Department of Mathematics

University of Mississippi

Undergraduate Courses

The official catalog of mathematics courses can be accessed here.

MATH 115. ELEMENTARY STATISTICS. This course will provide students with a basic understanding of the proper statistical techniques used to estimate population parameters. These techniques include ways of setting up a well-defined study, methods for organizing and displaying data, and how to summarize data by using descriptive statistics. In addition, students will learn the basic concepts of probability and probability distributions as well as how to create confidence intervals and complete hypothesis tests. The non- online sections meet twice weekly, with other work completed in a mathematics lab. Prerequisites: Minimum ACT mathematics score of 19 (SAT 450 or SATR 490) or the successful completion of DS 099, if required. (3)

MATH 120. QUANTITATIVE REASONING. Statistical reasoning, logical statements and arguments, personal business applications, linear programming, estimations, and approximation. Prerequisites: Successful completion of DS 099, if required. (3)

MATH 121. COLLEGE ALGEBRA. In this course, students will learn how to solve types of equations such as linear, quadratic, higher-order, rational, radical, exponential, and logarithmic equations. Students will also solve linear, polynomial, and rational inequalities. Other topics include the algebra of functions (including polynomial, rational, exponential, and logarithmic functions), the graphs of some of these functions, and solving systems of equations in two variables. The non-online sections meet twice weekly, with other work to be completed in the Jackson Avenue Center Mathematics Lab. Prerequisites: This course cannot be booked if completed Math 261 or Math 262 with a grade of C or better. Minimum ACT mathematics score of 19 (SAT 450 or SATR 490) or the successful completion of DS 099, if required. (3)

MATH 123. TRIGONOMETRY. In this course, students will learn to work with angles in degree and radian measure, write the ratio definitions of the six trigonometric functions, evaluate trigonometric functions of special angles, sketch graphs of trigonometric functions, verify trigonometric identities, solve trigonometric equations, solve triangles by a variety of methods, and solve application problems using trigonometric functions and identities. Prerequisites: Minimum ACT mathematics score of 19 (SAT 450 or SATR 490) or the successful completion of DS 099, if required. (3)

MATH 125. BASIC MATHEMATICS FOR SCIENCE AND ENGINEERING. This course is designed especially for students requiring a review of both algebra and trigonometry before beginning the calculus sequence. Students will solve a variety of algebraic equations and inequalities; examine and graph algebraic, exponential, logarithmic, and trigonometric functions; evaluate trigonometric functions and their inverses; verify trigonometric identities; and solve exponential, logarithmic, and trigonometric equations. Prerequisites: This course cannot be booked if completed Math 261 or Math 262 with a grade of C or better. Minimum ACT mathematics score of 19 (SAT 450 or SATR 490) or the successful completion of DS 099, if required. (3)

MATH 245. MATHEMATICS FOR ELEMENTARY TEACHERS I. Students are introduced to sets, the real number system and its subsystems. Prerequisites: Successful completion of DS 099, if required. Elementary or Special Education Majors, or Math Education Minors. (3)

MATH 246. MATHEMATICS FOR ELEMENTARY TEACHERS II. This course covers informal geometry; measurement and the metric system; probability and statistics. Prerequisites: Math 245 with a minimum grade of C. (3)

MATH 261. UNIFIED CALCULUS AND ANALYTIC GEOMETRY I. This course covers differential and integral calculus; analytic geometry introduced, covered in integrated plan where appropriate. Four-term sequence for engineering and science majors. After completing Math 261 with a C or higher, students may not receive credit for Math 121, Math 125, or Math 267. Prerequisites: Minimum ACT Mathematics score of 24 (SAT 560 or SATR 580); or B minimum in Math 121 and 123; or B minimum in Math 125.(3)

MATH 262. UNIFIED CALCULUS AND ANALYTIC GEOMETRY II. Differential and integral calculus; analytic geometry introduced, covered in integrated plan where appropriate. Four-term sequence for engineering and science majors. After completing Math 262 with a C or higher, students may not receive credit for Math 121, 125, or 268. Prerequisites: Math 271 or Math 261 with a minimum grade of C. (3)

MATH 263. UNIFIED CALCULUS AND ANALYTIC GEOMETRY III. Differential and integral calculus; analytic geometry introduced, covered in integrated plan where appropriate. Four-term sequence for engineering and science majors. Prerequisites: Math 262 with a minimum grade of C. (3)

MATH 264. UNIFIED CALCULUS AND ANALYTIC GEOMETRY IV. Differential and integral calculus; analytic geometry introduced, covered in integrated plan where appropriate. Four-term sequence for engineering and science majors. Prerequisites: Math 263 with a minimum grade of C. (3)

