Mathematics

**MATH/CS 101. Introduction to FORTRAN. 1 credit.**- Introduction to the programming language FORTRAN. Recommended for students who desire a short course in FORTRAN. This course is not open to students who have previously earned credit in CS/MATH 248 or equivalent.
***MATH 103. The Nature of Mathematics. 3 credits.**- Topics such as geometry, computing, algebra, number theory, history of mathematics, logic, probability, statistics, modeling and problem solving intended to give students insight into what mathematics is, what it attempts to accomplish and how mathematicians think.
***MATH 107-108. Fundamentals of Mathematics. 3 credits each semester.**- Sets, logic, numeration systems, number theory, probability and statistics, measurement, geometry, and an introduction to computers. This course will fulfill the requirements for licensure of prospective early childhood and middle school teachers, as well as provide a general introduction to mathematics for students in other majors.
*Prerequisite for MATH 108: MATH 107.* **MATH 135. Elementary Functions. 3 credits.**- Algebraic, exponential, logarithmic and trigonometric functions. Designed for freshmen who want to enroll in MATH 235 in the following semester. Not open to students who have previously earned credit in MATH 125, 145, 155, 156, 205 or 235, except with the consent of the department head.
**MATH 155. Functions and Probability. 3 credits.**- Polynomial, rational, exponential and logarithmic functions and applications, systems of equations and inequalities, sequences, counting, and probability.
*Prerequisite: Demonstration of proficiency in algebra at an intermediate level. A test is required to determine placement in MATH 155 or 156. Not open to students who have previously earned credit in MATH 125, 135, 145, 156, 205, 220 or 235.* **MATH 156. Functions and Probability. 3 credits.**- Covers same topics as MATH 155. MATH 156 will meet five times a week for students requiring more instructional time.
*Prerequisite: Demonstration of proficiency in algebra at an intermediate level. A test is required to determine placement in MATH 155 or 156. Not open to students who have previously earned credit in MATH 125, 135, 145, 155, 205, 220 or 235.* **MATH 167. Topics in Mathematics. 1-3 credits.**- Topics or projects in mathematics which are of interest to the lower-division student. May be repeated for credit when course content changes. Topics or projects selected may dictate
*Prerequisites. Students should consult the instructor prior to enrolling for this course.* ***MATH 205. Introductory Calculus I. 3 credits.**- Topics from differential calculus with applications to the social, behavioral or life sciences, and business or management.
*Prerequisite: Demonstration of strong preparation in algebra. Not open to computer science, mathematics or physics majors, or to students who have already earned credit in MATH 235. Not recommended for chemistry majors.* ***MATH 206. Introductory Calculus II. 3 credits.**- Topics from integral calculus with applications to the social, behavioral or life sciences, and business or management.
*Prerequisite: MATH 205. Not open to computer science, mathematics or physics majors, or to students who have already earned credit in MATH 236. Not recommended for chemistry majors.* ***MATH 220. Elementary Statistics. 3 credits.**- Descriptive statistics, frequency distributions, sampling, estimation and testing of hypotheses, regression, correlation, and an introduction to statistical analysis using computers.
*Prerequisite: Demonstration of strong preparation in algebra. Not open to majors in mathematics or computer science.* ***MATH 235-236. Analytic Geometry and Calculus I-II. 4 credits each semester.**- A course integrating the subject matter of analytic geometry, and differential and integral calculus.
*Prerequisite for MATH 235: MATH 135 or equivalent. Prerequisite for MATH 236: MATH 235 with grade of "C" or better.* **MATH 237. Analytic Geometry and Calculus III. 4 credits.**- A continuation of MATH 235-236 including sequences and infinite series.
*Prerequisite: MATH 236 with grade of "C" or better.* **MATH/CS 248. Computer Methods in Engineering and Science (3, 2). 4 credits.**- Programming in a high-level computer language such as BASIC or FORTRAN. Use of the computer to solve problems in areas basic to numerical work in engineering and science.
*Prerequisite or corequisite: MATH 206 or 236. This course is not open to students who have previously earned credit in MATH/CS 448.* **MATH 285. Data Analysis. 4 credits.**- Topics include experimental and survey design, distributions, variation, chance, sampling variation, computer simulation, bootstrapping, estimation and hypothesis testing using real data generated from classroom experiments and large databases.
*Prerequisite: MATH 206 or MATH 236, or permission of instructor. Not open to students who have already earned credit in MATH 220 or MATH 318.* **MATH 300. Linear Algebra. 3 credits.**- Vector spaces, linear transformations, matrices, determinants, systems of linear equations, and eigenvalues and eigenvectors.
