### Undergraduate course catalog

Some prerequisites can be overridden. If you don't meet a prerequisite, but think you are qualified to take a course, consult with one or more of: your advisor; the instructor; the department chair or associate chair.

**Math 1010**[3 credit hours]*APPLIED BUSINESS MATHEMATICS*Mathematics used in solving business problems related to simple and compound interest, annuities, payroll, taxes, promissory notes, consumer credit, insurance, markup and markdown, mortgage loans, discounting, financial statement ratios and break-even analysis.

Course is not applicable toward the undergraduate Mathematics major requirements.

**Math 1180**[3 credit hours]*MATHEMATICS FOR LIBERAL ARTS*A general liberal arts course for non-science students designed to acquaint students with the nature of mathematics and applications such as probability, statistics, functions and graphs.

Course is not applicable toward the undergraduate Mathematics major requirements.

**Core Mathematics Course****Math 1190**[1 credit hours]*MATH MODELING STUDY SKILLS*A course to provide the study skills needed to succeed in college mathematics. Students learn and apply skills such as reading textbooks, note-taking, and analyzing tests.

**Math 1200**[4 credit hours]*MATHEMATICAL MODELING AND PROBLEM SOLVING*Mathematical modeling of data using linear, quadratic, rational, and radical functions in their numerical, symbolic, graphic, and verbal forms. Problem solving methods and strategies will be emphasized.

Course is not applicable toward the undergraduate Mathematics major requirements. Math core course.

**Core Mathematics Course****Math 1210**[3 credit hours]*MATHEMATICS FOR EDUCATION MAJORS I*Principles of elementary number theory, base systems, foundations of arithmetic operations, fractions, decimals and problem solving techniques.

Course is not applicable toward the undergraduate Mathematics major requirements.

Prerequiste: MATH 1180 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1200 FOR LEVEL UG WITH MIN. GRADE OF C- OR AMPT FOR MIN. SCORE OF 46 OR AMRT FOR MIN. SCORE OF 46 OR A02 FOR MIN. SCORE OF 20 OR MTCA FOR MIN. SCORE OF 10 OR MTEA FOR MIN. SCORE OF 12 OR S02 FOR MIN. SCORE OF 480

**Core Mathematics Course****Math 1220**[3 credit hours]*MATHEMATICS FOR EDUCATION MAJORS II*Development of integers, rational numbers and real numbers; probability, statistics, informal geometry, geometric figures and measurements.

Course is not applicable toward the undergraduate Mathematics major requirements.

Prerequiste: MATH 1210 FOR LEVEL UG WITH MIN. GRADE OF C-

**Core Mathematics Course****Math 1320**[3 credit hours]*COLLEGE ALGEBRA*Number system; elementary theory of equations and inequalities; functions and relations; exponentials and logarithms; systems of equations and topics in analytic geometry. Course is not applicable toward the undergraduate Mathematics major requirements.

No credit given for students who have credit for MATH 1340.

Prerequiste: MATH 1200 FOR LEVEL UG WITH MIN. GRADE OF C- OR A02 FOR MIN. SCORE OF 20 OR S02 FOR MIN. SCORE OF 480 OR AMPT FOR MIN. SCORE OF 46 OR AMRT FOR MIN. SCORE OF 46 OR MTCA FOR MIN. SCORE OF 10

**Core Mathematics Course****Math 1330**[3 credit hours]*TRIGONOMETRY*Definitions and graphs of trigonometric functions and their inverses, solving trigonometric equations, applications and topics in analytic geometry. Course is not applicable toward the undergraduate Mathematics major requirements.

No credit given for students who have credit for MATH 1340.

Prerequiste: MATH 1320 FOR LEVEL UG WITH MIN. GRADE OF C- OR A02 FOR MIN. SCORE OF 22 OR S02 FOR MIN. SCORE OF 520 OR AMPT FOR MIN. SCORE OF 61 OR AMRT FOR MIN. SCORE OF 61 OR MTCA FOR MIN. SCORE OF 15

**Core Mathematics Course****Math 1340**[0-5 credit hours]*COLLEGE ALGEBRA AND TRIGONOMETRY*Functions and graphs, exponential and logarithmic functions, trigonometric functions and applications, systems of equations and topics in analytic geometry.

