# Course Descriptions - Department of Mathematics

## ELEMENTARY MATHEMATICS

__MATH 0901 Basic Algebra (0)__

Topics include: Operations with Real Numbers, Simplifying Algebraic Expressions, Linear Equations, Graphing Equations of Lines, Applications and Word Problems, Operations with Polynomials, Factoring Polynomials, Solving Quadratic Equations, Operations with Square Roots

*Prerequisites: By Placement Test Results
General Education Support Course*

MATH 1000 Algebra for College Students (3)

MATH 1000 Algebra for College Students (3)

Operations with real numbers, polynomial expressions, exponents, rational and radical expressions. Solutions of linear and nonlinear equations and inequalities. Solutions of linear and nonlinear systems of equations. Introduction to functions and their graphs. MATH 1000 is the one-semester non-extended format of Algebra for College Students. Fulfills the General Education Algebra requirement. Three degree credits.

General Education Foundation Course

Prerequisite: Placement by the Developmental Studies Office.

Prerequisite: Placement by the Developmental Studies Office.

__MATH 1001 Algebra for College Students__

Operations with real numbers, polynomial expressions, exponents, rational and radical expressions. Solutions of linear and nonlinear equations and inequalities. Solutions of linear and nonlinear systems of equations. Introduction to functions and their graphs. MATH 1001 is a component of the one-semester extended format of Algebra for College Students. MATH 1001 and MATH 1002, which must be taken concurrently, fulfill the General Education algebra requirement. Three institutional credits.

General Education Foundation Course

*Prerequisite: Placement by the Developmental Studies Office.*

Corequisite; MATH 1002.

Corequisite; MATH 1002.

__MATH 1010 Foundations of Mathematics (3)__

An introduction to mathematical reasoning including problem-solving strategies sets and set operations, logic, geometry, and statistics. Mathematics majors cannot receive credit for this course.

Approved General Education Distribution Course

*Prerequisite: MATH 1000 or placement by the Developmental Studies Office*

__MATH 1013 Finite Mathematics with Applications (3)__

Sets, counting, probability, matrices, and linear programming. Practical applications of contemporary mathematics and mathematical models. For non-science majors.

*Prerequisite: MATH 1000 or placement by the Developmental Studies Office.*

__Descriptive and inferential statistics: graphic treatment of data, characteristics of distributions, statistical models, correlation, regression, estimation and hypothesis testing. Computer applications.__

MATH 1016 Statistics (3)

MATH 1016 Statistics (3)

Approved General Education Distribution Course

*Prerequisite: MATH 1000 or placement by the Developmental Studies Office.*

__MATH 1017 Statistics Service Learning Module (1)__

Service learning is the process of incorporating student volunteerism within an academic framework while providing services to the community resulting in the development of skills, knowledge and experience.

*Corequisite: Must be taken in conjunction with MATH 1016.*

__MATH 1030 Problem Solving in Mathematics (3)__

Development and application of problem solving strategies to a variety of problems within and outside of mathematics making connections between mathematics and other content areas. Numerous and varied experiences with problem solving as a method of inquiry and applications.

*Prerequisite: Completion of any mathematics course 1000 level or above.*

__MATH 1044 Precalculus for Business (3)__

Equations, inequalities, and their applications. Functions and graphs, lines, parabolas and systems of equations, exponential and logarithmic functions, compound interest, present value, annuities and amortization of loans. Matrix algebra, Gauss-Jordan elimination and applications. Inverse of a matrix, solutions of systems of equations and inequalities. Problem solving methods. Students will be required to acquire a specified graphing calculator. Can not be used as a prerequisite for Math 2411

*Prerequisites: Math 1000 or equivalent*

Approved General Education Distribution Course

Approved General Education Distribution Course

__MATH 1054 Precalculus (3)__

Exponential and logarithmic functions. Trigonometric functions with emphasis on trigonometric identities and trigonometric analysis. Complex numbers, polar coordinates, plane vectors and trigonometric forms of complex numbers. Arithmetic and geometric sequences and series. Problem solving methods. Students will be required to acquire a specified graphing calculator.

