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### 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 0910**[4 hours]*ELEMENTARY ALGEBRA I*This course covers a review of operations with whole numbers, fractions, decimals, ratios and percents. Also covered are integer operations, variables, algebraic expressions, graphs and solving linear equations. Problem solving techniques are emphasized.

No credit toward graduation. Grades do not apply to student's GPA.

**Math 0950**[4 hours]*ELEMENTARY ALGEBRA II*This course introduces the student to functions, solving systems of linear equations, graphing, polynomials, rational and quadratic functions, rational numbers and mathematics modeling. Problem solving techniques are emphasized.

No credit toward graduation. Grades do not apply to student's GPA.

Prerequiste: MATH 0910 FOR LEVEL UG WITH MIN. GRADE OF D- OR MTEA FOR MIN. SCORE OF 05

**Math 0980**[4 hours]*INTERMEDIATE ALGEBRA*Review of algebra, linear and quadratic equations, graphs, exponents and radicals, exponential and log functions, simultaneous equations.

No credit toward graduation. Course is not applicable toward the undergraduate major in mathematics.

Prerequiste: MATH 0950 FOR LEVEL UG WITH MIN. GRADE OF D- OR MTEA FOR MIN. SCORE OF 10

**Math 0990**[1-4 hours]*INDEPENDENT STUDY*Course for students needing to complete only a portion of a developmental math class (MATH 0900 - 0980).

**Math 1010**[3 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 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 hours]*MATH MODELING STUDY SKILLS*A course to provide the study skills needed to college mathematics. Students learn and apply skills such as reading textbooks, note-taking, and analyzing tests.

**Math 1200**[4 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. Prerequisite: Satisfactory placement test score or satisfactory ACT score. Math core course.

**Core Mathematics Course****Math 1210**[3 hours]*MATHEMATICS FOR EDUCATION MAJORS I*Principles of elementary number theory, base systems, development of the rational numbers and problem solving techniques.

Course is not applicable toward the undergraduate Mathematics major requirements.

Prerequiste: MATH 0980 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 1200 FOR LEVEL UG WITH MIN. GRADE OF D- OR MTCA FOR MIN. SCORE OF 10 OR MTEA FOR MIN. SCORE OF 12 OR ACT MATH FOR MIN. SCORE OF 20 OR SAT MATH FOR MIN. SCORE OF 480 OR AMPT FOR MIN. SCORE OF 046 OR AMRT FOR MIN. SCORE OF 046

**Core Mathematics Course****Math 1220**[3 hours]*MATHEMATICS FOR EDUCATION MAJORS II*Development of the 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 D-

**Core Mathematics Course****Math 1260**[3 hours]*CALCULUS FOR BUSINESS WITH APPLICATIONS I*Equations and their graphs, linear systems, vectors and matrices, introduction to linear optimization, exponentials and logs, elementary probability, limits, functions, introductions to differential calculus.

Course is not applicable toward the undergraduate Mathematics major requirements.

Prerequiste: MATH 0980 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 1200 FOR LEVEL UG WITH MIN. GRADE OF D- OR MTCA FOR MIN. SCORE OF 10 OR MTEA FOR MIN. SCORE OF 12 OR ACT MATH FOR MIN. SCORE OF 20 OR SAT MATH FOR MIN. SCORE OF 480

**Core Mathematics Course****Math 1320**[3 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 0980 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 1200 FOR LEVEL UG WITH MIN. GRADE OF D- OR MTCA FOR MIN. SCORE OF 10 OR MTEA FOR MIN. SCORE OF 12 OR ACT MATH FOR MIN. SCORE OF 20 OR SAT MATH FOR MIN. SCORE OF 480 OR AMPT FOR MIN. SCORE OF 046 OR AMRT FOR MIN. SCORE OF 046

**Core Mathematics Course****Math 1330**[3 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 0980 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 1200 FOR LEVEL UG WITH MIN. GRADE OF D- OR MTCA FOR MIN. SCORE OF 10 OR MTEA FOR MIN. SCORE OF 12 OR ACT MATH FOR MIN. SCORE OF 20 OR SAT MATH FOR MIN. SCORE OF 480 OR AMPT FOR MIN. SCORE OF 061 OR AMRT FOR MIN. SCORE OF 061

**Core Mathematics Course****Math 1340**[4 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: MATH 0980 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 1200 FOR LEVEL UG WITH MIN. GRADE OF D- OR ACT MATH FOR MIN. SCORE OF 20 OR AMPT FOR MIN. SCORE OF 068 OR AMRT FOR MIN. SCORE OF 068

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

Prerequiste: MATH 1320 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 1260 FOR LEVEL UG WITH MIN. GRADE OF D- OR AMPT FOR MIN. SCORE OF 061 OR AMRT FOR MIN. SCORE OF 061