No credit for students who have credit for MATH 1320 or 1330.

Prerequiste: A02 FOR MIN. SCORE OF 24 OR S02 FOR MIN. SCORE OF 560 OR AMPT FOR MIN. SCORE OF 68 OR AMRT FOR MIN. SCORE OF 68 OR (MTCA FOR MIN. SCORE OF 12 AND MTTR FOR MIN. SCORE OF 9)

**Core Mathematics Course****Math 1730**[0-5 credit hours]*CALCULUS WITH APPLICATIONS TO BUSINESS AND FINANCE*An introduction to differential and integral calculus. Topics include limits, derivatives, maxima/minima, indefinite and definite integrals with an emphasis on business applications and technology use.

Prerequiste: MATH 1320 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1340 FOR LEVEL UG WITH MIN. GRADE OF C- OR MTCA FOR MIN. SCORE OF 15 OR A02 FOR MIN. SCORE OF 22 OR S02 FOR MIN. SCORE OF 520 OR AMPT FOR MIN. SCORE OF 61 OR AMRT FOR MIN. SCORE OF 61

**Core Mathematics Course****Math 1750**[0-4 credit hours]*CALCULUS FOR THE LIFE SCIENCES WITH APPLICATIONS I*Definitions of trigonometric functions, solving trigonometric equations, functions, limits and derivatives, exponential and logarithmic functions, and applications.

Course is not applicable toward the undergraduate Mathematics major requirements.

Prerequiste: MATH 1320 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1340 FOR LEVEL UG WITH MIN. GRADE OF C- OR MTCA FOR MIN. SCORE OF 12 OR A02 FOR MIN. SCORE OF 22 OR S02 FOR MIN. SCORE OF 520 OR AMPT FOR MIN. SCORE OF 61 OR AMRT FOR MIN. SCORE OF 61

**Core Mathematics Course****Math 1760**[0-3 credit hours]*CALCULUS FOR THE LIFE SCIENCES WITH APPLICATIONS II*Indefinite and definite integrals, probability, vectors, least squares, differential equations.

Course is not applicable toward the undergraduate Mathematics major requirements.

Prerequiste: MATH 1750 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1850 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1830 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1920 FOR LEVEL UG WITH MIN. GRADE OF C-

**Core Mathematics Course****Math 1830**[4 credit hours]*CALCULUS I FOR MATHEMATICIANS, SCIENTISTS AND EDUCATORS*Limits, differentiation, Fundamental Theorem of Calculus, Mean Value Theorem, curve sketching, maxima/minima, definite and indefinite integrals, applications. The emphasis is on the rigorous aspects and foundational ideas of calculus. Of interest to students requiring a conceptual understanding of calculus.

Course is not applicable toward the undergraduate Mathematics major requirements.

Prerequiste: MATH 1340 FOR LEVEL UG WITH MIN. GRADE OF C- OR (MATH 1320 FOR LEVEL UG WITH MIN. GRADE OF C- AND MATH 1330 FOR LEVEL UG WITH MIN. GRADE OF C-) OR AMPT FOR MIN. SCORE OF 76 OR AMRT FOR MIN. SCORE OF 76 OR (MTTR FOR MIN. SCORE OF 12 AND A02 FOR MIN. SCORE OF 27) OR (MTTR FOR MIN. SCORE OF 12 AND S02 FOR MIN. SCORE OF 610) OR (MTTR FOR MIN. SCORE OF 12 AND MTCA FOR MIN. SCORE OF 15)

**Core Mathematics Course****Math 1840**[4 credit hours]*CALCULUS II FOR MATHEMATICIANS, SCIENTISTS AND EDUCATORS*Applications and techniques of integration, polar coordinates and calculus of plane curves, infinite series and Taylor series, vectors and geometry of space. The emphasis is on the rigorous aspects and foundational ideas of calculus. Of interest to students requiring a conceptual understanding of calculus.

