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# 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 1310. 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 apply to course or gpa requirements for a major or minor in natural sciences and mathematics. Students may not receive credit for both MATH 1310 and MATH 1311. 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 to course or gpa requirements for a major or minor in natural sciences and mathematics. Principles of logic and proof, set theory, formal and informal geometry.

**MATH 1313: Finite Mathematics with Applications **

[TCCN—MATH 1324]

Cr. 3. (3-0). Prerequisite: credit for or placement out of MATH 1310. Students with prior credit for MATH 2331 will not receive credit for MATH 1313. May not apply to course or gpa requirements for a major or minor in natural sciences and 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 1310. Students with prior credit for MATH 1431 will not be permitted to enroll in or receive credit for MATH 1314. 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 1310. Students with prior credit in MATH 1432 may not receive credit for MATH 1330. 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 1330. 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 1431. Calculus of transcendental functions: additional techniques and applications of integration, indeterminate forms, improper integrals, Taylor's formula, and infinite series.

**MATH 1450: Accelerated Calculus **

Cr. 4 per semester. (3-2). Prerequisites: At least one semester of advanced placement high school calculus and placement out of MATH 1330. Credit may not be received for both MATH 1450 and MATH 1431. Students with credit in MATH 1451 may not enroll in or receive credit for either MATH 1432 or 2433. An accelerated calculus sequence. MATH 1450 will include topics normally covered in MATH 1431. MATH 1451 will include topics normally covered in MATH 1432 and 2433.

**MATH 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 1330. Credit may not be received for both MATH 1450 and MATH 1431. Students with credit in MATH 1451 may not enroll in or receive credit for either MATH 1432 or 2433. An accelerated calculus sequence. MATH 1450 will include topics normally covered in MATH 1431. MATH 1451 will include topics normally covered in MATH 1432 and 2433.

**MATH 2303: Concepts in Algebra**

Cr. 3. (3-0). Prerequisite: MATH 1312 or 1313. May not apply to course or gpa requirements for a major or minor in natural sciences and mathematics. Mathematical systems: classical and abstract algebra, systems of numeration, and basic number theory.

**MATH 2311: Introduction to Probability and Statistics**

[TCCN—MATH 1342]

Cr. 3. (3-0). Prerequisite: MATH 1310 or 1311. May not apply to course or gpa requirements for a major or minor in natural sciences and mathematics. Students with credit for MATH 3338 or 3339 may not enroll in or receive credit for MATH 2311. 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 1432. 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 1432. 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 1313 or consent of instructor. May not apply to course or gpa requirements for a major or minor in 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 1313 or consent of instructor. May not apply to course or gpa requirements for a major or minor in 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 1313 or consent of the instructor. May not apply to course or gpa requirements for a major or minor in 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 1313 or consent of instructor. May not apply to course or gpa requirements for a major or minor in 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 1313 or consent of instructor. May not apply to course or gpa requirements for a major or minor in natural sciences and mathematics. Basic probability, sampling, statistical prediction, and process control.

**MATH 3310: History of Mathematics **

Cr. 3. (3-0). Prerequisite: MATH 1431. May not apply to course or gpa requirements for a major or minor in natural sciences and mathematics. A survey of the history of mathematics from Euclid to Dedekind 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 1101. 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 1432. Students may not receive credit for both MATH 3321 and MATH 3331. 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.

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Effective beginning Fall 2013:**MATH 3325: Transition to Advanced Mathematics**Cr. 3. (3-0). Prerequisite: MATH 1432. An introduction to proof in mathematics: logic, sets, relations, functions and cardinality, a first look at epsilon-delta methods of proof. Writing and communication of mathematical ideas will be emphasized.

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Effective beginning Fall 2013 (see also listing below):**MATH 3330: Abstract Algebra**

Cr. 3. (3-0). Prerequisites: MATH 2331 and 3325 or consent of instructor. An introduction to groups and rings: groups, subgroups, quotients, products, homomorphisms and isomorphisms, ideals, integral domains and division rings.

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Effective through end of Summer 2013 (see also listing above):**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 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.

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Effective beginning Fall 2013 (see also listing below):**MATH 3333: Intermediate Analysis**

Cr. 3. (3-0). Prerequisites: MATH 2433 and 3325 or consent of instructor. A rigorous treatment of single variable calculus: topological properties of the real numbers, limits, continuity, differentiation, Riemann integration, the fundamental theorems of calculus, sequences and series.

