### Mathematics 3

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

• ### 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.

• ### Real Analysis:

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

• ### Algebra:

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

• ### Topics in mathematics:

This course will cover one of the following two areas. Please consult the department to determine which is offered in a given year:

• Differential Geometry:Curves (in the plane and in the space), curvature, global properties of curves, surfaces, the first fundamental form, isometries, the second  fundamental form, the normal and principal curvatures, the Gaussian and mean curvatures, the Gauss map, geodesics.

• 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.