Prerequiste: MATH 1830 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1850 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1920 FOR LEVEL UG WITH MIN. GRADE OF C-

**Core Mathematics Course****Math 1850**[0-4 credit hours]*SINGLE VARIABLE CALCULUS I*Limits, differentiation, Fundamental Theorem of Calculus, curve sketching, maxima/minima, definite and indefinite integrals, applications.

Course is not applicable toward the undergraduate Mathematics major requirements.

Prerequiste: MATH 1340 FOR LEVEL UG WITH MIN. GRADE OF C- OR (MATH 1320 FOR LEVEL UG WITH MIN. GRADE OF C- AND MATH 1330 FOR LEVEL UG WITH MIN. GRADE OF C-) OR AMPT FOR MIN. SCORE OF 76 OR AMRT FOR MIN. SCORE OF 76 OR (A02 FOR MIN. SCORE OF 27 AND MTTR FOR MIN. SCORE OF 12) OR (S02 FOR MIN. SCORE OF 610 AND MTTR FOR MIN. SCORE OF 12) OR (MTCA FOR MIN. SCORE OF 15 AND MTTR FOR MIN. SCORE OF 12)

**Core Mathematics Course****Math 1860**[0-4 credit hours]*SINGLE VARIABLE CALCULUS II*Applications and techniques of integration, polar coordinates and calculus of plane curves, infinite series and Taylor series, vectors and geometry of space.

Prerequiste: MATH 1830 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1850 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1920 FOR LEVEL UG WITH MIN. GRADE OF C-

**Core Mathematics Course****Math 1890**[3 credit hours]*ELEMENTARY LINEAR ALGEBRA*Matrix algebra, systems of linear equations, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors, applications, additional topics chosen from Google's page rank algorithm, Digital Image Compression, and others.

Prerequiste: MATH 1840 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1860 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1930 FOR LEVEL UG WITH MIN. GRADE OF C-

**Core Mathematics Course****Math 1920**[4 credit hours]*HONORS CALCULUS I*A more rigorous course in differential and integral calculus of one variable. Topics include limits, differentiation, Fundamental Theorem of Calculus, Mean Value Theorem, curve sketching, maxima/minima, definite and indefinite integrals, applications. The course stresses mathematical definitions and emphasizes proofs of standard theorems in calculus.

Prerequiste: MATH 1340 FOR LEVEL UG WITH MIN. GRADE OF C- OR (MATH 1320 FOR LEVEL UG WITH MIN. GRADE OF C- AND MATH 1330 FOR LEVEL UG WITH MIN. GRADE OF C-) OR AMPT FOR MIN. SCORE OF 76 OR AMRT FOR MIN. SCORE OF 76 OR (A02 FOR MIN. SCORE OF 27 AND MTTR FOR MIN. SCORE OF 12) OR (S02 FOR MIN. SCORE OF 610 AND MTTR FOR MIN. SCORE OF 12) OR (MTCA FOR MIN. SCORE OF 15 AND MTTR FOR MIN. SCORE OF 12)

**Core Mathematics Course****Math 1930**[4 credit hours]*HONORS CALCULUS II*A more rigorous course in differential and integral calculus of one variable. Topics include applications and techniques of integration, polar coordinates and calculus of plane curves, infinite series and Taylor series, vectors and geometry of space. The course stresses mathematical definitions and emphasizes proofs of standard theorems in calculus.

Prerequiste: MATH 1920 FOR LEVEL UG WITH MIN. GRADE OF C-

**Core Mathematics Course****Math 1980**[1-4 credit hours]*TOPICS IN MATHEMATICS*Selected topics in mathematics.

**Math 2190**[3 credit hours]*FOUNDATIONS OF MATHEMATICS*This course lays the logical and set-theoretic foundations for upper level mathematics courses. Topics include: logical connectives, quantifiers; techniques of proof; set operations; functions; equivalence classes; partitions, cardinality, natural numbers, rationals, real numbers.

Prerequiste: MATH 1830 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1850 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1920 FOR LEVEL UG WITH MIN. GRADE OF C-

**Writing Across the Curriculum Course****Math 2450**[0-4 credit hours]*CALCULUS FOR ENGINEERING TECHNOLOGY I*Differential calculus of algebraic and trigonometric functions, including limits, curve sketching, motion, maxima/minima, related rates, integral calculus of algebraic functions.

