UNDERGRADUATE COURSES

MATE 3000. FINITE MATHEMATICS. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3171.

Counting techniques, probability, matrix algebra, linear programming, and systems of linear equations.

MATE 3005. PRE-CALCULUS. Five credit hours. Five hours of lecture per week.

A preparatory course for the calculus covering the essentials of relations, functions, complex numbers, linear algebra, trigonometry and analytic geometry.

MATE 3020. INTRODUCTION TO THE FOUNDATIONS OF MATHEMATICS. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3031 or Consent of the Director of the Department.

An introductory course in set theory and logic. Topics include the propositional calculus and set algebra, finite and infinite sets, well-ordered sets, transfinite arithmetic, Peano's axioms, and development of the real number system.

MATE 3021. CALCULUS FOR BIOLOGICAL SCIENCES I. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3172 or its equivalent.

A basic course in differential and integral calculus of one real variable with applications. MATE 3022. CALCULUS FOR BIOLOGICAL SCIENCES II. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3021.

Integration techniques, topics in probability, functions of several variables, introduction to differential equations, and applications.

MATE 3030. INTRODUCTION TO GEOMETRY. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3032.

Brief review of Euclidean geometry, geometric constructions, similarity of figures, geometry of the triangle and of the circle, foundations of axiomatic geometry, and elements of non-Euclidean geometry.

MATE 3031. CALCULUS I. Four credit hours. Four hours of lecture per week. Prerequisite: MATE 3005 or MATE 3172.

Elementary differential and integral calculus of one real variable with applications.

MATE 3032. CALCULUS II. Four credit hours. Four hours of lecture per week. Prerequisite: MATE 3031.

Integration techniques, infinite series, vectors, polar coordinates, vector functions, and quadric surfaces; applications.

MATE 3040. THEORY OF NUMBERS. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3032.

Divisibility, number systems, Euclid's algorithm, factorization, the distribution of primes, perfect numbers and related topics, Euler's function, indeterminate problems, diophantine problems and congruences.

MATE 3048. MATHEMATICAL ANALYSIS. Four credit hours. Four hours of lecture per week. Prerequisite: MATE 3032. Corequisite: MATE 3010 or COMP 3010 or INGE 3016.

Theory and application of functions of several variables, vector calculus, first order differential equations, linear differential equations, the Laplace transform and numerical methods for solving or approximating solutions of differential equations.

MATE 3049. MATHEMATICAL ANALYSIS FOR MANAGEMENT SCIENCES. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3000 or MATE 3172.

Exponential functions and logarithms, the concepts of limit and continuity, differential and integral calculus of one variable, and functions of two variables with applications.

MATE 3063. CALCULUS III. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3032.

Differential and integral calculus of several variables, and an introduction to differential equations with applications.

MATE 3171. PRECALCULUS I. Three credit hours. Three hours of lecture per week. Properties and operations of real numbers; equations and inequalities; Cartesian coordinates and graphs; algebraic, exponential, and logarithmic functions and their graphs; trigonometry of right triangles.

MATE 3172. PRECALCULUS II. Three credit hours. Three hours of lecture per week. Pre-requisite: MATE 3171.

Analytic trigonometry; complex numbers; the fundamental theorem of algebra; conic sections; systems of equations; matrixes operations; sequences; and mathematical induction.

MATE 4000. ELEMENTS OF TOPOLOGY. Three credit hours. Three hours of lecture per week. Corequisite: MATE 4008

Introduction to topology including topological spaces, continuous functions and homeomorphisms, metric spaces, compact spaces, connected spaces, separation axioms, and elements of homotopy.

MATE 4003-4004. MATHEMATICS PRACTICE FOR COOP STUDENTS I-II. Three credit hours per semester. Prerequisite: Consent of the Director of the Department.

Practical experience in mathematics in cooperation with private industry or government, to be jointly supervised by the academic department, the COOP Program Coordinator, and an official from the COOP organization. A report will be required of the student and the official at the end of the semester.

MATE 4007. HIGHER GEOMETRY. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3063.

Coordinate systems in Euclidean 3-space, basic configurations, vectors and geometry of n-space, transformations, introduction to projective geometry, axioms of non-Euclidean geometries.

MATE 4008. INTRODUCTION TO ALGEBRAIC STRUCTURES. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3020. Introduction to algebraic systems; sets, semigroups, groups, rings, fields.

MATE 4009. ORDINARY DIFFERENTIAL EQUATIONS. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3063. Ordinary differential equations with applications: basic existence theorem, linear systems, the Laplace transform, series solutions, introduction to Fourier series and orthogonal functions.

MATE 4010. INTRODUCTION TO COMPLEX VARIABLES WITH APPLICATIONS. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3063.

This course is designed for students who desire a working knowledge of complex variables. Topics to be covered include analytic functions, singularities, residues, complex integration, power series, conformal mapping.

MATE 4020. PARTIAL DIFFERENTIAL EQUATIONS AND FOURIER SERIES. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 4009.

