ARISTOTLE UNIVERSITY OF THESSALONIKI
(G – THESSAL 01)
FACULTY OF SCIENCES
SCHOOL OF MATHEMATICS
E.C.T.S. GUIDE
European Community Course Credit Transfer System
ERASMUS/SOCRATES
European Community Action Scheme
for the Mobility of University Students
THESSALONIKI 2017
This Guide gives information on the Aristotle University of Thessaloniki and on the structure of the courses offered by the School of Mathematics, in order to help prospective ECTS students prepare for their study period at this institution. It also contains information on the city of Thessaloniki and other useful facts for all ECTS incoming students.
Assoc. Professor Efthimios Kappos, ECTS Coordinator for the School of Mathematics of the University, prepared the current version of this ECTS guide.
The preparation of the present ECTS guide was made possible by funds provided by the Aristotle University of Thessaloniki.
Table of Contents
A. Brief History of Thessaloniki and its Cultural Life
B. The Aristotle University of Thessaloniki
D. The University Student Union and its Services
H. Public Transport (Student Discount Card)
I. Accommodation for ECTS Students
E. Registration for Examinations
F. Undergraduate Programme of Studies
SUMMARY OF COURSE OFFERINGS BY SEMESTER
G. Postgraduate Programmes of Study
M.Sc. Course in «Pure Mathematics»
M. Sc. Course in «Statistics and Mathematical Modelling»
M. Sc. Course in «Theoretical Computer Science and Control and System Theory»
ECTS, the European Credit Transfer System, was implemented by the European Commission in order to develop procedures for organizing and improving academic recognition of studies abroad. Through the use of commonly understood measurements  credits and grades ECTS provides a means to interpret national systems of credit allocation, compare students learning achievements and transfer credit units from one institution to another. The ECTS system includes three core elements: information (on study programmes and student achievement), mutual agreement (between the partner institutions and the student) and the use of ECTS credits (to indicate student workload). Each ECTS department describes the courses it offers, not only in terms of content, but also assigning credits to each course.
The ECTS system is based on voluntary participation and a climate of mutual trust and confidence in the academic performance of partner institutions. The rules of ECTS are set out to create transparency, to build bridges between institutions, to enable studies abroad and to widen the choices available to students.
ECTS provides transparency through the following means:
· The information package, which supplies written information to students and staff on institution, schools/faculties, the organization and structure of studies and course units.
· ECTS credits which are a numerical value allocated to course units to describe the student workload required to complete them.
· The transcript of records, which shows students’ learning achievements in a way which is comprehensive, commonly understood and easily transferable from one institution to another.
· The learning agreement, covering the programme of study to be undertaken and the ECTS credits to be awarded for their satisfactory completion, committing both home and host institutions, as well as the student.
ECTS credits are a numerical value (between 1 and 60) allocated to course units to describe the student workload required to complete them. They reflect the quantity of work each course unit requires in relation to the total quantity of work necessary to complete a full year of academic study at the institution, that is, lecture, practical work, seminars, tutorials, fieldwork, private study  in the library or at home  and examinations or other assessment activities. ECTS is thus based on a full student workload and not limited to contact hours only.
From the 60 credits, which represent the workload of a full year of study, normally 30 credits are given for one semester. It is important to indicate that no special courses are set up for ECTS purposes, but that all ECTS courses are regular courses of the participating institution, as followed by home students under normal regulations.
It is up to the participating institutions to subdivide the credits for the different courses. ECTS credits should be allocated to all the course units available, whether compulsory or elective. Credits can also be allocated to project work, thesis and industrial placements, where these "units" are a normal part of the degree programme. Practical placements and optional courses, which do not form an integral part of the course of study, do not receive academic credit. Noncredit courses may, however, be mentioned in the transcript of records.
Credits are awarded only when the course has been completed and all required examinations have been successfully taken.
The students participating in ECTS will receive full credit for all academic work successfully carried out at any of the ECTS partner institution and they will be able to transfer these academic credits from one participating institution to another, on the basis of prior learning agreement on the content of study programmes abroad between students and the institutions involved.
All students of the participating schools who are willing to take part in the ECTS Pilot Scheme may do so provided their institution agrees, subject to limits of available places.
Students selected by each institution to participate in ECTS may only be awarded a student mobility grant if they fulfil the general conditions of eligibility for the ERASMUS grant. These are:
· Students must be citizens of one of the EU Member States or citizens of one of the EFTA countries (or recognized by one member State or one EFTA country as having an official status of refugee or stateless person or permanent resident); as to EFTA nationals, students will be eligible provided they are moving within the framework of ERASMUS from the respective EFTA home country to an EU Member State. EFTA nationals registered as students in ECTS participating institutions in other EFTA countries or in Community Member States are only eligible for participation in ECTS if they have established a right of permanent residence;
· Students shall not required to pay tuition fees at the host institution; the student may, however, be required to continue to pay his/her normal tuition fees to the home institution during the study period abroad;
· The national grand/loan to which a student may be entitled for study at his/her institution may not be discontinued, interrupted or reduced while the student is studying in another Member State and is receiving an ERASMUS grant;
· One study period abroad should not last less than three months or more than one year;
· Students in the first year of their studies are not eligible for receiving ERASMUS grants.
Most students participating in ECTS will go to one single host institution in one single EU Member State, study there for a limited period and then return to their home institution. Some may decide to stay at the host institution, possibly to gain a degree. Some may also decide to proceed to a third institution to continue their studies. In each of these three cases, students will be required to comply with the legal and institutional requirements of the country and institution where they take their degree.
When the three parties involved – the student, the home institution and the host institution – agree about the study programme abroad, they sign a learning agreement attached to the application form. This agreement, which describes the programme of the study abroad, must be signed before the student leaves for the host institution. Good practice in the use of the agreement is a vitally important aspect of ECTS.
The home institution provides the student with a guarantee that the home institution will give full academic recognition in respect of the course units listed on the agreement.
The host institution confirms that the programme of the study is acceptable and does not conflict with the host institution’s rules.
Students may have to modify the agreed programme of study upon arrival at the host institution for a variety of reasons: timetable clashes, unsuitability of chosen courses (in level or content) etc. The learning agreement form therefore provides for changes to the original agreed study programme/learning agreement.
It must be stressed that changes to the original agreed programmes of study should be made within a relatively short time after the student’s arrival at the host institution. A copy of the new learning agreement should be given to the student and the coordinator of the home and host institutions.
When the student has successfully completed the study programme previously agreed between the home and the host institutions and returns to the home institution, credit transfer will take place, and the student will continue the study course at the home institution without any loss of time or credit. If, on the other hand, the student decides to stay at the host institution and to take a degree there, he or she may have to adapt the study course due to the legal, institutional and school’s rules in the host country, institution and school.
USEFUL SERVICES TO STUDENTS
Anyone studying at Aristotle University of Thessaloniki may request the assistance of University services, such as the ones listed below, in order to solve any problems they may face during their studies. They can also themselves become volunteers, by offering their services to their colleagues or to fellow students in need.
Social Policy and Health Committee
The Social Policy and Health Committee (SPHC) aims to create conditions that will make the University an academic area accessible to all members of the university community, giving priority to space accessibility of disabled persons.
For this reason, qualified members of the teaching staff can train students with visual impairment to use electronic equipment linked with Braille printers installed in some of the University libraries. Also the SPHC tries its best to ensure the granting of books with voice output to such students.
The SPHC also provides a bus for disabled persons, in order to facilitate their movement around campus for classes and exams during the academic year. In this context, the University has created a Program for the Promotion of SelfHelp, which is run by a team of volunteers, the majority of whom are students. Email: selfhelp@auth.gr
Some years ago, the Social Policy and Health Committee established the institution of Voluntary Blood Donation, which also led to the creation of a Blood Bank in AHEPA hospital. Since May 2007, a second Blood Bank was founded in the Department of Physical Education in Serres, with the collaboration of the Social Policy and Health Committee and the General Hospital of Serres. Voluntary blood donation takes place twice a year, during the months of November and April, at the Ceremonial Hall of Aristotle University. The immediate target is to cover all needs for blood through voluntary blood donation, and currently covers 40% of total needs. Volunteering for blood donation, which is a safe procedure, without complications, is open to every person above 18 years of age who does not have any special health problems.
Email: socialcom@ad.auth.gr
fititikiline@ad.auth.gr
Website: http://spc.web.auth.gr
Tel / Fax: 2310 995386, 2310 995360
Observatory for the Academic Progress of Students belonging to Vulnerable Social Groups
The role of this Observatory is to assist:
 Students with disabilities
 Foreign students
 Minority students, foreign students of Greek descent or repatriated students
 Any other category of students who face problems hindering their studies
The above mentioned students can inform directly the Observatory – and also inform the Student Advisors of their Department – of any serious problem that they might face in the course of their studies, which arise either because of their disability or because of cultural, language or health problems.
Email: studobserv@ad.auth.gr
Website: http://acobservatory.web.auth.gr
Tel./Fax: 2310.995360
Counselling and Psychological Support Committee
The Counselling and Psychological Support Committee (PSC) aims to coordinate the organization and function of the university units that offer psychological assistance and counselling to AUTh students.
The services provided by the University Centre for Counselling and Psychological Support are offered to students and university staff alike.
The Committee works closely with other related Committees and organizes dialogue workshops with students, as well as with the administrative and other staff of the university community.
Among the future aims of the PSC is the operation of a campus hotline, in order to provide immediate assistance to people in crisis and to those facing personal difficulties that could feel safer to talk about their problems in anonymity and in the absence of visual contact.
PSC is located on the ground floor of the Lower University Student Club, in the Sanitary Service Section, offices 5 & 8.
Email: vpapadot@ad.auth.gr
Tel.: 2310 992643 & 2310992621
Fax: 2310 992607 & 210992621
Volunteer Committee
The Volunteer Committee has as its main goal to promote to the members of the university community of AUTh the idea of volunteering as a contemporary social imperative.
The Volunteer Committee has as its motivation the improvement of the daily life of everyone working in Aristotle University, students and teaching and administrative staff, in areas such as student affairs, environmental issues and social aid. It encourages all members of the university community to take the initiative, by submitting ideas and suggestions.
A number of cells of volunteers in various Departments and Faculties have already been created to this end, consisting of a faculty member and a student, in order to develop a body of volunteers in each Department / Faculty of AUTh.
Email: vrectacsecretary@auth.gr
Tel: 2310996713, 996708
Fax: 2310996729
.
One of Europe’s most ancient cities, and the second largest city in Greece, Thessaloniki was founded ca.315 BC by Cassander, King of Macedonia, who named it in honour of his wife, Thessaloniki, halfsister of Alexander the Great. It rapidly grew into the most important city in the kingdom, and its principal commercial port.
Macedonia had been a centre of intellectual and educational activity since the age of mythology. During the reign of kings Perdikkas II and Archelaos I (438399 BC), many important figures of Hellenic civilisation made their way to Macedonia, among them Hippocrates, the poet Melanippides, the tragic poets Euripides and Agathon, the epic poet Choirilos, the musician Timotheos and the painter Zeuxis.
Next came Aristotle, arguably the greatest of all the Greek philosophers. A native of the town of Stageira, not far from Thessaloniki on the Chalkidiki peninsula, his students included Alexander the Great, who was to carry Hellenic civilisation to most of the then known world.
During the Roman age, Thessaloniki was famous for its epigrammatists: Antipatros, Philippos and Epigonos. Saint Paul preached in Thessaloniki; and it was at nearby Philippi that in the year 50 of the Common Era he founded the first Christian Church in Europe. The Epistles to the Thessalonians, the two letters he later wrote to the people of Thessaloniki, are among the earliest documents of Christian writing.
With the foundation of the Byzantine Empire, Thessaloniki became its second urban centre, fostering and developing the intellectual and artistic movements that earned it the appellation of “the Athens of Medieval Hellenism”. Unfortunately, there are very few documentary references to the learned institutions that flourished here during this period, and what does exist is tucked away in local monasteries. Those who have studied the history of the city, however, affirm that Thessaloniki never ceased to be a centre of learning. The continuous development of the arts and sciences in the city was further supported by the presence, from the 11th century onwards, of numerous Orthodox monasteries in the surrounding area and on Mount Athos.
When Thessaloniki fell to the Ottomans, most of its leading lights fled to the Christian West. The city continued to be an important centre of Jewish life and culture, especially after the arrival of a large Sephardic community escaping persecution from Spain in the 15th century. During this period the little progress made in Greek education took place in the nearby Mount Athos, culminating in the foundation in 1749 at Karyes of the Athonite School, where students were taught theology, philosophy, Latin, mathematics and  for the first time  physics (by Evgenios Voulgaris).
It was not until the end of the 19th century, in the last years of the reign of Sultan Hamid II, that the Ottomans state assumed responsibility for education. In 1879 it founded a High School in Thessaloniki so that government officials would be trained there. The building that housed it is now the Old Building of the University’s School of Philosophy.
A victorious Greek army took Thessaloniki on October 26, 1912 at the end of the First Balkan War.
The year 1912 marked the beginning of a new period in Thessaloniki’s economic, social and cultural life, one that turned the city, now part of Greece, into the economic, political and cultural capital of Macedonia and Thrace and the second largest and most important city in Greece.
When it was founded in 1926, the Aristotle University of Thessaloniki opened its doors to just 65 students: by 1960, the student body had grown to 9000, climbing to 37,000 in 1976, while today it numbers more than 60,000 students. The city of Thessaloniki now has two other universities, the “University of Macedonia” and the “International Hellenic University” and one technological institute the “Alexander Technological Educational Institute of Thessaloniki”.
In the city there are numerous libraries, a variety of fine cultural and intellectual centres and institutions, museums, sculpture and art galleries, public and private theatres, conservatories and symphony orchestras. It also hosts a wealth of scientific and artistic events, especially during the annual “Dimitria” Festival.
Some of the features of the economic activity of the city, which has developed into one of the most important trade and communications centres in southeastern Europe, are the Port with its Free Zone, the European Centre for the Development of Vocational Training (CEDEFOP), “Makedonia” International Airport, and HELEXPO, the International Trade Fair Exhibition Centre. More information is available in http://www.thessaloniki.gr
The University of Thessaloniki was founded under the First Hellenic Republic, when the Fourth National Assembly passed a motion introduced by Alexandros Papanastasiou into law on June 14, 1925. Statute 3341 instituted five Schools: Theology, Philosophy, Law and Economics, Physics and Mathematics, and Medicine. To these were soon added Schools of Agronomy and Forestry, Veterinary Science, Engineering, and Dentistry.
The first to open its doors, in 1926, was the School of Philosophy (Faculty of Arts). This was followed a year later by the School of Physical and Mathematical Sciences, initially having only a School of Forestry, but by the 192829 academic year the Schools of Physics, Mathematics and Agronomy were added. The School of Law and Economics was also established in two stages, with the Faculty of Law in 192829 and the Faculty of Political and Economic Sciences a year later. In 1937 the Schools of Forestry and Agronomy were separated from the School of Physics and Mathematics and reconstituted as the School of Forestry and Agronomy. The School of Physics and Mathematics continued to grow, with the successive addition of the Schools of Chemistry, Natural Science (abolished in 197576), Pharmacology and in 197374, Biology and Geology. The Schools of Medicine and Theology, instituted by the original Law, opened in 1942. A Faculty of Dentistry was established in 195960 as part of the School of Medicine, but in 1970 broke off and instituted itself as a separate School in the following academic year (197071). The School of Veterinary Science  the only one in Greece  was founded in 1950. The School of Engineering, opened in 195556 with a single School of Civil Engineering, and successively expanded by the addition of the Schools of Architecture (195758), Agronomic and Survey Engineering (196263), Chemical Engineering (197273) and Electrical and Mechanical Engineering (197273), this last being divided four years later into a School of Electrical Engineering and a School of Mechanical Engineering.
The years 195152 saw the foundation of the Institute of Foreign Languages and Literatures, attached to the School of Philosophy; the School of English Language and Literature, inaugurated that same year, was followed three years later by the School of French Language and Literature and in 196061 by the corresponding Schools for Italian and German Language and Literature.
The Aristotle University of Thessaloniki is now the largest university in Greece, with over 60,000 students, a faculty of around 2000, 195 special educational staff, and 296 supplementary teaching personnel. The University also has a special technical administrative staff of around 700.
The University campus, where most of the university services are located, occupies an area of 43 hectares in the centre of the city. However, the particular requirements of certain of its schools, in conjunction with the already overcrowded campus, have led to the development of new installations  some still under construction and some already in use  with an eye to the future. Some of these offcampus buildings are located outside the city proper: the School of Fine Arts and the School of Physical Education and Sports, for example, will be located on a 20 hectare site near Thermi; while the School of Forestry and Environmental Science has moved to premises in the Finikas area.
The law “On the structure and operation of the Greek Universities”, which came into effect in the academic year 198283 and has subsequently been supplemented and modified by later legislation, introduced major changes in the structure and administration of the University and in its curriculum. The School of Physics and Mathematics, renamed the School of Sciences, has since the 199293 academic year included a School of Informatics. Today, the Aristotle University of Thessaloniki comprises the following Faculties and Schools:
1) Faculty of Theology:
* School of Theology
* School of Ecclesiastical and Social Theology
2) Faculty of Philosophy:
* School of Philology
* School of History and Archaeology
* School of Philosophy and Pedagogy
* School of Psychology
* School of English Language and Literature
* School of French Language and Literature
* School of German Language and Literature
* School of Italian Language and Literature
3) Faculty of Sciences:
* School of Mathematics
* School of Physics
* School of Chemistry
* School of Biology
* School of Geology
* School of Informatics
4) Faculty of Law, Economics and Political Sciences:
* School of Law
* School of Economics
* School of Political Sciences
5) Faculty of Agriculture
6) Faculty of Forestry and Natural Environment
7) Faculty of Veterinary Medicine
8) Faculty of Medicine
9) Faculty of Dentistry
10) Faculty of Engineering:
* School of Civil Engineering
* School of Architecture
* School of Rural and Surveying Engineering
* School of Mechanical Engineering
* School of Electrical and Computer Engineering
* School of Chemical Engineering
* School of Mathematics, Physics and Computational Sciences
* School of UrbanRegional Planning and Development Engineering (Veroia)
11) Faculty of Fine Arts:
* School of Visual and Applied Arts
* School of Music Studies
* School of Drama
* School of Film Studies
12) Faculty of Education:
* School of Primary Education
* School of Early Childhood Education
13) Independent Schools:
* School of Pharmacy
* School of Physical Education and Sports Sciences
* School of Physical Education and Sports Sciences (Serres)
* School of Journalism and Mass Media Studies
There are also the following University Units
1) School of Modern Greek Language
2) Institute of Modern Greek Studies
3) Centre for Byzantine Research
Each of these Schools offers at least a Bachelor’s degree (ptychio in Greek).
The School of Modern Greek Language offers both regular semester courses and intensive winter and summer programmes. Its programmes are addressed to the foreign students attending the University.
The “Manolis Triantafillidis” Institute of Modern Greek Studies is set up to study and cultivate Demotic Modern Greek and Modern Greek Literature.
The Aristotle University of Thessaloniki is a State University under the responsibility of the Ministry of Education. The decisionmaking bodies are:
1. The Senate.
Consists of the Rector, the three ViceRectors, the Deans of all the Schools, the Chairmen of all the Schools, representatives of the faculty, the technical administrative staff and the graduate student body, plus one undergraduate representative from each School.
2. The Rector’s Council.
Consists of the Rector, the three ViceRectors, one student representative and the University Registrar.
3. The Rector.
For the years 20142018, the Rector is Professor P. Mitkas and the ViceRectors are Professors Tzifopoulos, ArgyropoulouPataka, Varsakelis, Laopoulos and Klavanidou.
The respective faculty general assemblies take decisions on the academic affairs of each School. There is also student participation on issues of their concern. More information is available in http://www.auth.gr
Every year, about 160 students are admitted to the School of Mathematics strictly on the basis of their performance in the National Entrance Examinations administered by the Ministry of Education. There is a limited number of places reserved for transfer students, who are admitted after special examinations conducted by the University during the fall semester. Students at the Greek Universities pay no tuition and receive all textbooks for their courses free of charge. A limited number of places at statesponsored dormitories are available. Free meals are also offered to all registered students in the student mess hall. Financial aid in the form of honorary scholarships is available. Some of these grants are given to students strictly on the basis of academic performance regardless of financial need, while others are offered only to needy students who have demonstrated a highly satisfactory academic performance.
Successful candidates are invited to register within a time period fixed by the Ministry of Education, and are notified to this effect by means of a Presidential Decree issued each year and also published in the media.
No student already enrolled in any University School or School in Greece or elsewhere may be registered unless their prior registration is cancelled.
All University of Thessaloniki programmes are structured on a semester system, with two Semesters (Winter and Spring) of thirteen teaching weeks each in one academic year.
In the Academic Year 20172018, the Winter semester begins on October 2nd and ends on January 19th, while the Spring semester begins on February 12th and ends on June 1st.
There are three examination sessions annually, each lasting three weeks: the January session beginning on January 22nd, and ends on February 9th, the June session beginning on June 4th, and ends on June 22nd, and the September session beginning on September 3rd and ends on September 21^{st} 2018.
No lectures are given on the following official holidays: October 26th, October 28th, November 17, January 30th, March 25th, May 1st, and June 1st, and during the following holiday periods:
 Christmas and New Year’s (from December 24th to January 7th).
 Carnival (from February 19th to February 24th).
 Easter (from April 2nd to April 15th).
The University Library comprises the Central Library and its Library Branches, which are associated to University Departments, Laboratories, Reading Rooms and Clinics.
The Central Library Building has a Faculty Reading Room, a Central Reading Room on the ground floor and a Student Reading Room on the first floor.
The Central Reading Room is open to students for work relating to assigned projects; students must apply to the Administration for a special pass, presenting the authorization note signed by the professor who assigned the work.
The Student Reading Room is open to all students in the University, and may be used for work on students’ own books, textbooks, or the reference material available in the Reading Room itself. It is open morning and afternoon at the hours posted there.
The integration of the University Library into the Ptolemy II Library Network, begun in 1995, is expected to be completed soon; this will provide access to library materials via any computer hooked up to the system.
Anyone with access to the University network can freely browse the holdings of the libraries of the University of Thessaloniki and the University of Crete. The address is http:/www.lib.auth.gr
Student services are provided at the University Student Union, located in the eastern sector of the University Campus.
The Student Union building houses restaurants, a health service, a reading room, a cafeteria, a barber shop, a hairdresser’s with special student rates etc.
Board is provided subject to certain conditions; applications must be accompanied by the requisite documentation. Full details may be obtained from the Student Union offices.
Health care (medical, pharmaceutical and hospital) is provided for all undergraduate and postgraduate students. Students not already covered, directly or indirectly, by some other health care plan are issued Health Care Books upon registration. If a Health Book is lost, it may be replaced after an interval of two months. If this replacement book is lost, then a new one will be issued after the beginning of the following academic year.
There are three Student Residences on campus: Residence A, Residence B and Residence C. Admittance to these residences is subject to certain conditions, and applications must be accompanied by the proper documents. Full details are available from the USC Offices.
Oncampus organizations include theatre, film and chess clubs, as well as the traditional Greek dance group and the football, basketball and volleyball teams, all of which organize various events.
In addition, given that the University is located in the heart of Thessaloniki, students have the opportunity to enjoy the wealth and diversity of events that contribute to the artistic and cultural life of this great city.
Students may use the facilities of the University Gymnasium, located in the eastern sector of the campus. Information: at the Secretariat of the Gymnasium.
Covering about 9 hectares, the University Gymnasium facilities provide all members of the University, students and faculty alike, with opportunities for physical exercise. Varsity teams in various sports represent the University in competitions both in Greece and abroad. There is also a traditional Greek folk dance group.
Undergraduate and postgraduate students are entitled to a discount on domestic coach, rail and airfares.
At the time of registration, the Secretariat of each School will provide any student entitled to such discount with an interim special pass, valid for the named holder only and for one academic year. If this pass is lost, stolen or destroyed (for whatever reason), the student must declare its loss, theft or destruction to the Secretariat and a new card will be issued, after an interval of two months to allow for investigation into the circumstances of the said loss, theft or destruction.
The discount is valid for the duration of the academic year and for as many years as are normally required to complete the course of study, plus half that period again.
The discount granted is fixed by Ministerial decision on the basis of current fares for each form of transportation.
The Aristotle University of Thessaloniki can provide accommodation for ECTS students upon request. Students should ensure that the Secretariat of EEC European Educational Programmes receives their applications at least three months before the beginning of the semester.
In all schools, registration dates are: September 130 for the winter semester and January 131 for the spring semester.
The Senate has resolved that ERASMUS students are to be treated as home students; this means that they have the same rights and obligations as Greek students, including:
1) Free registration, tuition and books,
2) Discount card for urban and interurban transportation,
3) Health insurance card and free hospitalization and medication,
4) Free meals in the Student Refectory.
In addition, the University has reserved some places in special dormitories, which are available to Erasmus students for a small rental fee. The rent is payable by the week so that it is possible for the Erasmus student to stay in the dormitory for as long a period of time as he or she wishes or until he or she finds another arrangement.
For ERASMUSECTS students who wish to prepare for their studies in Greece, the University offers intensive and regular Greek Language courses.
The intensive courses are one month long; these run from midSeptember to midOctober and from early February to early March. For ECTS students, payment of the fees is covered by the University.
The regular courses (Beginners, Intermediate, and Advanced level) are yearlong courses and free of charge. These programmes focus on the teaching of the Modern Greek Language, and touch on aspects of Greek civilization and culture. Each of the three levels covers four (teaching) hours a day, five days a week.
A certificate of attendance is delivered at the end of the programme.
ERASMUS students may also, if they wish, follow the regular semester courses offered by the Modern Greek Language School. (For further information: School of Modern Greek Language, AUTH 54124 Thessaloniki, Tel: 00302310997571/ 00302310997572, fax: 00302310997573, http://www.gls.edu.gr).
The Office of European Education Programs is situated on the ground floor of the Administration Building. Opening hours: 08.00 – 14.30. Tel.: 00302310995291, 5293, 5289, 5306. Fax: 00302310995292.
More information is available in http://www.auth.gr
The School of Mathematics was established in 1928; together with the Schools of Physics, Chemistry, Biology, Geology and Informatics, it is one of the six Schools of the Faculty of Sciences.
For administrative purposes, the School of Mathematics is subdivided into the following five Departments:
1. Algebra, Number Theory and Mathematical Logic
2. Mathematical Analysis
3. Geometry
4. Numerical Analysis and Computer Sciences
5. Statistics and Operations Research
1. The Head of the School.
2. The Administrative Board.
It consists of the Head, the Deputy Head of the School and the five Department Heads, plus two student representatives.
3. The School’s Council.
The School’s Council comprises the teaching staff (25 faculty members) and student representatives.
Information:
School of Mathematics
Head of the School: Professor Nikolaos Karampetakis
Academic Secretary: A. Stergiou
Aristotle University of the Thessaloniki
Thessaloniki, Greece 54124
Tel.: 00302310997920
00302310997950
Fax: 00302310997952
Erasmus Programme
The ERASMUS Coordinator of the School is:
Efthimios Kappos
kappos@math.auth.gr
Tel: +302310997958
The Deputy ERASMUS Coordinator is:
Fani Petalidou
Tel: +30 2310 998104
Department of Algebra, Number Theory and Mathematical Logic
Professors 
Charalambous, H. (Head of Department) Papistas, A. Tzouvaras A. 


