|
Mathematics Courses
GEMA 112
BASIC MATHEMATICS - 3 semester hours F, Sp, Su
A course for students who plan to pursue a major in the humanities and social sciences. Problem solving, irrational numbers, real numbers, polynomials, equations, inequalities, ratios, proportions, geometry, graphs of linear and quadratic functions. This course cannot be used as an elective for mathematics majors.
Prerequisite: Two units of high school mathematics and placement criteria
GEMA 113
BASIC MATHEMATICS - 3 semester hours F, Sp, Su
The second part of a basic mathematics sequence. Set, deductive reasoning, computer literacy, probability, statistics, mathematics of finance.
Prerequisite: GEMA 112
MATH 111
INTRODUCTION TO COLLEGE ALGEBRA - 3 semester hours F, Sp, Su
The real number system, factoring, simplifying algebraic expressions, equations and inequalities, problem solving, system of linear equaltions, functions and their graphs
MATH 120
COLLEGE ALGEBRA AND TRIGONOMETRY - 3 semester hours F, Sp, Su
A pre-calculus course in algebra. Graphs, functions and their graphs, equations and inequalities, polynomial and rational functions, systems of equations and inequalities, and matrices.
Prerequisite: Two units of high school mathematics and placement criteria MATH 121
COLLEGE ALGEBRA AND TRIGONOMETRY - 3 semester hours F, Sp, Su
Exponential and logarthmic functions, trigonometric functions, analytic trigonometry, applications of trigonometry, sequences, series, probability.
Prerequisite: MATH 120 MATH 200
CALCULUS I - 3 semester hours F ,Sp, Su
Lines, functions and their graphs, limits, derivatives, continuity, the theory of limits, intermediate value theorem, derivatives of complete functions, power functions and trigonometric functions, implicit differentiation, related rates of change, first and second derivative tests, applications of maxima and minima, mean-value theorem and Newton's Method.
Prerequisite: MATH 121 MATH 201
CALCULUS II - 3 semester hours F ,Sp, Su
Antiderivatives, approximations of area, definite integral, fundamental theorem of calculus, integration by substitution, area between two curves, volumes, arc length, work power and energy, transcendental functions and their inverses, integration by parts, trigonometric substitutions, integration of rational functions, and using the integral tables.
Prerequisite: MATH 200
MATH 212
INTRODUCTION TO CALCULUS - 3 semester hours F, Sp, Su
Calculus for Non-Science and Non-Mathematics majors. Fundamental concepts of limits, continuity, differentiability and integrability of functions and their application to problems in various disciplines. This course cannot be taken as a Mathematics elective by Mathematics majors.
Prerequisite: MATH 120 and MATH 121 MATH 284
DISCRETE MATHEMATICS I - 3 semester hours F
Binary number systems; computer codes; computer arithmetic; logic truth tables; sets and relations; Boolean algebra; logic gates; simplifications of logic circuits, graphs, and directed graphs equivalence relations.
Prerequisite: MATH 121 MATH 285
DISCRETE MATHEMATICS II - 3 semester hours Sp
Duality, mathematical induction and contradiction, recurrence relations, posets and sorting, vectors and matrices, planar and non-planar graphs, networks, error propagation, combinatorics, circuits, lattices, algebraic systems and machines, algorithms for flowcharting and programming.
Prerequisite: MATH 284 MATH 290
FOUNDATIONS OF MATHEMATICS - 3 semester hours Sp
A study of the development of mathematical concepts and of the great mathematicians who introduced these concepts; development of integral and differential calculus, development of concepts in modern algebra and the use of rigorous set theory as the foundation for analysis, algebra and topology.
Prerequisite: MATH 201 or concurrent with MATH 201
MATH 300
CALCULUS III - 3 semester hours F, Sp, Su
Conic sections and polar coordinates, indeterminate forms, improper integrals, Taylor's theorem, L'Hopital's rule, Taylor's polynomials, sequences and series, absolute and conditional convergence, differentiation and integration of power series, vectors in the plane and in space, and cylindrical and spherical coordinates.
