# Course Listings

**MATH 91 - Pre-calculus: **

This course of pre-calculus includes Fundamental concepts of algebra, equations and inequalities, functions, complex numbers, polynomial and rational functions, coordinate geometry, exponential and logarithmic functions, trigonometry and trigonometric functions, conic sections. Applications and word problem applications of the included topics are an essential part of the course.

**MATH 100 - Elementary Mathematics:**

Set theory. Real numbers. Inequalities. Straight lines and circles. Complex Numbers. Systems of linear equation, Elementary matrices, and their applications.

**MATH 101 - Calculus I:**

This is the first course of a three-semester calculus sequence (MATH-101, MATH-102, and MATH-211). Topics of this course include limit and continuity of functions of a single variable; the intermediate value theorem; derivatives; differentiation methods; Rolle's theorem and the mean value theorem; applications of differentiation and differentials; indefinite and definite integrals; the fundamental theorem of calculus; area between curves as an application of definite integral.

**MATH 102 - Calculus II:**

This continuation of MATH-101 is the second course in a three-semester calculus sequence. Topics include; indeterminate forms and L’Hospital’s Rule; integration by parts; techniques of integration; applications of integration; improper integrals; infinite sequences, infinite series, power series; plane curves; polar coordinates; graphing and area in polar coordinates.

**MATH 103 - Biomathematics (Only for Biology students):**

Functions and their graphs, the derivative, applications of the derivative, simple integrations, law of growth and decay.

**MATH 105 - Applied Calculus (Only for students from the College of women):**

Trigonometry, analytical geometry in two dimensions, linear equations, functions and their graphs, derivatives and its geometric interpretation, simple integration and its applications.

**MATH-111 Introductory Linear Algebra :**

This is a first course in linear algebra, covering linear equations, matrices, determinants, linear (Euclidean) spaces, bases and dimension, eigenvalues and eigenvectors, matrix diagonalization, and three-dimensional geometry (cross products, lines and planes, applications).

**MATH 115 - Finite Mathematics (Non Mathematics Major) :**

Sets and operations on them; the Cartesian plane; systems of linear equations; systems of linear inequalities in two variables; geometric approach to linear programming problems in two variables; the simplex method of solving linear programming problems; basic principles of counting; permutations; combinations; discrete probability and simple applications related to Medical Science.

**MATH 211 - Calculus III:**

This continuation of Math 102 completes the three-semester calculus sequence. Topics include; vector functions, calculus of functions of several variables including partial differentiation and multiple integrals, Lagrange multipliers, applications of partial differentiation, line integrals, Green's theorem, surface integrals, Stoke’s theorem, and Divergence theorem.

**MATH 226 - Euclidean Plane Geometry:**

Historical background, fundamentals of plane Euclidean geometry, triangles, quadrilaterals, circles, locus problems, geometric constructions, transformations, symmetry, analytic geometry.

**MATH 240 - Ordinary Differential Equations:**

Differential equations of first order; linear differential equations of higher order; power seriesand their use in solving differential equations; Laplace transform and its use in solvingdifferential equations.

**MATH 250 - Introduction to the Foundations of Mathematics :**

Formal logic and predicate calculus, set theory, mathematical proofs, mathematical induction, relations, equivalence relations and partitions, functions, the integers, the rational and real numbers, denumerable sets, cardinal numbers, partial ordering.

**MATH 261 - Introduction to Abstract Algebra I:**

Groups and their basic properties; subgroups; permutation groups; equivalence relations; Lagrange’s Theorem; direct product of groups; factor groups; group homomorphism; group isomorphism.

**MATH 262 - Introduction to Abstract Algebra II:**

Rings and fields; integral domains; the field of quotients of an integral domain; rings ofpolynomials; factorization of polynomials over a field; ring homomorphism; ideals; factor rings;introduction to field extensions.

