**MA 0003. Developmental Mathematics. (3)**

(MA 0003 is a developmental course designed to prepare a student for university mathematics courses at the level of MA 1313 College Algebra: credit received for this course will not be applicable toward a degree.) Three hours lecture. Real numbers fractions, decimal fractions, percent, algebraic expressions, factoring, algebraic fractions, linear equations/inequalities, integral exponents, quadratic equations.

**MA 0103. Intermediate Algebra. (3)**

(MA 0103 is designed to prepare a student for MA 1313 College Algebra.) Two hours lecture. Two hours laboratory. Real numbers, algebraic expressions, factoring, algebraic fractions, linear equations/inequalities, quadratic equations, Pythagorean Theorem. Does not count toward any degree.

**MA 1001. First Year Seminar. (1)**

One hour lecture. First-year seminar explores a diverse array of topics that provide students with an opportunity to learn about a specific discipline from skilled faculty members.

**MA 1103. College Algebra Linked Lab - Corequisite Model. (3)**

(Prerequisite: MACT 17 or 18 and ACT 20 or above.) Two hours lecture. Two hours laboratory. Review of fundamentals; linear and quadratic equations; inequalities; functions; simultaneous equations; topics in the theory of equations.

**MA 1213. Math in Your World. (3)**

(Prerequisites: ACT Math Sub-score 19 or above or grade of C or better in MA 0103.) Topics will include but are not limited to ratios & proportions, unit conversions, formula manipulation, logical reasoning, financial literacy, general number sense, and the use of Excel to solve real world problems.

**MA 1313. College Algebra. (3)**

(Students with credit in MA 1713 will not receive credit for this course. Prerequisite: ACT Math sub-score 19, or grade of C or better in MA 0103.) Two hours lecture. Two hours laboratory. Review of fundamentals; linear and quadratic equations; inequalities; functions; simultaneous equations; topics in the theory of equations. For college algebra placement exam go to: www.math.msstate.edu/capt/.

**MA 1323. Trigonometry. (3)**

(Students with credit in MA 1713 will not receive credit for this course. Prerequisite: ACT Math sub-score 24, or grade of C or better in MA 1103 or 1313.) Three hours lecture. The trigonometric functions: identities; trigonometric equations: applications.

**MA 1413. Structure of the Real Number System. (3)**

(Prerequisite: a C or better in MA 1103 or 1313 or an ACT Math sub-score of 24.) Three hours lecture. The nature of mathematics; introductory logic; structure and development of the real number system. (Course is meant primarily for Elementary and Special Education majors).

**MA 1423. Problem Solving with Real Numbers. (3)**

(Prerequisite: a C or better in MA 1413.) Three hours lecture. Proportions, percent problems, probability, counting principles, statistics. (For Elementary and Special Education majors only.)

**MA 1433. Informal Geometry and Measurement. (3)**

(Prerequisites: a C or better in both MA 1413 and MA 1423.) Three hours lecture. Measurements and informal geometry. (For Elementary and Special Education majors only.)

**MA 1453. Precalculus with Graphing Calculators. (3)**

(Prerequisites: Math ACT 24 or C or better in MA 1323 or score of at least 70 on the Precalculus Qualifying Exam.) Three hours lecture. Properties, applications, and graphs of linear, quadratic, polynomial, exponential, logarithmic, and trigonometric functions; trigonometric identities, equations and inverses; inequalities. (Degree credit will not be granted for MA 1453 and either MA 1313 or MA 1323. This course is intended to prepare students to take MA 1713 Calculus I.)

**MA 1613. Calculus for Business and Life Sciences I. (3)**

(Prerequisite: ACT Math sub-score 24, or grade of C or better in MA1103 or 1313.) Three hours lecture. Algebraic and some transcendental functions, solutions of systems of linear equations, limits, continuity, derivatives, applications.

**MA 1713. Calculus I. (3)**

(Prerequisite: ACT Math sub-score 26, or grade of C or better in MA 1323 or 1453.) Three hours lecture. Analytic geometry; functions; limits; continuity; derivatives of algebraic functions. Application of the derivative. Honors section available through invitation.

**MA 1723. Calculus II. (3)**

(Prerequisite: Grade of C or better in MA 1713.) Three hours lecture. Anti-differentiation; the definite integral; applications of the definite integral; differentiation and integration of transcendental functions. Honors section available through invitation.

