## Undergraduate Courses (Mathematics 640)

*Note:*Some upper-level courses may be given in alternate years. Check with department advisers.

**50:640:041. Elementary Algebra (NC)**

for students who do not have the usual background in mathematics for college admission.

The system of integers, exponentiation, graphing, solution of equations, and basic notions of geometry.

**50:640:042. Intermediate Algebra (NC)**

Prerequisite:50:640:041 or placement by Basic Skills Test.

Study of algebraic operations on polynomials, integral and rational exponents, linear and quadratic equations, systems of equations, and the function concept.

**50:640:103. Fundamental Mathematics Systems I (R) (3)**

Particularly suitable for students of Elementary education.

Sets, logic, number systems, and algebraic structures.

**50:640:104. Fundamental Mathematics Systems II (R) (3) **

Informal geometry, measurement, coordinate geometry, transformational geometry, introduction to computers.

**50:640:105. Finite Mathematics (R) (3) **

Particularly suitable for business and economics majors.

Introduction to important and fundamental areas of mathematics that do not require calculus. Topics include set theory, functions and relations, and the algebra of vectors and matrices with applications to systems of linear equations, linear programming, and game theory.

**50:640:106. An Introduction to Mathematical Thought (R) (3) **

for the student who has serious interest in learning something about mathematical thought and its applications, but who is not planning to major in mathematics.

An understanding of the topics chosen for illustrating mathematical thinking within the reach of the student with the usual high school background.

**50:640:108. Numbers and Beyond (R)(3)
**This course is designed for students who are considering secondary certification. In addition, it also satisfies the 3-credit mathematics requirement for any other major.

a study of the properties and qualities of number systems and spatial relationships in geometry. Topics needed to explore the developmental beauty of mathematics will be discussed. Some of these are logic and reasoning, set theory and number theory, functions (not limited to linear), sequences, basic concepts from calculus, group and field concepts, and spatial concepts such as rotations, translations, and geometric objects.

**50:640:110. Joy of Math (R)(3)
**The course “The Joy of Math” aims to explain mathematical ideas gently, clearly and with abundance of examples, hands-on activities, images and clips to attract the attention of a big audience. The course satisfies Gen Ed requirement for Logic and Quantitative Reasoning and has an Engaged Civic Learning component.

**50:640:113. College Algebra (R) (3) **

Prerequisite:50:640:042 or appropriate score on the Mathematics Placement Examination. Credit not given for both this course and 50:640:115. a non-required preparatory course for those students who must take 50:640:118.

a study of real numbers with regard to algebraic operations and order properties. Introduction to complex numbers and logarithmic and exponential functions.

**50:640:114. Trigonometry and Analytic Geometry (R) (3) **

Elements of plane trigonometry and trigonometric identities. Plane loci, properties of the conic sections, and transformations of co-ordinates. The line, plane, and quadric surface in three dimensions.

**50:640:115. Precalculus College Mathematics (R) (3) **

Prerequisite:50:640:042 or appropriate score on the Mathematics PlacementExamination. Credit not given for both this course and 50:640:113. a non-required preparatory course for those students who must take 50:640:121-122.

Algebraic expressions, algebraic equations, functions, graphing, and exponential, logarithmic, and trigonometric functions.

**50:640:116. Elements of Calculus (R) (3) **

Prerequisite: 50:640:113 or 115. Students who plan to take more than one term of calculus should follow the sequence 50:640:121-122. Credit will not, in general, be given for more than one of the courses 50:640:116, 121, or 118.

a one-term survey of the elements of calculus, with emphasis on applications. Topics include Elementary functions and their derivatives, rate of change, curve tracing, velocity, minimum and maximum, law of growth and decay, antiderivatives, and definite integral.