Approved General Education Distribution Course

*Prerequisites: MATH 1000, or the equivalent, or a qualifying score on the placement examination.*

## LOGIC AND FOUNDATIONS

__
MATH 2110 Discrete Structures (3)
__Sets, logic, relations, methods of proof, counting techniques, recursively defined relations, Boolean algebra, applications to computing.

*Prerequisite: MATH 1054 or equivalent.*

__MATH 3110 Introduction to Proofs (3)__

This course will introduce the student to the motivation and logic behind mathematical proofs. Proofs will be built around topics from basic combinatorics, elementary number theory, elementary abstract algebra and basic graph theory.

*Prerequisite: MATH 2411 or equivalent.*

MATH 3120 Combinatorics (3)

MATH 3120 Combinatorics (3)

Sets, counting, permutations and combinations, generating functions, recurrence relations, graphs and their coloring, circuits, trees, and searching. Applications to computing and operations research.

*Prerequisite: MATH 2110.*

__A survey of classical and computational logic. The propositional calculus. Introduction to programming in logic. Fundamentals of neural networks.__

MATH 3155 Mathematical Logic (3)

MATH 3155 Mathematical Logic (3)

*Prerequisite: MATH 2110.*

## ALGEBRA

__MATH 2995 Matrix and Linear Algebra (3)__

Systems of linear equations, matrices, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors, applications.

*Prerequisite: MATH 2411*

__MATH 3225 Computational Methods In Matrix and Linear Algebra II (3)__

Continuation of topics discussed in MATH 2995. Additional topics: inner product spaces, canonical forms, derivatives in higher dimension, systems of differential equations, spectral theory, and their applications in science and economics.

*Prerequisites: MATH 2412, MATH 2995.*

__MATH 3247 Abstract Algebra I (3)__

Elementary group theory: subgroups, cyclic and permutation groups, direct products, Lagrange’s Theorem, normal subgroups and quotient groups, homomorphisms and isomorphisms, the Sylow Theorems; use of a computer.

*Prerequisite: MATH 2110 or permission of instructor.*

__MATH 3248 Abstract Algebra II (3)
__Rings, integral domains, fields, ideals and quotient rings, rings of polynomials, homomorphisms, extension field and vector spaces; use of computer.

*Prerequisite: MATH 3247 or permission of instructor.*

## GEOMETRY

__MATH 3342 Euclidean and Non-Euclidean Geometry (3)
__Euclidean geometry, from Euclid’s to Hilbert’s axioms; coordinate geometry; transformations; non-Euclidean geometries; finite geometries.

*Prerequisite: MATH 2110.*

## ANALYSIS

__MATH 2400 Calculus for Business and Economics (3)
__Single variable differential and integral calculus. Algebraic, exponential and logarithmic functions, derivatives, integrals. Applications of calculus to economics and managerial science. May not be substituted for MATH 2411, 2412 sequence.

*Prerequisite: Permission of MIS Program Coordinator and MATH 1054 or the equivalent.*

__MATH 2411 Calculus I (3)__

Functions, limits, and continuity, differentiation of algebraic and trigonometric functions, tangent and normal lines, Newton’s method, optimization and related rate problems. Applications to the physical, biological and managerial sciences. Computer applications.

*Prerequisite: MATH 1054 or a qualifying score on the placement test.*

MATH 2412 Calculus II (3)

MATH 2412 Calculus II (3)

Antiderivatives, definite integrals, integration of algebraic and transcendental functions, numerical integration, elementary differential equations. Area, volume, arc length, surface area. Applications to the physical, biological and managerial sciences. Computer applications.

