Courses Offered by Mathematics Department
(Beginning with Fall 2016)

Math 101 
Calculus I 
(4+2+0) 4 
ECTS 6 
Functions, limits, continuity, differentiation and applications, integration, fundamental theorem of calculus, techniques and applications of integration, improper integrals and series, Taylor polynomials, power series, basic transcendental functions. 
Math 102 
Calculus II 
(4+2+0) 4 
ECTS 6 
Vector calculus, functions of several variables, directional derivatives, gradient, Lagrange multipliers, multiple integrals and applications, change of variables, coordinate systems, line integrals, Green's theorem and its applications. 
Math 105 
Introduction to Finite Mathematics 
(4+2+0) 4 
ECTS 6 
Systems of linear equations and inequalities, matrices, determinants, inverses, Gaussian elimination, geometric approach to linear programming, basic combinatorics, binomial theorem, finite probability theory, conditional probability, Bayes' theorem, random variables, expected value, variance, decision theory. 
Math 106 
Introduction to Calculus for Social Sciences 
(4+2+0) 4 
ECTS 6 
Functions of one variable, properties of quadratic, cubic, exponential and logarithmic functions, compound interest and annuities, limits, continuity and differentiation, applied maximum and minimum problems, basic integration techniques, sequences and series. 
Math 111 
Introduction to Mathematical Structures 
(4+2+0) 4 
ECTS 8 
Propositional logic, truth tables, equivalences, quantifiers, rules of inference, proof
methods, sets, power sets, functions, sequences, countability, cardinality, divisibility,
modular arithmetic, primes, mathematical induction, strong induction and wellordering
principle, recursive definitions, axiomatic systems, Euclid's postulates and
nonEuclidean geometries. 
Math 131 
Calculus of a single variable 
(4+2+0) 4 
ECTS 8 
Sequences, limits and continuity, differentiation and its applications, integration and
its applications, fundamental theorem of calculus, transcendental functions, improper
integrals. 
Math 132 
Calculus of several variables 
(4+2+0) 4 
ECTS 8 
Vectors and geometry in space, vectorvalued functions and motion in space,
functions of several variables, partial derivatives, multiple integrals, vector fields. 
Math 162 
Discrete Mathematics 
(4+2+0) 4 
ECTS 8 
Counting, the pigeonhole principle, permutations, combinations, binomial
coefficients, generalized permutations and combinations, discrete probability,
linear recurrence relations, generating functions, inclusionexclusion, relations,
closures of relations, equivalence relations, construction of integers and rationals,
partial orderings, graphs. 
Math 201 
Matrix Theory 
(4+2+0) 4 
ECTS 5 
Systems of linear equations, Gaussian elimination, matrix algebra
determinants, inverse of a matrix, Cramer's rule, rank and nullity, the
eigenvalue problem, introduction to linear programming. 
Math 202 
Differential Equations 
(4+2+0) 4 
ECTS 7 
Firstorder differential equations, linear equations, homogeneous and nonhomogeneous, series solutions, the Laplace transform, systems of firstorder linear equations, boundary value problems, Fourier series. 
Prerequisite: 
(Math 101 or Math 131) and (Math 201 or Math 221) 
Math 221 
Linear Algebra 
(4+2+0) 4 
ECTS 8 
Vector spaces, bases, linear transformations, matrices, subspaces, systems of linear
equations, echelon and reduced echelon forms, dimension, fundamental subspaces,
rank, change of coordinates, determinants, cofactor expansion, minors, eigenvalues,
eigenvectors, diagonalization, inner product spaces, orthogonality, GramSchmidt
orthogonalization process, adjoint, unitary and orthogonal transformations, dual
spaces. 
Math 222 
Group Theory 
(4+2+0) 4 
ECTS 8 
Groups, subgroups, cyclic groups, generating sets, permutations, orbits, cycles,
alternating groups, cosets, Lagrange's Theorem, direct products, finite abelian groups,
homomorphisms, normal subgroups, factor groups, simple groups, group actions,
isomorphism theorems, Sylow's theorems. 
Math 231 
Advanced Calculus I 
(4+2+0) 4 
ECTS 8 
Sequences and functions, compact sets, continuity, uniform continuity, limits of
functions, discontinuities, differentiation, derivatives for functions of several
variables, differentiation of composite functions, Taylor's Theorem, definite integrals,
substitution in multiple integrals, improper integrals. 
Math 234 
Advanced Calculus II 
(4+2+0) 4 
ECTS 8 
Infinite series, conditionally convergent series, double series, uniform convergence,
series and sequences of functions, power series, improper integrals with parameters,
differentiation of transformations, linear functions, differentials and inverses of
transformations, inverse and implicit function theorems. 
Math 323 
Rings, Fields and Galois Theory 
(4+2+0) 4 
ECTS 8 
Rings, integral domains, field of fractions, polynomials, factorization, ideals, factor
rings, homomorphisms, prime and maximal ideals, extension fields, algebraic
extensions, finite fields, unique factorization domains, Euclidean domains, Gaussian
integers, field automorphisms, splitting fields, Galois theory, insolvability of the
quintic equations. 
Prerequisite: 
Math 222 or consent of the instructor 
Math 324 
Representation Theory of Finite Groups 
(3+2+0) 3 
ECTS 6 
Representations, irreducibility, Maschke's theorem, semisimplicity, characters,
character tables, orthogonality relations, induction and restriction of characters,
Mackey decomposition theorem, algebraic integers, Burnside's p^aq^btheorem,
Frobenius' normal complement theorem. 
