Courses: Mathematics (MATH)College: Natural Sciences & Mathematics. Any TCCN equivalents are indicated in square brackets [ ].

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1 Courses: Mathematics (MATH)College: Natural Sciences & Mathematics Any TCCN equivalents are indicated in square brackets [ ]. MATH 1300: Fundamentals of Mathematics Cr. 3. (3-0). A survey of precollege algebra. Topics include signed numbers, operations with algebraic expressions, first-degree equations and inequalities in one variable, factoring, the Cartesian coordinate system, systems of first-degree equations in two variables solved by graphical and algebraic means, exponents and radicals, an introduction to quadratic equations, and stated problems. This course may not be used to satisfy any degree requirements. MATH 1310: College Algebra [TCCN MATH 1314] Cr. 3. (3-0). Prerequisite: satisfactory score on placement examination. Students with credit in MATH 1330 or MATH 1431 will not be allowed to enroll or receive credit in MATH Quadratic equations, inequalities, logarithmic and exponential functions, graphs, elements of theory of equations, systems of equations. MATH 1311: Elementary Mathematical Modeling (formerly MATH 1315) Cr. 3. (3-0). Prerequisites: two credits of high school algebra, one credit of geometry and satisfactory score on the placement examination. May not be applied to a major or minor in Mathematics. Students may not receive credit for both MATH 1310 and MATH Functions, graphs, differences and rates of change, mathematical models, mathematics of finance, optimization, and mathematics of decision-making. MATH 1312: Introduction to Mathematical Reasoning Cr. 3. (3-0). Prerequisite: credit for or placement out of MATH 1310 or MATH 1311, May not apply toward a degree from the College of Natural Sciences and Mathematics. Principles of logic and proof, set theory, formal and informal geometry. MATH 1313: Finite Mathematics with Applications [TCCN MATH 1324]

2 Cr. 3. (3-0). Prerequisite: credit for or placement out of MATH Students with prior credit for MATH 2331 (formerly 2431) or INDE 2331 will not receive credit for MATH May not apply to a major or minor in mathematics. Systems of linear equations, introduction to linear programming, mathematics of finance, topics in probability and statistics. MATH 1314: Calculus for Business and the Life Sciences [TCCN MATH 1325] Cr. 3. (3-0). Prerequisite: credit for or placement out of MATH Students with prior credit for MATH 1431 will not be permitted to enroll in or receive credit for MATH Curve sketching and graphical analysis, differentiation and integration of elementary functions, topics in functions of several variables, applications in business and the natural and social sciences. MATH 1330: Precalculus [TCCN MATH 2312 or MATH 2412] Cr. 3. (3-0). Prerequisite: credit for or placement out of MATH Students with prior credit in MATH 1432 may not receive credit for MATH Functions, graphs, trigonometry, and analytic geometry. MATH 1397: Topics in Mathematics Cr. 3. (3-0). Prerequisite: consent of instructor. Restricted to nonadvanced undergraduates. May be repeated with approval of department chair. MATH 1431: Calculus I [TCCN MATH 2413] Cr. 4. (4-0). Prerequisite: MATH Calculus of rational functions, limits, derivatives, applications of the derivative, antiderivatives, the definite integral with applications, mean value theorem, fundamental theorem of calculus, and numerical integration. MATH 1432: Calculus II [TCCN MATH 2414] Cr. 4. (4-0). Prerequisite: MATH Calculus of transcendental functions: additional techniques and applications of integration, indeterminate forms, improper integrals, Taylor's formula, and infinite series.