Prerequiste: MATH 1340 FOR LEVEL UG WITH MIN. GRADE OF C- OR (MATH 1320 FOR LEVEL UG WITH MIN. GRADE OF C- AND MATH 1330 FOR LEVEL UG WITH MIN. GRADE OF C-) OR AMPT FOR MIN. SCORE OF 76 OR AMRT FOR MIN. SCORE OF 76 OR (A02 FOR MIN. SCORE OF 22 AND MTTR FOR MIN. SCORE OF 12) OR (S02 FOR MIN. SCORE OF 520 AND MTTR FOR MIN. SCORE OF 12) OR (MTCA FOR MIN. SCORE OF 15 AND MTTR FOR MIN. SCORE OF 12)

**Core Mathematics Course****Math 2460**[0-4 credit hours]*CALCULUS FOR ENGINEERING TECHNOLOGY II*Transcendental functions, methods of integration, applications of the integral, polar coordinates, vectors and vector operation, lines and planes, parametric equations.

Prerequiste: MATH 2450 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1850 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1920 FOR LEVEL UG WITH MIN. GRADE OF C-

**Core Mathematics Course****Math 2600**[3 credit hours]*INTRODUCTION TO STATISTICS*An introduction to descriptive and inferential statistical methods including point and interval estimation, hypothesis testing and regression.

No credit allowed if taken after MATH 3610 or 4680; credit not allowed for both MATH 2600 and 2630. Course is not applicable toward the undergraduate Mathematics major requirements.

Prerequiste: MATH 1200 FOR LEVEL UG WITH MIN. GRADE OF C- OR A02 FOR MIN. SCORE OF 20 OR S02 FOR MIN. SCORE OF 480 OR AMPT FOR MIN. SCORE OF 46 OR AMRT FOR MIN. SCORE OF 46 OR MTCA FOR MIN. SCORE OF 10

**Core Mathematics Course****Math 2620**[3 credit hours]*DISCRETE PROBABILITY*Sample spaces, events, counting techniques, probability distributions and their applications.

No credit if taken after 4680. Course is not applicable toward the undergraduate Mathematics major requirements.

Prerequiste: MATH 1180 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1200 FOR LEVEL UG WITH MIN. GRADE OF C- OR MTCA FOR MIN. SCORE OF 10 OR MTEA FOR MIN. SCORE OF 12 OR A02 FOR MIN. SCORE OF 20 OR S02 FOR MIN. SCORE OF 480 OR AMPT FOR MIN. SCORE OF 46 OR AMRT FOR MIN. SCORE OF 46

**Math 2640**[3 credit hours]*STATISTICS FOR APPLIED SCIENCE*Introduction to statistical methods. Modeling relationships between variables. Basic concepts in probability. Introduction to design of experiments, surveys and observational studies. Overview of statistical procedures used in applied science literature.

Prerequiste: MATH 1200 FOR LEVEL UG WITH MIN. GRADE OF C- OR A02 FOR MIN. SCORE OF 20 OR S02 FOR MIN. SCORE OF 480 OR AMPT FOR MIN. SCORE OF 46 OR AMRT FOR MIN. SCORE OF 46 OR MTCA FOR MIN. SCORE OF 10

**Math 2850**[4 credit hours]*ELEMENTARY MULTIVARIABLE CALCULUS*Geometry of functions of several variables, partial differentiation, multiple integrals, vector algebra and calculus (including Theorems of Green, Gauss and Stokes), and applications.

Prerequiste: MATH 1840 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1860 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1930 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 2860**[3 credit hours]*ELEMENTARY DIFFERENTIAL EQUATIONS*An introduction to the analysis and solution of ordinary differential equations with emphasis on the fundamental techniques for solving linear differential equations.

Prerequiste: MATH 2850 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 2950 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 2890**[3 credit hours]*NUMERICAL METHODS AND LINEAR ALGEBRA*Topics include: matrices, characteristic roots, solution of linear and nonlinear equations, curve fitting, integration, differentiation and numerical solution of ordinary differential equations. MATLAB is introduced and used to analyze problems. Additional topics are chosen from Google's page rank algorithm, Digital Image Compression, and others.

