Department of Mathematics
The department offers a number of mathematics courses which may be used
to satisfy liberal studies and degree requirements. The following year sequences
are available: MATH 107-108, MATH 135-235, MATH 155-220, MATH 156-220, MATH
205-206 and MATH 235-236. Each of these year sequences is constructed to
build increasingly higher levels of mathematical sophistication or present
a balanced and well-rounded selection of mathematical topics. Students should
therefore complete an entire sequence, except when a change of sequences
is necessitated by a change in the student's major program.
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 120. Introduction to Probability. 1 credit.
Counting, rules of probability, equally likely outcomes, conditional probability,
independent events, probability distributions and expected values. Not open
to those who have previously earned credit in MATH 115, 145, 155 or 156.
MATH 135. Elementary Functions. 3 credits.
Algebraic, exponential, logarithmic and trigonometric functions. Designed
for freshmen who wish 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 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 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
*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: MATH 120 and strong preparation
in algebra, MATH 155 or 156. Not open to majors in mathematics or computer
*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: MATH 206 or 236. This course is not
open to students who have previously earned credit in MATH/CS 448.
MATH/CS 252. Discrete Structures. 3 credits.
Introduction to the mathematical structures used in computer science. Topics
include logic and set theory, algebraic structures, automata theory and
computability. Prerequisite or corequisite: CS 238, MATH/CS 248 or equivalent.
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 335. Introduction to Topology. 3 credits.
Metric spaces, limits, continuous maps and homeomorphisms, connectedness,
compact topological spaces and applications. Prerequisite: MATH 237.
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 340. Mathematical Modeling I. 3 credits.
Use of matrices and computers to model problems in the physical, biological,
social and management sciences. Linear and non-linear optimization methods
will be stressed, along with computer visualization. Prerequisite: MATH/CS
MATH 341. Mathematical Modeling II. 3 credits.
Applications of differential equations and 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 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: Junior standing in mathematics
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
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, t he 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 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. Abstract Algebra I. 3 credits.
An introduction to groups, rings and fields. Prerequisite: Junior standing
in mathematics or consent of the instructor.
MATH 431. Abstract Algebra II. 3 credits.
A continuation of MATH 430. Vector spaces and additional topics selected
from groups, rings and fields. Prerequisite: MATH 430.
MATH/CS 448-449. Numerical Mathematics and Computer Applications. 3 credits
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.
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.
Catalog Table of Contents
JMU Home Page
Last reviewed: Sept. 10, 1994
Information Publisher: Academic Services