3 MATH 1450:1451: Accelerated Calculus Cr. 4 per semester. (3-2). Prerequisites: At least one semester of advanced placement high school calculus and placement out of MATH Credit may not be received for both MATH 1450 and MATH Students with credit in MATH 1451 may not enroll in or receive credit for either MATH 1432 or MATH An accelerated calculus sequence. MATH 1450 will include topics normally covered in MATH MATH 1451 will include topics normally covered in MATH 1432 and MATH MATH 2303: Concepts in Algebra Cr. 3. (3-0). Prerequisite: MATH 1312 or MATH May not apply toward a major or minor in mathematics. Mathematical systems: classical and abstract algebra, systems of numeration, and basicnumber theory. MATH 2311: Introduction to Probability and Statistics [TCCN MATH 1342] Cr. 3. (3-0). Prerequisite: MATH 1310 or MATH 1311 May not apply toward a degree in mathematics. Students with credit for MATH 3338 or MATH 3339 may not enroll in or receive credit for MATH Probability, correct probabilistic reasoning, distributions, graphical and descriptive methods, sampling estimation, hypotheses and statistical inference. MATH 2331: Linear Algebra [TCCN MATH 2318] Cr. 3. (3-0). Prerequisite: credit for or concurrent enrollment in MATH Solutions of systems of linear equations, matrices, vector spaces, linear transformations, similarity eigenvalues and eigenvectors. MATH 2433: Calculus III [TCCN MATH 2415] Cr. 4. (4-0). Prerequisite: MATH Calculus of functions of several variables: calculus of vector-valued functions, partial differentiation, multiple integrals. MATH 3303: Elements of Algebra and Number Theory Cr. 3. (3-0). Prerequisite: MATH 1312 or MATH 1313 or consent of instructor. May not apply toward a major or minor in mathematics.

4 May not satisfy mathematics requirements in the College of Natural Sciences and Mathematics. Topics in number theory and abstract algebra. MATH 3304: Elements of Mathematical Analysis Cr. 3. (3-0). Prerequisite: MATH 1312 or MATH 1313 or consent of instructor. May not apply toward a major or minor in mathematics. May not satisfy mathematics requirements in the College of Natural Sciences and Mathematics. Basic concepts of calculus including limits, derivatives, and integrals; selected applications. MATH 3305: Formal and Informal Geometry Cr. 3. (3-0). Prerequisite: MATH 1312 or MATH 1313 or consent of the instructor. May not apply toward a major or minor in mathematics. May not satisfy mathematics requirements in the College of Natural Sciences and Mathematics. Review of ruler and compass construction, formal axiomatic systems, finite geometries. Euclid's Elements, non-euclidean geometry, analytic and transformational geometry. MATH 3306: Problem Solving in Mathematics Cr. 3. (3-0). Prerequisite: MATH 1312 or MATH 1313 or consent of instructor. May not apply toward a major or minor in mathematics. May not satisfy mathematics requirements in the College of Natural Sciences and Mathematics. Strategies for solving problems in mathematics: reduction to smaller problems; analogy in mathematics; conjecture and proof; the processes of abstraction, generalization, and specialization. MATH 3307: Statistical Applications Cr. 3. (3-0). Prerequisite: MATH 1312 or MATH 1313 or consent of instructor. May not apply toward a major or minor in mathematics. May not satisfy mathematics requirements in the College of Natural Sciences and Mathematics. Basic probability, sampling, statistical prediction, and process control. MATH 3310: History of Mathematics Cr. 3. (3-0). Prerequisite: MATH May not apply toward a major or minor in mathematics. May not satisfy mathematics requirements in the College of Natural Sciences and Mathematics. A survey of the history of mathematics from Euclid to Dedekind

5 focusing on the development of the real number system and its relation to the Euclidean line. MATH 3311: Functions and Modeling Cr. 3. (3-0). Prerequisites: MATH 1432 and CUIN Ideas and activities that reinforce interrelationships among topics in mathematics, especially as taught in secondary education. Recurrent themes will be the use of transformations, data analysis methods, and technology. MATH 3321: Engineering Mathematics Cr. 3. (3-0). Prerequisites: MATH Students may not receive credit for both MATH 3321 and MATH First order ordinary differential equations and initial value problems; higher order differential equations; vector spaces, matrices, determinants, eigenvectors and eigenvalues; applications to systems of first order equations; Laplace transforms. MATH 3330: Abstract Algebra Cr. 3. (3-0). Prerequisite: MATH 2331 (formerly 2431). Introduction to groups, rings, and fields. MATH 3331: Differential Equations Cr. 3. (3-0). Prerequisites: MATH 2433 and MATH 2331 (formerly 2431). Systems of ordinary differential equations; existence, uniqueness and stability of solutions; initial value problems; bifurcation theory; Jordan form; higher order equations; Laplace transforms. Computer assignments are required. MATH 3333: Intermediate Analysis Cr. 3. (3-0). Prerequisite: MATH Properties of real number system, properties of continuous functions, and sequences of functions. MATH 3334: Advanced Multivariable Calculus Cr. 3. (3-0). Prerequisite: MATH Topology of n-space; continuity, uniform continuity and uniform convergence; extremal problems; Taylor's theorem for multivariate functions; multiple integrals; transformations and their derivatives; implicit functions. MATH 3335: Vector Analysis

