ARISTOTLE
UNIVERSITY OF THESSALONIKI (G Ð 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 2016
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.
Instructions: Navigation on this site is through
the Table of Contents below. Use the back button of your web browser to get
back to the Table of Contents.
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 ÇPure MathematicsÈ
M. Sc. Course in ÇStatistics and Mathematical
ModellingÈ
M. Sc. Course in ÇTheoretical Computer Science
and Control and System TheoryÈ..
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:
á
The
information package, which supplies written information to students and
staff on institution, schools/faculties, the organization and structure of
studies and course units.
á
ECTS credits which
are a numerical value allocated to course units to describe the student
workload required to complete them.
á
The
transcript of records, which shows studentsÕ learning achievements in a
way which is comprehensive, commonly understood and easily transferable from
one institution to another.
á
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:
á 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;
á 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;
á 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;
á One study period abroad should not
last less than three months or more than one year;
á 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 Ð the student, the home institution and the host
institution Ð 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 institutionÕs 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 studentÕs 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 schoolÕs 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 Ð and also inform the Student Advisors of their
Department Ð 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 EuropeÕs 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 Òthe
Athens of Medieval HellenismÓ. 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 UniversityÕs 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 ThessalonikiÕs 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 ÒUniversity of MacedoniaÓ and the ÒInternational
Hellenic UniversityÓ and one technological institute the ÒAlexander Technological
Educational Institute of ThessalonikiÓ.
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 ÒDimitriaÓ
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),
ÒMakedoniaÓ 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 educa_tional
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 FinikaÕs area.
The law ÒOn the structure and
operation of the Greek UniversitiesÓ, 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 BachelorÕs
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 ÒManolis TriantafillidisÓ
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 RectorÕs 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 200 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 20142015, the winter semester begins on September 29th and
ends on January 18th,
while the spring semester begins on February 16th and ends on May 31st.
There are three examination sessions
annually, each lasting three weeks: the January
session beginning on January 19th, and ends on February 10th, the June session
beginning on June 2nd, and ends on June 23rd, and the September session
beginning on September 1^{st} and ends on September 22nd.
No lectures are given on the
following official holidays: October 26th, October 28th, November 17, January
30th, March 25th, May 1st, and June 1st, or during the
following holiday periods:
 Christmas and New YearÕs (from
December 24th to January 7th).

Carnival (from February 19th to February 24th).
 Easter (from April 6th to April
19th).
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 studentsÕ 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
hair dresserÕs 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 Ð 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 SchoolÕs Council.
The SchoolÕs Council comprises the
teaching staff (25 faculty members) and student representatives.
Information:
School
of Mathematics
Head of the School: Professor Nikolaos
Karampetakis
Academic
Secretary: M. EkklisiaraZisi
Aristotle
University of the Thessaloniki
Thessaloniki,
Greece 54124
Tel.:
00302310997964
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 
Lazaridis, G. 
Department of Mathematical Analysis
Professors 
Betsakos, D. Daskaloyiannis,
K. Mandouvalos,
N. 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) 
Lecturer Department Secretary 
Petalidou, F. Tsitsilianou M. 


Department of Numerical Analysis and Computer
Sciences
Professors 
Karampetakis,
N. Poulakis, D. (Head of the
Department) 
Associate Professors 
GousidouKoutita,
M. 
Assistant Professor 
Rachonis,
G. 


Department Secretary Technical Assistants 
Tsitsilianou
M. Porfiriadis,
P. Chatziemmanouil,
I. 


Department of Statistics and Operations Research
Professors 
Antoniou, I. Kalpazidou, S. Moyssiadis, C. Tsaklidis, G. 
Associate
Professors 
Farmakis, N. (Head of Department) 
Assistant
Professor 
KolyvaMahaira, F. Papadopoulou, A. 
Lecturer


DepartmentÕs
Secretary: 
Lazaridis, G. 
Technical
Staff: 
Bratsas Ch. Vlachou Th. 


