### Mathematics 3

Our third year program in mathematics is made of 4 separate courses (2 in each semester).

###### MAT311: Algebra

Sets, equivalence relations, groups, rings, fields, integral domains, homorphisms, isomorphisms, and their elementary properties.

###### MAT313: Real Analysis

Topology of the real line, continuity and uniform continuity, Heine-Borel, Bolzano-Weierstrass, uniform convergence, introduction to metric spaces.

###### MAM311: Complex Analysis

This is a common course required by both MAP and MAT majors. Revision of complex numbers, Cauchy- Riemann equations, analytic and harmonic functions, elementary functions and their properties, branches of logarithmic functions, complex differentiation, integration in the complex plane, Cauchy’s Theorem and integral formula, Taylor and Laurent series, Residue theory and applications. Fourier Integrals.

###### MAT315: Topics in mathematics

This course will cover the following two areas:

• Topology: Revision on sets and functions, topological spaces (fundamental concepts, closure, interior, neighborhood, bases, subspaces, continuity), lower separation axioms (T0,T1 and T2 spaces).

• Discrete Mathematics: Permutations, combinations, generating functions, recursions, inclusion-exclusion, congruences, residue classes, graphs, Pythagorean triples, sums of 2 and 4 squares, Diophantine equations, continued fractions.