Department Secretary 
Tsitsilianou M. 
Department of Mathematical Analysis
Professors 
Betsakos, D. Marias, M. Siskakis, A. (Head of Department) 


Assistant Professor
Lecturer 
Galanopoulos, P.
Fotiadis, A.



Department Secretary 
Tsitsilianou M. 
Department of Geometry
Associate Professors 
Kappos, E. Stamatakis, S. (Head of Department)

Assistant Professor
Department Secretary 
Petalidou, F.
Tsitsilianou M.



Department of Numerical Analysis and Computer Sciences
Professors 
Karampetakis, N. Poulakis, D. 

Associate Professors 
GousidouKoutita, M. (Head of the Department) 

Assistant Professor 
Rachonis, G. 




Department Secretary Technical Assistants 
Tsitsilianou M. Porfiriadis, P. Tzounakis P.







Department of Statistics and Operations Research
Professors 
Antoniou, I. Kalpazidou, S. Tsaklidis, G.

Associate Professors 
KolyvaMahaira, F. 
Assistant Professor 
Papadopoulou, A. 
Lecturer 

Department’s Secretary: 
Tsitsilianou M.

Technical Staff:

Bratsas Ch. Vlachou Th.



Teachers of Foreign Language
To be announced
Secretarial Staff
Secretary 
Stergiou, A. Tel: +30 2310 997920 

Secretarial staff: 
Mantzouni, G. Tel: +30 2310 997920 Sotiriadou, A. Tel: +30 2310 997842 Tsianaka, O. Tel: +30 2310 997983 Tsitsilianou M. Tel: +30 2310 998096 Vlachou, Th., Tel: +30 2310997930