6 Cr. 3. (3-0). Prerequisite: MATH 2433 or approval of department chair. Algebra and calculus of vectors, vector differential operators, Green's and Stokes' theorems, curvilinear coordinates, tensors. MATH 3336: Discrete Mathematics Cr. 3. (3-0). Prerequisite: MATH 2331 (formerly 2431) or equivalent. Topics selected from logic, set theory, combinatorics, and graph theory. MATH 3338: Probability Cr. 3. (3-0). Prerequisite: MATH Students with credit for MATH 3341 may not receive credit for MATH Sample spaces, events, and probabilities, random variables and distributions, expectations, variances and covariance's; basic discrete and continuous distributions; the central limit theorem. MATH 3339: Statistics for the Sciences Cr. 3. (3-0). Prerequisite: MATH Graphical and descriptive methods in statistics, probability, random variables and distributions, sampling, estimation, hypothesis testing, regression, analysis of variance, exploratory and diagnostic methods, statistical computing. MATH 3340: Introduction to Fixed Income Mathematics Cr. 3. (3-0). Prerequisite: MATH Bonds and bank certificates of deposit, arbitrage, bond and annuity valuation, total return, market risk, risk management, term structure construction, liability management. MATH 3341: Applied Probability Cr. 3. (3-0). Prerequisite: MATH Students with credit for MATH 3341 may not receive credit for MATH Random variables and their distributions, expectation, relationships among important distributions, survival and hazard functions, joint distributions, marginal and conditional distributions, covariance, moment generating functions, the Central Limit Theorem. Applications to financial mathematics. MATH 3363: Introduction to Partial Differential Equations Cr. 3. (3-0). Prerequisites: MATH 2433 and either MATH 3321 or MATH Partial differential equations and boundary value

7 problems, Fourier series, the heat equation, vibrations of continuous systems, the potential equation, spectral methods. MATH 3364: Introduction to Complex Analysis Cr. 3. (3-0). Prerequisite: MATH The complex number system, analytic functions, the Cauchy integral theorem, series representation, residue theory, and conformal mapping. MATH 3379: Introduction to Higher Geometry Cr. 3. (3-0). Prerequisite: MATH 1432 or approval of department chair. Synthetic and algebraic geometry; harmonic division, cross ratio; groups of projective transformations. MATH 3397: Selected Topics in Mathematics Cr. 3. (3-0). Prerequisite: consent of instructor. May be repeated with approval of department chair. MATH : Senior Research Project Cr. 3. per semester. Prerequisite: approval of department chair. Directed research project culminating in a departmentally approved report. MATH : Senior Honors Thesis Cr. 3 per semester. Prerequisite: approval of department chair. MATH 4198:4298:4398:4498: Special Problems Cr. 1-4 per semester or more by concurrent enrollment. Prerequisite: approval of department chair. MATH 4315: Graph Theory with Applications Cr. 3. (3-0). Prerequisite: MATH 3330 or MATH Introduction to basic concepts, results, methods, and applications of graph theory. MATH 4320: Introduction to Stochastic Processes Cr. 3. (3-0). Prerequisite: MATH Generating functions, discrete and continuous versions of Poisson and Markov processes, branching and renewal processes, introduction to stochastic calculus and diffusion. 4331;4332: Introduction to Real Analysis