Prerequisite: MATH 201 MATH 301
MULTIVARIATE CALCULUS - 3 semester hours F, Sp
Vector functions, vector differentiation, parametric equations, differentiation of functions of two and three variables, multiple integration, the triple integral, introduction to vector analysis, ordinary differential equations and Euler's Method.
Prerequisite: MATH 300
MATH 325
LINEAR ALGEBRA - 3 semester hours F, Sp
Systems of linear equations, matrices, determinants, vector spaces, bases, dimensions, linear independence, eigenvalues and eigenvectors, and linear transformations.
Prerequisite: MATH 200 or MATH 212 MATH 340
MODERN GEOMETRY - 3 semester hours F, Su
Axioms and theorems of Euclidean geometry and deductive logic, polygonal relationships, tesselations, geometry in three dimensions, measurement, motion, magnification and similarity, topology, number patterns and LOGO in geometry.
Prerequisite: MATH 121 MATH 341
MODERN GEOMETRY - 3 semester hours Sp
Euclidean geometry, logic and incidence geometry, Hilbert’s axioms, projective geometry, neutral geometry, parallel postulate - history and independence, Non-Euclidean geometry, geometric transformations, hyperbolic geometry and philosophical implications.
Prerequisite: MATH 340 MATH 350
DIFFERENTIAL EQUATIONS - 3 semester hours Sp
Solutions of ordinary differential equations with applications to the sciences.
Prerequisite: MATH 201 MATH 392
INTRODUCTION TO LINEAR PROGRAMMING - 3 semester hours F
Matrices, vectors and vector spaces, linear programming; simplex method; duality, degeneracy, game theory, applications to transportation, warehouse, nutrition, and investment problems.
Prerequisite: MATH 201 MATH 400
ADVANCED CALCULUS - 3 semester hours F
Sets and functions, series and sequences of real numbers, limits and continuity in metric spaces, vector functions and multiple integrals, proofs.
Prerequisite: MATH 301 MATH 401
ADVANCED CALCULUS - 3 semester hours Sp
Line and surface integrals, Green’s and Stokes’ theorems, convergence of series, uniform convergence, improper integrals, introduction to completeness, compactness and connectedness; special topics and proofs.
Prerequisite: MATH 400 MATH 425
MODERN ALGEBRA - 3 semester hours F
Abstract groups, subgroups, cyclic groups, groups of symmetries, even and odd permutations, the alternating group cosets, normal subgroups, Lagrange's theorem, quotient groups, solvable groups, mappings, group homomorphisms, isomorphisms.
Prerequisite: MATH 201 MATH 426
MODERN ALGEBRA - 3 semester hours Sp
Rings, ring homomorphisms, subrings, ideals, quotient rings, integral domains, polynomial extensions of rings, fields and field extensions.
Prerequisite: MATH 425 MATH 432
THEORY OF FUNCTIONS - 3 semester hours Sp
Topics on the functions of complex variables and infinite series.
Prerequisite: MATH 301 MATH 445
INTRODUCTION TO POINT SET TOPOLOGY - 3 semester hours F, Sp
Metric spaces, separation axioms, connectedness, compactness, homeomorphisms and product spaces.
Prerequisite: MATH 300 or MATH 425 MATH 452
NUMERICAL ANALYSIS - 3 semester hours Sp
A survey of modern numerical methods with emphasis on those best suited for digital computer application. Polynomial interpolation, iterative methods for solving simultaneous linear and non-linear equations, solutions of algebraic equations, solutions to differential equations.
Prerequisite: MATH 201 MATH 495
MATHEMATICS SEMINAR - 3 semester hours F, Sp
Required of all senior mathematics majors. A capstone course designed (1) review, unify, and extend concepts and skills developed in previous mathematics courses; (2) give students additional experience in presenting mathematical concepts in oral and written form and improving problem-solving skills; (3) assess students’comprehensive mathematical knowledge through the administration of a departmental Field Test. Students will be expected to achieve a satisfactory level of performance on the Field Test in order to be eligible for graduation.