*Prerequisite: MATH 2411 or permission of the instructor.*

__MATH 3451 Calculus III (3)__

Indeterminate forms, vector algebra and calculus in the plane and 3-space, analytic space geometry, multivariable functions, partial derivatives, gradients. Optimization problems. Applications to the physical sciences. Computer applications.

*Prerequisite: MATH 2412 or permission of the instructor.*

__MATH 3452 Calculus IV (3)__

Infinite sequences and series, convergence tests, series of functions, power series, Taylor series and polynomials, numerical approximations. Multiple integrals, integral transformations. Vector integral calculus, line and surface integrals, theorems of Green, Gauss and Stokes. Applications to the physical sciences. Computer applications.

*Prerequisite: MATH 3451 or permission of the instructor.*

__MATH 3455 Differential Equations (3)__

First order equations, linear equations, numerical methods, Laplace Transforms and systems of equations. Emphasis on applications of differential equations to the solution of scientific problems from such areas as physical science, biology, economics, psychology and social science.

*Prerequisite: MATH 2412 or permission of the instructor.*

__MATH 3940 Numerical Analysis (3)__

Solution of equations and systems of equations, analysis of errors in numerical methods, numerical differentiation and integration, approximation, interpolation, solutions of differential equations. Use of computers.

*Prerequisites: MATH 2412 and CPS 2231 or the equivalent.*

__Study of power series solution to differential equations, Bessel functions, Legendre polynomials, partial differential equations, boundary value problems, Fourier series and integrals, the Sturm-Liouville problem and the Gamma function. Computer applications and simulations.__

MATH 4404 Introduction to Applied Mathematics (3)

MATH 4404 Introduction to Applied Mathematics (3)

*Prerequisite: MATH 3452 or MATH 3455 or permission of instructor.*

__MATH 4451 Advanced Calculus I (3)__

Fundamental concepts of calculus. Functions of one variable, sequences, limits, continuity, differentiation and integration.

*Prerequisite or corequisite: MATH 3452 or permission of instructor.*

__MATH 4452 Advanced Calculus II (3)__

Functions of several variables, partial differentiation, transformations, power series, uniform convergence, line and surface integrals, and vector analysis, including standard theorems and applications.

*Prerequisite: MATH 3452 or permission of the instructor.*

__MATH 4465 Complex Variables (3)__

Complex numbers, analytic functions, elementary functions and transformations, complex integration, power series, residues, poles, conformal mapping, and applications.

*Prerequisite or corequisite: MATH 3452 or permission of the instructor.*

## PROBABILITY AND STATISTICS

__MATH 2026 Statistical Decision Theory (3)
__An introduction to statistical concepts and methods and their effective application to real-world problems. The construction and evaluation of decision rules as a basis for decision-making. Computer facilities utilized.

*Prerequisite: MATH 1054.*

__MATH 2036 Non-Parametric Statistics (3)__

An introduction to useful and simple techniques that have wide applicability, including models and statistical procedures; one, two, and K-sample techniques; goodness of fit tests; correlation and regression. Use of computers.

*Prerequisite: One course in statistics.*

__MATH 2526 Applied Statistics (3)__

Statistical techniques of univariate and bivariate data analysis, probability, discrete and continuous random variables, sampling distributions, estimation, hypothesis tests about a single population parameter and simple correlation and regression. Computer assisted statistical analysis and interpretation of the results.

*Prerequisite: MATH 2411 or permission of the instructor.*

MATH 3500 Statistical Software (1)

MATH 3500 Statistical Software (1)

Introduction to the statistical software SAS or SPSS. Students learn the fundamentals of the SAS or SPSS software and its applications to descriptive and inferential statistical analysis of various real world problems from social and industrial fields.

*Prerequisite: MATH 2526*

__MATH 3511 Games and Gambling (3)__

Games of chance, combinatorics, probability and game theory. Standard and unusual games are played and then subjected to rational analysis in the face of uncertainty. Historical anecdotes. Role of games in artificial intelligence. Utilization of campus computing equipment.