Separation of variables in the solution of partial differential equations, orthogonal expansions, Fourier series in certain function spaces, and an introduction to boundary value problems.

MATE 4021. FUNDAMENTALS OF MATHEMATICAL LOGIC. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3020 or Consent of the Director of the Department.

An introductory course to the fundamental problems of logic, such as variables, the sentencial calculus, the theory of identity, the theory of classes, the theory of relations, and the deductive method.

MATE 4023. MATHEMATICS EDUCATION I. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 4008.

Strategies for teaching mathematics at the elementary and secondary levels; analysis of innovative programs of instruction in mathematics; the use of computers in the teaching of mathematics.

MATE 4031. INTRODUCTION TO LINEAR ALGEBRA. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3032.

Euclidean vector spaces, matrices and linear equations, spectral decomposition of normal operators.

MATE 4050. UNDERGRADUATE SEMINAR. One credit hour. One hour of lecture per week. Prerequisite: Consent of the Department Director.

Introduction to the methods of mathematical research; application of abstract methods to concrete situations. Recommended for all students who intend to pursue graduate studies in Mathematics.

MATE 4051. ADVANCED CALCULUS I. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3063.

A rigorous treatment of the basic ideas and techniques of mathematical analysis, including such topics as point set algebra, the real number system, functions, sequences, limits, continuity, theorems and continuous functions, uniform continuity, differentiation, Riemann integration, the Riemann-Stieltjes integral, power series, uniform convergency.

MATE 4052. ADVANCED CALCULUS II. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 4051.

Continuation of a rigorous treatment of the basic ideas and techniques of mathematical analysis, including such topics as functions of several variables, implicit functions, Jacobians and transformations of multiple integrals, line and surface integrals, improper integrals, linear function spaces, Fourier series and orthogonal functions.

MATE 4061. NUMERICAL ANALYSIS I. Three credit hours. Three hours of lecture per week. Prerequisites: MATE 3063 and (COMP 3010 or INGE 3016).

Roots of equations, interpolation and approximation procedures, numerical integration, numerical solution of initial value problems for ordinary differential equations of first and second order, direct and iterative methods for solving systems of linear equations.

MATE 4062. NUMERICAL ANALYSIS II. Three credit hours. Three hours of lecture per week. Prerequisites: MATE 4031 and MATE 4061.

The numerical solution of Fredholm integral equations: extension of the difference calculus to functions of several variables; brief study of analytical methods for the solution of the partial differential equations of mathematical physics; the numerical solution of boundary value problems; introduction to the numerical solution of eigen value problems.

MATE 4071. INTRODUCTION TO MATHEMATICS OF MODERN SCIENCE I. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 4009.

Brief explanation of certain mathematical topics essential for science and engineering: infinite series, elliptic integrals, Fourier series, solution of equations, partial differentiation, multiple and line integrals.

MATE 4072. INTRODUCTION TO MATHEMATICS OF MODERN SCIENCE II. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 4009. Laplace transforms; Gamma, Beta and Bessel functions; partial differential equations and boundary value problems; vector analysis; probability, empirical formulas, and curve fitting.

MATE 4120. HISTORY OF MATHEMATICS. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3032.

A survey of the historical development of the elementary branches of Mathematics.

MATE 4997. SPECIAL TOPICS IN MATHEMATICS. One to three credit hours. One to three hours of lecture per week. Prerequiste: Consent of the Director of the Department.

Introduction to topics of Mathematics which are not normally covered in regular courses in the curriculum, and which would serve to stimulate further advanced studies in Mathematics.

MATE 5016. GAME THEORY. Three credit hours. Three hours of lecture per week.

Mathematical theory and solution of different classes of games, such as two-person, rectangular or matrix, and multipersonal games.

MATE 5047. INTERMEDIATE DIFFERENTIAL EQUATIONS. Three credit hours. Three hours of lecture per week. Prerequisites: MATE 4009 and MATE 4031 or its equivalent.

Existence, continuity and differentiability of solutions; stability and Lyapunov's theorem.

MATE 5049. CALCULUS OF VARIATIONS. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 4009.

Origin and historical development of the calculus of variations; first variation of a functional; canonical forms of Euler's equations; second variation: sufficient conditions for weak and strong extremals; applications to problems in geometry, mechanisms and physics.

MATE 5055. VECTOR ANALYSIS. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3063.

Introduction to vector analysis as a tool for mathematicians. The algebra and calculus of vectors, including gradient, divergence and curl, Stokes' and Green's theorems, curvilinear coordinates, and simple n- dimensional space. Applications in physics and geometry.

MATE 5056. TENSOR ANALYSIS. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3063.

Cartesian tensors, Cartesian tensor fields, gradient vector, Laplacian, covariant and contravariant tensor fields, the differencial line-element and the fundamental tensors, covariant differentiation and the Riemann-Christoffel tensor.

MATE 5150. LINEAR ALGEBRA. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 4008.