Prerequisite: Senior academic standing or by permission of instructor MATH 499
GRE MATHEMATICS REVIEW - 3 semester hours Sp, Su
Whole numbers, fractions, decimals, percents, signed numbers, averages and medians, powers, exponents and roots, algebraic expressions, equations, verbal problems, counting problems, ratio and proportions, sequence and progressions, inequalities, lines, polygons, tri-angles, quadrilaterals, circles, area and perimeter, coordinate geometry, tables, circle, line and bar graphs, cumulative graphs, analytical reasoning tactics, and logical reasoning tactics. A considerable part of the course will be devoted to practice tests similar to quantitative tests of GRE in order to develop the problem-solving and test-taking techniques required.
Mathematics Education Courses
MAED 300
PRACTICUM - 1 - 3 semester hours
This course is designed to provide an introduction to teaching mathematics at the secondary level. Each student will observe and analyze real school situations within the context of trends, issues, theories, and information available in the content and professional literature of mathematics. At the discretion of the classroom teacher the student may also participate in classroom activities. MAED 460
THE TEACHING OF MATH IN ELEMENTARY SCHOOLS- 3 semester hours F
Methods, materials, and experiences will be provided to equip the student to teach mathematics in a variety of settings, such as self-contained, open or departmentalized class environments at the early childhood and elementary levels. The activities of the course will develop techniques and strategies of teaching concepts associated with sets, number, numeration systems, intuitive geometry, arithmetic operation, mensuration, functions and relations, graphs, spatial relations, logic number theory and patterns, probability and statistics. Concepts from the psychology of learning will be explored.
Prerequisite: GEMA 113 or MATH 121 MAED 464
TEACHING MATHEMATICS IN MIDDLE SCHOOLS - 3 semester hours
A study of modern instructional strategies for teaching, planning and directing mathematics in the middle school.
Prerequisite: EDUC 301 MAED 470
THE TEACHING OF THE METRIC SYSTEM - 1-3 semester hours Sp
A study of the history and development of the (SI) metric system, basic metric units, prefixes, symbols, decimal relationships of units, interdisciplinary applications; teaching strategies using aids from teachers, students, and commercial agencies, emphasis on thinking metric.
Prerequisite: One year of college mathematics or consent of instructor MAED 473
THE TEACHING OF MATHEMATICS IN SECONDARY SCHOOLS I 3 sem. hrs F
A study of modern instructional strategies for teaching, planning and directing mathematics learning in secondary schools. Prerequisite: EDUC 301 MAED 474
THE TEACHING OF MATHEMATICS IN SECONDARY SCHOOLS II 3 sem. hrs Sp
Selected topics in mathematics curriculum and instruction with emphasis on current problems and issues in mathematics. Topics also include methods of evaluation, diagnosis, and remediation.
Prerequisite: MAED 473 MAED 478
STUDENT TEACHING - 8 semester hours
This course is designed to provide supervised field experience for pre-service secondary teachers to enable them to become competent at the entry level in the roles, functions, and skills of classroom mathematics teachers.
Statistics Courses
STAT 210
ELEMENTARY STATISTICS - 3 semester hours F, Sp, Su
An introductory statistics course without a calculus prerequisite. Presentation of data, frequency distributions, descriptive statistics, elementary concepts of probability, random variables, binomial and normal distributions, sampling procedures, student's t-test, linear correlation. Interpretation of examples of data which occur in daily life. This course cannot be taken as a mathematics elective by mathematics majors.
Prerequisites: GEMA 112 and GEMA 113 or the equivalent
STAT 310
ELEMENTARY STATISTICS II - 3 semester hours
An applied statistics course designed for students who have some background in college algebra. Sampling of attributes, comparison of several samples, one-way analysis of variance, sign test, median test, Kruskal-Wallis test and test for randomness, simple regression analysis and test of correlation coefficients. Some use of Statistical packages for the Social Sciences.
Prerequisite: STAT 210 or equivalent STAT 330
INTRODUCTION TO PROBABILITY AND STATISTICS - 3 semester hours F, Su
An introductory course in probability and statistics with an elementary calculus prerequisite. Elementary descriptive statistics, basic probability rules, conditional probability, independence, Bayes' theorem, discrete and continuous probability distributions, probability density functions, binomial, Poisson, hypergeometric, negative binomial, geometric and normal distributions.
