THIRD YEAR LEVEL

(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 MAT 211.

MAP 312: Advanced Numerical Differentiation and Integration.

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 223.

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 212.

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; L^P-spaces. [Optional module] 22 credits, one 3-hour paper. Prerequisites: MAT 211, MAT 212 and MAT 224.

MAT 334: History and Fundamental Concepts of Mathematics.

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 MAT 212.

______________________________________________________