COMP 3010. INTRODUCTION TO COMPUTER PROGRAMMING I. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3171 or MATE 3005 or consent of the Director of the Department. Introduction to the components of the computer. Programming in a block-structured high-level language to solve numerical and non-numerical problems; design, coding, verification and documentation of programs emphasizing programming style.

COMP 3029. PROGRAMMING LANGUAGES. Three credit hours. Three hours of lecture per week. Prerequisite: COMP 3110 or INGE 3016.

Basic aspects of programming languages including data, operations, sequence control, data control, storage management, operational environments, syntax, and semantics.

COMP 3057. COMPUTER FUNDAMENTALS. Three credit hours. Two hours of lecture and one two-hour laboratory per week.

Historical development of computers; functions of the main hardware components and systems software; elementary concepts of programming. The laboratory will provide practical experience with some applications of the computer.

COMP 3075. INTRODUCTION TO DATA STRUCTURES. Three credit hours. Three hours of lecture per week. Prerequisite: COMP 3110 or its equivalent.

Basic concepts of data. Linear and orthogonal lists. Representation of trees and graphs. Recovery and allocation of memory for storage. Symbol tables. Searching and sorting techniques. Data structures in programming languages. Efficiency of sorting algorithms.

COMP 3110. INTRODUCTION TO COMPUTERS II. Three credit hours. Three hours of lecture per week. Prerequisite: COMP 3010 or its equivalent.

Design, verification and testing of large programs. Programming techniques include recursion, modularity, use of pointers, and backtracking.

COMP 4006. SYSTEMS ORGANIZATION AND PROGRAMMING. Three credit hours. Three lectures per week. Prerequisite: COMP 4016. Analysis and design of computer systems, including assembly input-output, compiling, multi- programming and multi-processor systems.

COMP 4016. ASSEMBLY LANGUAGE PROGRAMMING. Three credit hours. Three hours of lecture per week. Prerequisite: COMP 3010 or its equivalent.

Machine language programming; assembly language programming and assembly systems; subroutines; macros.

COMP 4025. COMPUTING MODELS. Three credit hours. Three hours of lecture per week. Prerequisite: ADMI 4025 or INGE 3025 or COMP 3010.

Various models for the modern use of computers, including operations research, and applications of probability and statistics.

COMP 4998. TOPICS IN COMPUTER SCIENCE. One to three credit hours. One to three hours of lecture per week. Prerequisite: consent of the Director of the Department.

The course will cover one or more topics chosen from the following general areas: hardware, computer systems organization, software, data, theory of computation, computer mathematics, information systems, computing methodologies.

COMP 5045. AUTOMATA AND FORMAL LANGUAGES. Three credit hours. Three hours of lecture per week. Prerequisite: consent of the Director of the Department.

Finite automata and regular languages; pushdown automata and context-free languages; Turing machines and recursively enumerable sets; linearly bounded automata and context-sensitive languages; computability and the halting problem; undecidable problems.

COMP 5055. PARALLEL COMPUTATION. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 4061 and consent of the Director of the Department.

Introduction to the use of supercomputers: parallel architecture, design of algorithms for scientific computation and their implementation with parallel multiprocessors, and performance analysis.

ESMA 3015. ELEMENTARY STATISTICS. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3171.

Nature and meaning of statistics; elements of probability; normal and binomial distributions; organization of data; measures of location and variability; elements of statistical inference; simple regression and correlation. Statistical analysis through computers.

ESMA 3101. APPLIED STATISTICS I. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3171.

Basic concepts of methods of applied statistics. Descriptive statistics: probability; random variables; probability distribution. Statistical analysis through computers.

ESMA 3102. APPLIED STATISTICS II. Three credit hours. Three hours of lecture per week. Prerequisite: ESMA 3101 or ESMA 3015 or its equivalent.

Sampling, elements of estimation and tests of hypotheses, regression and correlation analysis, chi-square and contingency tables.

ESMA 4001. MATHEMATICAL STATISTICS I. Three credit hours. Three hours of lecture per week. Prerequisite: MATE 3063.

Nature of statistics, probability, discrete and continuous random variables in one or more dimensions, probability distributions, expected value, and variance.

ESMA 4002. MATHEMATICAL STATISTIC II. Three credit hours. Three hours of lecture per week. Prerequisite: ESMA 4001.

Random sampling and sampling distributions, methods of estimation, tests of hypotheses, linear models, design of experiments, analysis of variance, and contingency tables.

ESMA 4038. SAMPLING METHODS. Three credit hours. Three hours of lecture per week. Prerequisite: ESMA 4002 or MATE 3012 or ESTA 3002 or ININ 4012.

Introduction to the theory and application of statistical sampling methods.

ESMA 5015. STOCHASTIC SIMULATION. Three credit hours. Three hours of lecture per week. Prerequisite: ESMA 4001. Basic methods of simulation, modeling of complex systems, simulation languages, generation of random numbers, model validity, analysis of solutions, variance reduction techniques, and the design of experiments.