MATH 267. CALCULUS FOR BUSINESS, ECONOMICS, AND ACCOUNTANCY I. This course covers differential and integral calculus with an emphasis on business applications. The course meets twice weekly, with other work completed online. Prerequisites: This course cannot be booked if completed Math 261 with a grade of C or better. Minimum ACT mathematics score of 19 (SAT 450 or SATR 490) or the successful completion of DS 099, if required. (3)

MATH 268. CALCULUS FOR BUSINESS, ECONOMICS, AND ACCOUNTANCY II. Differential and integral calculus with an emphasis on business applications. Prerequisites: Only for accountancy majors; Math 261 or Math 267 or Math 271 with a minimum grade of C. (3)

MATH 269. INTRODUCTION TO LINEAR PROGRAMMING. Selected topics in quantitative methods with an emphasis on business applications. Topics include Gauss-Jordan elimination, simplex solutions for linear programming models and transportation and assignment algorithms. Prerequisites: Math 261 or Math 267 or Math 271 with a minimum grade of C. (3)

MATH 271. CALCULUS OF DECISION MAKING I. Differential calculus with an emphasis on its uses in decision making. Topics will include techniques to analyze functions of one variable and maximize functions of several variables subject to constraints, using the Lagrange method. Other topics may include elementary encryption techniques. Students may not receive credit for both Math 267 and Math 271. (3)

MATH 272. CALCULUS OF DECISION MAKING II. Integral calculus with an emphasis on its uses in decision making. Other topics may include markets and auctions. Nash equilibria and game theory and discrete forms on optimization. Students may not receive credit for both Math 268 and Math 272. Prerequisites: Math 271 with a minimum grade of C. (3)

MATH 281. COMPUTER LABORATORY FOR CALCULUS I. Investigation of the techniques in Calculus I (Math 261) through the use of a computer. (1)

MATH 282. COMPUTER LABORATORY FOR CALCULUS II. Investigation of the techniques in Calculus II (Math 262) through the use of a computer. (1)

MATH 283. COMPUTER LABORATORY FOR CALCULUS III. Investigation of the techniques in Calculus III (Math 263) through the use of a computer. (1)

MATH 284. COMPUTER LABORATORY FOR CALCULUS IV. Investigation of the techniques in Calculus IV (Math 264) through the use of a computer. (1)

MATH 301. DISCRETE MATHEMATICS. This course covers elementary counting principles, mathematical induction and other proof methods, relations and functions, and graphs. Prerequisites: Math 301 or Math 305 with a minimum grade of C. (3)

MATH 302. APPLIED MODERN ALGEBRA. This course covers elementary group theory with applications, including modular arithmetic, public key encryption, Polya enumeration, and an introduction to coding theory. Prerequisites: Math 301 or Math 305 with a minimum grade of C. (3)

MATH 305. FOUNDATIONS OF MATHEMATICS. Set theory with emphasis on functions, techniques used in mathematical problems, cardinal numbers. Prerequisites: Math 262 with a minimum grade of C. (3)

MATH 319. INTRODUCTION TO LINEAR ALGEBRA. Vectors, matrices, determinants, linear transformations, introduction to vector spaces. Prerequisites: Math 262 with a minimum grade of C. (3)

MATH 353. ELEMENTARY DIFFERENTIAL EQUATIONS. This course covers equations of first and second order; linear equations with constant coefficients; solution in series. Corequisite: Math 263. (3)

MATH 368. INTRODUCTION TO OPERATIONS RESEARCH. An introduction to the mathematics involved in optimal decision making and the modeling of deterministic systems. Major topics to include linear programming, the simplex method, transportation algorithms, integer programming, network theory, and CPM/PERT. Prerequisites: Math 319 with a minimum grade of C. (3)

MATH 375. INTRODUCTION TO STATISTICAL METHODS. Probability; distributions; joint probability distributions; conditional distributions; marginal distributions; independence; probability distributions; simple regression; simple correlation; and tests of significance; introduction to the use of statistical software packages. Prerequisites: Math 261 with a minimum grade of C. (3)

MATH 390. TECHNIQUES IN TEACHING SECONDARY LEVEL MATH. Teaching techniques for algebra, geometry, trigonometry, and calculus are presented and discussed. For mathematics education majors only. (3)

MATH 397. SPECIAL PROBLEMS. May be repeated twice for credit for a total of 6 hours. Prerequisites: Math 305 with a minimum grade of C. (1-3)