**MATH ****264**** - ****Introduction to Combinatorial Mathematics****:**

This introductory course covers basic topics in combinations such as sets, permutations, and combinations; basic counting principles; binomial coefficients; and basic graph theory including graphs, degrees, paths and cycles, connectivity, Eulerian and Hamiltonian graphs, and trees.

**MATH 313 - Applied Mathematical Analysis:**

Gamma and Beta functions. Hypergeometric functions. Bessel functions. Orthogonal polynomials. Fractional calculus.

**MATH 315 - Mathematical Electromagnetic Theory:**

Electrostatics. Dielectrics. Magnetostatics. Induced magnetism. Steady currents. Maxwell's equations. Quasi-stationary Fields. Electromagnetic waves. Notion of electric charges.

**MATH 316 - Elements of Mathematical Modelling:**

The basic idea of mathematical modeling of real world problems; modeling change with difference equation; modeling using graphs, proportionality, curve-fitting, and optimization; experimental modeling; modeling with a differential equation; discrete optimization modeling; modeling with systems of differential equations (interactive dynamical systems).

**MATH 325 - Combinatorics:**

Topics of this course include; the pigeonhole principle; counting principles; permutations and combinations; identities involving binomial coefficients; the inclusion-exclusion principle; recurrence relations; generating functions.

**MATH 326 - Graph Theory:**

Topics of this course include; graphs and their basic components; directed and undirected graphs; isomorphism of graphs; planar graphs; edge- and vertex-colorings; Hamiltonian cycles and the Eulerian graphs; trees; matching theory; digraphs; chromatics number; connectivity of graphs; networks.

**MATH 327 - Theory of Numbers:**

Greatest common divisor; the division algorithm; the Euclidean algorithm; perfect numbers; multiplicative functions; Euler phi function; Mobius function; Mobius inversion formula; linear congruences; the Chinese Remainder theorem; Fermat theorem; Public key cryptography; quadratic residue; quadratic reciprocity; Pythagorean triples; sums of two squares.

**MATH 329 - Introduction to Real Analysis:**

This course is a rigorous treatment of the calculus of functions of one real variable. Emphasis is on proofs and understanding. The course topics include: the real number system, the completeness property, elements of the topology of the real line (open and closed sets and the Heine-Borel Theorem), sequences of real numbers, limits of functions of a single real variable, continuity, uniform continuity, properties of continuous functions, differentiation, the Riemann integral.

**MATH 330 - Functions of Complex Variables:**

Complex numbers; analytic functions, elementary functions; contour integration; Cauchy theorem; Cauchy integral formula; power series; Laurent series; calculus of residues.

**MATH 340 - Theory of Differential Equations :**

Series solutions near regular singular points; nonlinear differential equations; systems of linear differential equations; the theory of first-order equations; stability of equilibria; boundary value problems.

**MATH 343 - Classical Mechanics:**

Rectilinear motion of a particle with variable acceleration. Simple harmonic motion. Damped and forced oscillations. Motion of a particle in a plane using Cartesian, polar and intrinsic coordinates. Central orbits. Kepler's laws. Moments and products of intertia. Kinetic energy and angular momentum of rigid body. The general equations of motion. Two-dimensional problems. Generalized coordinates and Lagrange equations of motion. Small oscillations.

**MATH 345 - Abstract Algebra:**

An overview of rings and fields; integral domains; the field of quotients of an integral domain; rings of polynomials; factorization of polynomials over a field; ring homomorphism; ideals; factor rings; Modules.

**MATH 346 - Group Theory :**

Topics of this course include permutation groups; conjugacy classes; the simplicity of the alternating group of order n > 4; direct products; the fundamental theorem of finite Abelian groups; the Sylow theorems; groups of small orders.

**MATH 352 - Numerical Analysis:**

Numerical solution of nonlinear equations; numerical solution of systems of equations; polynomial interpolation; least-squares approximation, numerical integration.

**MATH 354 - Methods in Applied Mathematics:**

Vector calculus, Asymptotic expansions, Calculus of variations, Applications of ODEs to sciences.