**50:640:118. Calculus for Business and Economics (R) (3) **Prerequisite:50:640:113 or appropriate score on the Mathematics Placement Examination. Students who plan to take more than one term of calculus should follow the sequence 50:640:121-122. Credit will not, in general, be given for more than one of the courses 50:640:116, 121, or 118.

a one-term survey of the elements of calculus with emphasis on applications in business, economics, and life sciences. Topics covered are basic algebra, derivatives, maximum/ minimum problems, integration, and partial differentiation.

**50:640:121. Calculus I (R) (4) **

Prerequisite:50:640:115 or accepted score on the Mathematics Placement Examination. Students who plan to take more than one term of calculus should follow the sequence 50:640:121-122. Credit will not, in general, be given for more than one of the courses 50:640:116, 121, or 118.

An introduction to analytic geometry, differentiation of algebraic and transcendental functions, applications of differentiation, and a brief introduction to integration.

**50:640:122. Calculus II (R) (4)**

Prerequisite:50:640:121 or equivalent.

An extensive introduction to integration and the definite integral, transcendental functions, methods of integration, applications, and infinite series.

**50:640:129. Linear Mathematics for Business and Economics (R) (3) **Prerequisite:50:640:113 or accepted score on the Mathematics Placement Examination. a mathematics foundations course for the student majoring in business and economics.

Basic algebra, matrices, and linear programming with applications to problems in business and economics.

**50:640:182. Elements of Probability (R) (3) **

a one-term survey of the elements of the mathematical theory of probability with emphasis on applications. Topics include sets, subsets, Venn diagrams, partitions, independent events, sample spaces and weights, conditional probabilities, the binomial theorem, methods in combinatorial probability, the binomial distribution, and expected value.

**50:640:221. Calculus III (4) **

Prerequisite:50:640:122.

Solid analytic geometry, partial differentiation, multiple integrals, series, and applications.

**50:640:237. Discrete Mathematics (3) **

Prerequisite:50:640:113 or placement.

Sets, relations, and functions. Mathematical induction. Recursion. Propositional logic. Introduction to first order logic. Boolean algebra. Elements of combinatorics. Introduction to graphs and trees.

**50:640:250. Introduction to Linear Algebra (3) **

Prerequisite:50:640:121 or permission of instructor.

Vector spaces, the calculus of matrices, and the theory of determinants.

**50:640:253. Linear Algebra with Applications (3) **

Prerequisite:50:640:121 or permission of instructor.

The topics from 640:250 plus applications using MatLab. Students may not receive credits for this course and 640:250.

**50:640:300. Mathematical Reasoning with Proofs (3)
**Prerequisite:50:640:121 and 122

Course develops two fundamental components of “writing mathematics”:reasoning (thinking about the proof) and writing (formulating and writing the ideas precisely using logical statements). Begins with illustrative examples and general guidelines.

**50:640:311-312. Advanced Calculus I, II (3,3) **

Prerequisite:50:640:221.

a study of convergence, uniform convergence, and continuity, with applications to series expansions in one and several variables; partial differentiation; multiple, line, and surface integrals.

**50:640:314. Elementary Differential Equations (3) **

Prerequisite:50:640:221 or permission of instructor.

Theory of ordinary differential equations. Power series methods and existence and uniqueness theorems. Applications to problems in economics, biology, chemistry, physics, and engineering.

**50:640:331. Probability and Stochastic Processes (3)**

Pre- or co-requisites:50:640:122 and 50:640:300, or permission of instructor. This course provides a mathematically precise introduction to the basic concepts and essential introductory results of probability: a branch of math aimed at the description and study of random phenomena. The basic principles of stochastic modelling are described. Properties and applications of some standard stochastic models are analyzed. The concepts of conditional probabilities and independence are presented. The expectation and variance of random variables and their properties are discussed. Two fundamental limit theorems for long-time averages of independent, identically distributed random variables are stated and proven. The course concludes with an introduction to Markov chains and their long-run behavior.

**50:640:351-352. Introduction to Modern Algebra (3,3) **

Prerequisite:50:640:250 or permission of instructor.