**Math 2950**[4 credit hours]*HONORS CALCULUS III*A more rigorous course in calculus of functions of several variable. Topics include geometry of functions of several variables, partial differentiation, multiple integrals, vector algebra and calculus (including Theorems of Green, Gauss and Stokes), and applications. The course stresses mathematical definitions and emphasizes proofs of standard theorems in calculus.

Prerequiste: MATH 1930 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 3000**[3 credit hours]*SYMBOLIC LOGIC*A study of propositional and predicate logic, the symbolic techniques used to evaluate deductive arguments. Topics may include computability, set theory, Bayesianism and other formal systems with mathematical or philosophical relevance.

Prerequiste: MATH 1180 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 3190**[3 credit hours]*INTRODUCTION TO MATHEMATICAL ANALYSIS*This course is intended to introduce students to mathematical analysis. The focus will be on learning to write clear, rigorous proofs. Topics include set theory and logic, the real number system and its topology, sequences, limits and continuity.

Prerequiste: MATH 1840 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1860 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1930 FOR LEVEL UG WITH MIN. GRADE OF C-

**Writing Across the Curriculum Course****Math 3200**[3 credit hours]*NUMBER THEORY*Divisibility, congruences, diophantine equations, numerical functions, quadratic reciprocity.

Prerequiste: MATH 2190 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 3190 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 3320**[3 credit hours]*INTRODUCTION TO ABSTRACT ALGEBRA*Sets and mappings, integers, groups, rings and applications.

Prerequiste: MATH 2190 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 3190 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 3440**[3 credit hours]*FUNDAMENTALS OF MODERN GEOMETRY I*Euclidean geometry from a modern viewpoint, constructions and transformations. Primarily for students in secondary education.

**Math 3450**[3 credit hours]*FUNDAMENTALS OF MODERN GEOMETRY II*Euclidean geometry from a modern viewpoint, constructions and transformations. Primarily for students in secondary education.

Prerequiste: MATH 3440 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 3510**[3 credit hours]*HISTORY OF MATHEMATICS*Contributions to the development of mathematics by various groups and individuals from the earliest history to the present, with special emphasis on the elementary branches: arithmetic, algebra, geometry and calculus.

**Math 3610**[3 credit hours]*STATISTICAL METHODS I*Basic probability, sampling, descriptive statistics, statistical inference, regression, correlation, analysis of variance, goodness of fit, model formulation and testing.

Prerequiste: MATH 1840 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1860 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1930 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 3190 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 3620**[3 credit hours]*STATISTICAL METHODS II*Multiple regression, analysis of covariance, standard experimental designs, contingency tables, nonparametric methods and methods for sample surveys.

Prerequiste: MATH 3610 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 3820**[3 credit hours]*HONORS ELEMENTARY DIFFERENTIAL EQUATIONS*Theory, applications and systems of ordinary differential equations. The course stresses mathematical definitions and emphasizes proofs of standard theorems in the subject.

Prerequiste: MATH 2950 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 3920**[1-3 credit hours]*JUNIOR READINGS*Selected subjects in mathematics of special interest to students and the professor.

**Math 4300**[3 credit hours]*LINEAR ALGEBRA I*Theory of vector spaces and linear transformations, including such topics as matrices, determinants, inner products, eigenvalues and eigenvectors, and rational and Jordan canonical forms.

Prerequiste: MATH 2190 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 3190 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 4310**[3 credit hours]*LINEAR ALGEBRA II*Hermitian and normal operators, multilinear forms, spectral theorem and other topics.

Prerequiste: MATH 4300 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 4330**[3 credit hours]*ABSTRACT ALGEBRA I*Arithmetic of the integers, unique factorization and modular arithmetic; group theory including normal subgroups, factor groups, cyclic groups, permutations, homomorphisms, the isomorphism theorems, abelian groups and p-groups.

**Math 4340**[3 credit hours]*ABSTRACT ALGEBRA II*Ring theory including integral domains, field of quotients, homomorphisms, ideals, Euclidean domains, polynomial rings, vector spaces, roots of polynomials and field extensions.

