Mathematics courses Description

 

Math 411 Seminar

This course provides a forum for the exchange of mathematical ideas between faculty and students under the guidance of the course instructor. The course culminates in the presentation by each student of a one written report on a selected topic or problem reflecting some independent work and evidence of familiarity with the mathematical literature. Students may work with other faculty members in the preparation of written reports.

Prerequisite: Approval of the department.

 Math 430 Numerical Analysis (3) (NEW).  

Iterative techniques in solving system of equations, approximation theory, approximating eigenvalues and eigenvectors, numerical solution of boundary value problems, numerical solutions to partial differential equations, an introduction to finite element method.

 Prerequisite: Math 330

Math 431 Complex Variables (3) no changes.

Complex numbers and the complex plane, arguments and roots, roots of  unity, De Moivre’s theorem, limits, continuity, differentiability, Cauchy-Riemann conditions and analytic functions, elementary functions, branch cuts, convergence of complex series, complex integration: line integrals, Cauchy’s theorem, Cauchy’s integral formula, Morera’s and Liouville’s theorems, Taylor’s and  Laurent’s series, residues and poles, Rouche’s theorem, fundamental theorem of algebra, evaluation of real and improper integrals, meromorphic functions.

 Prerequisite: Math 333

 Math 432 Topology (3) minor changes.

Topological Spaces: basis for a topology, the order topology, the subspace topology, closed sets and limit points, continuous functions, product topology, metric topology, connected spaces, compact spaces, limit point compactness, countability and separation Axioms.

Prerequisite: Math 333   (change prerequisite from Math 233)

Math 433 Discrete Dynamical Systems (3) (NEW).

 Dynamics of first order difference equations, linear difference equations of higher order, systems of difference equations, stability theory and chaos in one and two-dimensional maps. Discrete nonlinear models.

Prerequisite: Math 331, Math 234

Math 434 Advanced Linear Algebra (3) major changes.

Vector spaces over arbitrary fields, bases, dimension, linear transformations and matrices. Inner products, quadratic forms, normal and Jordan canonical forms, generalized inverses.

 Prerequisite: Math 234

 Math 435 Introduction to Number Theory (3)minor changes.

 The integers, divisibility and primes, Euclidean algorithm, and the fundamental theorem of arithmetic, congruences, arithmetic and multiplicative functions, primitive roots, quadratic residues and reciprocity, Diophantine equation.

 Prerequisite: Math 233

 Math 437: Idependent studies

Prerequisite: Approval of the department.

 Math 438 Special Topics

Special topics in mathematics will be offered according to student needs.

Prerequisite: Approval of the department.

 Math 439  Non-Euclidean Geometry (3) (NEW).

Historical background of non-Euclidean Geometry, alternative concepts for parallelism, an improbable logical case, hyperbolic geometry and elliptic geometry: angle sum theorem, models for hyperbolic geometry and elliptic geometry, circular inversion, plane geometry, absolute geometry, projective geometry, projective transformations, multidimensional projective geometry, solid geometry, hyperbolic and elliptic solid geometry, Discrete geometry, Hilberts axioms, an introduction to  spherical geometry.

 Prerequisite: Math 339

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