(a) Applied Mathematics
MAP 311: Special and Orthogonal Functions.
Bessel functions, Legendre functions and other Orthogonal
functions; Sturm-Liouville system; Eigenvalues and Eigenvectors. 16 credits; one 3-hour paper. Prerequisites: MAP 221 and
MAP 312: Advanced Numerical Differentiation and
Advanced Numerical Differentiation and Integration;
Singular integrals and Gaussian integration; Methods for solving sums and
series; approximating solutions to difference equations. 16 credits; one 3-hour
paper. Prerequisites: MAP 221 and MAT 211.
MAP 321: Partial
Differential Equations; Conformal Mapping;
Calculus of Variation.
Partial differential equations; Complex variables;
Conformal mapping; Calculus of variations. 16 credits; one 3-hour paper.
Prerequisites: MAP 311.
MAP 322: Numerical Solutions to Differential Equations.
Numerical solutions to differential equations of the first
and higher order; Least-squares polynomial approximation; Boundary value
problems. 16 credits; one 3-hour paper. Prerequisites: MAP 312.
(b) Pure Mathematics
MAT 331 and MAT 332 are compulsory components; in addition
students have to choose between MAT 333 and MAT 334. Note MAT 334 is intended
mainly for prospective teachers of Mathematics.
MAT 331: Abstract Algebra
Groups; Rings; Fields and Algebras. [Compulsory module] 22 credits; one 3-hour paper. Prerequisites: MAT 212 and
MAT 332: Complex Analysis.
Functions of complex variable; Derivatives; Cauchy-Riemann
equations; Integration; Cauchy’s theorem; Contour integrals; Taylor and Laurent
expansions; Residue theory; conformal mappings and applications; Analytical
continuation and Riemann surfaces. [Compulsory module]. 22 credits; one 3-hour paper. Prerequisites: MAT 211 and
MAT 333: Real Analysis.
Metric spaces; Introduction to normed spaces; Function
spaces; Stone Weierstrass theorem; Some fixed point theorems and applications;
Inverse and implicit function theorems; Lebesgue integral; LP-spaces.
[Optional module] 22 credits, one 3-hour paper. Prerequisites: MAT 211, MAT
212 and MAT 224.
MAT 334: History and Fundamental Concepts of
Overview of some numerical systems; Babylonian, Egyptian
and Pythagorean mathematics; the Axiomatic method; Euclid’s elements and
non-Euclidean geometry; Hindu, Arabian and European mathematics; Analytic
geometry; Algebraic structure; Sets and the fundamental concepts of mathematics;
Crises in the foundations of mathematics; Philosophies of mathematics. [Optional
module] 22 credits; one 3-hour paper. Prerequisites: MAT 211 and