**MATH 310. Elementary Theory of Numbers. 3 credits.**- Properties of integers and prime numbers, divisibility, congruence, residues and selected topics.
**MATH 315. The Real Number System. 3 credits.**- A development of the real number system through a systematic approach to the natural numbers, integers, rationals and irrationals.
**MATH 318. Introduction to Probability and Statistics. 3 credits.**- Descriptive statistics, counting, probability, random variables, sampling distributions, estimation, hypothesis testing, power functions, regression and correlation.
*Prerequisite: MATH 236.* **MATH 321. Analysis of Variance and Experimental Design. 3 credits.**- Introduction to basic concepts in statistics with applications of statistical techniques including estimation, test of hypothesis, analysis of variance and topics in experimental design.
*Prerequisite: MATH 220, 318 or equivalent.* **MATH 322. Applied Linear Regression. 3 credits.**- Introduction to basic concepts and methods in regression analysis and the application of these models to real-life situations.
*Prerequisite: MATH 220, 318 or equivalent.* **MATH 323. Exploratory Data Analysis. 3 credits.**- Introduction to box plots, stem-and-leaf displays, re-expression, median polish, smoothing and robust regression. Applications and interactive computing will be an integral part of the course.
*Prerequisite: MATH 220 or 318.* **MATH 324. Applied Nonparametric Statistics. 3 credits.**- Methods of analyzing data from non-normal populations including binomial tests, contingency tables, use of ranks, Kolmogorov-Smirnov type statistics and selected topics.
*Prerequisite: MATH 220, 318 or equivalent.* **MATH 325. Survey Sampling Methods. 3 credits.**- Theory and practice of sampling including stratified random samples, discussion of simple random samples, cluster sampling, estimating sample size, ratio estimates, subsampling, two-state sampling and analysis of sampling error.
*Prerequisite: MATH 220 or 318.* **MATH 326. Statistical Quality Control. 3 credits.**- Uses and concepts of probability and sampling procedures. Acceptance sampling by attributes and variables, Shewhart concepts of process control, control chart process capability studies, reliability and life testing. Design of sampling plans.
*Prerequisite: MATH 318.* **MATH 336. Elementary Differential Equations. 3 credits.**- Development of techniques for obtaining, analyzing and graphing solutions to differential equations, with emphasis on first and second order equations.
*Prerequisite: MATH 237.* **MATH 337. Applied Calculus. 3 credits.**- Vector analysis, including line and surface integrals, Green's theorem, the divergence theorem and Stokes' theorem. Potential theory.
*Prerequisite: MATH 237.* **MATH 340. Mathematical Modeling I. 3 credits.**- Use of matrices and computers to model problems in the physical, biological, social and management sciences. Linear and nonlinear optimization methods will be stressed, along with computer visualization.
*Prerequisite: MATH/CS 248.* **MATH 341. Mathematical Modeling II. 3 credits.**- Applications of differential equations, of elementary probability and statistics to the development and analysis of continuous and discrete models that arise in the physical, biological, social and management sciences.
*Prerequisite: MATH 340; or MATH/CS 248 and MATH 300 and MATH 336 and either MATH 318 or MATH 285.* **MATH 352-353. Discrete Mathematics. 3 credits each semester.**- Logic, set theory, relations and functions, counting, recurrence relations, Boolean algebras and switching functions, graphs, and trees.
*Prerequisite or corequisite for MATH 352: MATH 237 or consent of instructor. Prerequisite for MATH 353: MATH 352.* **MATH 360. Complex Variables with Applications. 3 credits.**- Introduction to algebraic properties of complex numbers, analytic functions, harmonic functions, mappings of elementary functions, contour integration, series, residues, and poles and conformal mappings. Emphasis on computations and applications to fluid and heat flow.
*Prerequisite: MATH 237.* **MATH 387. Fourier Analysis and Partial Differential Equations. 3 credits.**- Elementary applied partial differential equations, the heat equation, Laplace's equation, the wave equation; Fourier series and boundary value problems. Both theory and problem-solving will be included.
*Prerequisite: MATH 336.* **MATH 410-411. Advanced Calculus. 3 credits each semester.**- Limits, continuity, differentiation, sequences, series, integration and selected topics.
*Prerequisite for MATH 410: MATH 300 and one of 310, 315 or 352 or consent of the instructor. Prerequisite for MATH 411: MATH 410.* **MATH 415. History of Mathematics. 3 credits.**- Topics in the history of mathematics spanning ancient times to the present.