**MA 2113. Introduction to Statistics. (3)**

(Prerequisite: ACT Math sub-score 24, or a grade of C or better in MA 1313.) Two hours lecture. Two hours laboratory. Introduction to statistical techniques: descriptive statistics, random variables, probability distributions, estimation, confidence intervals, hypothesis testing, and measurement of association. Computer instruction for statistical analysis. (Same as ST 2113).

**MA 2733. Calculus III. (3)**

(Prerequisite: Grade of C or better in MA 1723.) Three hours lecture. Parametric and Polar Equations; infinite series; introduction to vectors; vector functions. Honors section available through invitation.

**MA 2743. Calculus IV. (3)**

(Prerequisite: Grade of C or better in MA 2733.) Three hours lecture. Differential calculus of functions of several variables; multiple integration; vector calculus. Honors section available through invitation.

**MA 2923. Introduction to Modern Scientific Computing. (3)**

(Prerequisite: MA 1713 or equivalent.) Three hours lecture. Basic programming skills and applications to scientific computing; iteration and recursion; accuracy and efficiency issues; matrix operations; data interpolation; unconstrained optimization; regression analysis; multiple local minima problems. Prior programming experience is not required.

**MA 2990. Special Topics in Mathematics. (1-9)**

Credit and title to be arranged. This course is to be used on a limited basis to offer developing subject matter areas not covered in existing courses. (Courses limited to two offerings under one title within two academic years.)

**MA 3053. Foundations of Mathematics. (3)**

(Prerequisite: MA 1723.) Three hours lecture. The logical structure of mathematics; the nature of a mathematical proof; applications to the basic principles of algebra and calculus.

**MA 3113. Introduction to Linear Algebra. (3)**

(Prerequisite: MA 1723.) Three hours lecture. Basic principles of linear algebra; vector spaces; matrices; matrix algebra; linear transformations; systems of linear equations; eigenvalues and eigenvectors; orthogonality and Gram-Schmidt process.

**MA 3123. Introduction to Statistical Inference. (3)**

(Prerequisite: ACT Math sub-score 24, or grade of C or better in MA 1313.) Two hours lecture. Two hours laboratory. Basic concepts and methods of statistics, including descriptive statistics, probability, random variables, sampling distribution, estimation, hypothesis testing, introduction to analysis of variance, simple linear regression. (Same as ST 3123.)

**MA 3163. Introduction to Modern Algebra. (3)**

(Prerequisite: MA 3113 and MA 3053.) Three hours lecture. Rings, integral domains, and fields with special emphasis on the integers, rational numbers, real numbers and complex numbers; theory of polynomials.

**MA 3253. Differential Equations I. (3)**

(Prerequisite: MA 2743 or co-registration in MA 2743.) Origin and solution of differential equations; series solutions; Laplace Transform methods; applications.

**MA 3353. Differential Equations II. (3)**

(Prerequisite: MA 3253.) Three hours lecture. Systems of differential equations; matrix representations; infinite series solution of ordinary differential equations; selected special functions; boundary-value problems; orthogonal functions: Fourier series.

**MA 3463. Foundations of Geometry. (3)**

(Prerequisite: MA 1723 and MA 3053.) Three hours lecture. The structural nature of geometry; modern methods in geometry: finite geometrics.

**MA 3513. History of Mathematics. (3)**

(Prerequisite: MA 2733 or co-registration in MA 2733.) Three hours lecture. A historical development of mathematicians and their most important contributions will be emphasized.

**MA 4000. Directed Individual Study. (1-6)**

Hours and credits to be arranged.

**MA 4133/6133. Discrete Mathematics. (3)**

(Prerequisites: MA 3163 or consent of instructor.) Three hours lecture. Sets, relations, functions, combinatorics, review of group and ring theory, Burnside’s theorem, Polya’s counting theory, group codes, finite fields, cyclic codes, and error-correcting codes.

**MA 4143/6143. Graph Theory. (3)**

(Prerequisites: MA 3113 or consent of instructor.) Three hours lecture. Basic concepts, graphs, and matrices, algebraic graph theory, planarity and nonplanarity, Hamiltonian graphs, digraphs, network flows, and applications.

**MA 4153/6153. Matrices and Linear Algebra. (3)**

(Prerequisites: MA 3113 and MA 3253.) Three hours lecture. Linear transformations and matrices; eigenvalues and similarity transformations; linear functionals, bilinear and quadratic forms; orthogonal and unitary transformations; normal matrices; applications of linear algebra.