Mailing Address: School of Mathematics
Aristotle University of Thessaloniki
Thessaloniki 54124
Greece
The Library of the School of Mathematics, located in the western wing of the Sciences Building (Building 22), has a collection of more than 25,000 titles, and subscribes to 396 periodicals. Open Monday to Thursday from 9:00 until 18:00, and until 15:00 on Friday.
Lending facilities are restricted. Some books, chiefly textbooks used in the School, may be taken out upon presentation of the student’s ordinary or student identity card.
Other books and all periodicals must be read in the Library Reading Room.
Information on the Mathematics School is also available via Internet, at:
http:// www.math.auth.gr
Students may use the computers in the Informatics Laboratory on the first floor of the Biology building.
The School also operates an FTP Server that provides, free of charge, a variety of software on different computer platforms. The address is:
ftp:// ftp.math.auth.gr
Students must register for examination in all courses they are taking (compulsory, compulsory elective, elective and free elective–see below) at the beginning of each semester. This is done electronically on the site of the School, within a period specified by the Secretariat. The number of courses for which students may register is limited.
Students who do not register for their chosen courses in time will not be eligible to sit the examinations. In the January and June examination sessions, students are admitted only to examinations in the courses registered for at the beginning of that semester; in the September examination session, students are eligible for examination in courses for which they were registered in either of the two semesters of the academic year just completed.
A student who fails in any course may reregister for the same course in any semester when that course is taught (or in the conjugate semester, for students in their 8th or subsequent semester).
Curriculum regulations for students admitted in the 20142015 academic year will be announced by the Secretariat of the School.
The Undergraduate Programme in Mathematics is structured over eight semesters, and leads to the degree of “Diploma of Mathematics” (Ptychio).
There are four kinds of courses: compulsory, compulsory electives, electives and free electives. In order to complete the programme and be awarded the Diploma, students must successfully pass all the 24 compulsory courses plus 4 compulsory elective courses from four different departments and 12 elective courses. Of the elective courses, not more than 5 can be free elective. The total number of ECTS credits earned from all these courses must be at least 240. Additionally, every student must pass the course Introduction to Computer Programming (Fortran 90/95 or C++).
Listed below are all the courses offered by the School of Mathematics in the 20142015 academic year, with the following information for each: Name of Course, the indication GLSUD (Greece – Long Study University Diploma), number of semesters taught, the ECTS code and course number, the number of hours per week, the number of weeks per semester, the type of examination (written or otherwise), whether or not there is a laboratory component, the number of ECTS credits provided, an outline of the course and the name(s) of the instructor(s). This is followed by tables, setting out a summary of all the above information in compact and easytoread form.
Introduction to Algebra and Number Theory
GLSUD1 IALG  0102
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory
Description: Elements of set theory (sets  functions  relations  equivalence relations  partial ordered sets lattices). Natural numbers and Integers (Mathematical induction divisibility prime numbers Euclidean algorithm GCD LCM Fundamental theorem of arithmetic mod n). Elements of combinatorial theory. Elements of algebraic structures (Groups and subgroups, homomorphism of groups, rings and subrings, fields and subfields, multiplicative functions).
Instructor: H. Charalambous
Linear Algebra
GLSUD1 LALGI  0108
6h/w (5 hours’ lectures, 1 lab), 13 weeks, written exams, credits: 8
Compulsory
Description: Vector spaces  Finite dimensional vector spaces  Matrices  Determinants  Matrices and Linear Transformations  Systems of linear equations  Eigenvalues  Eigenvectors  Characteristic polynomial  Euclidean and unitary spaces.
Instructors: A. Papistas, H. Charalambous, A. Tzouvaras, P. Porfyriadis
Calculus I
GLSUD1 CI  0201
5h/w, 13 weeks, written exams, credits: 7
Compulsory
Description: Basic notions  Sequences and series of real numbers  Power series  Real functions  Limits  Continuity  The Derivative  Applications of the derivative  Taylor series  Study of functions.
Instructors: A. Siskakis
Introduction to Computer Programming (C++)
GLSUD1 ICPR  0430
3h/w, 13 weeks, written exams, credits: 5
Compulsory
Description: Introduction to C++: Computer hardware  Computer software  Programming languages  An introduction to problem solving with Fortran 90/95 or C++  The structure of a program  Simple input and output  Control structures  Iterations – Array processing (one dimensional and multidimensional matrices)  Functions  Subroutines  Modules  IMSL libraries  File organization (sequential files, direct access files)  Applications to mathematical problems.
Web link: http://users.auth.gr/~grahonis/C++.htm
Introduction to Fortran 90/95/2003 : Computer hardware  Computer software  Programming languages  An introduction to problem solving with Fortran 90/95/2003  The structure of a program  Simple input and output  Control structures  Iterations – Array processing (one dimensional and multidimensional matrices)  Functions  Subroutines  Modules  IMSL libraries  File organization (sequential files, direct access files)  Applications to mathematical problems.
Web link: http://eclass.auth.gr/courses/MATH104
Instructors: N. Karampetakis, G. Rahonis, P. Porfyriadis
Analysis of Mathematical texts in the English language
GLSUD1 0601
3h/w, 13 weeks, credits: 3
Elective
Description: Details to follow
Instructor: to be announced
Calculus II
GLSUD2 CII  0202
5h/w, 13 weeks, written exams, credits: 7
Compulsory
Description: The definite Riemann integral  Fundamental theorems of integral calculus  The indefinite integral modes of integration  Application of the definite integral (area, length of curves, area and volumes of revolution)  Improper integrals – Taylor series and power series, convergence. Differentiation and integration of power series.
Instructor: A. Fotiadis, M. Marias
Analytic Geometry I
GLSUD2 ANGI  0301
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory
Description: Vector spaces: The concept of a vector space  Basis  Dimension  Inner product  Vector product  Orientation. Affine spaces  Affine coordinates  Lines and planes in A^{2} and A^{3 } Affine transformations  Affine classification of Conics. Projective space – homogeneous coordinates. Euclidean vector and affine spaces. Inner products, Isometries.
Instructor: E. Kappos, F. Petalidou
Theoretical Informatics I
GLSUD2 ITI  0401
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory
Description: Sets, relations, algorithms. Analysis of algorithms. Alphabets, languages and regular languages. Finite automata: deterministic, nondeterministic and equivalence. Finite automata and regular expressions. Decidability results.
Instructor: G. Rahonis
Mathematical Programming
GLSUD2 MAPR  0501
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory
Description: Mathematical models  Linear programming  Graphical solution and graphical analysis of the sensitivity of the linear model  Simplex method  Sensitivity analysis  Introduction to Integer Programming  Transportation problem  Principles of dynamical programming  Nonlinear methods of optimization  Applications.
Instructor: A. Papadopoulou, C. Bratsas
Symbolic Programming Languages
G LSUD2 ISYMA  0461
3h/w, 13 weeks, written exams, credits: 5
Elective
Description: Introduction to computer algebra systems  Introduction to Mathematica  Building expressions Numerical calculations  Symbolic calculations  Symbolic manipulation of mathematical representations  Basic functions  List manipulation  Functions and programs  Mathematica packages  Special topics in Algebra (expansion  factorization  simplification  sets and matrices)  Analysis (equation solving  system equation solving  differentiation  integration  sums and products  limits  Taylor series) and Geometry (second order curves  second order surfaces  two and three dimensional plotting)  Introduction to other computer algebra systems such as Maple, Matlab, Reduce, Macsyma etc.
Instructor: N. Karampetakis, P. Porfyriadis
Algebraic Structures I
GLSUD3 ALG I  0106
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory
Description: Groups, subgroups, group generated by a set  Homeomorphisms of groups  Lagrange’s theorem  Order of a group element  Euler’s theorem, Fermat’s theorem  Normal subgroups  Isomorphism theorems  Cyclic groups and their classification  Action of a group on a set  Permutation groups  Dihedral groups  Direct sums of groups.
Instructor: A. Papistas
Calculus III
GLSUD3 CALIII  0203
4h/w, 13 weeks, written exams, credits: 7
Compulsory
Description: Functions of several variables  Limits and continuity  Partial derivatives  Differentiation of scalar and vector functions  The chain rule  Higher order partial derivatives  Directional derivatives  Taylor’s formula  Extremes of real valued functions  Lagrange multipliers  The implicit function theorem and the inverse function theorem.
Instructors: P. Galanopoulos, M. Marias
Topology of Metric Spaces
GLSUD3 ELTOP  0204
4h/w, 13 weeks, written exams, credits: 7
Compulsory
Description: Basic notions of Set Theory  Metric spaces  Topology of metric spaces  Convergence of sequences  Continuous functions  Compactness and Connectedness of metric spaces.
Instructors: A. Fotiadis
Analytic Geometry II
GLSUD3 INGII  0302
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory
Description: Applications in Euclidean spaces E^{2}, E, Ellipse  hyperbola and parabola  Tangents  Poles and polars  Conjugate diameters  Metric classification of figures of second degree in E^{2} Hyperboloids, paraboloids, ellipsoids, cylinders and cones of second degree  Tangent planes  Metric classification of figures of second degree in E^{3}.
Instructor: F. Petalidou, S. Stamatakis
Probability Theory I
GLSUD3 PROB  0502
4h/w, 13 weeks, written exams, credits: 7
Compulsory
Description: The sample distribution space  events  classical definition of mathematical probability  statistical regularity  axiomatic foundation of probability  Finite sample distribution spaces  combinatorics  geometric probabilities  Conditional probability  independence  Univariate random variables  distribution functions  function of a random variable  moments, momentgenerating function  probability generating function  Useful univariate distributions: Discrete (Bernoulli, Binomial, Hypergeometric, Geometric, Negative Binomial, Poisson), Continuous (Uniform, Normal, Exponential, Gamma)  Applications.
Instructor: I. Antoniou, G. Tsaklidis, F. KolyvaMachera
Introduction to Meteorology and Climatology
GLSUD3 METCLI – 1061
3h/w, 13 weeks, written exams, credits: 5
Free elective
Description: Climatic elements: solar and terrestrial radiation  Energy balance  airtemperature  atmospheric pressure  local winds  hydrologic cycle – evapotranspiration  water vapours  precipitation  Distribution of the climatic elements  Climate classifications  The climatic classification of Köppen and Thornthwaite  Climatic change theories.
Instructors: C. Fidas, P. Zanis.
Algebraic Structures II
GLSUD4 ALG II  0107
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory
Description: Rings, subrings and ring homeomorphisms  Ideals and sum and product of ideals Isomorphism theorems of rings Integral domains  Quotient field The ring of integers, the field of rational numbers Prime fields Prime and maximal ideals Principal ideal domains  Unique factorization domains Euclidean domains  Polynomial rings  Irreducible polynomials in Q[x], R[x], C[x] Field extensions  Algebraic and transcendental elements  Algebraic extensions and the minimal polynomial  Field constructions.
Instructor: H. Charalambous, A. Papistas
Calculus IV
GLSUD4 CIV – 0205
4h/w, 13 weeks, written exams, credits: 7
Compulsory
Description: Multiple integrals  Line integrals  Surface integrals  The integral theorems of Vector Analysis.
Instructors: P. Galanopoulos
Differential Equations
GLSUD4 DE  0206
4h/w, 13 weeks, written exams, credits: 7
Compulsory
Description: Differential equations of first order  The method of Picard  Linear differential equations of order n=2  Reduction of the order of a differential equation  Euler’s equations  Systems of differential equations. Laplace transforms.
Instructors: D. Betsakos
Statistics
GLSUD4 ST  0503
5h/w, 13 weeks, written exams, credits: 7
Compulsory
Description: Elements of probability theory  Distributions of some useful statistics  Descriptive statistics  Methods of point estimation  Confidence intervals and tests of hypotheses for the mean, the variance and the proportion for one and two samples  Test of GoodnessofFit  Contingency tables  Tests of homogeneity  The method of least squares Regression  Hypothesis testing and Confidence intervals in simple linear regression  Simple, multiple and partial correlation coefficient  Analysis of variance  The oneway layout  The twoway layout with and without interaction  Nonparametric methods  KolmogorovSmirnov tests, runs tests, rank tests and sign tests for one and two samples  Tests concerning k>2 independent and dependent samples  The Spearman correlation coefficient  Applications using statistical packages.
Instructor: F. KolyvaMachera, C. Bratsas
Mathematical Methods in Operational Research
GLSUD4 MMOR  0504
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory
Description: What is a stochastic process  Queuing Theory: birthdeath processes  some wellknown queuing systems  Markov Chains: nstep transition probabilities  classification of states  steadystate probabilities and mean first passage times  absorbing chains.
Instructor: A. Papadopoulou
General and Dynamic Meteorology
GLSUD4 GDM  1062
3h/w, 13 weeks, written exams, credits: 5
Free elective
Description: Chemical composition of air  Change of meteorological parameters of height – Barometric systems  General circulation of the atmosphere  Introduction to dynamic meteorology  Meteorological coordinate systems  The fundamental equations of motion Scale analysis  The geotropic wind. The gradient wind  The cyclostrophic wind  Thermal wind. Continuity equation  Pressure tendency equation  The concepts of circulation and vorticity  Absolute, relative and potential vorticity  The vorticity equation  Principles of weather modification  Conceptual and theoretical models  Operational and experimental weather modification projects.
Instructors: T.S. Karakostas.
Number Theory
GLSUD5 0136
3h/w, 13 weeks, written exams, credits: 5.5
Elective
Description: Unsolved problems in Number Theory. Linear congruences. Systems of linear congruences. Polynomial congruences. Arithmetic functions. Quadratic residues. Quadratic number fields. Applications.
Instructor: to be announced
Computational Methods in Algebra and Algebraic Geometry
GLSUD5 151
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory Elective
Description: Polynomial rings and ideals. Noetherian rings and the Hilbert Basis Theorem. Monomial orderings and polynomial division. Introduction to Gröbner bases. The Buchberger algorithm. Introduction to CoCoA. Applications to Algebra and Algebraic Geometry. Algebraic sets and the Nullstellensatz. Introduction to algebraic varieties.
Instructor: C. Tatakis
Introduction to Real Analysis
GLSUD5 REAN  0207
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory
Description: Real numbers  Countable and uncountable sets  Sequences and series  Permutations of series  Representations of real numbers  The Cantor set and Cantor’s function  Special classes of functions (monotone, bounded variation, absolutely continuous, convex)  Sequences and series of functions  uniform convergence and applications  Nowhere differentiable continuous functions – Spacefilling curves  equicontinuity  ArzelaAscoli theorem  Weierstrass approximation theorem  Lebesgue measure.
Instructor: D. Betsakos
Classical Differential Geometry I
GLSUD5 CDG  0303
5h/w, 13 weeks, written exams, credits: 7
Compulsory
Description: Definition of a curve  The method of moving frames  Fundamental Theorem of the Theory of Curves  Definition of a surface  Curves on surfaces  Fundamental forms  Asymptotic lines  Christoffel symbols  Theorema egregium  The Gauss mapping  Fundamental Theorem of Surface Theory.
Instructor: E. Kappos, S. Stamatakis
Numerical Analysis
GLSUD5 NA – 0402
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory
Description: Structure of Computational systems and algorithms, number systems and errors  Interpolation and approximation (interpolation by Lagrange and Newton polynomials)  Numerical integration (midpoint, trapezoid and Simpson’s rules, Romberg integration)  Numerical solution of nonlinear equations (bisection method, secant, regulafalsi and modified regulafalsi, Newton’s method)  Introduction to iterative methods for linear systems and ODE.
Instructor: M. GousidouKoutita
Probability Theory II
GLSUD5 PROBII  0505
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory
Description: The algebra of events  Probability Space  The axioms of Probability  Random variables  The notion of stochastic distribution  Multidimensional random variables  Multidimensional distribution functions  Marginal distributions  Denumerable multidimensional random variables  Continuous multidimensional distributions  Multidimensional normal distribution  Stochastic independence  Conditional Probability  Conditional density  Conditional distributions  Mean values for multidimensional random variables  Conditional mean values  Regression line  Mean square error  Random variable transforms  Compound distributions  Inequalities  Multiple Correlation coefficient  Ordered random variables  Characteristic functions  The sum of independent random variables  Characteristic functions of multidimensional random variables  Moment generating functions  Probability generating functions  Limit theory of random variables  Convergences  Relations between convergences  Central Limit Theorem – The Law of large numbers  The log log law.
Instructors: S. Kalpazidou, F. KolyvaMachera, G. Tsaklidis
Stochastic Strategies
GLSUD5 STOSTRA  0506
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory
Description: Stochastic problems  Stochastic networks  Stochastic problems of tools replacement and repairing  Renewal theory  Inventory.
Instructor: G. Tsaklidis
Stochastic Processes with Complete Connections and Learning Theory
GLSUD5 SPCCLT  0507
3h/w, 13weeks, written exams, credits: 5
Elective
Description: Stochastic processes with complete connections  Definition  Basic notions  The homogeneous case  Stochastic properties  Application of stochastic processes with complete connections to Learning Theory  Introduction to Learning theory  some notions of learning theory  The modelling of the learning phenomenon, The model of the stimulus choice.
Instructor: S. Kalpazidou
Regression Models and Applications to Knowledge Processing
GLSUD5 ANVARE  0531
4h/w, 13 weeks, written exams, credits: 5.5
Compulsory elective (for the Department of Statistics and Operational Research)
Description: Multiple linear regression: parameter estimation  confidence intervals of the estimators  tests of hypotheses  orthogonal polynomials  best model selection criteria  stepwise regression  Analysis of variance: one factor parametric models  two or more factors  block randomized experimental designs.
Instructor: I. Antoniou, C. Bratsas
Seismology
GLSUD5 SEIS  1063
3h/w, 13 weeks, written exams  lab., credits: 5
Free Elective
Description: Theory of elastic waves  Quantification of earthquakes – Theory of plate tectonics  Seismotectonics of the Aegean area  Macroseismic effects of earthquakes.
Instructor: P. Chatjidimitriou, T. Tsapanos.
Theoretical Mechanics
GLSUD5 THMI  1064
3h/w, 13 weeks, written exams, credits: 5
Free Elective
Description: Kinematics of a mass particle  Forces and laws of motion  Conservation theorems  Systems with one degree of freedom  Oscillations  Stability of equilibrium points  Phase diagrams  Central forces  Kepler’s problem  Systems of mass particles – Noninertial frames of reference.