MATH 401. COMBINATORICS. This course explores the counting methods of Math 301 in further depth. Additional topics may include Ramsey theory, combinatorial designs, graph theory, matroid theory, and other related topics. Prerequisites: Math 301 with a minimum grade of C. (3)

MATH 425. INTRODUCTION TO ABSTRACT ALGEBRA. Real number system, groups, rings, integral domains, fields. Prerequisites: Math 263 with a minimum grade of C. (3)

MATH 454. INTERMEDIATE DIFFERENTIAL EQUATIONS. Certain special methods of solution; systems of equations; elementary partial differential equations; equations occurring in physical sciences. Prerequisites: Math 353 with minimum grade of C. (3)

MATH 459. INTRODUCTION TO COMPLEX ANALYSIS. Complex numbers, complex differentiation, the Cauchy-Riemann equations and applications; the Cauchy integral formula, contour integration, series. Prerequisites: Math 264 with minimum grade of C. (3)

MATH 461. NUMERICAL MATHEMATICAL ANALYSIS I. (3)

MATH 462. NUMERICAL MATHEMATICAL ANALYSIS II. (3)

MATH 464. INTRODUCTION TO DYNAMICS AND CHAOS. The course is an introduction to nonlinear dynamics and chaos theory. It will cover stability in nonlinear systems of differential equations, bifurcation theory, chaos, strange attractors, iteration of nonlinear mappings, fractals, and applications. This course will be of interest to students majoring either in natural sciences or mathematics. Prerequisites: Math 353 with minimum grade of C. (3)

MATH 475. INTRODUCTION TO MATHEMATICAL STATISTICS. Data analysis; moment characteristics; statistical distributions, including Bernoulli, Poisson, and Normal; least squares, simple correlation, and bivariate analysis; applications. Prerequisites: Math 375 and Math 262, both with a minimum grade of C. (3)

MATH 480. INTRODUCTION TO ACTUARIAL SCIENCE. A course to develop knowledge of the fundamental probability tools for quantitatively assessing risk with emphasis on the application of these tools to problems encountered in actuarial science. Topics include general probability concepts, univariate distributions, multivariate distribution, and risk management concepts. Prerequisites: Math 475 with minimum grade of C. (3)

MATH 501. GENERAL TOPOLOGY I. Metric spaces, continuity, separation axioms, connectedness, compactness, and other related topics. Prerequisites: Math 305 with a minimum grade of C. (3)

MATH 502. GENERAL TOPOLOGY II. Algebraic invariants in topology. Prerequisites: Math 501 with a minimum grade of C. (3)

MATH 513. THEORY OF NUMBERS I. Divisibility; properties of prime numbers; congruences and modular arithmetic; quadratic reciprocity; and representation of integers as sums of squares. Prerequisites: Math 305. (3)

MATH 514. THEORY OF NUMBERS II. Arithmetic functions and their distribution; distribution of prime numbers; Dirichlet characters and primes in arithmetic progression; and partitions. Prerequisites: Math 513 and Math 555. (3)

MATH 519. MATRICES. Basic matrix theory, eigenvalues, eigenvectors, normal and Hermitian matrices, similarity, Sylvester’s Law of Inertia, normal forms, functions of matrices. Prerequisites: Math 319 with a minimum grade of C. (3)

MATH 520. LINEAR ALGEBRA. An introduction to vector spaces and linear transformations; eigenvalues, and the spectral theorem. (3)

MATH 525. MODERN ALGEBRA I. General theory of groups. Prerequisites: Math 305 with a minimum grade of C. (3)

MATH 526. MODERN ALGEBRA II. General theory of rings and fields. Prerequisites: Math 525 with a minimum grade of C. (3)

MATH 533. TOPICS IN EUCLIDEAN GEOMETRY. A study of incidence geometry; distance and congruence; separation; angular measure, congruences between triangles; inequalities; parallel postulate; similarities between triangles; circles area. Prerequisites: Math 305 with a minimum grade of C. (3)

MATH 537. NON-EUCLIDEAN GEOMETRY. Brief review of the foundation of Euclidean plane geometry with special emphasis given the Fifth Postulate; hyperbolic plane geometry; elliptic plane geometry. (3)

MATH 540. HISTORY OF MATHEMATICS. Development of mathematics, especially algebra, geometry, and analysis; lives and works of Euclid, Pythagoras, Cardan, Descartes, Newton, Fuler, and Gauss. Prerequisite requirements for this course may also be satisfied by consent of instructor. Prerequisites: Junior standing (60 hr), Math 305 with minimum grade of C. (3)

MATH 545. SELECTED TOPICS IN MATHEMATICS FOR SECONDARY SCHOOL TEACHERS. High-school subjects from an advanced point of view and their relation to the more advanced subjects. May be repeated once for credit. (3)