Prerequiste: MATH 4330 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 4350**[3 credit hours]*APPLIED LINEAR ALGEBRA*Matrices, systems of equations, vector spaces, linear transformations, determinants, eigenvalues and eigenvectors, singular value decomposition, pseudoinverses, rank, numerical methods and applications to various areas, e.g., the Google Matrix or Digital Image Compression or others.

Prerequiste: MATH 1890 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 2890 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 4380**[3 credit hours]*DISCRETE STRUCTURES AND ANALYSIS OF ALGORITHMS*Discrete mathematical structures for applications in computer science such as graph theory, combinatorics, and groups theory, asymptotics, recurrence relations and analysis of algorithms.

Prerequiste: MATH 3320 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 4330 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 4450**[3 credit hours]*INTRODUCTION TO TOPOLOGY I*Metric spaces, topological spaces, continuous maps, bases and subbases, closure and interior operators, products, subspaces, sums, quotients, separation axioms, compactness and local compactness.

**Math 4460**[3 credit hours]*INTRODUCTION TO TOPOLOGY II*Connectedness and local connectedness, convergence, metrization, function spaces. The fundamental groups and its properties, covering spaces, classical applications, e.g. Jordan Curve Theorem, Fundamental Theorem of Algebra, Brouwer's Fixed Point Theorem.

Prerequiste: (MATH 4450 FOR LEVEL UG WITH MIN. GRADE OF C- AND MATH 3320 FOR LEVEL UG WITH MIN. GRADE OF C-) OR (MATH 4450 FOR LEVEL UG WITH MIN. GRADE OF C- AND MATH 4330 FOR LEVEL UG WITH MIN. GRADE OF C-)

**Math 4540**[3 credit hours]*CLASSICAL DIFFERENTIAL GEOMETRY I*Smooth curves in Euclidean space including the Frenet formulae. Immersed surfaces with the Gauss map, principal curvatures and the fundamental forms. Special surfaces including ruled surfaces and minimal surfaces. Intrinsic Geometry including the Gauss Theorem Egregium.

Prerequiste: MATH 2860 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 3820 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 4550**[3 credit hours]*CLASSICAL DIFFERENTIAL GEOMETRY II*Tensors, vector fields, and the Cartan approach to surface theory, Bonnet's Theorem and the construction of surfaces via solutions of the Gauss Equation. Geodesics parallel transport, and Jacobi Fields. Theorems of a global nature such as Hilbert's Theorem or the Theorem of Hopf-Rinow.

Prerequiste: MATH 4540 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 4600**[3 credit hours]*APPLICATIONS OF STATISTICS I*Real data applications of statistical methods. Emphasis is placed on exploratory data analysis and the use of computing facilities to analyze data and produce statistical reports. Statistical packages used include: MINITAB, SAS, and/or S-PLUS; programming is performed in C or Fortran.

**Math 4610**[3 credit hours]*APPLICATIONS OF STATISTICS II*Continuation of Applications of Statistics I.

Prerequiste: MATH 4600 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 4620**[3 credit hours]*THEORY OF INTEREST*This course covers the measurement of interest, certain annuities, yield rates, amortization and sinking funds, bonds and other securities and application of interest theory.

**Math 4640**[3 credit hours]*STATISTICAL COMPUTING*Error analysis of statistical algorithms. Numerical linear algebra for linear models. Approximation methods for distribution function probabilities and quantiles. Uniform and non-uniform random number generation. Introduction to simulation methods.

**Math 4680**[3 credit hours]*INTRODUCTION TO THEORY OF PROBABILITY*Probability spaces, random variables, probability distributions, moments and moment generating functions, limit theorems, transformations and sampling distributions.

Prerequiste: MATH 2850 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 2950 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 4690**[3 credit hours]*INTRODUCTION TO MATHEMATICAL STATISTICS*Sampling distributions, point and interval estimation, hypothesis testing, regression and analysis of variance.