Instructor: C. Varvoglis.
Complex Analysis
GLSUD6 COMAN 0208
4h/w, 13 weeks, written exams, credits: 7
Compulsory
Description: Complex numbers, the complex plane, topology of the plane, elementary complex functions  Holomorphic functions, CauchyRiemann equations  The complex integral, Cauchy's theorem and integral formula  The maximum principle, theorems of Morera and Liouville, the Schwarz lemma  Power series, the identity theorem  Laurent series, singularities, residues.
Instructor: A. Siskakis
Compulsory Electives
Group Theory
GLSUD6 GTH  0131
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory Elective (Department of Algebra, Number Theory and Math. Logic)
Description: The groups D_{n}, S_{n}, GL(n,K)  Action of a group on a set. Counting formulae  Applications: orbits and decoration problems, symmetric groups, crystallographic and wallpaper groups  Sylow theorems  Applications: groups of small order  Simple groups  Normal and solvable series  Solvable groups  Exact sequences  Finitely generated abelian groups.
Instructor: A. Papistas
Measure Theory
GLSUD6 METHE  0231
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory Elective (Department of Mathematical Analysis)
Description: Lebesgue measure on the real line  Measurable functions  Lebesgue integral  Monotone and dominated convergence theorems  Comparison of integrals of Riemann and Lebesgue  The fundamental theorem of Calculus for Lebesgue integral  Abstract measure theory  Signed and complex measures  Product measures  Fubini’s theorem.
Instructor: D. Betsakos
Elements of Functional Analysis
GLSUD6 FA – 0232
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory elective (Department of Mathematical Analysis)
Description: Metric spaces, review of basic notions. The orem of Baire. Normed spaces, Banach spaces, examples. Inner product spaces and Hilbert spaces. Linear operators and linear functionals. Dual space. HahnBanach, BanachSteinhaus, open map and closed graph theorems..
Basic notions  Metric spaces  Normed spaces  Inner product spaces  Linear operators and functionals  Norms in B(X,Y), HahnBanach, BanachSteinhaus, open mapping and closed graph Theorems.
Instructor: G. Stylogiannis
Linear Geometry I
GLSUD6 LINGEO  0331
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory Elective (Department of Geometry)
Description: Multidimensional affine spaces – Affine subspaces – Affine mappings.
Instructor: Th. Theofanidis
Classical Differential Geometry II
GLSUD6 CDGII  0332
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory elective (Department of Geometry)
Description: The Darboux frame  Normal curvature, geodesic curvature, geodesic torsion  Principal curvatures, Gauss curvature and mean curvature  Lines of curvature  Dupin indicatrix and conjugate directions  Geodesics  LeviCivita parallelism  The GaussBonnet formula.
Instructor: S. Stamatakis
Computational Mathematics
GLSUD6 COMMA  0431
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory elective (Department of Numerical Analysis and Computer Science)
Description: Interpolation and approximation with piecewise polynomials and splines, Numerical linear algebra: Gauss elimination for linear systems, pivoting, LU factorization and an introduction to the stability of systems and algorithms, norms of vectors and matrices, condition number, iterative methods, introduction to the numerical solution of eigenvalueeigenvector problem, numerical solution of ODEs (existence and uniqueness of initial value problem). Euler method, Taylor method, RungeKutta methods and multistep methods.
Instructor: M. GousidouKoutita
Theoretical Informatics II
GLSUD6 ITI  0432
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory elective (Department of Numerical Analysis and Computer Science)
Description: Minimization of finite automata. Algebraic grammars. Syntactic trees. Algebraic languages and their properties. Relations between algebraic and identifiable languages. Stack automata.
Instructor: Postdoc
Matrix Theory
GLSUD6 MATRIX  0532
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory elective (Department of Statistics and Operational Research)
Description: Prerequisite matrix theory  Matrix polynomials and normal forms  Functions of matrices  Inner products and matrix norms  Normal matrices  polar decomposition  singular value decomposition  Kronecker and Hadamard products  Nonnegative matrices  Generalized inverses.
Instructor: G. Tsaklidis
Deterministic Methods of Optimization
GLSUD6 DEMEOP  0533
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory elective (Department of Statistics and Operational Research)
Description: Introductory concepts: Convex and Concave functions. Solving NLPs with one variable. Iterative methods of finding extrema of functions in R^{n}, n>1.
Instructor: G. Tsaklidis
Electives
Stochastic Processes
GLSUD6 STPR  0563
3h/w, 13weeks, written exams, credits: 5
Elective
Description: Definition of a stochastic process  Classification of stochastic processes  Stochastic dependence  Martingales  The Markov property  The strong Markov property  Classification of states  Classifications of Markov chains  The matrix method  Regular chains  Cyclic chains  Inverse Markov chains  General properties of Markov chains  Extension of the Markov property  The ergodic behaviour  Random walks  GaltonWatson Processes (or Branching Processes), Processes with independent increments  The Poisson process  The Wiener process  Brownian motion  Continuous parameter Markov processes  The transition probability function  Kolmogorov’s equations  Feller’s algorithm  Noteworthy classes of Markov processes  Renewal Processes  Diffusion processes  Applications.
Instructor: S. Kalpazidou
Didactics of Mathematics
GLSUD6 DIMA  0963
3h/w, 13 weeks, written exams, credits: 5
Free elective
Description: This course is an introduction to the general didactics of mathematics and concentrates on the following: Mathematics as a scientific discipline and as a school subject, emphasising the epistemological aspects  Cognitive approach to the learning of Mathematics  Ethnomathematics aspects of mathematics education  Elementarization of Mathematics  Methods of teaching mathematics.
Instructor: S. Kalpazidou
Mathematical Software and Knowledge Representation Languages
GLSUD6 0967
3h/w, 13 weeks, written exams, credits: 5
Elective
Description: Introduction to software for the simulation and investigation of mathematical problems suitable for secondary school students, such as Sketchpad, Cabri and GeoGebra. Ontology web languages and applications to the semantic web.
Instructor: G. Makris
Special Topics A
GLSUD6 ST  1161
3h/w, 13 weeks, written exams, credits: 5
Elective
Description: The instructor, in collaboration with the student, specifies a subject.
Instructor: Any one of the teaching staff upon decision to teach the course.
Free Electives
Continuum Mechanics
GLSUD6 CM  1066
3h/w, 13 weeks, written exams, credits: 5
Free elective
Description: Introduction to Tensor Analysis  Lagrangian and Eulerian description of the motion  Local and total derivatives  Streamlines and pathlines of particles  Potential flow  Strain tensor  Displacement vector  Rate of deformation tensor  Velocity distribution in infinitesimal regions  Circulation and turbulent flow  The equation of continuity  Mass forces, stress vector and stress tensor  Equations of motion of a continuum  Ideal and Newtonian fluids  Euler and NavierStokes equations  Applications  examples.
Instructor: E. Meletlidou
Compulsory Electives
Mathematical Logic
GLSUD7 MALO – 0133
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory Elective (Department of Algebra, Number Theory and Math. Logic)
Description: Propositional calculus: language of PC. Truth values, logical inference. Sufficiency of connectives. Axiomatization of PC, completeness. Independence of the axioms. Predicate calculus. Firstorder languages. Structures, models, truth. Axiomatization of firstorder predicate calculus, completeness.
Instructor: A. Tzouvaras
General Topology
GLSUD7 GTO – 0233
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory Elective (Department of Mathematical Analysis)
Description: Topological spaces. Types of points. Countability and separability axioms. Continuity and convergence. Topologies derived from other topologies. Compact spaces. Connected spaces. Function spaces
Instructor: Ch. Papacristodoulos
Differential Manifolds I
GLSUD7 DMI – 0304
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory Elective (Department of Geometry)
Description: Topological spaces  Differentiation in Euclidean spaces  Differentiable Manifolds  Differential of functions and mapping  Tangent space  Tensor Algebra  Tensor fields  Lie brackets  Covariant derivative of vector and tensor fields  Connections  Parallel displacement  Geodesics  The curvature tensor.
Instructor: F. Petalidou
Classical Control Theory
GLSUD7 CLCOTH  0433
3h/w, 13 weeks, written exam, credits: 5.5
Compulsory elective (Department of Numerical Analysis and Computer Science)
Description: Introduction to the concepts of Systems, Signals and Automatic Control, (brief historical review, basic structure of feedback control, examples)  Mathematical concepts and tools for the study of continuous and discretetime signals and systems. (Laplace transform, ztransform, applications, block diagrams and signal flow graphs)  Classification of signals and systems. Continuous and discrete time signals and systems  Time invariance, linearity  Classical analysis of systems and control in the time and frequency domains  Linear time invariant singleinput, singleoutput systems described by ordinary, linear differential equations  Input output relation and the transfer function description of a linear time invariant system – Free, forced and total response of systems in the time domain  Stability of linear time invariant systems and algebraic stability criteria  Routh test for stability  Frequency response of linear time invariant systems  Closed loop systems  Root locus  Nyquist stability Criterion  Stabilizability and Stabilization of systems via precompensation and output feedback  Synthesis of controllers and parametrization of stabilising controllers.
Instructor: N. Karampetakis
Error Correcting Codes
GLSUD7 ECC – 0465
3h/w, 13 weeks, written exam, credits: 5.5
Compulsory elective (Department of Numerical Analysis and Computer Science)
Description: Hamming distance. Perfect codes, equivalence of codes, linear codes, generator matrices, message encoding, parity check matrices, decoding matrices, majority decoding, weight enumerator. Shannon’s theorem, lower bound on codes, code generation, Singleton’s bound, MDS codes, Plotkin’s bound, Griesmer’s bound, Hamming codes, Golay codes, ReedMuller codes.
Instructor: D. Poulakis
Mathematical Statistics
GLSUD7 MASTI  0534
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory elective (Department of Statistics and Operation Research)
Description: Distributions of functions of random variables  Normal distribution and the derived distributions from the normal  The exponential family  Sufficiency of a statistic for a parameter or for functions of parameters. The RaoBlackwel theorem  Completeness and uniqueness  Unbiased estimators with minimum variance  The CramerRao inequality  Efficient statistics  Consistent statistics  Maximum likelihood and moment estimators and their properties  Prior and posterior distributions and Bayes estimators  The minimax principle  Interval estimation. General methods for construction of confidence intervals  Approximate confidence intervals  Confidence regions.
Instructor: F. KolyvaMachera
Electives
Computational Geometry
GLSUD7 0471
3h/w, 13 weeks, written exams, credits: 5
Elective
Description: Bézier curves, cubic and Hermite interpolation, approximating curves, piecwise Bézier curves, curve synthesis, Bsplines and applications. Parametric surfaces, rational Bézier curves, Bézier surfaces, rational Bsplines, surface synthesis.
Instructor: P. Dospra
Stochastic Methods in Finance
GLSUD7 STMFIN  0562
3h/w, 13 weeks, written exams, credits: 5
Elective
Description: Introduction to probability theory  rates, time value of money  Options and derivatives  Options evaluation  Conditional mean value  Martingales  Selffinanced processes  Brownian motion  The BlackSchool model  Stochastic differential equations  Stochastic integration  Evaluation of the European option.
Instructor: A. Papadopoulou
Special Topics A and B
GLSUD7 SPETO – 1161, 1162
3h/w, 13 weeks, written exams, credits: 5
Elective
Description: The instructor, in collaboration with the student, specifies a subject.
Instructor: Any one of the teaching staff upon decision to teach the course.
Free Electives
Observational Astronomy and Astrophysics
GLSUD7 QBASTR  1067
3h/w, 13 weeks, written exams, credits: 5
Free elective
Description: Sun as a typical star. Stars: Characteristics, classification, distances, photometry, HR diagram  Stellar evolution: Equations of state, gravitational collapse, nucleosynthesis, neutron stars, black holes  Interstellar medium: Transfer equation, dispersion phenomena  Galaxies. Experimental astronomy: The celestial sphere. Telescopes  Classification of galaxies using the Palomar Sky Survey plates.
Instructors: J. Seiradakis
Compulsory Electives
Set Theory
GLSUD8 SETTH – 0132
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory Elective (Department of Algebra, Number Theory and Math. Logic)
Description: Paradoxes in naïve set theory. ZermeloFraenkel axiomatic set theory (ZF). The ZF universe and the foundation axiom. Comparison of size of sets. Equinumerable sets. SchroderBernstein theorem and Cantor’s theorem. Wellordered sets, ordinal numbers and operations with ordinals. Transfinite induction and Iinduction. Cardinals and operations with cardinals. The axiom of choice and its equivalent forms (wellordering principle, Zorn’s lemma, Hausdorff’s maximum principle.)
Instructor: A. Tzouvaras
Galois Theory
GLSUD8 GALTHE  0134
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory Elective (Department of Algebra, Number Theory and Math. Logic)
Description: Construction of fields. Algebraic extensions  Classical Greek problems: constructions with ruler and compass. Galois extensions  Applications: solvability of algebraic equations  The fundamental theorem of Algebra  Roots of unity  Finite fields.
Instructor: H. Charalambous
Advanced Topics in Linear Algebra
GLSUD8 ADVLA – 0137
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory Elective (Department of Algebra, Number Theory and Math. Logic)
Description: Infinitedimensional vector spaces. Quotient spaces. Isomorphism theorems. Dual spaces. Invariant subspaces. Jordan canonical form. Applications.
Instructor: A. Papistas
Fourier Analysis
GLSUD8 FOURAN  0234
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory elective (Department of Mathematical Analysis)
Description: Trigonometric series. Fourier coefficients, convergence criteria. Summability of Fourier series. Fourier series and space. Applications.
Instructor: P. Galanopoulos
Partial Differential Equations
GLSUD8 PDE  0235
3h/w, 13weeks, written exams, credits: 5.5
Compulsory elective (Department of Mathematical Analysis)
Description: Introduction, some simple PDEs. Wellposed problems. Classical solutions. Weak solutions and regularity. Four important linear PDEs
1) The equation of transport. Initial value problems, the inhomogeneous problem
2) The Laplace and Poisson equations. Fundamental solutions. Elements of the theory of distributions. Mean value formulae. Eigenvalues of harmonic functions. The strong maximum principle and uniqueness of some boundary value problems for Poisson’s equation. Mollifiers and smoothness. Local estimates for the derivatives of harmonic functions. Liouville’s theorem. The Harnack inequality. Green’s function for a halfspace and a ball.
3) The heat equation. Fundamental solution. Similar issues to the case (2)
4) The wave equation
Instructor: A. Fotiadis
Harmonic Analysis
GLSUD8 HARAN  0266
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory elective (Department of Mathematical Analysis)
Description: Harmonic functions on R^{n }  Poisson kernels  Harmonic extensions of the upper halfspace  Singular integral operators and the CalderonZygmund theory.
Instructor: M. Marias
Differential Manifolds II
GLSUD8 DIFMAII  0333
3h/w, 13weeks, written exams, credits: 5.5
Compulsory elective (Department of Geometry)
Description: Riemannian metrics Affine connections Parallel transport Curvature tensor HopfRinow theorem Geodesics and Jacobi fields.
Instructor: F. Petalidou
Cryptography
GLSUD8 CRYPT 0434
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory elective (Department of Numerical Analysis and Computer Science)
Description: Basic concepts Historical examples of cryptosystems  The RC4 and DES cryptosystems  Basic computational number theory  The RSA and Rabin cryptosystems  The DiffieHellman Key Exchange Protocol  The ElGamal and MasseyOmura cryptosystems  Hash functions  The RSA, ElGamal and DSA Digital Signatures.
Instructor: D. Poulakis
Electives
Modern Control Theory
GLSUD8 MOCQNTR  0462
3h/w, 13weeks, written exam., credits: 5
Elective
Description: State space models of LTI continuous time systems. Single input – single output systems. Multivariable systems. Block diagrams and realizations of state space models. Examples. System equivalence and state space coordinate transformations. Examples. Eigenvalues and eigenvectors. Diagonalization of matrices and diagonalization of state space models by coordinate transformations. State space realizations of transfer functions. State space system responses. Unit impulse and unit step response of state space models. LTI systems. Free and forced response of state space models. Canonical forms of state space models. Controllability. Observability. Controllability and Observability criteria. Stabilization of state space models and decoupling zeros. Stability of state space models. Eigenvalue criteria for stability. Asymptotic and BIO stability. State feedback. Eigenvalue assignment by state feedback. Constant output feedback. State Observers and state reconstruction. Stabilization by state observers and state feedback. The separation principle.
Instructor: N. Karampetakis
Sampling
GSLUD8 SAM  0566
3h/w, 13 weeks, written exams, credits: 5
Elective
Description: What is Sampling? Estimation and Estimators  Simple Random Sampling in order to estimate Population (and Subpopulations) Mean  Percentages and Variance  Ratio Estimators and Regression, with socioeconomic applications  Coefficient of Variation  Stratified Sampling with proportional and optimal drawing of sample  Systematic Sampling with administrative applications and applications in populations where the studied random variables have some trend  Cluster Sampling, introduction and study of the cases with 1 and 2 level sampling techniques  Comparison of the studied sampling methods. Indices and their screening, general introduction to indices and a specialized study on price indices  The currency unit ECU as a weighted index.
Instructor: N. Farmakis
Information Theory and Chaos
GSLUD8 ITCH  0570
3h/w, 13 weeks, written exams, credits: 5
Elective
Description: Observation information. Probability and uncertainty. Messages, analogue and digital timeseries, harmonic analysis, wavelets, sampling. Entropy, conditional information, mutual information and interdependence. Uncertainty, predictability, complexity, innovation. Stochastic processes and dynamical systems as sources of information. Ergodicity, mixing, Bernoulli, Kolmogorov and Markov processes. Chaos, noise. Communication channels as transformations of stochastic processes. Markov channel models. Coding, requirements for code generation. Selected applications in Statistics, Physics, Biology. Learning, decision making and games. Graphs and communication networks.
Instructor: I. Antoniou
Statistical Inference
GLSUD8 STIF – 0569
3h/w, 13 weeks, written exams, credits: 5
Elective
Description: Introduction to testing hypothesis  Selecting the test procedure  Testing simple hypothesis  NeymanPearson’s fundamental lemma  Uniformly most powerful tests  Tests for the parameters of one or two normal populations  Likelihood ratio tests.
Instructor: Postdoc
Special Topics B
GLSUD8 SPETOPB – 1162
3h/w, 13 weeks, written exams, credits: 5
Elective
Description: The instructor, in collaboration with the student, specifies a subject.
Instructor: Can be any one of the teaching staff if he/she accepts to teach the course.
FIRST SEMESTER 
Code 
Courses 
Hrs/Credits 