**MATH 355 - Operational Mathematics:**

Equation of Laplace, Fourier and Hankel transforms, Boundary value problems, applications.

**MATH 361 - Theoretical Fluid Dynamics:**

Equations of motion. Two-dimensional motion. Streaming motions. Sources and sinks. Theorem of Schwarz and Christoffel. Stoke’s stream function and three-dimensional motion.

**MATH 362 - Computational Linear Algebra:**

Gauss elimination; Doolittle's and Choleski's methods; special structured matrices; iterative methods of Jacobi, Gauss-Seidel, SOR, conjugate gradient, and GMRES; the linear least squares problem; matrix eigenvalue problem.

**MATH 363 - Advanced Linear Algebra :**

Abstract vector spaces over arbitrary fields; bases and dimensions; linear transformations; dual spaces; invariant subspaces; inner product spaces; diagonalization.

**MATH 370 - Geometry I:**

Historical background, Euclid’s axioms, Euclid re-examined: Hilbert’s axioms, Non-Euclidean Geometries, Neutral Geometry, Transformations of the Euclidean plane (isometries, homothecies, similarities), Projective Geometry.

**MATH 375 - Introduction to Topology:**

The course is a traditional first course in topology covering “point-set topology”. It covers metric and topological spaces, continuity, topological equivalence (homeomorphism), compactness, connectedness, and completeness.

**MATH 401 - Analysis:**

Uniform convergence of sequences and series of functions; convergence properties of power series; Abel’s theorem; Weierstrass approximation theorem; Picard’s existence theorem for ODE; equicontinuity and Arzela’s theorem; Lebesgue measure and integral; the L2 theory of Fourier series.

**MATH 402 - Set Theory:**

Formation of set theory. Propositional calculus. Quantification. Calculus of classes. Set of natural numbers. Relations and maps. Axiom of choice. Zorn’s dilemma. Well-ordering principle. Ordinals and cardinals.

**MATH 403 - Advanced Linesr Algebra:**

Linear transformations, change of bases matrices, dual spaces, irreducible polynomials, vector spaces as F[x] modules, characteristic polynomial decomposition companion matrices, rational and Jordan canonical forms.

**MATH 404 - Analysis of Functions of Several Variables:**

Sets and functions in R^n; continuous and differentiable functions between Euclidean spaces R^n andtheir properties; higher derivatives; the Implicit and Inverse function theorems; Taylor's theoremfor functions of several variables; maxima and minima; integration over subsets of R^n; evaluation of multiple integrals; change of variables.

**MATH 406 - Algebraic Coding Theory:**

Topics of this course include the basics of coding theory; linear codes; decoding algorithms for linear codes; basic examples of linear codes such as Hamming codes, Reed Solomon codes, BCH Codes and decoding algorithms for BCH codes; cyclic codes; important bounds for linear codes.

**MATH 407 - Tensor Analysis:**

Orthogonal Transformations. Cartesian tensors. Generalised N-dimensional spaces. Contravariant and covariant tensors. Tensor algebra. Tensor densities. Covariant differentiation. The Riemann Christoffel curvature tensor. Metrical connection. The Laplacian. Einstein tensor. Geodesics.

**MATH 408 - Topology:**

Topological spaces, product spaces, quotient spaces, convergence, separation axioms, first and second countable spaces, compactness, connectedness, and fundamental groups.

**MATH 409 - Geometry II:**

Analytic projective geometry. Affine, hyperbolic and elliptic geometries.

**MATH 410 - Theory of Relativity:**

Review of tensor analysis. The principle of special relativity. Lorentz transformations. minkowski geometry. Relativistic mechanics and electrodynamics. Introduction to the general theory of relativity. The principle of equivalence, metric in a gravitational field, Einstein's law of gravitation. Shwarzchild solution.

**MATH 412 - Theory of Elasticity:**

Analysis of stress and strain. Principal axes. Compatibility equations. Generalized Hooke's law. Beltrami-Michell equations. The fundamental boundary value problems. Applications.