Prerequiste: MATH 4680 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 4710**[3 credit hours]*METHODS OF NUMERICAL ANALYSIS I*Floating point arithmetic; polynomial interpolation; numerical solution of nonlinear equations; Newton's method. Likely topics include: numerical differentiation and integration; solving systems of linear equations; Gaussian elimination; LU decomposition; Gauss-Seidel method.

Prerequiste: MATH 2860 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 3820 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 4720**[3 credit hours]*METHODS OF NUMERICAL ANALYSIS II*Likely topics include: Computation of eigenvalues and eigenvectors; solving systems of nonlinear equations; least squares approximations; rational approximations; cubic splines; fast Fourier transforms; numerical solutions to initial value problems; ordinary and partial differential equations.

Prerequiste: MATH 4710 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 4740**[3 credit hours]*ADVANCED APPLIED MATHEMATICS I*Series and numerical solutions to ordinary differential equations, special functions, orthogonal functions, Sturm-Liouville problems, self-adjointness, vector analysis.

Prerequiste: MATH 2860 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 3820 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 4750**[3 credit hours]*ADVANCED APPLIED MATHEMATICS II*Continuation of vector analysis, introduction to complex analysis, partial differential equations, Fourier series and integrals.

Prerequiste: MATH 4740 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 4760**[3 credit hours]*ACTUARIAL MATHEMATICS I*Survival distributions and life tables, life insurance, life annuities, benefit premiums and reserves and multiple life functions are some topics covered in this course.

Prerequiste: MATH 4680 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 4770**[3 credit hours]*ACTUARIAL MATHEMATICS II*Continuation of Actuarial Mathematics I. Multiple decrement models, collective risk models and applications of risk theory.

Prerequiste: MATH 4760 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 4800**[3 credit hours]*ORDINARY DIFFERENTIAL EQUATIONS*Modern theory of differential equations; transforms and matrix methods; existence theorems and series solutions; and other selected topics.

**Math 4810**[3 credit hours]*PARTIAL DIFFERENTIAL EQUATIONS*First and second order equations; numerical methods; separation of variables; solutions of heat and wave equations using eigenfunction techniques; and other selected topics.

**Math 4820**[3 credit hours]*INTRODUCTION TO REAL ANALYSIS I*The real number system; continuity and differentiability of functions; convergence of sequences and series; applications.

**Math 4830**[3 credit hours]*INTRODUCTION TO REAL ANALYSIS II*Riemann Integral; limits of functions; elementary metric space theory including compactness, connectedness and completeness. Optional topics include differentiable functions on Rn; the Implicit and Inverse Function Theorems.

Prerequiste: MATH 4820 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 4860**[3 credit hours]*CALCULUS OF VARIATIONS AND OPTIMAL CONTROL I*Conditions for an extrema (Euler's equations, Erdman corner conditions, conditions of Legendre, Jacobi, and Weierstrass, fields of extremals, Hilbert's invariant integral); Raleigh-Ritz method; isoperimetric problems; Lagrange, Mayer-Bolza problems. Recommended: MATH 4820.

Prerequiste: MATH 1890 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 2890 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 4870**[3 credit hours]*CALCULUS OF VARIATIONS AND OPTIMAL CONTROL II*Pontryagin's maximum principle; necessary and sufficient conditions for optimal control, controllability, time optimal control, existence of optimal controls, relationship to the calculus of variations.

Prerequiste: MATH 4860 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 4880**[3 credit hours]*COMPLEX VARIABLES*Analytic functions; Cauchy's theorem; Taylor and Laurent series; residues; contour integrals; conformal mappings, analytic continuation and applications.

Prerequiste: MATH 2860 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 3860 FOR LEVEL UG WITH MIN. GRADE OF C-

**Math 4900**[1-3 credit hours]*SENIOR SEMINAR*Seminar on a topic not usually covered in a course. Library research and paper to be expected.

**Math 4920**[1-3 credit hours]*SENIOR READINGS*Selected subjects in mathematics of special interest to students and the professor. (By arrangement with professor and student.)

**Math 4960**[1-3 credit hours]*ACTUARIAL SCIENCE PROBLEM SEMINAR*The primary activity will be student solution and presentation of problems of a type given on actuarial exams.