# Department of Mathematics

University of Mississippi

MATH 110. QUANTITATIVE REASONING. Statistical reasoning, logical statements and arguments, personal business applications, linear programming, estimations, and approximation. (3)

MATH 115. ELEMENTARY STATISTICS. Descriptive statistics; probability distributions; sampling distributions; estimation; hypothesis testing; and linear regression. (3)

MATH 121. COLLEGE ALGEBRA. College algebra. (3)

MATH 123. TRIGONOMETRY. College trigonometry. (3)

MATH 125. BASIC MATHEMATICS FOR SCIENCE AND ENGINEERING. A unified freshman course designed especially for those students requiring a review of both algebra and trigonometry before beginning the calculus sequence. (3)

MATH 245. MATHEMATICS FOR ELEMENTARY TEACHERS I. Introduction to sets; the real number system and its subsystems. For elementary and special education majors only. (3)

MATH 246. MATHEMATICS FOR ELEMENTARY TEACHERS II. Informal geometry; measurement and the metric system; probability and statistics. For elementary and special education majors only. Prerequisite: Math 245 with minimum grade of C. (3)

MATH 261. UNIFIED CALCULUS AND ANALYTIC GEOMETRY I. Differential and integral calculus; analytic geometry introduced, covered in integrated plan where appropriate. Four-term sequence for engineering and science majors. Prerequisite: 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. Prerequisite: Math 261 with 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. Prerequisite: Math 262 with 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. Prerequisite: Math 263 with minimum grade of C. (3)

MATH 267. CALCULUS FOR BUSINESS, ECONOMICS, AND ACCOUNTANCY I. Differential and integral calculus with an emphasis on business applications. (3)

MATH 268. CALCULUS FOR BUSINESS, ECONOMICS, AND ACCOUNTANCY II. Differential and integral calculus with an emphasis on business applications. Prerequisite: Math 267 with 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. Prerequisite: Math 267 with 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. Prerequisite: Math 271 with 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. Elementary counting principles; mathematical induction; inclusion- exclusion principles; and graphs. Prerequisite: Math 261 with minimum grade of C. (3)

MATH 302. APPLIED MODERN ALGEBRA. Languages, generating functions, recurrence relations, optimization, rings, groups, coding theory, and Polya theory. Prerequisite: Math 301 with minimum grade of C. (3)

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

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

MATH 353. ELEMENTARY DIFFERENTIAL EQUATIONS. Equations of first and second order; linear equations with constant coefficients; solution in series. (3) Corequisite: Math 264.

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. Prerequisite: Math 319 with 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. Prerequisite: Math 261 with 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. Prerequisite: Math 305 with minimum grade of C. (1-3)

MATH 401. COMBINATORICS. An introduction to the mathematics of finite sets, Ramsey theory, Latin squares, graph theory, matroid theory, and other related topics. Prerequisite: Math 305 with minimum grade of C, Math 301 with minimum grade of C. (3)

MATH 425. INTRODUCTION TO ABSTRACT ALGEBRA. Real number system, groups, rings, integral domains, fields. Prerequisite: Math 263 with 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. Prerequisite: 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. Prerequisite: 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. Prerequisite: 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. Prerequisite: Math 375 with minimum grade of C, Math 262 with 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. Prerequisite: Math 475 with minimum grade of C. (3)

MATH 501. GENERAL TOPOLOGY I. Metric spaces, continuity, separation axioms, connectedness, compactness, and other related topics. Prerequisite: Math 555 with minimum grade of C. (3)

MATH 502. GENERAL TOPOLOGY II. Introduction to algebraic topology. Prerequisite: Math 501 with minimum grade of C. (3)

MATH 513. THEORY OF NUMBERS I. Congruences; divisibility; properties of prime numbers; arithmetical functions; quadratic residues. Prerequisite: Math 305. (3)

MATH 514. THEORY OF NUMBERS II. Diophantine equations, distribution of prime numbers, and an introduction to algebraic number theory. Prerequisite: Math 513. (3)

MATH 519. MATRICES. Basic matrix theory, eigenvalues, eigenvectors, normal and Hermitian matrices, similarity, Sylvesterâ€™s Law of Inertia, normal forms, functions of matrices. Prerequisite: Math 319 with 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 properties of groups. (3)

MATH 526. MODERN ALGEBRA II. General properties of rings and fields. Prerequisite: Math 525. (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. Prerequisite: Math 305 with 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. Prerequisite: 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. (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. Prerequisite requirements for this course may also be satisfied by consent of instructor. Prerequisite: 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. Prerequisite: Math 555 with minimum grade of C. (3)

MATH 564. DYNAMICAL SYSTEMS. 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. Prerequisite: Math 353 with minimum grade of C or Graduate Standing. (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. Prerequisite: Math 556 with minimum grade of C. (3)

MATH 568. INTRODUCTION TO FUNCTIONAL ANALYSIS II. Topics in Banach space theory. Prerequisite: Math 567 with 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. Prerequisite: Math 261 with minimum grade of C, Math 262 with minimum grade of C, Math 263 with minimum grade of C, Math 264 with 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, Tchebycheffâ€™s inequality, Central Limit Theorem. Prerequisite: Math 261 with minimum grade of C, Math 262 with minimum grade of C, Math 263 with minimum grade of C, Math 264 with 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. Prerequisite: Math 573 with minimum grade of C. (3)

MATH 575. MATHEMATICAL STATISTICS I. Mathematical treatment of statistical and moment characteristics; frequency distribution; least squares; correlation; sampling theory. Prerequisite: Math 262 with minimum grade of C. (3)

MATH 576. MATHEMATICAL STATISTICS II. Mathematical treatment of statistical and moment characteristics; frequency distribution; least squares; correlation; sampling theory. Prerequisite: Math 575 with 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. Prerequisite: Math 573 with 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. (1-3)

MATH 597. SPECIAL PROBLEMS I. (1-3)

MATH 598. SPECIAL PROBLEMS II. (1-3)

MATH 599. SPECIAL PROBLEMS III. (1-3)