The study of groups, rings, field, and linear spaces.

**50:640:356. Theory of Numbers (3)**

Prerequisite:Permission of instructor.

Properties of the natural numbers, simple continued fractions, congruences, and Elementary arithmetical functions.

**50:640:357. Computational Mathematics (3) **

Prerequisite:50:640:250 or permission of instructor. Alternate substitute for 50:640:356. Recommended also for students majoring in computer science as an elective.

Designed to emphasize the computational aspect of number theory. The most important topics to treat are the prime numbers, pseudo primes, and their applications, especially cryptography; prime factorization of composite numbers via several different methods explored. Computer simulation emphasized.

**50:640:358. Advanced Discrete Mathematics (3) **

Prerequisite:50:640:237.

Graphs and trees, generating functions, recursion theory, and difference equations. Regular and context-free languages. Finite and pushdown automata. Turing machines.

**50:640:363-364. Foundations of Applied Mathematics I, II (3,3) **

Prerequisite:50:640:314.

Covers integral theorems of vector analysis, complex variables, series solutions to differential equations, Laplace and Fourier transforms, and use of mathematical software languages such as Maple and Mathematica.

**50:640:375. Fourier Series (3) **

Prerequisite:50:640:314.

Introduction to the solution of boundary value problems in the partial differential equations of mathematics, physics, and engineering by means of Fourier series, Fourier transforms, and orthogonal functions.

**50:640:396. Honors Program in Mathematics (3)**

**50:640:403. Introductory Theory of Functions of a Complex Variable (3) **Prerequisite:50:640:311 or permission of instructor.

Topological concepts, analytic functions, Elementary conformal mappings, line integrals, Cauchy’s theorem, Cauchy’s integral formula, the calculus of residues. Taylor and Laurent series, normal families, Riemann mapping theorem, and harmonic functions.

**50:640:427. Advanced Differential Equations (3) **

Prerequisites:50:640:250 and 314.

Autonomous and nonautonomous systems of differential equations; phase plane analysis and stability of critical points; the perturbation method applied to nonlinear equations; modeling and analysis of environmental, biological, chemical, and economic systems. An article that is interdisciplinary in nature is discussed in detail.

**50:640:432. Introduction to Differential Geometry (3) **

Prerequisite:Permission of instructor.

Space, curves, curvature, torsions, Frenet formulas, curvilinear coordinates, fundamental forms, mean and Gaussian curvature, and the general theory of surfaces.

**50:640:435. Geometry (3) **

Prerequisites:50:640:121, 122, 221, or permission of instructor.

Euclidean and non-Euclidean geometries, geometric transformations. Complex language in geometry. Moebius transformations. Symme-tries and tessellations. Projective geometry. Regular polytopes.

**50:640:441. Introductory Topology (3) **

Prerequisite:Permission of instructor.

a study of the standard topics of the set theoretic topology.

**50:640:463-464. Partial Differential Equations and Boundary Value Problems (3,3)**

Prerequisites:50:640:363-364.

An advanced course in methods of applied mathematics. Covers differential equations, orthogonal functions, Sturm-Liouville boundary value problems, Green’s functions, variational methods, and other topics.

**50:640:477-478. Mathematical Theory of Probability (3,3)**

Prerequisites:50:640:121 and 50:960:336 or permission of instructor.

Mathematical theory of discrete and continuous probabilities.

**50:640:491,492. Mathematics Seminar I, II (3,3) **

Prerequisite:Permission of instructor.

Members of the seminar present individually developed reports on topics of mathematical interest.

**50:640:493-494. Individual Study in Mathematics (BA, BA)**

**50:640:495-496. Honors Program in Mathematics (3,3)**

**50:640:497. Visualizing Mathematics by Computer (3) **

Prerequisites:50:640:121, 122, 221, or permission of instructor. Recommended also for students majoring in computer science as an elective.

a comprehensive introduction to symbolic computational packages and scientific visualization through examples from calculus and geometry. Covers 2-D, 3-D, and animated computer graphics using Maple, Mathematica, and Geomview. No programming knowledge required.