8 Cr. 3 per semester. (3-0). Prerequisite: MATH 3334 or consent of instructor. Properties of continuous functions, partial differentiation, line integrals, improper integrals, infinite series, and Stieltjes integrals. MATH 4333: Advanced Abstract Algebra Cr. 3. (3-0). Prerequisites: MATH 3330 and consent of instructor. Direct products, Sylow theory, ideals, extensions of rings, factorization of ring elements, modules, and Galois theory. MATH 4335;4336: Partial Differential Equations Cr. 3 per semester. (3-0). Prerequisite: MATH Existence and uniqueness for Cauchy and Dirichlet problems; classification of equations; potential-theoretic methods; other topics at the discretion of the instructor. MATH 4337: Topology Cr. 3. (3-0). Prerequisite: MATH 3333 or MATH 3334 or consent of instructor. Metric spaces, completeness, general topological spaces, continuity, compactness, connectedness. MATH 4340: Nonlinear Dynamics and Chaos Cr. 3. (3-0). Prerequisite: MATH 3331 or consent of instructor. Dynamical systems associated with one-dimensional maps of the interval and the circle; elementary bifurcation theory; modeling of real phenomena. MATH 4350;4351: Differential Geometry Cr. 3 per semester. (3-0). Prerequisites: MATH 2433 and MATH 2331 (formerly 2431) or equivalent. Frenet frames, metric tensors, Christoffel symbols, Gaussian curvature, differential forms, moving frames, Euler characteristics, the Gauss-Bonnet theorem and the Euler-Poincare index theorem. MATH 4355: Mathematics of Signal Representation Cr. 3. (3-0). Prerequisites: MATH 2433 and either MATH 2331 (formerly 2431) or MATH Fourier series of real-valued functions, the integral Fourier transform, time-invariant linear systems, band-limited and time-limited signals, filtering and its connection with Fourier inversion, Shannon's sampling theorem, discrete and fast Fourier transforms, relationship with signal processing.

9 MATH 4360: Integral Equations Cr. 3. (3-0). Prerequisites: MATH 3331 and MATH Relation to differential equations; Fredholm, Hilbert-Schmidt, and Volterra type equations; special devices and approximation methods. MATH 4362: Theory of Ordinary Differential Equations Cr. 3. (3-0). Prerequisites: MATH 3331 and MATH Existence, uniqueness, and continuity of solutions of single equations and systems of equations; other topics at the discretion of the instructor. MATH 4364;4365: Numerical Analysis Cr. 3 per semester. (3-0). Prerequisites: MATH 2331 (formerly 2431), MATH 3331; COSC 1301 or COSC 2101 or equivalent; or consent of instructor. Topics selected from numerical linear algebra, approximation of functions, numerical integration and differentiation, interpolation, approximate solutions of ordinary and partial differential equations, Fourier methods, optimization. MATH 4370: Mathematics of Financial Derivatives Cr. 3. (3-0). Prerequisites: MATH 2433 and either MATH 3338 or MATH Stochastic processes for modeling the dynamics of returns of financial instruments and commodities. Use of Ito's calculus and Black-Scholes Model to value contingent claims and real options in capital budgeting. MATH 4377: Advanced Linear Algebra I Cr. 3. (3-0). Prerequisites: MATH 2331 and a minimum of three semester hours of 3000-level mathematics. Linear systems of equations, matrices, determinants, vector spaces and linear transformations, eigenvalues and eigenvectors. 4378: Advanced Linear Algebra II Cr. 3. (3-0). Prerequisite: MATH Similarity of matrices, diagonalization, Hermitian and positive definite matrices, normal matrices, and canonical forms, with applications. MATH 4380: A Mathematical Introduction to Options Cr. 3. (3-0). Prerequisites: MATH 2433 and MATH Arbitragefree pricing, stock price dynamics, call-put parity, Black-Scholes formula, hedging, pricing of European and American options.

10 MATH 4383: Number Theory Cr. 3. (3-0). Prerequisite: MATH 3330 or consent of instructor. Perfect numbers, quadratic reciprocity, quadratic residues, algebraic numbers, and continued fractions. MATH 4385;4386: Mathematical Statistics Cr. 3 per semester. (3-0). Prerequisite: MATH 3339 or equivalent. Linear models-estimation, testing and application to designs of experiments, nonparametric statistical models. MATH 4389: Survey of Undergraduate Mathematics Cr. 3. (3-0). Prerequisites: MATH 3330, 3331, 3333, and three hours of 4000-level Mathematics. A review of some of the most important topics in the undergraduate mathematics curriculum. MATH 4390: Applied Mathematics Seminar Cr. 3. (3-0). Prerequisite: completion of 27 advanced semester hours in the Applied Analysis Option. A team approach to a case study of a real-world problem; emphasis on mathematical modeling and analysis and on written and oral communication; completion of a technical report. MATH 4397: Selected Topics in Mathematics Cr. 3. (3-0). Prerequisites: consent of instructor and MATH 3333, 3334, or MATH May be repeated with approval of department chair. Catalog Publish Date: August 15, 2009 This Page Last Updated: August 17, 2009