Code 
Courses 
Hrs/Credits 

0102 0108 0201 0430

Compulsory Introduction to Algebra Linear Algebra Calculus I Introduction to Computer Programming 
3 6 5 3


5.5 8 7 5


0601 
Electives Analysis of Mathematical texts in the English language 
3 

3 
SECOND SEMESTER 
Code 
Courses 
Hrs/Credits 

Code 
Courses 
Hrs/Credits 

0202 0301 0401 0430 0501

Compulsory Calculus II Analytic Geometry I Theoretical Informatics I Introduction to Comp. Progr. (rep.) Mathematical Programming

5 3 3 3 3


7 5.5 5.5 5 5.5 

0461

Electives Symbolic Programming Languages

3


5

THIRD SEMESTER 
Code 
Courses 
Hrs/Credits 

Code 
Courses 
Hrs/Credits 

0106 0203 0204 0302 0502 
Compulsory Algebraic Structures I Calculus III Topology of Metric Spaces Analytical Geometry II Probability Theory I

3 4 4 3 4


5.5 7 7 5.5 7 

1061 
Free Elective Introduction to Meteorology and Climatology 
3 

5 
FOURTH SEMESTER 
Code 
Courses 
Hrs/Credits 

Code 
Courses 
Hrs/Credits 

0107 0205 0206 0503 0504 
Compulsory Algebraic Structures II Calculus IV Differential Equations Statistics Mathematical Methods in Operational Research

3 4 4 5 3


5.5 7 7 7 5.5 

1062

Free Electives General and Dynamic Meteorology

3


5

FIFTH SEMESTER 
Code 
Courses 
Hrs/Credits 

Code 
Courses 
Hrs/Credits 

0207 0303 0402 0505 0506
1063 1064 
Compulsory Introduction to Real Analysis Classical Differential Geometry I Numerical Analysis Probability Theory II Stochastic Strategies
Free Electives Seismology Theoretical Mechanics

3 5 3 3 3
3 3 

5.5 7 5.5 5.5 5.5
5 5 

0136 0151
0531
0507

Compulsory Electives Number Theory Computational Methods in Algebra and Algebraic Geometry Regression Models and Applications to Knowledge Processing
Electives Stochastic Processes with Complete Connections and Learning Theory

3 3
3
3


5.5 5.5
5.5
5

SIXTH SEMESTER 
Code 
Courses 
Hrs/Credits 

Code 
Courses 
Hrs/credits 

0208
0563 0963 0967 1161
1066

Compulsory Complex Analysis
Electives Stochastic Processes Didactics of Mathematics Mathematical Software and Knowledge Representation Languages Special Topics A
Free Electives Continuum Mechanics 
4
3 3 3 
3


7
5 5 5 5
5


0131 0231 0232 0331 0332 0431 0532 0533

Compulsory Electives Group Theory Measure Theory Elements of Functional Analysis Linear Geometry I Classical Differential Geometry II Computational Mathematics Matrix Theory Deterministic Methods of Optimization

3 3 3 3 3 3 3 3 3


5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5

SEVENTH SEMESTER 
Code 
Courses 
Hrs/Credits 

Code 
Courses 
Hrs/Credits 

0471 0562 1161 1162 1070

Electives Computational Geometry Stochastic Methods in Finance Special Topics A Special Topics B Practical Training 
3 3   


5 5 5 5 2


0133 0233 0266 0304 0433 0465 0534 0535

Compulsory Electives Mathematical Logic General Topology Harmonic Analysis Differential Manifolds I Classical Control Theory Error Correcting Codes Mathematical Statistics Stochastic Operations Research

3 3 3 3 3 3 3 3


5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5

EIGHTH SEMESTER 
Code 
Courses 
Hrs/Credits 

Code 
Courses 
Hrs/Credits 

0462 0566 0569 0570 0962 1162 1070 
Electives Modern Control Theory Introduction to Sampling Statistical Inference Information Theory and Chaos History of Mathematics Special Topics B Practical Training

3 3 3 3 3  


5 5 5 5 5 5 2


0132 0234 0235 0333 0434

Compulsory Electives Set Theory Fourier Analysis Partial Differential Equations Differential Manifolds II Cryptography
Free Electives