*Prerequisite: Junior standing in mathematics or consent of the instructor.* **MATH 420. Foundations of Euclidean Geometry. 3 credits.**- A study of the structure and content of Euclidean geometry from an advanced standpoint.
*Prerequisite: MATH 310, 315 or 352 or consent of the instructor.* **MATH 421. Applied Multivariate Statistical Analysis. 3 credits.**- Multivariate statistical methods, with applications. Topics include canonical correlation, clustering, discriminant analysis, factor analysis, multivariate analysis of variance, multiple regression, multidimensional scaling and principal component analysis.
*Prerequisite: MATH 321 or MATH 322.* **MATH 423. Stochastic Processes. 3 credits.**- Sequences and classes of random variables. Applications to physical, biological, social and management sciences. Topics include Markov chains, branching processes, the Poisson process, queuing systems and renewal processes.
*Prerequisite: MATH 318 and MATH 300 or equivalent.* **MATH 424. Statistical Decision Theory. 3 credits.**- Development and use of probability and statistics for strategic decision making with applications. Topics include decision flow diagrams, analysis of risk and risk aversion, utility theory, Bayesian statistical methods, the economics of sampling, sensitivity analysis and collective decision making.
*Prerequisite: MATH 318.* **MATH 426. Probability and Mathematical Statistics I. 3 credits.**- Probability spaces, random variables, discrete and continuous probability distributions, mathematical expectation, moment generating functions, moments of linear combinations of random variables and sampling distributions.
*Prerequisite: MATH 318.* **MATH 427. Probability and Mathematical Statistics II. 3 credits.**- Sampling theory and distributions, theory and applications of estimation and hypothesis testing, regression and correlation, and analysis of variance.
*Prerequisite: MATH 426.* **MATH 429. Practicum in Statistics. 1-3 credits.**- Practical statistical experience under the supervision of a statistics faculty member.
*Prerequisite: 6 hours of statistics courses at the 300 or 400 level.* **MATH 430-431. Abstract Algebra. 3 credits each semester.**- An introduction to groups, rings and fields.
*Prerequisite for MATH 430: MATH 300 and one of 310, 315, or 352 or consent of the instructor. Prerequisite for MATH 431: MATH 430.* **MATH 435. Introduction to Topology. 3 credits.**- Metric spaces, limits, continuous maps and homeomorphisms, connectedness, compact topological spaces and applications.
*Prerequisite: MATH 300 and one of 310, 315 or 352 or consent of the instructor. (Formerly MATH 335.)* **MATH/CS 448-449. Numerical Mathematics and Computer Applications. 3 credits each semester.**- Numerical solutions and error analysis of typical problems such as finding zeros of nonlinear functions, solving systems of linear and nonlinear equations, interpolation, approximation, integration, solving ordinary differential equations, optimization, Monte Carlo methods.
*Prerequisite: for MATH/CS 448: MATH 237, MATH 300, and either CS 238 or MATH/CS 248. Prerequisite: for MATH/CS 449: MATH/CS 448 and MATH 336.* **MATH 450. Theory of Ordinary Differential Equations. 3 credits.**- Theory of existence, uniqueness, continuous dependence and stability for differential equations with applications to the sciences.
*Prerequisite: MATH 300, MATH 336 and MATH 410.* **MATH 467. Selected Topics in Mathematics. 1-3 credits each semester.**- Topics in advanced mathematics which are of special interest to the student but not covered in the regularly offered courses. Offered only with approval of the department head; may be repeated for credit when course content changes.
**MATH 475. Fundamental Concepts of Geometry. 3 credits.**- Origin and development of geometry, axiomatic systems, mathematical proof and special topics from incidence geometry.
*Prerequisite: MATH 310, 315 or 352 or consent of the instructor.* **MATH 483. Selected Topics in Applied Mathematics. 3 credits.**- Topics in applied mathematics not covered in the regularly offered courses. Offered only with the approval of the department head; may be repeated for credit when course content changes.
*Prerequisite: Junior standing and consent of the instructor.* **MATH 485. Selected Topics in Statistics. 1-3 credits.**- Topics in statistics which are of interest but not otherwise covered in the regular statistics offerings of the department. Offered only with approval of the department head; may be repeated for credit when course content changes.
*Prerequisite: Junior standing and consent of the instructor.* **MATH 497-498. Independent Study. 1-3 credits each semester.**- Independent study in mathematics under faculty supervision. Offered only with consent of the department head.
**MATH 499. Honors. 6 credits. Year course.**

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Undergraduate Catalog Contents

1996-97 Undergraduate Catalog

Last reviewed: 30 November 1996

Information Publisher: Division of Academic Affairs

James Madison University