**50:640:499. Mathematics on the Web (3) **

Prerequisites:50:640:121, 122, 221, 250, or permission of instructor. Recommended also for students majoring in computer science as an elective.

Designed to get acquainted with using the World Wide Web for finding mathematical information and communicating mathematics.

## Courses (Statistics 960)

**50:960:183. Elementary Applied Statistics (R) (3) **

No prerequisite beyond the usual three years of high school mathematics. Credit will not be given for both this course and 50:830:215.

Frequency distribution, graphical representations, measures of central tendency and variability, elements of probability, the normal curve and its applications, sample versus population, estimating and testing hypotheses, regression and correlation analysis, nonparametric tests. Emphasis on applications.

**50:960:283. Introduction to Statistics I (R) (3) **

Prerequisite:50:640: 113 or 115. Intended primarily for business majors and information systems/ computer science majors.

Elementary course in the principles and methods of statistics. Topics include measures of central tendency and dispersion, probability theory, random variables and probability distribution, binomial and normal distributions, central limit theorem, confidence intervals, and testing of hypotheses on mean( s) and proportion( s).

**50:960:284. Introduction to Statistics II (R) (3) **

Prerequisite:50:960:283. Intended primarily for business majors and information systems/ computer science majors.

a second introductory statistics course. Emphasizes the application of statistical techniques to data analysis. Topics include analysis of variance, nonparametric statistics, simple linear regression, correlation, multiple regression, time series, and index numbers.

**50:960:336. Applied Statistics (3) **

Prerequisite:50:640:122. Intended primarily for applied mathematics majors but open to all qualified students. Descriptive statistics, probability, random variables, probability distributions, estimation and tests of hypotheses, regression and correlation analysis. Emphasis on applications of these techniques to problems in the biological, physical, and social sciences.

**50:960:337. Managerial Statistics (Intermediate) (3) **

Prerequisite:50:960:283 or permission of instructor.

An intermediate course oriented to business and managerial decisions and research in social sciences. Statistical decision making, a priori and a posteriori probabilities, quality control sampling, power curve solutions, sequential decisions, and research design. Design of sample surveys and study of replicated sampling plans.

**50:960:340 Special Topics in Statistics (3)**

Prerequisite:50:960:284.

Aimed at students with any major who want to go beyond the first two statistics courses. Instructor will provide proper description.

**50:960:384 Statistical Data Analysis (3)**

Prerequisite:50:960:284.

Aimed at students who want to go beyond the first two statistics courses. Application of statistical techniques to analyze data. Topics include correlation and regression analysis, regression diagnostics, model building, design of experiments, categorical data analysis. Use of computer packages for visual analysis and interpretation of data.

**50:960:390. Introductory Computing for Statistics (1)**

Prerequisite:50:960:283 and Corequisite (or Prerequisite):50:960:284.

Aimed at students who want to learn statistical computing along with or after the second statistics course. Purpose of the course is to introduce statistical computing using packages (like Excel, SAS, etc.). It includes computing basic univariate statistics, generating random numbers, computing point estimates and confidence interval, testing of hypothesis, basic ANOVA and regression.

**50:960:452. Introduction to Biostatistics (3) **

No prerequisite beyond the usual three years of high school mathematics.

Introduction to the principles and methods of statistical inference for advanced undergraduate and graduate students in biological science. Topics include discussion of random variables, probability distributions, population, sample, measures of central tendency and dispersion, point and interval estimation, testing hypothesis, two-sample comparison, analysis of variance, linear regression and correlation model, and nonparametric methods. Emphasizes applications of statistical principles and analyses for biological science.

**50:960:467 Introduction to Applied Multivariate Analysis (3) **

Prerequisite:50:960:284.