*Prerequisite: A course in statistics or computer science.*

__MATH 3526 Applied Statistics II (3)__

Statistical inference about a single population and about two populations, analysis of variance, chi-square tests, non-parametric statistical techniques, simple linear regression and correlation, categorical data analysis, introduction to multiple regression.

*Prerequisite: MATH 2526 or equivalent*

__MATH 3544 Probability and Mathematical Statistics (3)__

Descriptive statistics and frequency distribution of a random variable. Sampling distribution of a statistic. Probability: sample spaces, random variables, probability laws and probability ditributions of discrete and continuous random variables. Binomial, Poisson, Geometric, Negative Binomial, Hypergeometric, Uniform, Normal, Gamma, Chi-Square and Beta distributions. Mathematical expectation of distributions such as Binomial, Poisson, Gamma, Normal, Chi-Square, Student’s t and F distributions.

*Prerequisite: MATH 2412 or permission of instructor.*

__MATH 3560 Regression Analysis (3)__

Introduction to linear regression models with one or more independent variables. Analysis of variance (ANOVA). Estimation of parameters, model building, analysis and diagnostics. Introduction to non-linear estimation. Use of computer software.

*Prerequisites: MATH 3526 and MATH 2995*

__MATH 3570 Multivariate Analysis (3)__

Review of multiple regression and hypothesis testing in multiple regression. Multiple, partial and multiple-partial correlation. Polynomial regression, one-way analysis of variance, two-way analysis of variance, analysis of covariance. Logistic regression, discriminant analysis, path analysis and factor analysis.

*Prerequisites: MATH 2995 and a course in statistics.*

__MATH 3580 Experimental Design (3)__

Introduction to the principles of experimental design and analysis of data from designed experiments with emphasis on applications. Topics include single factor experiments, repeated measures, randomized block designs, Latin squares, factorial experiments, nested models and split-plot designs. Statistical software packages will be utilized.

*Prerequisite: MATH 3526*

__Planning and designing sample surveys, the population and the sample, random sampling, systematic sampling, stratified random sampling, ratio estimation, cluster sampling with equal and unequal probability, probability proportional to size sampling, sample design and estimation methodology and sample survey methodology.__

MATH 3590 Sampling Techniques (3)

MATH 3590 Sampling Techniques (3)

*Prerequisite: MATH 2526 or equivalent.*

__MATH 4500 Non-Parametric Statistical Methods (3)__

The dichotomous data problem, the one-sample and two-sample location problems, distribution-free rank test for dispersion and the difference in two populations; the one-way layout distribution-free tests, multiple comparisons and the two-way layout distribution-free tests. Computers will be utilized.

*Prerequisite: MATH 3526 or equivalent.*

__MATH 4545 Applications of Mathematical Statistics (3)__

Applications of mathematical statistics to decision making in economics, quality control, psychology, and the natural sciences. Estimation, linear statistical models, designing experiments in the analysis of enumerative data, regression and analysis of variance, goodness-of-fit tests, randomized block design and non-parametric statistics.

*Prerequisite: MATH 3544.*

__MATH 4550 Statistical Quality Control (3)__

Shewhart’s control charts, moving average charts, statistical process-control techniques, capability, stability and quality; charts for binomial and Poisson data counts, three-way control charts, acceptance sampling, estimating fraction nonconforming.. Computers will be utilized.

*Prerequisite: MATH 3526 or equivalent.*

__MATH 4560__

__Actuarial Mathematics (3)__

Mathematics of interest, present value of basic annuities, loan repayment, the sinking-fund method, Makeham’s formula, bond prices and amortization, spot rates, stocks and options, futures and forward contracts, foreign currency exchange rates. Practical applications in the mathematics of financial analysis.

*Prerequisite: MATH 3544*

## NUMBER THEORY

__
MATH 3624 Number Theory (3)
__Properties of the integers: divisibility, primes, theory of congruence, Diophantine equations, number theoretic functions with a historical study of important problems. Use of computers.