Teachers of Foreign Languge
Secretarial Staff
Secretary 
EkklisiaraZisi,
M. 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.00302310997930 




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 studentÕs 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 electiveÐsee 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 ÒDiploma
of MathematicsÓ (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 Ð
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
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).
Instructor:
H. Charalambous
Linear Algebra
GLSUD1 LALGI  0108
6h/w (5 hoursÕ 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 Ð 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 Ð 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
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  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  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  LagrangeÕs theorem  Order of a group element  EulerÕs theorem, FermatÕs
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  TaylorÕs 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 Ð 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 Ð evapotranspiration  water vapours  precipitation 
Distribution of the climatic elements  Climate classifications  The climatic
classification of Koppen 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
Calculus
IV
GLSUD4 CIV
Ð 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 Pickard  Linear differential equations of order n=2  Reduction of
the order of a differential equation  EulerÕs equations  Systems of
differential equations.
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 Ð 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: Postdoc
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 CantorÕs function  Special classes of functions
(monotone, bounded variation, absolutely continuous, convex)  Sequences and
series of functions  uniform convergence and applications  Nowhere differentiable
continuous functions Ð 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 Ð 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 SimpsonÕs rules, Romberg integration)  Numerical
solution of nonlinear equations (bisection method, secant, regulafalsi and
modified regulafalsi, NewtonÕs 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 Ð 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 Ð 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  KeplerÕs problem  Systems of mass particles Ð 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  FubiniÕs theorem.
Instructor:
D. Betsakos
Elements of Functional Analysis
GLSUD6 FA Ð 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: Postdoc
Linear Geometry I
GLSUD6 LINGEO  0331
3h/w, 13
weeks, written exams, credits: 5.5
Compulsory
Elective (Department of Geometry)
Description:
Multidimensional affine spaces Ð Affine subspaces Ð Affine mappings.
Instructor: Postdoc
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
Dynamical
Systems
GLSUD6
DS Ð 0236
3h/w, 13 weeks,
written exams, credits: 5
Elective
Description: Part I: Continuous and discrete dynamical systems.
Recursions. Fixed points and periodic points. SharkovskiiÕs theorem. Chaotic
behaviour. Examples, cantor sets, fractals, the logistic function etc. Symbolic
dynamics. Statistical and topological behaviour of orbits.
Part II: Normal families of analytic functions. Rational functions
recursions. Dynamical behaviour, Julia and Fatou sets, properties, the
Mandelbrot set.
Instructor: A. Siskakis
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 
KolmogorovÕs equations  FellerÕs 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
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 Ð 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 Ð 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. Functiomn spaces
Instructor:
Postdoc
Differential Manifolds I
GLSUD7 DMI Ð 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 Ð 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 Ð 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. ShannonÕs
theorem, lower bound on codes, code generation, SingletonÕs bound, MDS codes,
PlotkinÕs bound, GriesmerÕs 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
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 Ð 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 Ð 0132
3h/w, 13 weeks, written exams, credits: 5.5
Compulsory Elective (Department of Algebra,
Number Theory and Math. Logic)
Description: Paradoxes in na•ve set theory. ZermeloFraenkel axiomatic set theory
(ZF). The ZF universe and the foundation axiom. Comparison of size of sets.
Equinumerable sets. SchroderBernstein theorem and CantorÕs 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, ZornÕs lemma, HausdorffÕs
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 (why 8^{th} semester and why not free elective!!??)
GLSUD8 ADVLA Ð 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
PoissonÕs equation. Mollifiers and smoothness. Local estimates for the
derivatives of harmonic functions. LiouvilleÕs theorem. The Harnack inequality.
GreenÕs 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 Ð 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 socioecono_mic 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 Ð 0569
3h/w, 13 weeks, written exams, credits: 5
Elective
Description: Introduction to testing hypothesis  Selecting
the test procedure  Testing simple hypothesis  NeymanPearsonÕs 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 Ð 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 


Electives 



SECOND SEMESTER 
Code 
Courses 
Hrs/Credits 

Code 
Courses 
Hrs/Credits 

0202 0301 0401 0501 
Compulsory Calculus II
Analytic Geometry I Theoretical Informatics I Mathematical Programming 
5 3 3 3 

7 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 0531 0507 
Compulsory Electives Number Theory Regression Models and Applications to Knowledge Processing
Electives Stochastic Processes with Complete
Connections and Learning Theory 
3 4 3 

5.5 5.5 5 
SIXTH SEMESTER 
Code 
Courses 
Hrs/Credits 

Code 
Courses 
Hrs/credits 

0208 0236 0563 0963 1161 1066 
Compulsory Complex Analysis
Electives Dynamical Systems Stochastic Processes Didactics of Mathematics Special Topics A Free Electives Continuum Mechanics 
4 3 3 3  3 