**MA 4163/6163. Group Theory. (3)**

(Prerequisite: MA 3163 or consent of the instructor.) Three hours lecture. Elementary properties: normal subgroups; factor groups; homomorphisms and isomorphisms; Abelian groups; Sylow theorems; composition series; solvable groups.

**MA 4173/6173. Number Theory. (3)**

(Prerequisite: MA 3113.) Three hours lecture. Divisibility: congruences; quadratic reciprocity; Diophantine equations; continued fractions.

**MA 4213. Senior Seminar in Mathematics. (3)**

(Prerequisites: MA 3163 and MA 3253 and MA 4633.) Three hours lecture. Students explore topics in current mathematical research, write expository articles, and give oral presentations. Refinement of specialized writing skills needed for effective mathematical communication.

**MA 4243/6243 Data Analysis I. (3)**

(Prerequisite: MA 2743. Co-requisite: MA 3113.) Three hours lecture. Data description and descriptive statistics, probability and probability distributions, parametric one-sample and two-sample inference procedures, simple linear regressions, one-way ANOVA. Use of SAS. (Same as ST 4243/6243.)

**MA 4253/6253 Data Analysis II. (3)**

(Prerequisites: MA 4243/6243 and MA 3113.) Three hours lecture. Multiple linear regression; fixed, mixed and random effect models; block designs; two-factor analysis of variance; three-factor analysis of variance; analysis of covariance. Use of SAS. (Same as ST 4253/6253.)

**MA 4313/6313. Numerical Analysis I. (3)**

(Prerequisites: CSE 1213, MA 3113, and MA 2743.) Three hours lecture. Matrix operations; error analysis; norms of vectors and matrices; transformations; matrix functions; numerical solutions of systems of linear equations; stability; matrix inversion; eigenvalue problems; approximations.

**MA 4323/6323. Numerical Analysis II. (3)**

(Prerequisites: CSE 1213 or equivalent. MA 3113 and MA 3253.) Three hours lecture. Numerical solution of equations; error analysis; finite difference methods; numerical differentiation and integration; series expansions; difference equations; numerical solution of differential equations.

**MA 4373/6373. Introduction to Partial Differential Equations. (3)**

(Prerequisite: MA 3253.) Three hours lecture. Linear operators: linear first order equations; the wave equation; Green’s function and Sturm-Liouville problems; Fourier series; the heat equation; Laplace’s equation.

**MA 4523/6523. Introduction to Probability. (3)**

(Prerequisite: MA 2733.) Three hours lecture. Basic concepts of probability, conditional probability, independence, random variables, discrete and continuous probability distributions, moment generating function, moments, special distributions, central limit theorem. (Same as ST 4523/6523.)

**MA 4533/6533. Introductory Probability and Random Processes. (3)**

(Prerequisites: MA 3113 and MA 2743). Three hours lecture. Probability, law of large numbers, central limit theorem, sampling distributions, confidence intervals, hypothesis testing, linear regression, random processes, correlation functions, frequency and time domain analysis. (Credit can not be earned for this course and MA/ST 4523/6523.)

**MA 4543/6543. Introduction to Mathematical Statistics I. (3)**

(Prerequisite: MA 2743.) Three hours lecture. Combinatorics; probability, random variables, discrete and continuous distributions, generating functions, moments, special distributions, multivariate distributions, independence, distributions of functions of random variables. (Same as ST 4543/6543.)

**MA 4573/6573. Introduction to Mathematical Statistics II. (3)**

(Prerequisite: MA 4543/6543.) Three hours lecture. Continuation of MA-ST 4543/6543. Transformations, sampling distributions, limiting distributions, point estimation, interval estimation, hypothesis testing, likelihood ratio tests, analysis of variance, regression, chi-square tests. (Same as ST 4573/6573.)

**MA 4633/6633. Advanced Calculus I. (3)**

(Prerequisite: MA 2743 and MA 3053.) Three hours lecture. Theoretical investigation of functions; limits; differentiability and related topics in calculus.

**MA 4643/6643. Advanced Calculus II. (3)**

(Prerequisite: MA 4633/6633.) Three hours lecture. Rigorous development of the definite integral; sequences and series of functions; convergence criteria; improper integrals.

**MA 4733/6733. Linear Programming. (3)**

(Prerequisites: MA 3113.) Three hours lecture. Theory and application of linear programming; simplex algorithm, revised simplex algorithm, duality and sensitivity analysis, transportation and assignment problem algorithms, integer and goal programming. (Same as IE 4733/6733.)