Prerequisite: MATH 201 STAT 380
PROBABILITY AND STATISTICS I - 3 semester hours Sp
Mathematical derivations, computational formulas, and applications and interpretations associated with the techniques of probability theory and elementary statistical inference will be emphasized. Moment-generating functions, basic sampling distribution theory, t and chi-square distributions, one-sample estimation and tests of hypotheses.
Prerequisites: MATH 201, STAT 330 STAT 382
INTRODUCTION TO SAMPLING METHODS - 3 semester hours Sp
A course that presents the basic ideas of sampling: random, stratified, systematic and cluster sampling, ratio and regression estimates, estimation of sample size, sampling methods in social, economic and biological surveys, sources of error in surveys.
Prerequisite: STAT 380 STAT 385
ANALYSIS OF VARIANCE - 3 semester hours Sp
A survey of the theory, methodology, and practical applications of analysis of variance (ANOVA). Topics will include: one-factor and two-factor ANOVA; multiple comparisons; two-factor and three-factor balanced factorial designs with interactions; random, fixed and mixed-effect models; contrasts and confounding; and the regression approach to ANOVA.
Prerequisite: STAT 310 or STAT 380 STAT 410
ADVANCED STATISTICAL METHODS - 3 semester hours F, Su
A course designed for students who plan to apply statistical methods in the context of research problems in social sciences, natural sciences, agriculture and education. Uses of computers and packaged computer programs are emphasized.
Prerequisite: STAT 310 or STAT 385
STAT 480
PROBABILITY AND STATISTICS II - 3 semester hours F
A course emphasizing the statistical techniques which are useful in the treatment of multiple samples. Topics include the properties of joint discrete and continuous probability distributions, conditional and marginal distributions, covariance, independent random variables, estimation and hypothesis testing of population parameters in the two-sample case, chi-square tests, and simple linear regression and correlation.
Prerequisite: STAT 380 STAT 481
NONPARAMETRIC STATISTICS - 3 semester hours F
A course which examines statistical techniques which are applicable even if the form of the sampled population is unknown. Wilcoxon rank-sum test, Mann-Whitney U-test, sign test, Wilcoxon signed-rank test, tests for randomness, Spearman's correlation, Kolmogorov-Smirnov statistics, Tukey's quick test, Friedman and Cochran's test, computer programs.
Prerequisite: STAT 380 STAT 482
APPLIED MULTIVARIATE STATISTICS - 3 semester hours Sp
A course in multivariate methods using matrix algebra and applied statistics to analyze several correlated measurements made on each experimental unit. Multivariate normal distribution, estimation and hypotheses testing in multiple regression, Hotelling's T, one-way multivariate analysis of variance, introduction to discriminant and factor analysis, principal components and canonical correlations. Multivariate analysis programs from BMD and SPSS will also be discussed.
Prerequisite: STAT 311 or STAT 410 STAT 484
APPLIED PROBABILITY - 3 semester hours Sp
A course designed to apply probability theory to the study of phenomena in engineering, management science, operations research, and the physical and social sciences. Markov's inequality, conditional expectation, Markov chains, Chapman-Kolmogorov equation, interarrival and waiting time distributions.
Prerequisite: STAT 480 STAT 490
PROBABILITY THEORY - 3 semester hours Sp
A rigorous development of the theory of probability, emphasizing the axiomatic development of the subject. Formal probability systems, conditional probability, sequences of events, independence of events, random variables, probability density and distribution functions, joint distributions, independence of random variables, functions and transformations of random variables, fundamental limit theorems.
Prerequisites: At least two 400-level courses or consent of the instructor
Computer Science Courses
CSCI-120
Introduction to Problem Solving Using Computers - 3 Semester hours F, Sp, Su
This is a first exposure to the use of an algorithm to solve a problem. Emphasis is in the techniques: sequence, conditional and iteration, implemented through an procedural language like BASIC, Pascal or C. This course must provide a solid foundation to approach more complicate problems using an advanced language.