3 3 3 3 3


5.5 5.5 5.5 5.5 5.5

There are two postgraduate programmes in the School of Mathematics of the Aristotle University of Thessaloniki:
® The postgraduate programme in «Mathematics» with three possible tracks, offered since the fall of 2002.
® The postgraduate programme in «Web Science» which has been running since the fall of 2009.
The postgraduate programme in «Mathematics» leads to the award of a Master’s Degree or to a Doctorate in Mathematics. The objective of the programme is the advancement of knowledge and the development of mathematical research and applications.
The Master’s Degree has the following three tracks:
1. Pure Mathematics.
2. Statistics and Mathematical Modelling.
3. Theoretical Computer Science and Control and Systems Theory.
The nominal duration of the Master’s Degree on Mathematics is three semesters of study. Students are expected to complete the coursework during the first two semesters and prepare a Master’s Degree dissertation during the third semester.
The requirements for the award of the Master’s Degree are:
1. For the «Pure Mathematics» track: satisfactory completion of at least 6 courses from categories A, B, C which must include one each from A, B, C of this track.
2. For the «Statistics and Mathematical Modelling» track: satisfactory completion of at least 6 courses from the category SΜ.
3. For the «Theoretical Computer Science and Control Theory» track: satisfactory completion of at least 6 courses from categories A and B, containing at least one each from the categories A and B of this track.
The postgraduate programme in «Web Science» awards a Master’s degree in Web Science. The objective of the programme is to pursue research in Mathematics and all the other disciplines which are involved in the Web, in order to contribute to the development of Greece and the whole world and to contribute to the organization, classification and development of the Web Science.
The duration of the Master’s Degree on «Web Science » is typically three semesters of study. Students are expected to complete the coursework during the first two semesters and write a Master’s Degree dissertation during the third semester. For each of the three semesters of both programmes the number of ECTS credits earned must be at least 30.
Listed below are all the courses offered by the Department of Mathematics in the 20142015 academic year, with the following information: code GMDUD (GreeceMaster’s Degree University Diploma), semester taught, the ECTS code and course number, the number of hours per week, the number of weeks per semester, the type of examination (written), whether or not there is a laboratory component, the number of ECTS credits provided, and an outline of the course. All courses are taught in Greek.
Information on the Postgraduate Programmes may be obtained from the Director of Postgraduate Studies, Professor E. Kappos:
email kappos@math.auth.gr
Tel. 00302310997958
Information is also available via Internet at:
To enquire about the programme, you can contact the ERASMUS coordinators of the School, Profs E. Kappos or F. Petalidou.
Code: Group A: Algebra, Group B: Analysis, Group C: Geometry
Fall Semester
A.2 Algebraic Number Theory
A.5 Representation Theory of Lie Algebras
B.9 Complex Analysis
B.11 Functional Analysis
B.12 Hyperbolic Analysis and Geometry
C.4 Differentiable Manifolds
C.8 Global Differential Geometry
Spring Semester
A.1 Algebraic Geometry
A.12 Topics in Mathematical Logic
B.13 Spaces of Analytic Functions
C.3 Line Geometry
C.9 Symplectic and Poisson Geometry
Third Semester
Master’s Degree Dissertation.
Semester A
A.2 Analytic Number Theory
GMScUD1 0864
3h/w, 13 weeks, written exam., credits 10
Elective
Description: Elements of Group theory, Ring theory and Number theory. Field extensions, Elements of Galois theory. Module theory over commutative rings. Noetherian modules and rings. Algebraic number fields. Integral elements over commutative rings. The ring of algebraic integers of an algebraic number field. Simple extensions. The discriminant of an algebraic number field. Integral bases. Ideals and class group of an algebraic number field. Units. Prime ideals and decomposition of an ideal into product of prime ideals. Ramification theory of Galois extensions of algebraic number fields. Quadratic and Cyclotomic extensions over Q. Abelian extensions.
References:
1. D. S. Dummit and R. M. Foote, Abstract Algebra, John Willey and Sons, Inc., 2005.
2. H. Cohen, Computational Algebraic Number Theory, Springer, 2001.
3. M.Hazewinkel, N. Gubareni and V. V. Kirichenco, Algebras, Rings and Modules, Kluwer Academic Publishers, New York, 2005.
4. G. Janusz, Algebraic Number Fields, AMS, 1995.
5. C. Lakkis, Number Theory, Thessaloniki, 1990 (in Greek)
6. P. Ribenboim, Classical Theory of Algebraic Numbers, Springer, 2000.
7. Th. TheohariApostolidi, Lectures in Number Theory, 2011 (in Greek)
8. Th. TheohariApostolidi and H. Charalambous, Galois Theory, 2016, www.kallipos.gr (in Greek)
Instructor: Th. TheohariApostolidi
A.5 Representation Theory of Lie Algebras
GMDUD2 0634
3h/w, 13 weeks, written exams, 10 credits
Elective
Description: 1. Introduction: Introduction to Lie groups, construction of Lie algebras from Lie groups, basic definitions, derivations, ideals, solvable and nilpotent Lie algebras, example of the Lie algebra sl_{n}(C) 2. Simple and semisimple Lie Algebras: Cartan subalgebras, Killing forms, Weyl group, Dynkin diagrams, classification of semisimple Lie algebras 3. Enveloping Algebras: Definition of enveloping algebras, PoincaréBirkhoffWitt theorem, exponential mapping of Lie algebras to a Lie groups, Casimirs, Hopf structure of enveloping algebra 4. Representations and modules: Theorem of AdoIwasawa, finitedimensional irreducible representations, adjoint representation, tensor representations, induced representations, representations of solvable  nilpotent and semisimple algebras, Verma modules 5. Applications: Symmetries of integrable systems, BäcklundLie symmetries, Lax operators in Hamiltonian systems, LiePoisson algebras, Symmetries of quantum systems and Lie algebras su(2), su(3).
References
1. J. E. Humphreys, Introduction to Lie Algebras and Representation theory, Springer Graduate Texts in Mathematics (1972).
2. W Fulton and J Harris, Representation Theory, Grad. Texts in Maths, Springer (1991).
3. B. C. Hall, Lie Groups, Lie Algebras and Representations, Grad. Texts in Maths. Springer (2003).
4. R. W. Carter et al., Lecture Notes on Lie Groups and Lie Algebras, London Math. Soc. Student Texts 32 (1995).
5. N. Jacobson, Lie Algebras, Dover (1962).
6. A. Roy Chowdhury, Lie Algebraic Methods in Integrable Systems, Chapman & Hall (2000).
7. A. O. Barut and Raczka, Theory of Group Representations and Applications, World Scientific (1986).
Instructor: C. Daskaloyiannis
B.9 Complex Analysis
GMDUD2 0641
3h/w, 13 weeks, written exams, 10 credits
Elective
Description: Analytic functions. The general form of Cauchy’s theorem. Local uniform convergence of analytic functions, the theorem of Weierstrass. Infinite products, canonical decomposition, Blaschke products. Runge’s approximation theorem. Normal families of analytic functions, Montel’s theorem. Conformal mappings, the Riemann mapping theorem, the MittagLeffler theorem. Harmonic functions, the maximum principle, the Dirichlet problem, subharmonic functions. Schwarz’s symmetry principle, theorems of Bloch, Schottky, MontelCaratheodory and Picard.
Prerequisites: Elements of complex functions, topology of metric spaces.
References
1. Ahlfors L. V., Complex Analysis, McGrawHill 1979.
2. Caratheodory C., Theory of Functions I and II, Chelsea Publishing Company 1960.
3. Sarason D., Complex Function Theory, Second Edition, Amer. Math. Soc. 2007.
4. Saks S. and Zygmund A., Analytic Functions, Elsevier 1971.
Instructor: D. Betsakos
B.11 Functional Analysis
GMDUD1 0644
3h/w, 13 weeks, 10 credits
Elective
Description: Topological vector spaces, linear operators and functionals. Dual space. The HahnBanach theorem, second dual space. Finitedimensional spaces. Locally convex spaces. Quotient space, Uniform Boundedness, Open Mapping and Closed Graph theorems. Weak and weak* topologies, BanachAlaoglu theorem, KreinMilman theorem, adjoint operator, compact operators.
Reference
W. Rudin: Functional Analysis
Instructor: P. Galanopoulos
B.12 Hyperbolic Analysis and Geometry
GMDUD1 0648
3h/w, 13 weeks, written exams, 10 credits
Elective
Description: Möbius transformations, basic models of hyperbolic geometry, isometries, distance formulas, comparison with Euclidean geometry, groups of isometries, fundamental domains, the limit set, hyperbolic surfaces, heat kernel estimates.
References
1. Anderson J.W. (2007) Hyperbolic Geometry. 2^{nd} ed. Springer.
2. C. Series (2013) Hyperbolic Geometry. Notes Warwick University. Available at: http://homepages.warwick.ac.uk/~masbb/Papers/MA448.pdf
3. Davies E.B. and N. Mandouvalos (1988). Heat kernels bounds on Hyperbolic Space and Kleinian groups. Proc. London Math. Soc. 57 (No 3): 182208.
Instructor: A. Fotiadis
C.4 Differentiable Manifolds
GMDUD2 0658
3h/w, 13 weeks, written exams, 10 credits
Elective
Description: Differentiable Manifolds (review of basic notions). Riemannian metrics. Affine connections. Geodesics, curvature. Riemannian submanifolds. Complete manifolds: theorems of HopfRinow and Hadamard. Spaces of constant curvature.
References
1. M. P. do Carmo, Riemannian Geometry, Birkhäuser 1992.
2. John M. Lee, Riemannian manifolds. An introduction to curvature, GTM 176, SpringerVerlag 1997.
3. W. Boothby, An introduction to differentiable manifolds and Riemannian geometry, Academic Press 1975.
4. Loring W. Tu, An introduction to Manifolds, Universitext, Springer 2011.
5. John M. Lee, Introduction to Smooth Manifolds, GTM 218, Springer 2003.
Ιnstructor: F. Petalidou
C.8 Global Differential Geometry
GMDUD1 0655
3h/w, 13 weeks, written exams, 10 credits
Elective
Description: Elements of the theory of differentiable manifolds: Triangulation of manifolds, closed surfaces. Characterizations of the sphere (Theorems of Liebmann etc.) The GaußBonnet theorem and its applications, Minkowski΄s integral formulae. The index method (Poincaré). Congruence theorems for ovaloids, rigidity of ovaloids. Uniqueness theorems for the problems of Minkowski and Christoffel. The maximum principle method, complete surfaces. The HopfRinow theorem. The CohnVossen inequality.
Prerequisites: Classical Differential Geometry I and II.
References
1. Blaschke W. und Leichtweiß K. Elementare Differentialgeometrie. Springer (1973).
2. Hopf H. Differential Geometry in the Large. Lecture Notes in Mathematics N^{o} 1000. Springer (1983).
3. Hsiung C.C. A First Course in Differential Geometry. Wiley (1981).
4. Huck H. et al. Beweismethoden der Differentialgeometrie im Großen. Lecture Notes in Mathematics N^{o} 335 Springer (1973).
5. Klingenberg W. A Course in Differential Geometry. Springer (1978).
6. Stephanidis N. Differential Geometry, Vol. II, Thessaloniki (1987). (in Greek).
Instructors: S. Stamatakis, G. Stamou
Semester B
A.1 Algebraic Geometry
GMDUD2 0637
3h/w, 13 weeks, written exam, 10 credits
Elective
Description: Commutative rings: principal ideal domains, unique factorization rings. Resultants, Noetherian rings. Elements of general topology: open and closed sets, domains, covers of a set. Continuous functions. Afiine varieties: algebraic sets in A^{n}, algebraic and semialgebraic varieties. Hilbert’s Nullstellensatz, coordinate ring, Noetherian topological spaces. Projective varieties: algebraic sets in P^{n}, projective Nullstellensatz, projective cover of a variety. Morphisms: regular functions, function fields of a variety. Basic properties of morphisms, finite morphisms, rational maps. Products of varieties: product of affine varieties, product of projective varieties. Segre embedding, image of a projective variety. Dimension of a variety: dimension of topological spaces, Krull dimension of a ring, dimension of the intersection of a variety with a hypersurface, dimension and morphisms.
References
1. Cox D. A., Little J. B. and O’Shea D. B. (1998) Ideals, Varieties and Algorithms. Introduction to Computational Algebraic Geometry and Commutative Algebra. SpringerVerlag.
2. Dieudonné J. (1974) Cours de Géométrie Algébrique. PUF.
3. Fulton. W. (1978). Algebraic Curves. Benjamin.
4. Harris J. (1992). Algebraic Geometry. Springer Verlag.
5. Kendig K. (1977). Elementary Algebraic Geometry. Springer Verlag.
6. Mumford D. (1995) Algebraic Geometry I. Complex Projective Varieties. Springer Verlag.
7. Perrin D. (1995) Géométrie Algébrique. InterÉditions/Éditions CNRS.
8. Shafarevich I. R. (1994). Basic Algebraic Geometry. Springer Verlag.
9. Smith K. E., Kahanpää, Kekäläinen and Traves W. (2000). An Invitation to Algebraic Geometry. Springer Verlag.
10. Kunz E. (1985). Introduction to Commutative Algebra and Algebraic Geometry. Birkhäuser.
Instructor: D. Poulakis
A.12 Topics in Mathematical Logic
GMDUD2 0639
3h/w, 13 weeks, 10 credits
Elective
Description: The intuitive notion of total and partial algorithm and the consequent concepts of computable function, computable set and computably enumerable set that arise from it. First formalization of computable functions through recursive functions. The class of primitive recursive functions and sets. The Ackermann function and the general class of recursive functions and sets. Recursively enumerable (r.e.) sets and their various characterizations. Arithmetization of recursive functions and Kleene's Normal Form theorem. The Halting Problem, the smn theorem and the Rice theorem. Kleene's FixedPoint theorems. Second formalization of computable functions through Turing Machines. Turingcomputable functions and their equivalence with the class of recursive functions. The ChuchTuring Thesis.
Instructor: A. Tzouvaras
B.13 Spaces of Analytic Functions
GMDUD2 0863
3h/w, 13 weeks, 10 credits
Elective
Description: Basic properties of some important Banach spaces of analytic functions on the unit disk. Study of functions on the basis of their growth properties, their Taylor coefficients, derivative, geometric properties and the existence of boundary values. Such spaces are Bloch spaces, Dirichlet spaces, Hardy spaces and spaces of bounded mean oscillation.
References
1. P. Duren, Theory of H^{p} spaces, Dover 2000
2. K. Zhu, Operator theory in function spaces, 2^{nd} ed. AMS 2007.
3. P. Koosis, Introduction to Hp spaces, 2^{nd} ed. Cambridge University Press 1998
4. K. Hoffman, Banach spaces of analytic functions, Dover 1990.
Instructor: A. Siskakis
C.3 Line Geometry
GMDUD2 0666
3h/w, 13 weeks, 10 credits
Elective
Description: Α. Introduction: CayleyKlein geometries and the Erlangen program. The ndimensional affine space. The ndimensional projective space. Plücker coordinates.
B. Ruled surfaces: Parameter of distribution and striction curve of a ruled surface. Developable surfaces. The Sannia and the Kruppa moving frame. Derivative equations. Complete system of invariants. Minding isometries. Closed ruled surfaces. Linear and angular opening. Right helicoid. Edlinger surfaces.
C. Line congruences: Moving frame and the integrability conditions. Focal surfaces. Curvature and mean curvature of a line congruence. The middle surface and the middle envelope. The Sannia and the Kruppa principal surfaces. Integral formulae. Closed line congruences. Specific line congruences.
Prerequisites: Classical Differential Geometry I and II
References
1. Farouki R.: Pythagorean – Hodograph Curves: Algebra and Geometry Inseparable. Springer (2008)
2. Finikow S. P.: Theorie der Kongruenzen. AkademieVerlag (1959)
3. Hoschek J.: Liniengeometrie. Bibliographisches Institut (1971)
4. Pottmann H., Wallner J.: Computational Line Geometry. Springer (2001)
5. Stephanidis N.: Differential Geometry. Vol II, Thessaloniki (1987) (in Greek)
Instructor: S. Stamatakis
C.9 Symplectic and Poisson Geometry
GMDUD2
3h/w, 13 weeks, 10 credits
Elective
Description: Symplectic vector spaces and symplectic forms. Symplectomorphisms. Generating functions. Theorem of Darboux. Lagrangian submanifolds. Contact forms and manifolds, Kähler manifolds. Elements of Hamiltonian mechanics. The moment map. MarsdenWeinstein reduction. Poisson brackets and Poisson manifolds.
References
1. A. Cannas da Silva: Lectures on Symplectic Geometry (LNM1764 2001, 2008)
2. R. Berndt: An Introduction to Symplectic Geometry (AMS 2007)
3. Arnold V.I. Mathematical Methods of Classical Mechanics (2^{nd} ed.) (Springer 1982)
Instructor: E. Kappos
Semester C
Master’s Degree Dissertation
GMDUD2 0600
13 weeks, 30 credits.
Semester A
SM.02 Time Series Analysis
SM.07 Dynamic Modelling
SM.10 Optimal Control Theory (see TCSCST track)
SM.14 Quantic Information and Computation
SM.22 Statistics and Decision Making
Semester B
SM.06 Sampling and Statistical Processing
SM.24 Stochastic Methods
SM.27 Special Topics I: Information Theory, Entropy and Complexity
Semester C
Master’s Degree Dissertation
Semester A
SM.02 Time Series Analysis
GMDUD1 0747
3h/w, 13 weeks, written exams, 10 credits
Elective
Description: Introduction. Basic characteristics of TS. Linear stochastic processes. Stationary linear models. Nonstationary linear models. Forecasting. Spectral analysis. Nonlinear analysis of TS.
References
1. Brockwell P.J. and R.A. Davis (2002). Introduction to Time Series and Forecasting. 2^{nd} edition. Springer Verlag, New York.
2. Cryer J. (1986). Time Series Analysis. Wadsworth Pub Co.
3. Kantz H. and T. Schreiber (1999). Nonlinear Time Series Analysis. Cambridge University Press.
4. Tong H. (1997). NonLinear Time Series: A Dynamical System Approach (Oxford Statistical Science Series, 6). Oxford University Press.
5. Vandaele W. (1997). Applied Time Series and BoxJenkins Models. Academic Press, New York.
Instructors: D. Kugiumtzis
SM.07 Dynamic Modelling
GMDUD1 0750
3h/w, 13 weeks, written exams, 10 credits
Elective
Description: Phenomenological Laws, Scientific Method, Mathematical Modelling, the Prediction Problem. Differential Equations, Difference Equations and Dynamical Systems. Classification, Stability, Solutions (Analytic, Approximate, Numerical), Simulations. Selective Applications. Chaos, Random Number Generators, Population Dynamics and Chemical Reactions, Economics, Biology, Signals and Filters, Cellular Automata, Dynamics of Communication Νetworks.
Τhe Objectives of the course are:
1) The understanding of Mathematical modelling in terms of Dynamical Systems in discrete time (Difference Equations) and in continuous time (Differential Equations).
2) The exploration of the possibilities and the identification of the difficulties to find solutions of dynamical models
3) The relevance of approximations and errors in applications.
References
1. Arnold V.I. (1978) Ordinary Differential Equations, MIT Press, Cambridge, MA.
2. Blum L., Cucker F., Shub M., Smale S. (1988), Complexity and Real Computation. Springer, New York.
3. Gustafson K. (1999), Introduction to Partial Differential Equations and Hilbert Space Methods. Dover, New York.
4. Hirsch M., Smale S. (1974), Differential Equations, Dynamical Systems and Linear Algebra. Academic Press, London.
5. Hörmander Lars, The Analysis of Linear Partial Differential Operators:
Vol.1: Distribution Theory and Fourier Analysis. Springer (1990).
Vol.2: Differential Operators with Constant Coefficients. Springer (1999).
Vol.3: PseudoDifferential Operators. Springer (1985).
Vol.4: Fourier Integral Operators. Springer (1994)
6. Kalman R. (1968), On the Mathematics of Model Building, in “Neural Networks”. ed. by E. Caianelo, Springer New York.
7. Katok A., Hasselblatt B.1995, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, Cambridge, UK.
8. Kulesovic M.R.S., Merino O. (2002), Discrete Dynamical Systems and Difference Equations with Mathematicα. CRC Press.
9. Polyanin A.D., Zaitsev V.F. (2002), Handbook of Exact Solutions for Ordinary Differential Equations, CRC Press.
10. Sobolev S. (1989), Partial Differential Equations of Mathematical Physics. Dover, New York.
11. Wolfram S. (2002), A New Kind of Science. Wolfram Media, Champaign, Illinois.
12. Vvedesnsky D. (1992), Partial Differential Equations with Mathematica. Addison Wesley, New York.
Instructor: I. Antoniou.
SM.10 Optimal Control Theory (see TCSCST track, Course B.8)
SM.14 Quantic Information and Computation
GMDUD1 0751
3h/w, 13 weeks, written exams, 10 credits
Elective
Description: Introduction to Quantum Mechanics: Mathematical Introduction (Hilbert Spaces, Spectrum of selfadjoint and unitary operators, Lie group U(N), control theory of groups), Quantum states and observables, the state space of Hilbert space, the state space as a set of definite operators.
Quantum information theory: Quantum computer structure, quantum hits and registers, quantum gates, Toffoli theorem, invertible gates, quantum circuits and networks, Deutsch theory of elementary gates, decomposition in elementary gates, quantum codes, error correction and decoherence.
Quantum algorithms: Shannon entropy, Quantum entropy, Quantum transportation, Quantum cryptography.
References
1. Alicki R., Fannes M., Quantum Dynamical Systems, Oxford University Press, Oxford U.K.
2. Bohm A. (1993), Quantum Mechanics, Foundations and Applications, 3d ed, Springer, Berlin.
3. Fock V.A. (1986), Fundamentals of Quantum Mechanics Mir Publishers, Moscow.
4. Jammer M. (1974), The philosophy of Quantum Mechanics, Wiley, NewYork.
5. Jauch J.M. (1973), Foundations of Quantum Mechanics, AddisonWesley, Reading, Massatussetts.
6. Mackey G.W. (1957), Quantum Mechanics and Hilbert Space, Αmerican Mathematical Monthly 64, 4557.
7. Mackey G.W. (1963), The Mathematical Foundations of Quantum Mechanics, Benjamin, New York.
8. Prugovecki E. (1981), Quantum Mechanics in Hilbert Space, Academic Press, New York.
9. Von Neumann J. (1932), Mathematical Foundation of Quantum Mechanics. Princeton Univ. Press, New Jersey.