**MA 4753/6753. Applied Complex Variables. (3)**

(Prerequisite: MA 2743.) Three hours lecture. Analytic functions: Taylor and Laurent expansions; Cauchy theorems and integrals; residues; contour integration; introduction to conformal mapping.

**MA 4933/6933. Mathematical Analysis I. (3)**

(Prerequisite: MA 4633/6633 or equivalent.) Three hours lecture. Metric and topological spaces; functions of bounded variation and differentiability in normed spaces.

**MA 4943/6943. Mathematical Analysis II. (3)**

(Prerequisite: MA 4933/6933.) Three hours lecture. Riemann-Stieltjes integration, sequences and series of functions; implicit function theorem; multiple integration.

**MA 4953/6953. Elementary Topology. (3)**

(Prerequisite: MA 4633/6633.) Three hours lecture. Definition of a topological space, metric space, continuity in metric spaces and topological spaces; sequences; accumulation points; compactness, separability.

**MA 4990/6990 Special Topics in Mathematics. (1-9)**

Credit and title to be arranged. This course is to be used on a limited basis to offer developing subject matter areas not covered in existing courses. (Courses limited to two offerings under one title within two academic years.)

**MA 7000 Directed Individual Study in Mathematics. (1-6)**

Hours and credits to be arranged.

**MA 8000 Thesis Research/ Thesis in Mathematics: (1-13)**

Hours and credits to be arranged.

**MA 8113. Modern Higher Algebra I. (3)**

(Prerequisite: MA 4163/6163.) Three hours lecture. A study of the basic mathematical systems with emphasis on rings, fields, and vector spaces.

**MA 8123. Modern Higher Algebra II. (3)**

(Prerequisite: MA 8113). Three hours lecture. A continuation of the topics introduced in MA 8113.

**MA 8203. Foundations of Applied Mathematics I. (3)**

(Prerequisites: MA 3113, MA 3253 or consent of instructor.) Three hours lecture. Principles of applied mathematics including topics from perturbation theory, calculus of variations, and partial differential equations. Emphasis of applications from heat transfer, mechanics, fluids.

**MA 8213. Foundations of Applied Mathematics II. (3)**

(Prerequisite: MA 8203.) Three hours lecture. A continuation of MA 8203 including topics from wave propagation, stability, and similarity methods.

**MA 8253. Operational Mathematics. (3)**

(Prerequisite: MA 4753/6753). Three hours lecture. Theory and applications of Laplace, Fourier, and other integral transformations: introduction to the theory of generalized functions.

**Courses numbered MA 8273, 8283, 8293 and 8313 have as prerequisites at least one of the courses MA 4633/6633, MA 4153/6153, 4753/6753.*

**MA 8273. Special Functions. (3)**

Three hours lecture. Infinite products: asymptotic series; origin and properties of the special functions of mathematical physics.

**MA 8283. Calculus of Variations. (3)**

Three hours lecture. Functionals: weak and strong extrema; necessary conditions for extrema; sufficient conditions for extrema; constrained extrema; direct methods; applications.

**MA 8293. Integral Equations. (3)**

Three hours lecture. Equations of Fredholm type: symmetric kernels; Hilbert-Schmidt theory; singular integral equations; applications; selected topics.

**MA 8313. Ordinary Differential Equations I. (3)**

Three hours lecture. Linear systems of differential equations; existence and uniqueness; second order systems; systems with constant coefficients; periodic systems; matrix comparison theorems; applications and selected topics.

**MA 8323. Ordinary Differential Equations II. (3)**

(Prerequisite: MA 8313.) Three hours lecture. Existence, uniqueness, continuation of solutions of nonlinear systems; properties of solutions of linear and nonlinear equations including boundedness, oscillation, asymptotic behavior, stability, and periodicity; application.

**MA 8333. Partial Differential Equations I. (3)**

(Prerequisite: MA 4373/6373 or consent of instructor.) Three hours lecture. Solution techniques; existence and uniqueness of solutions to elliptic, parabolic, and hyperbolic equations; Green’s functions.

**MA 8343. Partial Differential Equations II. (3)**

(Prerequisite: MA 8333.) Three hours lecture. A continuation of the topics introduced in MA 8333.

**MA 8363. Numerical Solution of Systems of Nonlinear Equations. (3)**

(Prerequisites: MA 4313/6313 and MA 4323/6323.) Three hours lecture. Basic concepts in the numerical solution of systems of nonlinear equations with applications to unconstrained optimization.