**Math 1750**[4 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 D- OR MATH 1340 FOR LEVEL UG WITH MIN. GRADE OF D- OR MTCA FOR MIN. SCORE OF 12 OR ACT MATH FOR MIN. SCORE OF 22 OR SAT MATH FOR MIN. SCORE OF 520 OR AMPT FOR MIN. SCORE OF 061 OR AMRT FOR MIN. SCORE OF 061

**Core Mathematics Course****Math 1760**[3 hours]*CALCULUS FOR THE LIFE SCIENCES WITH APPLICATIONS II*Indefinite and definite integrals, probability, functions of several variables, least squares, differential equations.

Course is not applicable toward the undergraduate Mathematics major requirements.

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

**Core Mathematics Course****Math 1780**[1 hours]*INTRODUCTION TO MAPLE*Brief review of the computer algebra system Maple; graphing; simplifying algebraic expressions; finding solutions of equations symbolically, graphically and numerically; various typical problems from precalculus and beginning calculus.

**Math 1830**[4 hours]*CALCULUS I FOR MATHEMATICIANS, SCIENTISTS AND EDUCATORS*Limits of sequences and functions, derivatives, Mean Value Theorem, curve sketching, definite and indefinite integral, Fundamental Theorem of Calculus. Of interest to students requiring a conceptual understanding of calculus. Not for major credit.

Prerequiste: MATH 1340 FOR LEVEL UG WITH MIN. GRADE OF D- OR (MATH 1320 FOR LEVEL UG WITH MIN. GRADE OF D- AND MATH 1330 FOR LEVEL UG WITH MIN. GRADE OF D-) OR AMPT FOR MIN. SCORE OF 076 OR AMRT FOR MIN. SCORE OF 076

**Core Mathematics Course****Math 1840**[4 hours]*CALCULUS II FOR MATHEMATICIANS, SCIENTISTS AND EDUCATORS*Techniques of integration, polar coordinates and calculus or plane curves, infinite series and Taylor series. Of interest to students requiring a conceptual understanding of calculus.

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

**Core Mathematics Course****Math 1850**[4 hours]*SINGLE VARIABLE CALCULUS I*Limits, differentiation, Fundamental Theorem of Calculus, Mean Value Theorem, 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 D- OR MATH 1320 FOR LEVEL UG WITH MIN. GRADE OF D- AND MATH 1330 FOR LEVEL UG WITH MIN. GRADE OF D- OR AMPT FOR MIN. SCORE OF 076 OR AMRT FOR MIN. SCORE OF 076

**Core Mathematics Course****Math 1860**[4 hours]*SINGLE VARIABLE CALCULUS II*Inverse functions, techniques and applications of integration, polar coordinates, sequences and series.

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

**Core Mathematics Course****Math 1890**[3 hours]*ELEMENTARY LINEAR ALGEBRA*Matrix algebra, systems of linear equations, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors, and applications.

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

**Core Mathematics Course****Math 1920**[4 hours]*HONORS CALCULUS I*Theory and applications of derivatives and integrals of a function of one variable.

**Core Mathematics Course****Math 1930**[4 hours]*HONORS CALCULUS II*Theory and applications of derivatives and integrals of a function of one variable.

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

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

**Math 2190**[3 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 D- OR MATH 1850 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 1920 FOR LEVEL UG WITH MIN. GRADE OF D-

**Writing Across the Curriculum Course****Math 2450**[4 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: AMPT FOR MIN. SCORE OF 076 OR AMRT FOR MIN. SCORE OF 076

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

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

**Core Mathematics Course****Math 2600**[3 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 0980 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 1180 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 1200 FOR LEVEL UG WITH MIN. GRADE OF D- OR MTCA FOR MIN. SCORE OF 10 OR MTEA FOR MIN. SCORE OF 12 OR ACT MATH FOR MIN. SCORE OF 20 OR SAT MATH FOR MIN. SCORE OF 480 OR AMPT FOR MIN. SCORE OF 046 OR AMRT FOR MIN. SCORE OF 046

**Core Mathematics Course****Math 2620**[3 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 0980 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 1180 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 1200 FOR LEVEL UG WITH MIN. GRADE OF D- OR MTCA FOR MIN. SCORE OF 10 OR MTEA FOR MIN. SCORE OF 12 OR ACT MATH FOR MIN. SCORE OF 20 OR SAT MATH FOR MIN. SCORE OF 480

**Math 2630**[3 hours]*STATISTICS FOR BUSINESS AND ECONOMICS*An introduction to descriptive and inferential statistical methods, including numerical and graphical data description, basic probability concepts and distributions, point and interval estimation and hypothesis testing. Credit not allowed for both MATH 2600 & 2630.