Aimed at students with any major who want to go beyond the first two statistics courses. Introduction to applied multivariate analysis through multivariate normal distribution. Topics include comparison of mean vector, multiple linear regression, discriminant analysis, principal components, factor analysis, and other applied multivariate topics. Use of statistical packages to perform all the multivariate computation and its interpretation.

**50:960:476. Introduction to Sampling (3) **

Prerequisite:50:960:283 or 50:960:336 or permission of instructor.

Application of the principles of sampling to economic procurement or assessment of data. Introduction to various sampling procedures. Emphasis on the design and control phases of investigation. Applications of the techniques to large-scale surveys, accounting and auditing, and operations research.

**50:960:481, 482. Mathematical Theory of Statistics (3,3) **

Prerequisite:First course in calculus or permission of instructor.

*First term:*theory of probability, discrete and continuous probability distributions, introduction to statistical inference.

*Second term:*further study of distribution functions, correlation and regression, analysis of variance and design of experiments, nonparametric methods, sequential sampling.

**50:960:483. Statistical Quality Control (3) **

Prerequisite:50:960:283 or permission of instructor.

Basic course in modern statistical quality control. Statistical measures, histogram analysis, construction and analysis of control charts for variables and attributes, use of Dodge-Roming and military standards acceptance sampling plans, statistical aspects of tolerances.

**50:960:484 Statistical Computing by SAS (3)**

Prerequisite:50:960:283 and Corequisite (or Prerequisite):50:960:284.

Aimed at students who want to learn statistical computing along with or after the second statistics course. Topics include introduction to SAS for reading data, creating data sets and handling other data steps. Using SAS to perform basic regression and model building techniques. Carrying out ANOVA procedures for different design of experiments. Exposure to basic analysis of categorical, time series and other types of data.

**50:960:485-486. Number Problems in Mathematical Theory of Statistics (2,2)**

To be used as laboratory in conjunction with 50:960:481-482.

Numerical problems applied to data in student’s field of study where possible. Emphasis on application of mathematical statistical distributions and methods.

**50:960:487-488. Introduction to Operations Resarch (3,3) **

Prerequisites:50:960:283,284 or permission of instructor.

a two-term introduction to techniques of operations research involved in construction and solution of models in inventory, linear programming, nonlinear programming, queuing, sequencing, network, replacement, reliability, Markov chains, and competitive problems.

**50:960:489.** **Statistical Models (3)**

Prerequisite:50:640:331.

Introduction to multiple linear regression and its diagnostics, estimation, and testing in regression. Analysis of variance models (ANOVA), regularized regression:ridge and lasso, and generalized linear models.

**50:960:490. Experimental Design and Analysis (3) **

Prerequisites:50:960:283,284 or permission of instructor.

An advanced course in statistics with applications in all fields of study. Analysis of variance and covariance, experimental framework and layout, simple randomized designs, randomized blocks. Latin squares, Graeco-Latin squares, factorials, balanced and partially balanced designs, gains in precision and estimation.

**50:960:491** **Time Series and Forecasting (3)**

Prerequisite:50:960:489.

Introduction to time series models, stationary processes, measure of dependence, tests of randomness, forecasting, estimation, model selection, ARIMA and ARMA models, and bootstrapping and smoothing.

**50:960:492** **Actuarial Models (3)**

Prerequisite:50:960:489.

Distribution theory and its convolution, application to loss models, failure times and censored data models, survival models:parametric and nonparametric, estimation, and model building.

**50:960:495. Independent Study in Statistics (3) **

Prerequisites:50:960:283,284 and permission of instructor.

Intended for students who want to concentrate on special methods of statistical analysis and their applications to real world problems.

**50:960:496. Independent Study in Operations Resarch (3) **

Prerequisites:50:960:487-488 and permission of instructor.

Intended to meet the needs of students who wish to study special techniques of operations research beyond the level of 50:960:487-488, or their applications to real world problems.