10. Benenti G., Casati G, Strini G. (2005), Principles of Quantum Computation and Information.
Vol I: Basic Concepts. World Scientific, Singapore.
Vol II: Basic Tools and Special Topics. World Scientific, Singapore.
11. Bernstein E., Vazirani U. (1997), Quantum Complexity Theory. SIAM J. Comput. 26, 14111473.
12. Chen G., Brylinsky R, editors (2002), Mathematics of Quantum Computation, Chapman and Hall/VRC, Florida, USA.
13. Feynman R.P. (1967), Quantum Mechanical Computers. Foundations of Physics, 16, 507531.
14. Ingarden R.S. (1976), Quantum Information Theory. Rep. Math. Physics 10, 4372.
15. Nielsen A.M., Chuang I.L. (2000), Quantum Computation and Quantum Information. Cambridge University Press, Cambridge UK.
16. Ohya M., Petz D. (2004), Quantum Entropy and its Use. 2^{nd} Printing, Springer, Berlin.
17. Vitanyi P. M. B. (2001), Quantum Kolmogorov Complexity based on Classical Descriptions. IEEE Transactions on Information Theory 47, 24642479.
Instructors: I. Antoniou, C. Panos
SM.22 Statistics and Decision Making
GMDUD1 0749
3h/w, 13 weeks, written exams, 10 credits
Elective
Description: The characteristic functions for the multivariate random variables. The multivariate normal distribution and related topics. Application in statistical analysis (Cochran’s theorem, ANOVA, regression, χ^{2}). Statistical inference: The NeymanPearson lemma. Likelihood ratio test and related procedures. Decision theory.
References
1. Lehman E.L. (1986), Testing Statistical hypotheses. John Wiley & Sons.
2. Patrick Billingsley (1995), Probability and Measure. John Wiley & Sons.
3. Feller W. (1971), An Introduction to probability theory and its Applications. John Wiley & Sons.
4. DacunhaCastelle P. and Duflo M. (1986), Probability and Statistics. Volumes I and II. SpringerVerlag.
5. F. KolyvaMachera (1998), Mathematical Statistics. Ziti, Thessaloniki. (in Greek).
Instructor: D. Ioannidis, F. KolyvaMachera.
Semester B
SM.06 Sampling and Statistical Processing
GMDUD2 0748
3h/w, 13 weeks, written exams, 10 credits
Elective
Description: Part 1: Sampling and its applications in Social and Economic Issues, Methods and Techniques of Sampling, Surveys from A to Z.
Part 2: Preparation of a questionnaire and checking of its reliability. Kinds of questions and specialization of their use. From the questionnaire data to the efiles via random variables and coding of answers. Elaboration of the filled data.
Part 3: Some issues of Sampling of specific content, like: “Searching for linear trend of sampling data”, “searching for periodicities of data”, “Creating equation of probabilities (2^{nd} degree model) from twodimensional data, etc.”, “Coefficient of Variation and its applications, e.g. symmetric model of probability density function”.
References
1. Farmakis Ν. (2009), Introduction to Sampling, Christodoulidis, Thessaloniki. (in Greek).
2. Farmakis Ν. (2009), Survey and Ethics, Christodoulidis, Thessaloniki. (in Greek).
3. Javeau C. (2000) Questionnaire Based Survey, Typothito, G. Dardanos, Athens (Greek translation)
4. Cochran W. (1977) Sampling Techniques, John Wiley, New York.
Instructor: N. Farmakis
SM.24 Stochastic Methods
GMDUD2 0746
3h/w, 13 weeks, written exams, 10 credits
Elective
Description: Renewal theory, limit theorems, Wald equation, key renewal theorem, renewal processes with reward, semiMarkovian processes, discrete and continuous time, martingales, Brownian motion.
References
1. Howard R.A. (1971). Dynamic Probabilistic Systems. Volumes I and II. John Wiley and Sons; New York.
2. Ross S.M. (1995). Stochastic Processes. John Wiley and Sons; New York.
3. Ross S.M. (2000). Introduction to Probability Models. 7^{th} edition. John Wiley and Sons; New York.
Instructors: A. Papadopoulou, G. Tsaklidis, P.C. Vassiliou.
SM.27 Special Topics I (Information Theory, Entropy and Complexity)
GMDUD2 860
3h/h, 13 weeks, 10 credits
Elective
Description: Information and entropy, uncertainty and variety, interdependence, mutual information and correlation. Information sources. Stochastic processes, dynamical systems and chaos. Entropy and innovation. Communication channels. Coding, cryptography and security. Network entropy and data analysis by networks. Syntactic and semiological processing. Quantum information and applications to networks.
References
Systems and Complexity:
1. Antoniou I. 1991, "Information and Dynamical Systems", p221236 in "Information Dynamics", ed. Atmanspacher H., Scheingraber H., Plenum, New York
2. Antoniou I., Christidis Th., Gustafson K. 2004, “Probability from Chaos”, Int. J. Quantum Chemistry 98,150159
3. Devaney R. 1992, A First Course in Chaotic Dynamical Systems. Theory and Experiment, AddisonWesley, Reading, Massachusetts
4. Honerkamp J. 1994, Stοchastic Dynamical Systems: Concepts, Numerical Methods, Data Analysis, Wiley, New York
5. Honerkamp J. 1998, Statistical Physics. An Advanced Approach with Applications, Springer, Berlin.
6. Katok A., Hasselblatt B. 1995, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, Cambridge, UK
7. Meyers R. (Ed.) 2009, Encyclopedia of Complexity and Systems Science, Springer, New York.
8. Skiadas Christos, Skiadas Charilaos 2009, Chaotic Modelling and Simulation. Analysis of Chaotic Models, Attractors and Forms, CRC Press, London
9. Sinai Ya. 1989, Kolmogorov’s Work on Ergodic Theory, Annals of Probability 17, 833839
Probability and Statistics:
1. Billingsley P. 1985, Probability and Measure, Wiley, New York
2. Cox R. 1961, The Algebra of Probable Inference, John Hopkins Press, Baltimore.
3. Doob J.L. 1953 Stochastic Processes, Wiley, New York.
4. Epstein R. 1977, The Theory of Gambling and Statistical Logic, Academic Press, London
5. Feller W. 1968, An Introduction to Probability Theory and Its Applications I, Wiley, New York
6. Feller W. 1971, An Introduction to Probability Theory and Its Applications II, Wiley, New York
7. Ferguson T. 1997, Mathematical Statistics: a Decision Theoretic Approach, Academic Press
8. Gardiner C. 1983, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, Springer, Berlin
9. Gheorghe A. 1990, Decision Processes in Dynamic Probabilistic Systems, Kluwer, Dodrecht
10. Whittle W. 2000, Probability via Expectation, 4th ed., Springer, Berlin
11. Van Kampen N. 1981, Stochastic Processes in Physics and Chemistry, North Holland, Amsterdam
Information and Entropy:
1. Applebaum D. 2008, Probability and Information. An Integrated Approach 2nd ed, Cambrigre Univ. Press, Cambridge, UK.
2. Ash, R. 1965, Information Theory, Wiley; Dover, New York 1990
3. Billingsley P. 1965, Ergodic Theory and Information, Wiley, New York
4. Blum L., Cucker F., Shub M., Smale S. (1998) Complexity and Real Computation, Springer, New York.
5. Cover T.,Thomas J. 2006, Elements of Information Theory, Wiley, New York
6. Cucker F., Smale S. 2001, On the Mathematical Foundations of Learning, Bull. Am. Math. Soc. 39, 149
7. Frieden R. 2004, Science from Fisher Information: A Unification, Cambridge University Press, Cambridge.
8. Kakihara Y. 1999, Abstract Methods in Information Theory, World Scientific, Singapore
9. Khinchin A. 1957, Mathematical Foundations of Information Theory, Dover, New York.
10. Kullback S. 1968, Information Theory and Statistics, Dover, New York.
11. Li M., Vitanyi P. 1993, An Introduction to Kolmogorov Complexity and its Applications, Springer. New York
12. MacKay D. 2003, Information Theory, Inference, and Learning Algorithms, Cambridge, UK.
13. Rényi A. 1961, On Measures of Entropy and Information, Proc. 4th Berkeley Symposium on Mathematics, Statistics and Probability, University of California Press, p 547561
14. Renyi A. 1984, A Diary in Information Theory, Wiley, New York.
15. Reza F. 1961, An Introduction to Information Theory, McGrawHill, New York
16. Rohlin V. 1967, Lectures on the Entropy Theory of Measure Preserving Transformations, Russ. Math. Surv. 22, No 5,152
17. Shannon C.,Weaver W. 1949, The Mathematical Theory of Communication, Univ. Illinois Press, Urbana.
18. Yaglom A.,Yaglom I. 1983, Probability and Information, Reidel, Dordrecht.
Digital Communication, WWW:
1. Negroponte N. 1995, Being Digital, Hodder London. Ελλην. Μεταφρ. Eκδ. Καστανιώτης, Αθηνα, 2000
2. Dertouzos M. 1997, What Will Be? How the World of Information Will Change Our Lives, Harper Collins, New York. Ελλην. Μεταφρ. Eκδ. Γκοβοστη 1998.
3. Dertouzos M. 2001, The Unfinished Revolution : How to Make Technology Work for Us—Instead of the Other Way Around,Harper Collins, New York. Ελλ. Μεταφρ. Eκδ. Λιβανη, Αθηνα, 2001
4. BernersLee T, Fischetti M. 1997, Weaving The Web , Harper Collins, New York. Ελλην. Μεταφρ. Eκδ. Γκοβοστη , Αθηνα, 2002.
5. Shadbolt N., Hall W., BernersLee T. 2006, The Semantic Web Revisted
Networks:
1. Antoniou I., Tsompa E. 2008, Statistical Analysis of Weighted Networks, Discrete Dynamics in Nature and Society 375452 doi:10.1155/2008/375452.
2. Baldi P., Frasconi P. and Smyth P., 2003, Modeling the Internet and the Web, Wiley, West Sussex.
3. Barabasi A.L. 2002, Linked: The new Science of Networks, Perseus, Cambridge Massachussetts.
4. Boccaletti S., Latora V., Moreno Y., Chavez M., Hwang D.U., 2006, Complex networks: Structure and dynamics, Physics Reports, 424, 175 – 308.
5. Bondy J. and Murty U. 2008, Graph Theory, Springer.
6. Bollobas B., 1985, Random Graphs, Academic Press, London.
7. Brandes U., Erlebach T. 2005, Network Analysis, SpringerVerlag Berlin Heidelberg.
8. Dehmer M. 2008, InformationTheoretic Concepts for the Analysis of Complex Networks, Applied Artificial Intelligence 22, 684–706
9. Dehmer Μ., Mowshowitz A. 2011, A history of Graph ΕntropyΜeasures, Information Sciences 181, 5778
10. De Nooy W., Mrvar A., Batagelj V., 2007, Explanatory Social Network Analysis with Pajek, Cambridge University Press, NY.
11. Dorogovtsev S., Mendes G. , 2003, Evolution of Networks, Oxford Univ. Press, UK.
12. Easley D. and Kleinberg J., 2010, Networks, Crowds, and Markets: Reasoning about a Highly Connected World, Cambridge University Press.
13. Li J., et.al. 2008, Network Entropy Based on Topology Configuration and Its Computation to Random Networks, Chin. Phys. Letters 25, 41774180
14. Rosen K. et al., 2000, Handbook of Discrete and Combinatorial Mathematics, CRC Press, USA.
15. Sole R. and Valverde S. 2004, Information Theory of Complex Networks: Evolution and Architectural Constraints, Lect. Notes Phys. 650, 189204
16. Tutzauer F. 2007, Entropy as a measure of centrality in networks characterized by pathtransfer flow, Social Networks 29, 249–265
Quantum Entropy, Information and Networks:
1. Bernstein E., Vazirani U. 1997, Quantum Complexity Theory, SIAM J. Comput. 26, 14111473.
2. Chen G., Brylinsky R. , editors 2002, Mathematics of Quantum Computation, Chapman and Hall/VRC, Florida, USA.
3. Gnutzman S., Smilansky U. 2006, Quantum graphs: applications to quantum chaos and universal spectral statistics, Adv. Phys. 55 527625
4. Mahler G., Weberruss V. 1995, Quantum Networks. Dynamics of Open Nanostructures, SpringerVerlag, Berlin
5. Ohya M., Volovich Ι. 2011, Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano and Biosystems, Springer, Berlin.
Instructor: I Antoniou
Semester C
Master’s Degree Dissertation
GMDUD3 0700
13 weeks, 30 credits
Semester: A
A.10 Formal Language Theory
A.11 Quantic Information and Computation
A.12 Cryptography
B.5 Geometric Control Theory
B.8 Optimal Control Theory
B.10 Convex Optimization
Semester: B
A.4 Automata over Semirings
A.9 Information Theory
A.15 Stochastic Methods
B.3 Numerical Methods with Applications to the Solution of ODEs and PDEs
B.9 Multivariable Control Systems
B.12 Predictive Control
B.15 Special Topics I: Robust Control
Semester: C
Master’s Degree Dissertation
Semester A
A.10 Formal Language Theory
GMDUDI
3h/w, 13 weeks, written exams, 10 credits
Elective
Description: Words. Infinite words and ωlanguages. Automata over infinite words, with Büchi and Muller acceptance conditions. ωRecognizable languages. Closure properties of ωrecognizable languages. The complement of an ωrecognizable language. Monadic secondorder logic. The expressive equivalence of sentences from monadic second order logic and automata over infinite words. Application of automata over infinite alphabets to modelchecking.
Instructor: G. Rahonis
A.11 Quantic Information and Computation
GMDUD1 0751
3h/w, 13 weeks, written exams, 10 credits
Elective
Description: Mathematical Foundation of Quantum Theory. Quantum Information and Von Neumann Entropy. Boole Algebras and Classical Gates. Quantum Logic and Quantum Gates. Quantum Algorithms. Quantum Teleportation and Cryptography. Realization of Quantum Computers. Perspectives of Quantum Information.
References:
Selected References on Quantum Theory:
Selected References on Quantum Theory Information and Quantum Computing:
Instructors: I. Antoniou, C. Panos, C. Daskalogiannis
A.12 Cryptography
GMDUD1 0840
3h/w, 13 weeks, written exams, 10 credits
Elective
Description: Classical Cryptosystems  Perfect Security  Feedback Shift Register  Basic Computational Number Theory  RSA Cryptosystem  Rabin Cryptosystem  Primality Testing  Factorization Methods  Discrete Logarithm  DiffieHellman Protocol  ElGamal Cryptosystem  OkamotoUchiyama Cryptosystem  Digital Signatures  Cryptographic Protocols.
Remark: The basic concepts of Linear Algebra, Algebraic Structures and Number Theory are needed for the aforementioned course.
References
4. N. Koblitz, A course in Number Theory and Cryptography, NewYork, Berlin, Heidelberg, SpringerVerlag (1987).
5. J. A. Buchmann, Introduction to Cryptography, NewYork, Berlin, Heidelberg, SpringerVerlag (2001).
6. N. P. Smart, Cryptography, McGraw Hill; Boston (2003).
7. E. Bach, J. Shallit, Algorithmic Number Theory, Vol 1, MIT Press (1997).
Instructor: D. Poulakis.
B.5 Geometric Control Theory
GMDUD2 0673
3h/w, 13 weeks, 10 credits
Elective
Description: Elements of differential geometry: manifolds, tangent bundles, vector fields and differential form. Control system formulations, distributions and fibrations. Controllability and analysis of reachable sets. Lyapunov stability theory, index theory for vector fields, Hopf theorem. Singular perturbations. Feedback equivalence and linearization. Aspects of global control design.
References
1. H. Khalil: Nonlinear Systems, Prentice Hall, 2001
2. S. Sastry: Nonlinear Systems, Analysis, Stability and Control, Springer 1999.
3. M. Vidyasagar: Nonlinear Systems Analysis, Prentice Hall 1978, SIAM 2001.
4. E. Kappos: Global Controlled Dynamics, A Geometric and Topological Analysis, web 2008.
Instructor: E. Kappos
B.8 Optimal Control Theory
GMDUD1 0844
3h/w, 13 weeks, written exams, 10 credits
Elective
Description: The optimal control problem, basic mathematical notion from the variational calculus, minimization of functionals, EulerLagrange equation, minimization of functional under constraints, optimal control of continuous or discrete time systems with or without state/input constraints, the minimum principle of Pontryagin, the linear quadratic (LQ) regulation and tracking problem, the Riccati equation, minimum time control, HamiltonJacobiBellman theory: exact and approximate solutions, convexification, dynamic programming, state observation in a stochastic environment, Kalman filter, the linear quadratic Gaussian (LQG) problem, applications to practical problems (energyefficient buildings, traffic control, robotics, intelligent web.)
References
1. Burl J.B. (1998). Linear Optimal Control: H_{2} and H_{∞} Methods. AddisonWesley.
2. Lewis F.L. (1995). Optimal Control. 2^{nd} edition. John Wiley and Sons; New York.
3. Donald E. Kirk (1970), Optimal Control Theory : An Introduction, Prentice Hall.
5. A. Sinha, 2007, Linear systems : optimal and robust control, CRC Press
6. Karampetakis Ν., (2009), Optimal Control of Systems, Εκδόσεις Ζήτη. (in Greek)
Instructor: N. P. Karampetakis, G. Tsaklidis
B.10 Convex Optimization
GMDUD1 0850
3h/w, 13 weeks, written exams, 10 credits
Elective
Description: Introductory notions. Theory: convex sets, convex functions, convex optimisation problems in automatic control. Applications: solution of convex optimisation problems in robust control, LMI methods, bilinear matrix inequality methods. Algorithms: development of algorithms for the solution of convex optimisation problems, interior point algorithms, software.
References
1. Stephen Boyd, Lieven Vandenberghe: Convex Optimization, Cambridge University Press 2004
2. Edwin K. P. Chong, Stanislaw H. Zak, An Introduction to Optimization, 4th Edition, Wiley 2013
3. Giuseppe C. Calafiore, Laurent El Ghaoui, Optimization Models, Cambridge University Press 2014
Instructor: O. Kosmidou
Semester B
A.4 Automata over Semirings
GMDUD1 0865
3h/w, 13 weeks, written exam, 10 credits
Elective
Description: Semirings. Weighted automata over semirings. Recognizable series. Properties of recognizable series. The determinization problem for weighted automata. Decidability problems. Applications: fuzzy languages, digital image compression.
References
Droste M., Kuich W., Vogler H. (eds) Handbook of Weighted Automata, EATCS Monographs in Theoretical Computer Science, Springer 2009.
Instructor: G. Rahonis
A.9 Information Theory
GMDUD1 0865
3h/w, 13 weeks, written exam, 10 credits
Elective
Description: Information and entropy. Uncertainty and diversity. Mutual information and correlation, information sources, chaos and innovation, communication channels, coding, cryptography and security. Quantic information, network entropy, transmission entropy and data analysis in networks, applciations of quantic information in networks. Network entropy, syntactic and semantic processing.
References:
Instructor: I. Antoniou
A.15 Stochastic Methods see SM.24
Β.3 Numerical Methods with Applications to Ordinary and Partial Differential Equations
GMDUD2 0853
3h/w, 13 weeks, written exam. 10 credits
Elective
Description: Initial and boundary value problems. Numerical methods for the solution of ordinary differential equations with initial and boundary conditions. Methods of single step and multiple step, stability, predictorcorrector methods, stiff ODE. Linear and nonlinear methods. Shooting. Linear and nonlinear methods of finite differences. Variational techniques. Finite difference methods for elliptic, parabolic and hyperbolic problems. Introduction to the finite element method.
References
1. Faires J. Douglas & Burden L. Richard, (1993). Numerical Methods, PWSKENT Publ. Comp.
2. Lapidus Leon, Seinfeld H. John, (1971). Numerical Solution of Ordinary Differential Equations, Academic Press Inc.
3. Smith G.D., (1965, 1969, 1974). Numerical Solution of Partial Differential Equations, Oxford Univ. Press.
4. Mitchell A.R. & Griffiths D.F., (1980). The Finite Difference Method in Partial Differential Equations, John Wiley & Sons
Instructor: M. GousidouKoutita
Β.9 Multivariable System Theory
GMDUD1 0843
3h/w, 13 weeks, written exams, 10 credits
Elective
Description: Real rational vector spaces and rational matrices, polynomial matrix models of linear multivariable systems, pole and zero structure of rational matrices at infinity, dynamics of polynomial matrix models. Proper and Ωstable rational functions and matrices, feedback system stability and stabilization, some algebraic design problems.
References
Instructor: AI. Vardoulakis.
B.12 Predictive Control
GMDUD2 0848
3h/w, 13 weeks, written exam., credits 10
Elective
Description: Review of control concepts. Introduction to the analysis of discrete systems: discrete transfer functions, ztransform, conversion to analog signals, definition of stability, sampling systems, sample analysis, discrete PID, controller parametrizations. Discrete optimal control systems: linear quadratic control, guidance and regulation problems. Optimal state and model parameter estimation: controllability/observability, Kalman filter estimators (linear and nonlinear), model prediction. Predictive control  systems with constraints: constrained optimization, numerical solution, applications. Predictive control – stability, robustness: process model uncertainties, disturbance model uncertainties, stability and robustness. Predictive control – nonlinear systems: constrained optimization, numerical solution, applications. Numerical optimization in predictive control systems: parametrization of control actions, discretization of dynamical systems, numerical optimization methods.
Bibliography:
Rossiter J.A., “Model Based Predictive Control – A Practical Approach”, CRC Press, 2005.
Camacho E.F., and C. Bordons, “Model Predictive Control”, Springer, 1999. Kouvaritakis B., and M. Cannon, “NonLinear Predictive Control: Theory & Practice”, IEE Publishing, 2001.
Maciejowski, J., “Predictive Control with Constraints”, Pearson Education POD, 2002.
Kwon W.H., and S. Han, “Receding Horizon Control – Model Predictive Control for State Models”, Springer, 2005.
Instructor: P. Seferlis
B.15 Special Topics I (Robust Control)
GMDUD2 0848
3h/w, 13 weeks, written exam., credits 10
Elective
Description: Introductory notions of uncertain systems and robust control. Mathematical descriptions of uncertainty, additive and multiplicative uncertainty. Robustness analysis. Design of robust systems. LQG methods. LMI methods. Design of robust controllers using state observers. Multiple model methods. Robust pole assignment. Robust control of multiobjective functions. H_{∞} methods. Applications.
References:
1. J. Ackermann, “Robust Control: Systems with Uncertain Physical Parameters”, Springer Verlag, 1993.
2. B.R. Barmish, “New Tools for Robustness of Linear Systems”, McMillan, 1994.
3. S.P. Bhattacharya, H. Chapellat and L.H. Keel, “Robust Control: The Parametric Approach”, Prentice Hall.
4. G.E. Dullerud and F. Paganini, “A Course in Robust Control Theory”, Springer, 2000.
5. R.S. Sanshez – Pena and M. Sznaier, “Robust Systems – Theory and Applications”, Wiley, 1998.
6. Κοσμίδου Όλγα, Εύρωστος έλεγχος δυναμικών συστημάτων, Εκδόσεις Γκιούρδας, Β., ISBN: 960387826Χ, 2009.