Course is not applicable toward the undergraduate Mathematics major requirements.

Prerequiste: MATH 1270 FOR LEVEL UG WITH MIN. GRADE OF D-

**Math 2640**[3 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 1750 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 1830 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 1850 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 1920 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 2450 FOR LEVEL UG WITH MIN. GRADE OF D-

**Math 2850**[4 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 D- OR MATH 1860 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 1930 FOR LEVEL UG WITH MIN. GRADE OF D-

**Math 2860**[3 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 D-

**Math 2890**[3 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.

**Math 2950**[4 hours]*HONORS CALCULUS III*Theory and applications of the calculus of functions of two or more variables. The fundamental theorems of vector calculus.

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

**Math 3000**[3 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 D-

**Math 3190**[3 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 D- OR MATH 1860 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 1930 FOR LEVEL UG WITH MIN. GRADE OF D-

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

Prerequiste: MATH 3190 FOR LEVEL UG WITH MIN. GRADE OF D-

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

Prerequiste: MATH 3190 FOR LEVEL UG WITH MIN. GRADE OF D-

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

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

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

**Math 3510**[3 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 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 D- OR MATH 1860 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 1930 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 3190 FOR LEVEL UG WITH MIN. GRADE OF D-

**Math 3620**[3 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 D-

**Math 3820**[3 hours]*HONORS ELEMENTARY DIFFERENTIAL EQUATIONS*Theory, applications and systems of ordinary differential equations.

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

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

**Math 4300**[3 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 3190 FOR LEVEL UG WITH MIN. GRADE OF D-

**Math 4310**[3 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 D-

**Math 4330**[3 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.

Prerequiste: MATH 3190 FOR LEVEL UG WITH MIN. GRADE OF D-

**Math 4340**[3 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 D-

**Math 4350**[3 hours]*APPLIED LINEAR ALGEBRA*Matrices, systems of equations, vector spaces, linear transformations, determinants, eigenvalues and eigenvectors, generalized inverses, rank, numerical methods and applications to various areas of science.

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

**Math 4380**[3 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 D- OR MATH 4330 FOR LEVEL UG WITH MIN. GRADE OF D-

**Math 4450**[3 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.

Prerequiste: MATH 3190 FOR LEVEL UG WITH MIN. GRADE OF D-

**Math 4460**[3 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 D- OR MATH 3320 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 4330 FOR LEVEL UG WITH MIN. GRADE OF D-

**Math 4540**[3 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 D- OR MATH 3860 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 3820 FOR LEVEL UG WITH MIN. GRADE OF D-

**Math 4550**[3 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 D-

**Math 4600**[3 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 hours]*APPLICATIONS OF STATISTICS II*Continuation of Applications of Statistics I.

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

**Math 4620**[3 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 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 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 3190 FOR LEVEL UG WITH MIN. GRADE OF D- AND MATH 4350 FOR LEVEL UG WITH MIN. GRADE OF D-)

**Math 4690**[3 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 D-

**Math 4710**[3 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 D- OR MATH 3860 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 3820 FOR LEVEL UG WITH MIN. GRADE OF D-

**Math 4720**[3 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 D-

**Math 4740**[3 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 D- OR MATH 3860 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 3820 FOR LEVEL UG WITH MIN. GRADE OF D-

**Math 4750**[3 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 D-

**Math 4760**[3 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 D-

**Math 4770**[3 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 D-

**Math 4780**[3 hours]*ADVANCED CALCULUS*Extrema for functions of one or more variables, Lagrange multipliers, indeterminate forms, inverse and implicit function theorems, uniform convergences, power series, transformations, Jacobians, multiple integrals.

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

**Math 4800**[3 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 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 hours]*INTRODUCTION TO REAL ANALYSIS I*A rigorous treatment of the Calculus in one and several variables. Topics to include: the real number system; sequences and series; elementary metric space theory including compactness, connectedness and completeness; the Riemann Integral.

Prerequiste: MATH 3190 FOR LEVEL UG WITH MIN. GRADE OF D-

**Math 4830**[3 hours]*INTRODUCTION TO REAL ANALYSIS II*Differentiable functions on Rn; the Implicit and Inverse Function Theorems; sequences and series of continuous functions; Stone-Weierstrass Theorem; Arzela-Ascoli Theorem; introduction to measure theory; Lebesgue integration; the Lebesque Dominated Convergence Theorem.

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

**Math 4860**[3 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 D-

**Math 4870**[3 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 D-

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

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

**Math 4920**[1-3 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 hours]*ACTUARIAL SCIENCE PROBLEM SEMINAR*The primary activity will be student solution and presentation of problems of a type given on actuarial exams.