## Senior Year

**40412 Introduction to numerical analysis of differential equations**

Euler's method, multistep methods, Runge-Kutta methods, stiff equations, finite difference schemes.

**40217 40218 Advanced Calculus (I)(II)**

1.Divisibility and Congruences 2.Private-Key Cryptosystems 3.Primality and Factoring 4.Public-Key Cryptosystems 5.Pseudo-Random Numbers

**40423 Theory of Finite Fields and their Applications**

1.Algebraic Foundations 2.Structure of Finite Fields 3.Polynomials over Finite Fields 4.Irreducible Polynomials 5.Primitive Polynomials 6.Normal Bases over Finite Fields 7.Application in Coding Theory 8.Application in Cryptography 9.Application in Combinatorics

**40425 Mathematical Biology**

This course is an introduction to mathematical modeling, using applications in the biological sciences. We will cover linear difference and differential equations, and give an introduction to nonlinear phenomena and qualitative methods. Elementary knowledge of differential equations and linear algebra is assumed.

40430 History in Mathematics Prerequisites: Textbook

40430 History in Mathematics Prerequisites: Textbook

This subject-matter of this course is a historical summary of the development of mathematics, illustrated by the lives and discoveries of those to whom the progress of the science is mainly due. It is intended to give a short and popular account of those leading facts in the history of mathematics which students may desire to know. 1.The Beginnings 2.The Ancient Orient 3.Greece 4.The Orient after the Decline of Greek Society 5.The Historic Period Down to 1600 A.D. 6.The Seventeenth Century 7.The Eighteenth Century 8.The Ninteenth Century 9.The Twentieth Century

**40432 Differential Geometry (I)(II)**

Fourth year, Grade 3. this course is mainly to study course and surfaces in R3 ( Three dimential differential geometry ). It includes vector analysis course in R2 & R3, tangent plane, regular surfaces, geometry of the Gauss map, intrinsic geometry of surfaces, global differential geometry.

**40433 40434 Complex Analysis (I)(II)**

These courses may cover the contents of the geometric function theory and that of the value distribution theory.

**40435 40436 Real Analysis (I)(II)**

This course covers the essentials of real analysis. It will cover the basic theory of measure and Lebesgue integration are developed. Topics include Fatou's Lemma, dominated convergence theorems and classical function spaces.

**40437 Fourier analysis**

**Fourier series. Summability of Fourier series.Convergence of Fourier series. Uniqueness. Fourier transform. Cosine and Sinetransform. Convolution. Laplace transform. Some applications.**

**40445 40446 Advanced Probability Theory (I)(II)**

1.Probability 2.Measure 3.Integration 4.Random variables and expected values 5.Convergence of distributions 6.Derivatives and conditional probability 7.Stochastic processes.

**40449 40450 Actuarial Mathematics (I)(II)**

Applied probability and mathematics of investment to problems of premiums and reserves on annuities and insurance policies.

**40453 40454 Topics in Algebra (I) (II)**

Extends concepts of Algebra I and II and develops further applications. This course contains Galois theory: splitting fields, separable extensions, the main theorem of Galois theory, cyclotomic extensions, and solvability by radicals. Selected further topics, such as transcendental extensions, Wedderburn theory, and representations of finite groups. Prerequisite: Algebra (I)(II)

**40460 Multimedia Education and its Applications**

Introduction to multimedia. Multimedia tools. Developing multimedia. Producing and distributing multimedia. Multimedia issues and the future of multimedia. Hands-on Tutorial. Required course, 3 credits, fall semester.

**40461 40462 Fuzzy Mathematics and its Applications (I)(II)**

The purpose of this course is to provide the student with comprehensive coverage of the oriental foundations of fuzzy set theory and fuzzy logic. Topics include fuzzy set, fuzzy relations, fuzzy relation equations, fuzzy logic and fuzzy arithmetic.

**40463 Discrete Mathematics**

1.Fundamentals 2.Logic 3.Counting 4.Relations and Digraphs 5.Functions 6.Topics in Graph Theory 7.Order Relations and Structures 8.Trees 9.Semigroups and Groups 10.Languages and Finite-State Machines 11.Goups and Coding

**40472 Partial Differential Equations**

Fourth year (& Third year), this course in one semester course in Introductory Partial Differential Equations. It includes the reviews in basic concepts or some introduction in basic analysis, for example, the idea of distance between sets, double inteqral, solutions of ordinary differential equation, complex-valued functions, Fourier series. The essential parts are: 1.Second-order partial differential equations ( with canonical form ) 2.The wave equation ( hyperbolic equation with Cauchy problem, initial value problem ) 3.The potential equation ( Laplace equation with Dirichlet problems ) 4.The heat equations ( parabolic equation with boundary valued problem. ) 5.Approximate solution of P.D.E. 6.Servey of other topics ( other methods of solution, method of Green's Functions ) 7. Remarks about nonlinear P.D.E.

**40493 Seminar in Mathematics**

Material related mathematics. Consent of the instructors.

**40497 40498 Introduction to Operations Research (I)(II)**

This is a course for the fourth year of undergraduate. It will cover the following topics. OR Approach: modeling, constraints, objective and criterion. Problems of multiple criteria, optimization, model validation and systems design. OR Methodology: mathematical programming; optimum seeking; simulation, gaming; heuristic programming. OR Applications: theory of inventory; economic ordering under deterministic and stochastic demand. Production smoothing problem; linear and quadratic cost functions. Waiting line problems: single and multiple servers with Poisson input and output. Theory of games for two-person competitive situations.