CSCI-150
Programming in C++ I - 3 Semester hours F, Sp, Su
A formal approach to basic elements, syntax and semantics, of C++. Basic Input/Output. Statement, expressions, precedence rules. Basic control structures. Functions, void functions. Reference and value parameters.
Prerequisites: high school programming or CSCI-120
CSCI-250
Programming in C++ II - 3 Semester hours F, Sp
A continuation of CSCI-150, this time with more emphasis in data structures. Integers and floating point representations, source of numeric errors. Arrays and structures. Static and Automatic variables.
Prerequisites: CSCI-150
CSCI-260
Object Oriented Programming - 3 Semester hours F, Sp
Pointers and recursive programming. Fundamentals : objects and methods. Object Oriented features of C++ . Classes: data abstraction, hiding and encapsulation. Inheritance and derived classes. Static and dynamic binding. Polymorphism and virtual functions.
Prerequisites: CSCI-250
CSCI-387
Data Structures - 3 Semester hours Sp
This course emphasizes the implementation in a high level language of the most common data structures. Lists : sorted and unsorted. Stacks and Queues. Linked structures. Circular and doubly-linked lists. Use of recursion with data structures. Binary search trees. Advanced sorting and searching.
Prerequisites: CSCI-260, MATH-281
CSCI 303
Computer Organization and Assembly Language Programming - 3 Semester hours F
Machine representation of data and instructions. Machine organization, primary storage, registers, arithmetic logic unit, control unit, operations. Assembly language programming, interface to high level languages. Assemblers and loaders.
Prerequisite: CSCI 250
CSCI 388
Architecture and Operating Systems - 3 Semester hours F
A treatment of computer architecture. Introduction to operating systems. Computer system and operating system architectures, processes, inter-process communication, inter-process synchronization, mutual exclusion, deadlocks, memory hierarchy, virtual memory, CPU scheduling, file systems, I/O device management, security.
Prerequisite: CSCI 303 CSCI-389
Human-Computer Interaction - 3 Semester hours Sp
human information processing, user interface design principles, information presentation, visual, auditory and tactile displays, speech communication, data entry, controls, tools and feedback, human factors in computer programming, workspace design, environmental and legal considerations.
Prerequisites: CSCI-387
CSCI 356
Data Base Systems - 3 Semester hours Sp
Database Design, Entity-Relationship and Relational Model, Relational Algebra, Query Language SQL, Storage and File Structures, Query Processing, System Architectures.
Prerequisite: CSCI 250
CSCI 485
Programming Languages - 3 Semester hours Sp
Concepts for structuring data, computation, and whole programs. Object-oriented languages, functional languages, logic- and rule-based languages. Data types, type checking, exception handling, concurrent processes, synchronization, modularity, encapsulation, interfaces, separate compilation, inheritance, polymorphism, dynamic binding, sub typing, overloading, beta-reduction, unification.
Prerequisite: CSCI 387 CSCI 493
Senior Project - 3 Semester hours F, Sp
The investigation of special problems in computer science on an individual basis. The student must submit a proposal for this investigation. The result of the investigation will be printed in a report.
CSCI 495
Topics in Computer Science - 3 Semester hours F, Sp
Topics vary depending upon needs of students and current interest of the instructor. Students interested in the specific content of this course as offered in a particular term should consult the instructor.
Prerequisites: Consent of instructor.
CSCI 402
Introduction to Artificial Intelligence - 3 Semester hours F
Basic problem-solving strategies, heuristic search, problem reduction and AND/OR graphs, knowledge representation, expert systems, generating explanations, uncertainty reasoning, game playing, planning, machine learning, computer vision, and programming systems such as Lisp or Prolog.
Prerequisite: CSCI 387
CSCI 445
Computer Communication Networks - 3 Semester hours F
ISO model for communications. Protocols for physical, data link and network
communications. Sockets. TCP/ IP. Applications. Protocol correctness and efficiency. Error detection and recovery. Local-area and Wide-area networks.