7 5 5 5 5 5 

0131 0231 0232 0331 0332 0431 0432 0532 0533 
Compulsory Electives Group Theory Measure Theory Elements of Functional Analysis Linear Geometry I Classical Differential Geometry II Computational Mathematics Theoretical Informatics II 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 

0562 1161 1162 
Electives Stochastic Methods in Finance Special Topics A Special Topics B 
3   

5 5 5 

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 

0962 0264 0462 0566 0569 0570 1162 
Electives History of Mathematics Special Functions Modern Control Theory Introduction to Sampling Statistical Inference Information Theory and Chaos Special Topics B 
3 3 3 3 3 3  

5 5 5 5 5 5 5 

0132 0134 0137 0234 0235 0266 0333 0434 0465 
Compulsory
Electives Set Theory Galois Theory Advanced Topics in Linear Algebra Fourier Analysis Partial Differential Equations Harmonic Analysis Differential Manifolds II Cryptography Error Correcting Codes Free Electives 
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 
There are two postgraduate programmes
in the School of Mathematics of the Aristotle University of Thessaloniki:
¨ The postgraduate programme in ÇMathematicsÈ with three possible
tracks, offered since the fall of 2002.
¨ The postgraduate programme in ÇWeb ScienceÈ which has been running
since the fall of 2009.
The postgraduate programme in
ÇMathematicsÈ leads to the award of a MasterÕs 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 MasterÕs 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 MasterÕs
Degree on Mathematics is three semesters of study. Students are expected to
complete the coursework during the first two semesters and prepare a MasterÕs
Degree dissertation during the third semester.
The requirements for the award
of the MasterÕs Degree are:
1. For the ÇPure MathematicsÈ 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 ÇStatistics and Mathematical
ModellingÈ track: satisfactory completion of at least 6 courses from the
category S_.
3. For the ÇTheoretical Computer
Science and Control TheoryÈ 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 ÇWeb ScienceÈ awards a MasterÕs 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 MasterÕs
Degree on ÇWeb Science È is
typically three semesters of study. Students are expected to complete the
coursework during the first two semesters and write a MasterÕs 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 (GreeceMasterÕs 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.5 Representation Theory of Lie Algebras
A.6 Commutative Algebra
B.7 Theory of Measure
and Integral
B.9 Complex Analysis
B.12 Hyperbolic
Analysis and Geometry
C.4 Differentiable Manifolds
C.8 Global Differential Geometry
Spring Semester
A.1 Algebraic Geometry
A.3 Algebraic Topology (also C.1)
A.12
Topics in Mathematical Logic
B.2 Analysis on Manifolds
C.3 Line Geometry
Third Semester
MasterÕs Degree Dissertation.
Semester A
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, PoincarŽBirkhoffWitt 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, BŠcklundLie
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.
A.6 Commutative Algebra_
GMScUD1 0631_
3h/w, 13 weeks, written exam., credits 10_
Elective_Description: Historical aspects: connections with algebraic
number theory, algebraic geometry, invariant theory. Introductory material to
the theory of commutative rings and modules, homomorphisms, exact sequences,
tensor products, flat modules. Localization. Noetherian and Artinian rings and
modules, HilbertÕs Basis Theorem . Associated primes,
primary decomposition. Integral dependence and the Nullstellensatz. Filtrations
and the ArtinReesÕ Lemma. Completion, HenselÕs lemma and Cohen structure
theory. Dimension Theory and HilbertSamuel polynomials. Noether Normalization.
Discrete valuation rings and Dedekind domains.
Requirements: General knowledge of Algebraic Structures such as
groups and of Galois theory_
References:
1. M. F. Atiyah and I.
G. MacDonald (1994) Introduction to
Commutative Algebra, Addison Wesley. _
2. H. Matsumura, (1989)
Commutative Ring Theory, Cambridge
University Press. _
3. D. Eisenbud, (1997) Commutative Algebra with a View Toward Algebraic
Geometry, SpringerVerlag. _
Instructor: H. Charalambous
B.7 Theory of Measure and Integral
GMDUD1 0643
3h/w, 13 weeks, 10 credits
Elective
Description: Measures,
_algebras,
outer measures, Borel measures. Measurable and integrable functions. Dominated
convergence theorem. Product measure, FubiniÕs theorem. The Lebesgue integral
in R^{n}. Signed measure, Hahn decomposition theorem, RadonNikodym
theorem. Functions of bounded variation. Absolutely continuous and singular