MATH 555. ADVANCED CALCULUS I. Suprema and infima on the real line; limits, liminf, and limsup of a sequence of reals; convergent sequences; Cauchy sequences and series, absolute and conditional convergence of series. Prerequisites: Junior standing (60 hr), Math 305 with minimum grade of C. (3)

MATH 556. ADVANCED CALCULUS II. Limits, continuity, power series, partial differentiation; multiple, definite, improper, and line integrals; applications. Prerequisites: Junior standing (60 hr), Math 555 with minimum grade of C. (3)

MATH 564. INTRODUCTION TO DYNAMICAL SYSTEMS I. This course is an introduction to the theory of dynamical systems. The course will cover linear maps and differential equations, nonlinear systems, conservative dynamics, one-dimensional dynamics and connections with ergodic theory and number theory. Prerequisites: Math 353 with a minimum grade of C or Graduate Standing. (3)

MATH 565. INTRODUCTION TO DYNAMICAL SYSTEMS II. This course is the second semester of an introduction to the theory of dynamical systems. The course will cover some aspects of linear maps and differential equations, nonlinear systems, conservative dynamics, one-dimensional dynamics, and connections with ergodic theory and number theory. Prerequisites: Junior standing (60 hr), MATH 564. (3)

MATH 567. INTRODUCTION TO FUNCTIONAL ANALYSIS I. Hilbert spaces, Banach spaces, Hahn-Banach Theorem, Banach Steinhaus Theorem, Open Mapping Theorem, weak topologies, Banach-Alaoglu Theorem, and Classical Banach spaces. Prerequisites: Math 556 with a minimum grade of C. (3)

MATH 568. INTRODUCTION TO FUNCTIONAL ANALYSIS II. Topics in Banach space theory. Prerequisites: Math 567 with a minimum grade of C. (3)

MATH 572. INTRODUCTION TO PROBABILITY AND STATISTICS. Emphasis on standard statistical methods and the application of probability to statistical problems. Prerequisites: Math 261, Math 262, Math 263, and Math 264, all with a minimum grade of C. (3)

MATH 573. APPLIED PROBABILITY. Emphasis on understanding the theory of probability and knowing how to apply it. Proofs are given only when they are simple and illuminating. Among topics covered are joint, marginal, and conditional distributions, conditional and unconditional moments, independence, the weak law of large numbers, Tchebycheff’s inequality, Central Limit Theorem. Prerequisites: Math 261, Math 262, Math 263, and Math 264, all with a minimum grade of C. (3)

MATH 574. PROBABILITY. Topics introduced in Math 573 will be covered at a more sophisticated mathematical level. Additional topics will include the Borel-Cantelli Lemma, the Strong Law of Large Numbers, characteristic functions, Fourier transforms. Prerequisites: Math 573 with a minimum grade of C. (3)

MATH 575. MATHEMATICAL STATISTICS I. Mathematical treatment of statistical and moment characteristics; probability models; random variables; distribution theory; correlation; central limit theorem; and multiparameter models. Prerequisites: Junior standing (60 hr), Math 262 with a grade of C. (3)

MATH 576. MATHEMATICAL STATISTICS II. Mathematical treatment of statistical inference; maximum likelihood estimation and maximum likelihood ratio test; minimum variance unbiased estimators; most powerful tests; asymptotic normality and efficiency; and Baysian statistics. Prerequisites: Math 575 with a minimum grade of C. (3)

MATH 577. APPLIED STOCHASTIC PROCESSES. Emphasis on the application of the theory of stochastic processes to problems in engineering, physics, and economics. Discrete and continuous time Markov processes, Brownian Motion, Ergodic theory for stationary processes. Prerequisite requirements for this course may also be satisfied by consent of instructor. Prerequisites: Math 573 with a minimum grade of C. (3)

MATH 578. STOCHASTIC PROCESSES. Topics will include general diffusions, Martingales, and Stochastic differential equations. (3)

MATH 590. TECHNIQUES IN TEACHING COLLEGE MATHEMATICS. Directed studies of methods in the presentation of college mathematics topics, teaching and testing techniques. This course is required of all teaching assistants, each semester, and may not be used for credit toward a degree. Prerequisites: Junior standing (60 hr). (1-3)

MATH 597. SPECIAL PROBLEMS I. Prerequisites: Junior standing (60 hr). (1-3)

MATH 598. SPECIAL PROBLEMS II. Prerequisites: Junior standing (60 hr). (1-3)

MATH 599. SPECIAL PROBLEMS III. Prerequisites: Junior standing (60 hr). (1-3)