Prerequisite: CSCI 260 CSCI 460
Computability and Formal Language Theory - 3 Semester hours Sp
Formal models of computation such as finite state automata, pushdown automata and Turing machines. Formal definitions of languages, problems, and language classes including recursive, recursively enumerable, regular, and context free languages. Halting problems, undecidable problems, recursive functions, Chomsky hierarchy, Church's thesis and the limits of computability. Proofs of program properties including correctness.
Prerequisite: MATH 281 CSCI 462
Compiler Construction - 3 Semester hours F
Exploration of the design of programming language translators. Includes parsing, run-time
storage management, error recovery, and code generation and optimization.
Prerequisite: CSCI 485, CSCI 460
CSCI 480
Computer Graphics - 3 Semester hours F, Sp
Techniques of modeling objects for the purpose of computer rendering: boundary
representations, constructive solids geometry, hierarchical scene descriptions.
Mathematical techniques for curve and surface representation. Basic elements of
computer graphics rendering pipeline; architecture of modern graphics display devices.
Geometrical transformations such as rotation, scaling, translation, and their matrix
representations. Homogenous coordinates, projective and perspective transformations.
Algorithms for clipping, hidden surface removal, rasterization, and anti-aliasing.
Scan-line based and ray rendering algorithms. Lighting models for reflection, refraction,
transparency.
Prerequisite: CSCI 260, MATH 301, MATH 325
CSCI-482
Matrix Computations - 3 Semester hours F
This course is fundamental for students who will pursue graduate studies of applications of computers to science and engineering. Vector and Matrix Norms. Numerical Linear Algebra, condition number, singular values. Householder and Givens transformations. Orthogonalization and Least Squares methods. The eigenvalue problem. Basic iterative methods: Jacobi Gauss-Seidel and SOR.
Prerequisites: CSCI-250, MATH-325
CSCI 487
Software Design and Development - 3 Semester hours F, Sp
A formal approach to current techniques in software design and development. Students work in teams in the organization, management, and development of a large software project.
Prerequisite: CSCI 387 CSCI-492
Algorithms and Complexity - 3 Semester hours F, Sp
Recommended for students pursuing a graduate degree in Computer Science. Definitions of algorithm and its complexity. Proof of correctness of an algorithm. Average and worst case complexity. Complexity of search and sorting algorithms. Recurrence relations arising from basic algorithms. Linear and non-linear recurrences. Divide-and-conquer algorithms. Ordinary and Exponential Generating functions. Big-O notation and asymptotic approximations. An in-depth study of one of the following: number-theoretical, permutation, tree or graph algorithm.
Prerequisites: CSCI-387
MATH 280
Discrete Mathematics for Computer Science I - 3 Semester hours F
The purpose of this course is to introduce fundamental techniques in Discrete Mathematics for the application in Computer Science. Set theory, Order relations, Mathematical logic, Relations, Functions, Mathematical induction, Counting principle, Grammars and finite state automata, Boolean algebra.
Prerequisites: MATH 121
MATH 281
Discrete Mathematics for Computer Science II - 3 Semester hours Sp
Recursion and solution of recurrence relations, Generating functions, Introduction to graph theory, Trees, Analysis of algorithms, Fuzzy sets, Introduction to Coding theory
Prerequisites: MATH 280 STAT 340
Probability and Statistics for Computer Scientists - 3 Semester hours F
Introduction to the concepts of probability, random variables, estimation, hypothesis testing, regression, and analysis of variance with emphasis on application.
Prerequisites: MATH 201, MATH 281
MATH 490
Graph Theory - 3 Semester hours F
Introduction to Graphs and Digraphs, Trees, Networks, Matching and factorizations, Planar graphs, Coloring of graphs, Extremal graph theory
Prerequisites: MATH 201, MATH 281 In addition, students can chose any two out of the following Mathematics, Information System & Decision Science, and/ or Computer Engineering courses as elective. MATH 392, MATH 301, MATH 340, MATH 350, MATH 400, MATH 425, MATH 432,
MATH 445, CPEG 303, CPEG 307, CPEG 308, CPEG 410, CPEG 411, CPEG 415,
CISY 344, CISY 350, CISY 358, CISY 359, CISY 480, CISY 466. |