measures. Elementary theory of L^{p} spaces, duality.
References
1. Folland G. (1984). Real Analysis  Modern techniques and their
applications. _John Wiley and Sons, New York. _
2. Malliavin P. (1982).
ThŽorie de la mesure. _
3. Rudin W. (1986). Real
and Complex Analysis. 3^{rd} edition.
McGraw Hill; Boston. 4. Wheeden R.
and A. Zygmund (1977). Measure and Integral. Marcel Dekker. _
Instructor: P.
Galanopoulos
B.9 Complex Analysis
GMDUD2 0641
3h/w, 13 weeks,
written exams, 10 credits
Elective
Description:
Analytic functions. The general form of CauchyÕs theorem. Local uniform
convergence of analytic functions, the theorem of Weierstrass. Infinite products,
canonical decomposition, Blaschke products. RungeÕs approximation theorem.
Normal families of analytic functions, MontelÕs theorem. Conformal mappings,
the Riemann mapping theorem, the MittagLeffler theorem. Harmonic functions,
the maximum principle, the Dirichlet problem, subharmonic functions. SchwarzÕs
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.12 Hyperbolic Analysis and Geometry
GMDUD1 0648
3h/w, 13 weeks, written exams, 10 credits
Elective
Description: Mšbius 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, BirkhŠuser
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.
_nstructor: 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 Gau§Bonnet theorem and its
applications, Minkowski_s integral formulae. The index method (PoincarŽ).
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 Leichtwei§ 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 Gro§en. 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. HilbertÕs 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.
Bibliography:
1. Cox D. A., Little J.
B. and OÕShea D. B. (1998) Ideals,
Varieties and Algorithms. Introduction to Computational Algebraic Geometry and Commutative
Algebra. SpringerVerlag. _
2. DieudonnŽ J. (1974) Cours de GŽomŽtrie AlgŽbrique. 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) GŽomŽtrie AlgŽbrique.
Interƒditions/ƒditions CNRS. _
8. Shafarevich I. R.
(1994). Basic Algebraic Geometry.
Springer Verlag. _
9. Smith K. E.,
KahanpŠŠ, KekŠlŠinen and Traves W. (2000). An
Invitation to _Algebraic Geometry. Springer Verlag. _
10. Kunz E. (1985). Introduction to Commutative Algebra and
Algebraic _Geometry. BirkhŠuser._
Instructor: D. Poulakis
A.3, C.1 Algebraic
Topology
GMDUD2 0672
3h/w, 13 weeks,
written exam, 10 credits
Elective
Description: Homotopy notions and homotopy
equivalence, retractions and deformation retractions, homotopy extension. Basics
of categories and functors. Fundamental group: basic construction, the
Seifertvan Kampen theorem, covering spaces. Computations and applications.
Homology: singular and CW complexes. Simplicial and singular homology.
MayerVietoris sequence. Cohomology, products and duality.
Prerequisites: Basic notions of algebra and of general
topology.
References:
1. A. Hatcher: Algebraic Topology,
Cambridge University Press, 2002 (freely available at : http://www.math.cornell.edu/~hatcher/AT/ATpage.html )
2. W.S. Massey: A Basic Course in
Algebraic Topology, Springer 1991.
3. J. Rotman: An Introduction to
Algebraic Topology, Springer 1988.
4. G. Bredon: Topology and
Geometry, Springer 1993.
5. J.P. May: A Concise Course in
Algebraic Topology, University of Chicago Press, 1999 (Freely available at:
http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf )_
6. M.J. Greenberg, J.R. Harper: Algebraic
Topology  A First Course, Benjamin, 1981.
Instructor: E. Kappos
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.2 Analysis on
Manifolds
GMDUD2 0646
3h/w, 13 weeks, 10
credits
Elective
Description: Heat kernel
estimates: the laplacian, Gaussian estimates of the heat kernel, bounds on
compact manifolds, applications of heat kernel bounds. Estimates of the
eigenvalues on compact manifolds.
Bibliography:
Instructor: M. Marias
C.3 Line Geometry
GMDUD2 0666
3h/w, 13 weeks, 10 credits
Elective
Description: _. Introduction:
CayleyKlein geometries and the Erlangen program. The ndimensional affine
space. The ndimensional projective space. PlŸcker 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.
_.
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 Ð 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
Semester C
MasterÕs 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
Semester B
SM.06 Sampling and Statistical
Processing
SM.22 Statistics
and Decision Making
SM.24 Stochastic Methods
SM.27 Special Topics I: Information
Theory, Entropy and Complexity
Semester C
MasterÕs
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 Forecas_ting. 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 Uni_versity Press.
4. Tong H. (1997). NonLinear Time Series: A Dynamical