Instructor: O. Kosmidou
Semester C
Master’s Degree Dissertation
GMDUD3 0800
13 weeks, 30 credits
Semester : A
WS.01 Web Science Introduction
WS.04 Networks and Discrete Mathematics
WS.13 Web Languages and Technologies
Semester: B
WS.05 Statistical Analysis of Networks
WS.11 Knowledge Processing in the Web
WS.18 Special Topics: Biological Networks
Semester: C
Master’s Degree Dissertation
WS.01 Web Science Introduction
GMscUD1 WSI
36 hours/semester, 13 weeks, written exam and projects, credits: 8
Compulsory
Description: From Hyperlinks to Web Pages and the Semantic Web, Epistemology and Didactics of the Web. Research Methodology and Project Management, Web Economics and Business, Trust, Privacy, Security and Law. Web users Behaviour.
References:
1. Abelson, H., Ledeen, K., Lewis, H. 2008, Blown to bits: Your life, liberty, and happiness after the digital explosion, Upper Saddle River, NJ: AddisonWesley. http://www.bitsbook.com/
2. Amarantidis E., Antoniou I., Vafopoulos M. 2010, Stochastic Modeling of Web evolution, in SMTDA 2010 Conference Proceedings.
3. Antoniou I., Vafopoulos M. 2010, Web as a Complex System, in GRID 2010 Conference Proceedings, Dubna, Russia.
4. Antoniou I., Moissiadis C., Vafopoulos M. 2010, Statistics and the Web, in ESI 2010 Proceedings.
5. Antoniou I., Reeve M., Stenning V. 2000, “Information Society as a Complex System”, J. Univ. Comp. Sci. 6, 272288.
6. BernersLee, T., Fischetti M. 1999. Weaving the Web: the original design and ultimate destiny of the World Wide Web by its inventor. San Francisco: Harper SanFrancisco.
7. BernersLee T., Hall W., Hendler J., Shadbolt N., Weitzner D. 2006, Creating a Science of the Web, Science, Vol. 313. no. 5788.
8. BernersLee T., Hall W., Hendler J., O'Hara K., Shadbolt N., Weitzner D. 2006, A Framework for Web Science. Foundations and Trends in Web Science", 1 (1). pp.1130; Eλληνική Μετάφραση Βαφόπουλος Μ. 2008, Το πλαίσιο της επιστήμης του Web, εκδόσεις hyperconsult, ISBN 9789609303613.
9. BernersLee T. 1996. "WWW: Past, Present, and Future". Computer. 29 (10): 69.
10. Bizer C., Heath T., BernersLee T. 2009, Linked Data  The Story So Far, International Journal on Semantic Web and Information Systems http://tomheath.com/papers/bizerheathbernersleeijswislinkeddata.pdf
11. Bizer C., Maynard D. 2010, The Semantic Web Challenge , In Press Journal of Web Semantics: Science, Services and Agents on the World Wide Web, Available online 2 July 2011
12. Castells, Manuel. 2004. The network society: a crosscultural perspective. Cheltenham, UK: Edward Elgar Pub.
13. Castells Μ. 2007, "Communication, Power and Counterpower in the Network Society.” International Journal of Communication, vol. 1, pages 238266.
14. Golbeck, Jennifer. 2008. Trust on the World Wide Web: a survey. Hanover, MA: Now Publishers.
15. Grewal, David Singh. 2008. Network power: the social dynamics of globalization. New Haven: Yale University Press.
16. D. Lazer, A. Pentland, L. Adamic, S. Aral, A.L.Barabasi, D. Brewer, N. Christakis, etals 2009, Computational social science. Science 323:721723, 2009.
17. Lessig L. 2004, Free culture: how big media uses technology and the law to lock down culture and control creativity. New York: Penguin Press.
18. Linked Data W3C http://www.w3.org/standards/semanticweb/data
19. Linked Data talks, Tom Heath, http://tomheath.com/talks/html
20. Shadbolt N., and BernersLee Τ. 2008, Web Science Emerges  Studying the Web will reveal better ways to exploit information, prevent identity theft, revolutionize industry and manage our ever growing online lives", Scientific American October, 76.
http://eprints.ecs.soton.ac.uk/17143/1/Web_Science_Emerges.pdf
21. Easley D., Kleinberg J. 2010, Networks, Crowds, and Markets: Reasoning about a Highly Connected World, Cambridge University Press http://www.cs.cornell.edu/home/kleinber/networksbook/
22. Rappa M., Managing the digital enterprise http://digitalenterprise.org/
23. TorrentSellens J. 2009, Knowledge, networks and economic activity: an analysis of the effects of the network on the knowledgebased economy http://www.uoc.edu/uocpapers/8/dt/eng/torrent.html
Coordinatos: Metakides G. ,Bratsas C.
Instructors: Antoniou I., Bratsas C., Metakides G., Nouskalis G., Polychronis P., Varsakelis N.
WS.04 Networks and Discrete Mathematics
GMscUD1 NDM
64 hours/semester, written exams and projects, credits: 14
Compulsory
Description: An Introduction to: Graphs and Networks as the Structure of the Web  Information as the Fundamental Quantity in the Web  Digital Processing and the Knowledge Society  The Symmetric and the PublicKey Cryptosystems – The Digital Signatures and Some Cryptographic Protocols used in the Internet.
References
1. Albert R., Barabasi ΑL. (2002), Statistical Mechanics of Complex Networks, Rev. Mod. Physics 74, 4797.
2. Barabasi AL. (2002), Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life, Plume, New York.
3. Batagelj V. (2003), Course on Social Network Analysis Graphs and Networks, Padova, April 1011,
http://vlado.fmf.unilj.si/pub/networks/course/networks.pdf
4. Batagelj V. (2003), Course on Social Network Analysis Weights, April 1011,
http://vlado.fmf.unilj.si/Pub/Networks/course/weights.pdf
5. Bollobas B. (1998), Modern Graph Theory, Springer, Berlin.
6. Bollobas Β. (2001), Random Graphs. Cambridge University Press.
7. Bollobas B. , Riordan O. (2002), Mathematical Results on ScaleFree Random Graphs, in “Handbook of Graphs and Networks”, edited by Bornholdt S. , Schuster H., pp. 1—34, Weinheim, Germany: WileyVCH.
8. Diestel R. (2005), Graph Theory, Springer, Heidelberg.
9. Durret R (2007), Random Graph Dynamics, Cambridge University Press, UK.
10. C. Moyssiadis (2001), Combinatorics. The Art of Calculating Without Counting, Ziti, Thessaloniki. (in Greek).
11. Newman M. (2003), The structure and function of complex networks, SIAM Review 45, 167256.
12. Newman Μ., Barabasi AL., and Watts D., editors, (2006), The Structure and Dynamics of Networks. Princeton University Press, Princeton, New Jersey, USA.
13. Roberts F., Tesman (2004), Applied Combinatorics, Prentice Hall, New Jersey.
14. Rosen Κ. (1995), “Discrete Mathematics and Its Applications,” McGrawHill, New York.
15. Watts, D. J., and S. H. Strogatz (1998), Collective Dynamics of Small World Networks, Nature 393, 393, 440442. D. Stinson, Cryptography – Theory and Practice, Boca Raton, Florida, CRC Press (2002).
16. G. Zémor, Cours de Cryptographie, Paris, Cassini (2002).
17. B. Schneier, Applied Cryptography, J. Wiley and Sons (1996).
18. N. Koblitz, A course in Number Theory and Cryptography, NewYork, Berlin, Heidelberg, SpringerVerlag (1987).
19. J. A. Buchmann, Introduction to Cryptography, NewYork, Berlin, Heidelberg, SpringerVerlag (2001).
20. N. P. Smart, Cryptography, McGraw Hill; Boston (2003).
21. E. Bach, J. Shallit, Algorithmic Number Theory, Vol 1, The MIT Press (1997).
22. S. Y. Yan, Number Theory for Computing, Berlin, Heidelberg, SpringerVerlag (2002).
Coordinator: P. Moyssiadis
Instructors: I. Antoniou, V. Karagiannnis, P. Moyssiadis
WS.13 Web Languages and Technologies
GMscUD1 WLT
36 hours/semester, 13 weeks, written exam and projects, credits: 8
Compulsory
Description: Web Technologies, Privacy and Τrust. From Web 2.0 to Web 3.0 Technologies and Languages. Web Search and Retrieval, Web and Semantic Web Services and Architectures, Agents, Distributed and Cloud Computing. Future Internet
References:
1. Alonso G., Casati F., Kuno H., MachirajuV.. Web Services: Concepts, Architectures and Applications (DataCentric Systems and Applications). Springer; Softcover reprint of hardcover 1st ed. 2004 edition (2010).
2. Corella MA, Castells P. Semiautomatic semanticbased Web service classification. Business Process Management Workshops (Lecture Notes in Computer Science, vol. 4103), Dustdar S, Fiadeiro JL, Sheth A (ed.). Springer: Berlin, 2006; 459470. DOI: 10.1007/11837862_43.
3. T.Erl. SOA Design Patterns (The Prentice Hall ServiceOriented Computing Series from Thomas Erl). Prentice Hall; 1st edition (2009)
4. He M., Jennings N., and Leung H. "On AgentMediated Electronic Commerce". IEEE Transactions on Knowledge and Data Engineering, Vol. 15, No. 4, pp. 9851003, 2003.
5. Hebeler J., Fisher M., Blace R., PerezLopez A.. Semantic Web Programming. Wiley; 1st edition (2009).
6. Funk A, Bontcheva K. OntologyBased Categorization of Web Services with Machine Learning. Proceedings of the Seventh conference on International Language Resources and Evaluation, May 2010, Calzolari N, Choukri K, Maegaard B, Mariani J, Odijk J, Piperidis S, Rosner M, Tapias D (ed.). European Language Resources Association, 2010; 482488.
7. Kagal, L.; Pato, J.; , "Preserving Privacy Based on Semantic Policy Tools," Security & Privacy, IEEE , vol.8, no.4, pp.2530, JulyAug. 2010
8. Kehagias D., Giannoutakis K., Gravvanis G., Tzovaras D. Ontologybased Mechanism for Automatic Categorization of Web Services. Concurrency and Computation: Practice and Experience (Wiley) (2011, accepted for publication, online available:
http://onlinelibrary.wiley.com/doi/10.1002/cpe.1818/pdf ).
9. Kehagias D., Mavridou E., Giannoutakis K., Tzovaras D., “A WSDL structure based approach for semantic categorization of web service elements”, 6th Hellenic Conference on Artificial Intelligence, 47 (SETN10) May. 2010, Athens, Greece (Lecture Notes in Artificial Intelligence, vol. 6040) S. Konstantopoulos et al. (Eds.): pp. 333–338, 2010.
10. Kehagias D., Tzovaras D., Mavridou E., Kalogirou K., Becker M., “Implementing an open reference architecture based on web service mining for the integration of distributed applications and multiagent systems”, 2010 AAMAS Workshop on Agents and Data Mining Interaction, May 11, 2010, Toronto, Canada.
11. Kehagias D., Tzovaras D., Gravvanis G. Agentbased discovery, composition and orchestration of grid web services. In: Recent developments in Grid Technology and Applications, Nova Science Publishers, 2009.
12. Kehagias D., GarciaCastro A., Giakoumis D., Tzovaras D., “A Semantic Web Service Alignment Tool” 7th International Semantic Web Conference, October 2630, 2008, Karlsruhe, Germany.
13. Martin D, Burstein M, Mcdermott D, Mcilraith S, Paolucci M, Sycara K, Mcguinness DL, Sirin E, Srinivasan N. Bringing Semantics to Web Services with OWLS. World Wide Web 2007; 10 (3): 243277. DOI: 10.1007/s112800070033x.
14. Nguyen K, Cao J, Liu C. SemanticEnabled Organization of Web Services. APWeb 2008 (Lecture Notes in Computer Science, vol. 4976), Zhang Y. et al. (ed.). SpringerVerlag: Berlin, 2008; 511–521. DOI: 10.1007/9783540788492_51.
15. Singh M., Huhns M.. ServiceOriented Computing: Semantics, Processes, Agents. Wiley; 1st edition (2005).
16. Story H., Harbulot B., Jacobi I., and Jones M. FOAF+ SSL:RESTful Authentication for the Social Web. Semantic Web Conference, 2009.
17. Wooldridge M. An Introduction to Multiagent Systems. J. Wileyand Sons, 2002.
Coordinators: I. Stamatiou, D. Kehagias
Instructors: C. Bratsas, D. Kehagias
Semester: B
WS.05 Statistical Analysis of Networks
GMscUD2 STAN
68 hours/semester, 13weeks, written exam and projects, credits: 15
Compulsory
Description: Statistical Methods in the Study of Web  Sampling Techniques  Inference on Network Data  Time series Techniques and Statistical Analysis for the Study and Monitoring the Behaviour of the Web in Real Time  Statistical Models of Network Traffic – Development – Evolution. Games.
References:
Data Processing from Networks:
1. Aldenderfer M. 1984, Cluster Analysis, Sage publications, London.
2. Everitt B. 1977, Cluster Analysis, Heinenmann , London.
3. Chatfield C., Collins A. 1980, Introduction to Multivariate Analysis, Chapman and Hall, New York
4. Φαρμάκης Ν. 2009, Εισαγωγή στη Δειγματοληψία, Χριστοδουλίδης, Θεσσαλονίκη.
5. Φαρμάκης Ν. 2009, Δημοσκοπήσεις και Δεοντολογία, Χριστοδουλίδης, Θεσσαλονίκη.
6. Field A. 2000, Discovering Statistics using SPSS, 2nd Edition, Sage Publications, London.
7. Kinnear, P., Gray C. 2008, SPSS 15 Made Simple, Psychology Press, New York.
8. Kolaczyk, E. 2009, Statistical Analysis of Network Data: Methods and Models, Springer, New York, Springer.
9. ΚολυβάΜαχαίρα Φ. 1998, Μαθηματική Στατιστική 1 Εκτιμητική, Εκδ. Ζήτη, Θεσσαλονίκη.
10. Norusis M. 2003, SPSS 12.0 Statistical Procedures Companion, Prentice Hall, New Jersey.
11. Tabachnick B., Fidell G. 1996, Using Multivariate Statistics, 3^{rd} edition, Harper Collins, London.
Web Modeling:
1. Airoldi E. 2007, Getting Started in Probabilistic Graphical Models,http://www.ploscompbiol.org/article/info%3Adoi%2F10.1371%2Fjournal.pcbi.0030252
2. Baldi P., Frasconi P., Smyth P. 2003, Modeling the Internet and the Web. Probabilistic Methods and Algorithms, Wiley
3. Barbu V., Limnios N. 2008, Semi Markov Chains and Hidden Semi Markov Models towards applications, Springer, Berlin.
4. Bollobas B., Riordan O. 2006, Percolation, Cambridge University Press, UK
5. Bonato A. 2008, A Course on Web Graph, American Mathematical Society, Providence, Rhode Island.
6. Cowell, R., Dawid, A. Lauritzen P., Steffen L, Spiegelhalter, D. 1999, Probabilistic Networks and Expert systems, Springer, Berlin
7. Dorovtsev S., Mendes J. 2003, Evoluton of Networks. From Biological Nets to the Internet and the WWW, Oxford, UK
8. Heykin S. 1999, Neural Networks. A Comprehensive Foundation, Pearson Prentice Hall, New Jersey
9. Howard, R. 1971, Dynamic Probabilistic Systems 1: Markov Models, Dover, New York.
10. Howard R. 2007, Dynamic Probabilistic Systems 2: SemiMarkov and Decision Models, Dover, New York.
11. Jensen F. 1996, An introduction to Bayesian Νetworks, Springer, Berlin.
12. Lieberman E., Hauert C., Nowak M. 2005, Evolutionary dynamics on graphs, Nature 433, 312316
13. Newman M., Barabasi A.L., Watts D. 2006, The Structure and Dynamics of Networks, Princeton University Press, New Jersey
14. Pearl J. 1988, Probabilistic Reasoning in Intelligent Systems, 2nd ed., Morgan Kaufmann. San Mateo, CA.
15. Papadimitriou, C. H. (January 01, 2001). Algorithms, Games, and the Internet. Proceedings of the Annual Acm Symposium on Theory of Computing, 33, 749753.
16. D. Pham, L. Xing 1995, Neural Networks for Identification, Prediction and Control, SpringerVerlag, Berlin
17. Prigogine I. and Antoniou I. 2001, "Science, Evolution and Complexity", p 2136 in Genetics in Europe, Sommeteuropéen, Ed. Lombardo G., Merchetti M., Travagliati C., Ambasciato d’Italia – Brussels, Quaderni Europei No 2.
Coordinator: I. Antoniou, N. Farmakis
Instructors: I. Antoniou, N. Farmakis, V. Ivanov, F. KolyvaMachera, D, Kugiumtzis, A. Papadopoulou.
WS.11 Knowledge Processing in the Web
GMscUD2 KPW
36 hours/semester, 13 weeks, written exams and projects, credits: 7.5
Compulsory
Description: Logic and Programming are the foundations of Ontologies and Semantic processing. Semantic Web and
Linked data, Trust and privacy, Ambient Intelligence and the Future Internet
References:
1. Antoniou G., Van Harmelen F. 2008, A Semantic Web Primer 2nd ed., MIT Press.
2. Aarts, E., Harwig, R., and Schuurmans, M. 2001, Ambient Intelligence in The Invisible Future: The Seamless Integration of Technology into Everyday Life, McGrawHill, New York.
3. Allemang D., Hendler J. 2008, Semantic Web for the Working Ontologist: Effective Modeling in RDFS and OWL, Morgan Kaufmann, San Francisco, California.
4. Bizer C., Heath T., BernersLee T. 2009, Linked Data  The Story So Far. In: International Journal on Semantic Web & Information Systems 5, 122.
5. Bizer C., Lehmann J., Kobilarov G., Auer S., Becker C., Cyganiak R., Hellmann S. 2009, DBpedia  A Crystallization Point for the Web of Data. Journal of Web Semantics: Science, Services and Agents on the World Wide Web 7, 154–165.
6. Bratsas C., Bamidis P., Kehagias D., Kaimakamis E., Maglaveras N. 2011, "Dynamic Composition of Semantic Pathways for Medical Computational Problem Solving by Means of Semantic Rules", IEEE Transactions on Information Technology in Biomedicice, Vol. 15, No. 2, pp. 334343
7. Gershenfeld N., Krikorian R., Cohen D. 2004, The Internet of Things, Scientific American, vol. 291, no. 4, pp. 76–78.
8. Heath T., Bizer C. 2011 Linked Data: Evolving the Web into a Global Data Space. Synthesis Lectures on the Semantic Web: Theory and Technology, Morgan & Claypool Publishers, ISBN 978160845431, (Free HTML version).
9. Nikoletseas S., Rolim J. 2011, Theoretical Aspects of Distributed Computing in Sensor Networks, Springer
10. Reese G. 2009, Cloud Application Architectures: Building Applications and Infrastructure in the Cloud. O'Reilly Media Inc, Beijing, Sebastopol, CA.
11. SegaranΤ., Taylor J., Evans C. 2009, Programming the Semantic Web, O'Reilly Media Inc, Beijing, Sebastopol, CA.
12. Shadbolt N., BernersLee T. and Hall W. 2006. "The Semantic Web  The Semantic Web Revisited". IEEE Intelligent Systems. 21 (3): 96.
13. Staab S., Studer R. 2009, Handbook on Ontologies, International Handbooks on Information Systems, Springer Verlag, Heidelber, DOI: 10.1007/978354092673
14. Wilks Y. and Brewster C. 2009, "Natural Language Processing as a Foundation of the Semantic Web", Foundations and Trends in Web Science: Vol. 1: No 3–4, pp 199327.
Coordinatos: G. Metakides, C. Bratsas .
Instructors: C. Bratsas, G. Metakides
WS.18 Special Topics (Biological Networks)
GMscUD2 BIONET
36 hours/semester, 13 weeks, written exams and projects, credits: 7.5
Compulsory
Description: Biomedical Ontologies in the Web. Statistical Analysis of Biological Data, Life Networks Models, Metabolic and Phenotypic Networks. Brain Networks (Connectomics), and Semantic, Ecological networks. Web as Ecosystem
References:
1. Barrat A., Barthelemy M., Vespignani A. (2008), Dynamical Processes on Complex Networks, Cambridge University Press, Cambridge, UK
2. Barrat A., Boccaletti S., Caldarelli G., Chessa A., Latora V., Motter A. E. ed. (2008), Complex Networks: from Biology to Information Technology, J. Phys. A: Math. andTheor. 41, 220301
3. Barrett, C.L., Kim, T.Y., Kim, H.U., Palsson, B.Ø. & Lee, S.Y. (2006), "Systems biology as a foundation for genomescale synthetic biology", Current opinion in biotechnology, Vol. 17, No. 5, pp. 488492
4. Blow, N. (2009), "Systems biology: Untangling the protein web", Nature, Vol. 460, No. 7253, pp. 415418.
5. Bodenreider O. 2008, Biomedical ontologies in action: role in knowledge management, data integration and decision support, Yearbook Med. Inform. , 67–79.
6. Bratsas C., Koutkias V, Kaimakamis E, Bamidis P, Maglaveras N. 2007, Ontologybased Vector Space Model, and Fuzzy Query Expansion to Retrieve Knowledge on Medical Computational Problem Solutions ConfProc IEEE Eng Med BiolSoc 1:37947.
7. Bratsas C., Koutkias V., Kaimakamis E., Bamidis P., Pangalos G., Maglaveras N. 2007, KnowBaSICSM: An ontologybased system for semantic management of medical problems and computerised algorithmic solutions. Computer Methods and Programs in Biomedicine, 88(1):3951
8. Bratsas C., Frantzidis C., Papadelis C., Pappas C., Bamidis P. 2009, Towards a semantic framework for an integrative description of neuroscience patterns and studies: a case for emotion related data, published in Book Series Studies in Health Technology and Informatics Volume 150, ISO Press, pp. 322326, ISBN: 9781607500445
9. Bratsas C., Bamidis P., Kehagias D., Kaimakamis E., Maglaveras N. 2011, "Dynamic Composition of Semantic Pathways for Medical Computational Problem Solving by Means of Semantic Rules", IEEE Transactions on Information Technology in Biomedicice, Vol. 15, No. 2, pp. 334343
10.Gene Ontology Consortium. The Gene Ontology (GO) project in 2006. Nucleic Acids Res. 34 (database issue), D322–D326 (2006).
11.Hidalgo C.A., Blumm N., Barabasi A.L., and Christakis N.A. 2009. "A Dynamic Network Approach for the Study of Human Phenotypes". PLoS Computational Biology. 5 (4).
12.Kamburov A, Goldovsky L, Freilich S, Kapazoglou A, Kunin V, Enright AJ, Tsaftaris A, Ouzounis CA (2007) Denoising inferred functional association networks obtained by gene fusion analysis. BMC Genomics 8, 460.
13.Lewis, T. G. 2009. Network science: theory and practice. Hoboken, N.J.: John Wiley & Sons.
14.Meyerguz, Leonid, Jon Kleinberg, and Ron Elber. 2007. "The network of sequence flow between protein structures". Proceedings of the National Academy of Sciences of the United States of America. 104 (28): 11627.
15.Nordlie, Eilen; Gewaltig, MarcOliver; Plesser, Hans Ekkehard (2009). Friston, Karl J.. ed. "Towards Reproducible Descriptions of Neuronal Network Models". PLoS Computational Biology 5 (8): e1000456. doi:10.1371/journal.pcbi.1000456
16.Noy N., Shah N., Whetzel P., Dai B., Dorf M., Griffith N., Joquet C., Rubin D., Storey M.A., Chute C. Musen M. 2009, BioPortal: ontologies and integrated data resources at the click of a mouse. Nucleic Acids Res. 37: W170W173.
17.Petanidou Th., Kallimanis A., Tzanopoulos J, Sgardelis S.P, Pantis J.D. 2008, Longterm observation of a pollination network: fluctuation in species and interactions, relative invariance of network structure, and implications for estimates of specialization. Ecology Letters 11(6): 564575.
18.Royer L., Reimann M., Andreopoulos B., and Schroeder M. 2008. "Unraveling protein networks with power graph analysis". PLoS Computational Biology. 4 (7).
19.Schulz, S., Beisswanger, E., van den Hoek, L., Bodenreider, O., van Mulligen, E.M. 2009, Alignment of the UMLS semantic network with BioTop: Methodology and assessment, Bioinformatics, 25 (12), pp. i69i76.
20.B. Smith, W. Ceusters, B. Klagges, J. Kohler, A. Kumar and J. Lomax et al. 2005, Relations in biomedical ontologies, Genome Biol 6 () (5), p. R46
21.Yu A. 2006, Methods in biomedical ontology, Journal of Biomedical Informatics, Volume 39, Issue 3, Biomedical Ontologies, Pages 252266, ISSN 15320464, DOI: 10.1016/j.jbi.2005.11.006.
Coordinator: S. Sgardelis
Instructors: I. Αntoniou, C. Bamidis, C. Bratsas , D. Kehagias, A. Μazaris, I. Pantis, S. Sgardelis , Z. Scouras.
Semester: C
Master’s Degree Dissertation
13 weeks, credits 30.