## Undergraduate

**General Information - AIMS**

The famous Platonic inscription "μηδείς αγεωμέτρητος εισίτω" ("let no one ignorant of geometry enter") has been adopted, directly or indirectly, by all universities in the world and, appropriately, the Department of Mathematics and Statistics was one of the departments with which the University of Cyprus commenced its operation. The primary goal of the Department is the promotion, through scientific research and teaching, of the Mathematical Sciences.

The achievement of this goal is inextricably linked with the need to produce well-trained scientists who will contribute to the continuation of the cultural and economic progress of Cyprus. Because of the pivotal role of Mathematics and Statistics for Science, it is necessary to create a department of high calibre.

Following modern trends, the University of Cyprus encourages joint degree programmes between the Department of Mathematics and Statistics and other Departments (e.g., Computer Science, Economics) that offer various career possibilities. The ambition of the Department is to become a recognized research and teaching centre. Taking into consideration the high standards of secondary education in Cyprus, this should be regarded as an obligation.

Important steps in achieving this ambition are the development of links with corresponding institutions abroad and the creation of high-level programmes of studies. The undergraduate programme, which started in September 1992, was designed in such a way so as to be naturally extended into a graduate one, which was designed at a later stage and started in September 1997.

During its first years of operation, the Department has prepared the programme of studies, has established a seminar series in Mathematics and Statistics, has placed emphasis on the development of a modern and fully equipped library and has collaborated with other sectors of the University to develop the necessary institutional and technical (especially in electronic equipment) infrastructure.

**PROGRAMME OF STUDY**

The programme of studies contains the list of courses, the description of most courses, the regulations for obtaining the degrees in Mathematics and Mathematics and Statistics and the requirements for the minor in Mathematics.

The Department's objective is to offer an up-to-date and realistic programme leading to degrees whose standards are equivalent to those of well-established universities. The programme has been designed so that it can be easily adapted to future needs.

**COURSES**

The curriculum courses are divided into four levels and six groups. The level 101-199 corresponds mainly to courses of the first year of studies. The level 201-299 corresponds mainly to courses of the second year of studies. The levels 301-399 and 401-499 are defined accordingly. The level 001-099 corresponds to service courses (see table Β) and are not open to Mathematics or Statistics majors (except MAS007, see Degree Requirements).

The six groups to which the courses are divided, correspond (approximately) to the following areas of Mathematics: Analysis, Algebra, Geometry, Probability/Statistics, Numerical Analysis and Applied Mathematics. The second digit of the course number determines the area of mathematics that the course belongs to. The characteristic digit (second digit of course number) of the six areas are 0 & 1, 2, 3, 5 & 6, 7 and 8 respectively and they appear in table A.

Classes meet for four hours per week, one of which may be a recitation class. Each class corresponds to a number of credit units (c.u.) as they appear in table A.

**DEGREE REQUIREMENTS**

The following are required for the degree in Mathematics or Mathematics and Statistics:

- 17 compulsory courses for all students .

MAS101 - Calculus I

MAS102 - Calculus II

MAS121 - LinearAlgebra

MAS122 - Linear Algebra II

MAS131 - Basic Mathematics

MAS191 - Mathematics with computers

MAS201 - Multivariate Differential calculus

MAS202 - Multivariate Integral calculus

MAS203 - Ordinary Differential Equations

MAS251 - Probability I

MAS252 - Statistics I

MAS271 - Numerical Analysis I

MAS301 - Real Analysis

MAS302 - Complex Analysis I

MAS331 - Classical Differential geometry

MAS303 - Partial Differential Equations

MAS304 - Functional Analysis

MAS371 - Numerical Analysis II

- 9 courses that are related to different areas of concentration (Pure Mathematics, Applied Mathematics and Statistics). For the degree in Mathematics one of these courses, is PHY111 – General Physics I. Some of these courses are "free electives" within the department (see tables A and C1, C2, C3).
- The course CS031-Introduction to Programming.
- 25 c.u. (5 courses of 5 c.u. each) must be free electives from other departments.
- The student is required to take two foreign language courses (any language).

At most two "free electives" within the Department could be substituted, in exceptional cases and during the last year of studies, by graduate courses. For that, a grade average of at least 7 is required in the departmental courses as well as the approval of the instructor and the academic advisor.

One of the free electives from other Departments could be substituted by MAS007-History of Mathematics (5 c.u.). In this case the free electives from other Departments correspond to 20 c.u.

Students can complete their studies with more than 240 c.u. depending on the elective courses, within and out of the Department, that they choose to take.

Typical programmes of study for the Degree in Mathematics with emphasis in Pure Mathematics, with emphasis in Applied Mathematics and for the Degree in Mathematics and Statistics are given in tables C1, C2 and C3 respectively.

Click here for **Course Titles and Numbers for MAS Students** (Table A)

Click here for **Indicatory Undergraduate Programme - Pure Mathematics** (Table C1)

Click here for **Indicatory Undergraduate Programme - Applied Mathematics** (Table C2)

Click here for **Indicatory Undergraduate Programme - Statistics** (Table C3)

**OTHER REQUIREMENTS**

Students can not register simultaneously for more than 5 departmental courses.

**ADDITIONAL INFORMATION**

The Department offers sufficient number of courses to allow for the completion of the requirements for obtaining the degree in Mathematics or in Mathematics and Statistics in eight semesters with regular attendance. Regular attendance is considered to be the successful completion of an average of three courses in the Department of Mathematics and Statistics and one course offered by other departments, per semester. It should be noted that the students of the Department, after the completion of their studies, receive only one of the degrees offered by the Department.

**RESEARCH INTERESTS AND PROJECTS**

There are several research projects in the Department, and some of these are in cooperation with overseas universities. The projects which are currently in progress involve research in the following areas of Mathematics and Statistics:

• Algebraic and Discrete Geometry.

• Algebraic Topology.

• Applications of Lie Groups to Differential Equations, Integrable and Hamiltonian Systems.

• Applications of Statistics to Biomedical Sciences.

• Asymptotic Efficiency of Model Selection Criteria for Autoregressive Processes.

• Computational Complex Analysis, Numerical Conformal Mapping, Spline Functions and Applications.

• Computational Oceanography.

• Differential Geometry.

• Efficiency in Parametric-Semiparametric Models in Survival Analysis.

• Finite Elements.

• Group Representation Theory.

• Harmonic Analysis, Orthogonal Polynomials, Special Functions.

• Lie Groups/Algebras

• Numerical Simulation of Newtonian and Viscoelastic Flow Problems. Stability Analysis.

• Numerical Solution of Partial Differential Equations.

• Riemannian Geometry.

• Sampling.

• Several Complex Variables.

• Theory and Applications of Bootstrap Methods.

• Theory and Applications of U-Statistics.

• Theory and Practice of Wavelets in Statistics and Time Series Analysis, Functional Linear Models and Functional Data Analysis.