Prerequisite: 
Math 222 or consent of the instructor 
Math 325 
Matrix Groups 
(3+0+2) 3 
ECTS 6 
General linear groups, closed subgroups of real and complex general linear groups,
their topological properties, associated tangent spaces, exponential and logarithm
functions, manifolds, maximal tori, homomorphisms. 
Prerequisite: 
(Math 102 or Math 132) and Math 222 
Math 327 
Number Theory 
(3+2+0) 3 
ECTS 6 
Divisibility theory, Euclidean algorithm, congruences, solutions of polynomial
congruences, primitive roots, power residues, quadratic reciprocity law, arithmetical
functions, distribution of prime numbers, Pell's equation, quadratic forms, some
diophantine equations. 
Prerequisite: 
Math 111 or Math 162 
Math 331 
Metric Spaces 
(4+2+0) 4 
ECTS 8 
Topology, density, separability, convergence, compactness, connectedness,
continuity, open and closed maps, equicontinuity, ArzelaAscoli theorem,
contractions and fixed point theorems, completeness, Cantor's theorem, Baire
category theorem, completion. 
Math 332 
Lebesgue Integration 
(3+2+0) 3 
ECTS 6 
Elementary measure theory, sets of measure zero, Lebesgue measure, Lebesgue
measurable sets and functions, Lebesgue integral, convergence theorems, the space
L^1, absolutely continuous functions, functions of bounded variation, Hilbert space
L^2, Fourier series. 
Prerequisite: 
Math 234 or consent of the instructor 
Math 334 
Analysis on Manifolds 
(3+2+0) 3 
ECTS 6 
Differentiation, inverse and implicit function theorems, integration, manifolds,
differential forms, orientation, Stokes' theorem, Poincaré lemma, de Rham
cohomology. 
Prerequisite: 
Math 221 and Math 234 
Math 336 
Numerical Analysis 
(3+2+0) 3 
ECTS 6 
Solutions of nonlinear equations, bisection, Newton, and fixed point iterations, direct
solutions of linear systems, Gaussian elimination with partial pivoting, LU and
Cholesky factorizations, iterative solutions of linear systems, vector and matrix
norms, Neumann series, Jacobi, GaussSeidel and SOR iterations, projection methods,
steepest descents, conjugategradient and GMRES methods, matrix eigenvalue
problem, power method, Givens rotations, Jacobi iteration, Hessenberg form, QRiteration,
polynomial interpolation, Lagrange polynomials, Newton’s divided
differences, Chebyshev polynomials, least squares, spline interpolation. 
Prerequisite: 
(Math 101 or Math 131) and (Math 201 or Math 221) 
Math 338 
Complex Analysis I 
(4+2+0) 4 
ECTS 6 
Complex numbers, exponential forms, roots of complex numbers, functions of a
complex variable, limits, continuity, derivatives, CauchyReimann Equations, polar
coordinates, analytic functions, reflection principle, exponential and logarithmic
functions, branches, trigonometric and hyperbolic functions, linear transformations,
definite integrals, contour integrals, branch cuts, CauchyGoursat theorem, simply
connected domains, Cauchy integral formula, Liouville's Theorem, maximum
modulus principle, Taylor and Laurent series, residues and poles, Cauchy's residue
theorem, residue at infinity. 
Math 344 
Introduction to Probability and Statistics 
(3+2+0) 3 
ECTS 6 
Probability, conditional probability, Bayes’ theorem, independence, discrete and
continuous probability distributions, expected value, estimation, confidence intervals,
tests of hypothesis for one parameter, goodness of fit test, linear regression, analysis
of variance. 
Prerequisite: 
Math 102 or Math 132 
Math 345 
Probability 
(3+2+0) 3 
ECTS 6 
Axioms of probability, conditional probability, independence, discrete and continuous
random variables, jointly distributed random variables, expectation, limit theorems. 
Prerequisite: 
Math 344 or consent of the instructor 
Math 351 
Qualitative Theory of Ordinary Differential Equations 
(3+2+0) 3 
ECTS 6 
Existence and uniqueness theorems, phase portraits in the plane, linear systems and
canonical forms, nonlinear systems, linearization, stability of fixed points, limit
cycles, PoincaréBendixson theorem.

Math 352 
Partial Differential Equations 
(3+2+0) 3 
ECTS 6 
Wave equation, heat equation, Laplace equation, classification of second order linear
equations, initial value problems, boundary value problems, Fourier series, harmonic
functions, Green's functions. 
Prerequisite: 
(Math 132 and Math 202) or (Math 102 and Math 202) 
Math 361 
Combinatorics 
(3+2+0) 3 
ECTS 6 
Sieve methods, lattices, distributive lattices, incidence algebra, Mobius inversion
formula, Mobius algebras, generating functions, exponential formula, Lagrange
inversion formula, matrix tree theorem. 
Prerequisite: 
Math 201 or Math 221 
Math 363 
Graph Theory 
(3+2+0) 3 
ECTS 6 
Basic definitions, trees, Cayley's formula, connectedness, Eulerian and Hamiltonian
graphs, matchings, edge and vertex colouring, chromatic numbers, planar graphs,
directed graphs, networks. 
Prerequisite: 
Math 221 or consent of instructor 
FOR THE PART II OF THE COURSE CATALOGUE, SEE HERE.