*Prerequisite or corequisite: MATH 3451.*

## APPLICATIONS

__MATH 2800 Mathematical Software (1)__

Introduction to mathematical software. Students apply mathematical software and computer algebra systems to perform numerical and symbolic calculations and to solve computational problems in calculus, matrix theory, differential equations and numerical analysis.

*Prerequisite: MATH 2411*

__MATH 3815 Cryptology (3)
__History of cryptography, monoalphabetic substitution, multiliteral substitution systems, periodic polyalphabetic ciphers, digraphic substitution, transposition systems, aperiodic systems including simpler varieties of machine ciphers, code systems. Use of computers.

__MATH 3891 History of Mathematics (3)__

A study of the evolution of the major concepts and processes associated with elementary mathematics from geometry through the invention of calculus. Emphasis is on the mathematical content contributed by many civilizations.

*Prerequisite: MATH 2412*

Writing Emphasis Course

__MATH 4801 Independent Study in Mathematics (1)__

An advanced topic in undergraduate mathematics that is not covered in any of the courses offered by the mathematics department, and independently studied by the student under the supervision of faculty.

*Prerequisite: Permission of instructor*

__MATH 4802 Independent Study in Mathematics (2)__

An advanced topic in undergraduate mathematics that is not covered in any of the courses offered by the mathematics department, and independently studied by the student under the supervision of faculty.

*Prerequisite: Permission of instructor*

__MATH 4805 Mathematical Modeling with Applications (3)__

Techniques of mathematical model construction. An approach for translating real-world phenomena and problems into the language, of mathematics. Use of computers.

*Prerequisite: MATH 3544 or permission of instructor.*

__MATH 4809 Special Topics in Mathematics (3)__

Research study of areas in mathematics influenced by contemporary developments as well as interests and needs of students majoring in mathematics. The subject of a semester’s work varies, and course may be taken for credit more than once.

*Prerequisite: Permission of the instructor.*

__MATH 4815 Advanced Cryptanalysis (3)__

Overview of electronic cryptosystems, bitstream generation, irreducible and primitive polynomials, Galois fields, sequence complexity, the Berlekamp Massey Theorem, correlation immunity, the Likelihood Ratio Test, exponentiation ciphers, discrete logarithms, public key systems. Use of computers.

*Prerequisite: MATH 3815 or permission of instructor.*

__MATH 4890 Senior Seminar in Mathematics (3)__

A capstone seminar to integrate ideas, concepts, and methods from various areas of mathematics. Students will be required to choose a topic in mathematics or a related field for a research paper and presentation to the class. Students will be expected to communicate mathematical ideas by presenting solutions to problems, leading discussions and actively participating in class.

*Prerequisite: Senior status and completion of core requirements.*

Required for Mathematics Majors, Writing Emphasis Course (GE Capstone Course)

MATH 4892 The History of Modern Mathematics (3)

MATH 4892 The History of Modern Mathematics (3)

Selections from the major developments of modern mathematics in calculus, geometry, algebra, number theory, foundations, topology and probability through the first half of the 20th century. Primary materials written by great mathematicians on significant topics are analyzed.

*Prerequisite: Senior status and completion of mathematics core.*

__MATH 4999 Work-Study Cooperative Education in Mathematics/Statistics (3)__

The cooperative education program allows a student to earn academic credit while gaining valuable job experience by working in industry in an area related to his or her major. All co-op jobs must be approved by a faculty committee after consultation between a faculty coordinator and a job supervisor. Students must complete approximately 120 hours on the job during a regular semester or summer session and fulfill all requirements of the job supervisor and faculty coordinator.

*Prerequisite: Completion of minimum of 15 semester hours in mathematics/computer science including CPS 1031, MATH 3452, MATH 2110, MATH 4545. Minimum grade point average of 3.0 in major and 2.75 overall. Approval of faculty committee.*