**MATH 415 - Partial Differential Equations:**

First and second order linear partial differential equations; the method of characteristics; separation of variables method and its application to linear partial differential equations; Fourier series; boundary-value problems and Sturm-Liouville theory; Green’s formulas; well-posed and ill-posed problems.

**MATH 416 - Mathematical Modelling:**

Selection of mathematical models based on differential equations and linear systems; analysis of models; development of solution algorithms and sensitivity of models to perturbations in data; computer simulation for the visualization and interpretation of modeled physical phenomenon.

**MATH ****417**** - ****Spline Functions and Applications****:**

Polynomial interpolation; univariate piecewise polynomial and spline functions; bivariate piecewise polynomial functions; thin plate splines and radial basis functions; bivariate piecewise polyharmonic functions.

**MATH 420-** **Introduction to Dynamical Systems and Chaos:**

Dynamical systems: Phase space, attractors, basin of attraction, elementary bifurcation theory, stability theory; Chaos: Liapunov exponents, bifurcation of fixed points, chaotic systems and maps; Fractals: Iterated function systems, the contraction mapping theorem, fractal dimension, box counting theorem.

**MATH 438 - Applications of Graph Theory:**

Network flows. Timetable. Matching. Travelling salesman problem. Some computer algorithms.

**MATH 440 - Integral Equations:**

Topics of this course include basic concepts about integral equations; Fredholm and Volterra integral equations; Integral transformations; Approximation methods.

**MATH 450 - Ring Theory:**

Field quotients. Ideals, prime ideals, Direct sums. Modules, submodules, homomorphisms, free modules, vector spaces. Subdirect sums of rings, primitive rings, prime radical, density-Theorem (without proof), Jacobson radical, chain conditions, Wedderburn Artin Theorem.

**MATH 454 - Advanced Methods in Applied Mathematics:**

Fourier transform and inversion techniques, applications in signal processing. Laplace and Mellin transforms. Discrete linear systems and filters, discrete Fourier transforms. Fast Fourier transform. Perturbation methods.

**MATH 468 - Numerical Ordinary Differential Equations:**

Topics of this course include numerical integration (Quadratures); numerical differentiation; numerical solution of initial value ordinary differential equations (one-step methods and linear multi-step methods); numerical methods for solving two-point boundary-value problems ordinary differential equations.

**MATH 469 - Numerical Partial Differential Equations:**

Finite difference methods for parabolic, elliptic and hyperbolic differential equations; method of characteristics; stability; consistency; convergence.

**MATH 470 - Calculus of Variations:**

Fundamental problems; Euler’s equation; boundary conditions; second variation; isoperimetric problem; transformations; variational principles; applications.

**MATH 480 - Differential Geometry:**

This is a one-semester course in differential geometry for senior undergraduate students. Topics of this course include smooth curves in plane and space; moving Frenet frame; torsion and curvature; Frenet equations; smooth surfaces; first and second fundamental forms; structure equations; intrinsic geometry.

**MATH 481 - Functional Analysis:**

Metric spaces; properties of normed and Banach spaces; bounded and continuous linear operators; linear functionals; inner product and Hilbert spaces; Hilbert adjoint operators, Riesz representation theorem for Hilbert spaces; fundamental theorems for normed and Banach spaces.

**MATH ****484**** - ****Applied Cryptography****:**

This course is an introductory course to mathematical cryptography. It covers the following topics: an introduction to Cryptography: history and its present day use, discrete logarithms and Diffie-Hellman key exchange, integer factorization and RSA, digital signatures, elliptic curves and cryptography, and additional topics in cryptography.

**MATH 485 - Finite Planes**

Finite incidence structures. Incidence matrices. Block design. Projective and affine planes. Coolineations. Coordination and ternary rings. The Bruck-Ryser theorem.

**MATH 495 - Mathematical Logic**

Propositional calculus. First order logic. First order recursive arithmetic. Arithmatization of syntax. The incompleteness theorem and other applications.