System Approach (Ox_ford 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 _etworks.
_he 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.
Hšrmander 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 ÒNeural NetworksÓ. 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 Mathematic_. 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.
_nstructor: 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, _merican 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.
11. Vol I: Basic Concepts. World
Scientific, Singapore.
12. Vol II: Basic Tools and Special
Topics. World Scientific, Singapore.
13. Bernstein E., Vazirani U. (1997),
Quantum Complexity Theory. SIAM J. Comput. 26, 14111473.
14. Chen G., Brylinsky R, editors
(2002), Mathematics of Quantum Computation, Chapman and Hall/VRC, Florida, USA.
15. Feynman R.P. (1967), Quantum
Mechanical Computers. Foundations of Physics, 16, 507531.
16. Ingarden R.S. (1976), Quantum
Information Theory. Rep. Math. Physics 10, 4372.
17. Nielsen A.M., Chuang I.L.
(2000), Quantum Computation and Quantum Information. Cambridge University
Press, Cambridge UK.
18. Ohya M., Petz D. (2004), Quantum
Entropy and its Use. 2^{nd} Printing, Springer, Berlin.
19. Vitanyi P.
M. B. (2001), Quantum
Kolmogorov Complexity based on Classical
Descriptions. IEEE Transactions
on Information Theory 47, 24642479.
Instructors:
I. Antoniou, C. Panos
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: ÒSearching for linear trend of sampling dataÓ,
Òsearching for periodicities of dataÓ, ÒCreating equation of probabilities (2^{nd}
degree model) from twodimensional data, etc.Ó, ÒCoefficient of Variation and
its applications, e.g. symmetric model of probability density functionÓ.
References
1. Farmakis _.
(2009), Introduction to Sampling, Christodoulidis, Thessaloniki. (in
Greek).
2. Farmakis _.
(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.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 (CochranÕs theorem, ANOVA, regression, _^{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. Dacunha Castelle 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.
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 Wi_ley and Sons; New York.
2. Ross S.M. (1995). Stochastic
Processes. John Wi_ley and Sons; New York.
3. Ross S.M. (2000). Introduction to
Probability Models. 7^{th} edition. John Wi_ley 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, ÒProbability from
ChaosÓ, 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, St_chastic 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,
KolmogorovÕs 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. RŽnyi 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. _____. ______. E__.
____________, _____, 2000
2.
Dertouzos M. 1997, What Will Be? How the World of Information Will
Change Our Lives, Harper Collins, New York. _____.
______. E__. ________ 1998.
3.
Dertouzos M. 2001, The Unfinished Revolution :
How to Make Technology Work for UsÑInstead of the Other Way Around,Harper
Collins, New _York. ___. ______. E__. ______, _____, 2001
4.
BernersLee T, Fischetti M. 1997, Weaving The Web ,
Harper Collins, New _York. _____. ______. E__. ________ ,
_____, 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 Ð 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, 684Ð706 _
9. Dehmer _.,
Mowshowitz A. 2011, A history of Graph _ntropy_easures, _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, 249Ð265
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 _.
2011, Mathematical Foundations of Quantum Information _and Computation and Its
Applications to Nano and Biosystems, Springer, Berlin. _
Instructor: I Antoniou
Semester C
MasterÕs 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.13 Network Cryptography
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
MasterÕs
Degree Dissertation
Semester A
A.10 Formal Language Theory
GMDUDI
3h/w, 13 weeks,
written exams, 10 credits
Elective
Description: Alphabets. Infinite
words and _languages. Automata over infinite words, with BŸchi and Muller
acceptance conditions. _Recognizable languages. Closure properties of
_recognizable languages. The complement of an _recognizable language. Monadic
secondorder logic. The expressive equivalence of sentences from monadic
second order logic and automata over infinite alphabets. 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 Wi_ley 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 _.,
(2009), Optimal Control of Systems, _________ _____. (in Greek)
Instructor: N. P. Karampetakis, G. Tsaklidis
B.10 Convex Optimization
GMDUD1 0850
3h/w, 13 weeks, written exams, 10
credits
Elective
Description:
References