**MA 8383. Numerical Solution of Ordinary Differential Equations I. (3)**

(Prerequisites: MA 4313/6313 and MA 4323/6323.) Three hours lecture. General single-step, multistep, multi-value, and extrapolation methods for systems of nonlinear equations; convergence; error bounds; error estimates; stability; methods for stiff systems; current literature.

**MA 8443. Numerical Solution of Partial Differential Equations I. (3)**

(Prerequisites: MA 4313/6313, MA 4323/6323, and MA 4373/6373 or consent of instructor.) Three hours lecture. Basic concepts in the finite difference and finite element methods; methods for parabolic, hyperbolic and elliptic equations; analysis of stability and convergence.

**MA 8453. Numerical Solution of Partial Differential Equations II. (3)**

(Prerequisite: MA 8443.) Three hours lecture. Methods for elliptic equations; iterative procedures; integral equation methods; methods for hyperbolic equations; stability; dissipation and dispersion.

**MA 8463. Numerical Linear Algebra. (3)**

(Prerequisite: MA 4323/6323.) Three hours lecture. Gaussian elimination and its variants; iterative methods for linear systems; the lease-squares problem; QR factorization; singular value decomposition; principal component analysis; eigenvalue problems; iterative methods for eigenvalue problems; applications to data mining.

**MA 8633. Real Analysis I. (3)**

(Prerequisite: MA 4943/6943.) Three hours lecture. Lebesgue measure and Lebesgue integrals; convergence theorems, differentiation and L spaces.

**MA 8643. Real Analysis II. (3)**

(Prerequisite: MA 8633.) Three hours lecture. General measures; the Radon-Nikodym theorem and other topics.

**MA 8663. Functional Analysis I. (3)**

(Prerequisite: MA 8643.) Three hours lecture. Hilbert spaces; Banach spaces; locally convex spaces; Hahn-Banach and closed graph theorems; principle of uniform boundedness; weak topologies.

**MA 8673. Functional Analysis II. (3)**

(Prerequisite: MA 8663.) Three hours lecture. Continuation of topics introduced in MA 8663.

**MA 8713. Complex Analysis I. (3)**

(Prerequisite MA 4943/6943 or consent of instructor.) Three hours lecture. Complex numbers: functions of a complex variable; continuity; differentiation and integration of complex functions; transformations in the complex plane.

**MA 8723. Complex Analysis II. (3)**

(Prerequisite: MA 8713.) Three hours lecture. Series; analytic continuation; Riemann surfaces; theory of residues.

**MA 8913. Introduction to Topology I. (3)**

(Prerequisite: MA 4643/6643 or MA 4953/6953.) Three hours lecture. Basic general topology; introduction of homotopy and homology groups.

**MA 8923. Introduction to Topology II. (3)**

(Prerequisite: MA 8913.) Three hours lecture. Continuation of topics introduced in MA 8913.

**MA 8981. Teaching Seminar. (1)**

One hour lecture. Preparation for service as instructors in mathematics and statistics courses; includes practice lectures and exam preparation. (May be taken for credit more than once.)

**MA 8990 Special Topics in Mathematics: (1-9)**

Credit and title to be arranged. This course is to be used on a limited basis to offer developing subject matter areas not covered in existing courses. (Courses limited to two offerings under one title within two academic years.)

**MA 9000 Dissertation Research /Dissertation in Mathematics. (1-13)**

Hours and credits to be arranged.

**MA 9313. Selected Topics in Ordinary Differential Equations. (3)**

(Prerequisite: MA 8313 and consent of instructor). (May be taken for credit more than once.) Three hours lecture. Topics to be chosen from such areas as Bifurcation Theory, Biological Modeling, Control Theory, Dynamical Systems, Functional Differential Equations, Nonlinear Oscillations, and Quantitative Behavior.

**MA 9333. Selected Topics in Partial Differential Equations. (3)**

(Prerequisite: MA 8333 and consent of instructor). (May be taken for credit more than once.) Three hours lecture. Topics to be chosen from such areas as Bifurcation Theory, Boundary Integral Methods, Evolution Equations, Maximum and Variational Principles, and Spectral Methods.

**MA 9413. Selected Topics in Numerical Analysis. (3)**

(Prerequisite: Consent of instructor.) (May be taken for credit more than once). Three hours lecture. Current topics in Numerical Analysis. The subject matter may vary from year to year.

**MA 9633. Selected Topics in Analysis. (3)**

(Prerequisite: MA 8643 and consent of instructor). (May be taken for credit more than once.) Three hours lecture. Topics will be chosen from areas of analysis of current interest.