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Effective through end of Summer 2013 (see also listing above):**MATH 3333: Intermediate Analysis **

Cr. 3. (3-0). Prerequisite: MATH 2433. Properties of real number system, properties of continuous functions, and sequences of functions.

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Effective beginning Fall 2013 (see also listing below):**MATH 3334: Advanced Multivariable Calculus**

Cr. 3. (3-0). Prerequisite: MATH 3333. Basic theory underlying multivariable calculus: a brief overview of the topology of n-space, limits, continuity and differentiation of functions of several variables, Taylor's theorem, the inverse and implicit function theorems, integration.

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Effective through end of Summer 2013 (see also listing above):**MATH 3334: Advanced Multivariable Calculus**

Cr. 3. (3-0). Prerequisite: MATH 3333. 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**

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 1432. Sample spaces, events, and probabilities; random variables and distributions, expectations, variances and covariances; basic discrete and continuous distributions; the central limit theorem.

**MATH 3339: Statistics for the Sciences**

Cr. 3. (3-0). Prerequisite: MATH 1432. 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 1432. Bonds and bank certificates of deposit, arbitrage, bond and annuity valuation, total return, market risk, risk management, term structure construction, liability management.

**MATH 3363: Introduction to Partial Differential Equations **

Cr. 3. (3-0). Prerequisites: MATH 2433 and either MATH 3321 or 3331. Partial differential equations and boundary value 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 3331. 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. Synthetic and algebraic geometry; harmonic division, cross ratio; groups of projective transformation

**MATH 3396: Senior Research Project**

Cr. 3. per semester. Prerequisite: approval of department chair. Directed research project culminating in a departmentally approved report. MATH 3396 and MATH 4396 must be satisfied in order for any to apply to a degree.

**MATH 3397: Selected Topics in Mathematics**

Cr. 3. (3-0). Prerequisite: consent of instructor. May be repeated with approval of department chair.

**MATH 3399: Senior Honors Thesis **

Cr. 3 per semester. Prerequisite: approval of department chair. MATH 3399 and MATH 4399 must be satisfied in order for any to apply to a degree.

**MATH 4399: Senior Honors Thesis**

Cr. 3 per semester. Prerequisites: MATH 3399 and approval of department chair. MATH 3399 and MATH 4399 must be satisfied in order for any to apply to a degree.

**MATH 4198: Independent Study**

Cr. 1 per semester or more by concurrent enrollment. Prerequisite: approval of department chai

**MATH 4298: Independent Study**

Cr. 2 per semester or more by concurrent enrollment. Prerequisite: approval of department chai

**MATH 4309: Mathematical Biology**

Cr. 3. (3-0). Prerequisite: MATH 3331 and BIOL 3306 or consent of instructor. Topics in mathematical biology, epidemiology, population models, models of genetics and evolution, network theory, pattern formation, and neuroscience. Students may not receive credit for both MATH 4309 and BIOL 4309.

**MATH 4310: Biostatistics**

Cr. 3. (3-0). Prerequisite: MATH 3339 and BIOL 3306 or consent of instructor. Statistics for biological and biomedical data, exploratory methods, generalized linear models, analysis of variance, cross-sectional studies, and nonparametric methods. Students may not receive credit for both MATH 4310 and BIOL 4310.

**MATH 4315: Graph Theory with Applications**

Cr. 3. (3-0). Prerequisite: MATH 3330 or 3336. Introduction to basic concepts, results, methods, and applications of graph theory.

**MATH 4320: Introduction to Stochastic Processes**

Cr. 3. (3-0). Prerequisites: MATH 3338. Generating functions, discrete and continuous versions of Poisson and Markov processes, branching and renewal processes, introduction to stochastic calculus and diffusion.

**MATH 4331: Introduction to Real Analysis**

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 4332: Introduction to Real Analysis**

Cr. 3 per semester. (3-0). Prerequisites: MATH 4331 and 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: Partial Differential Equations**

Cr. 3 per semester. (3-0). Prerequisite: MATH 3331. Existence and uniqueness for Cauchy and Dirichlet problems; classification of equations; potential-theoretic methods; other topics at the discretion of the instructor.

**MATH 4336: Partial Differential Equations**

Cr. 3 per semester. (3-0). Prerequisites: MATH 4335 and MATH 3331. 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 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: Differential Geometry**

Cr. 3 per semester. (3-0). Prerequisites: MATH 2433 and 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 4351: Differential Geometry**

Cr. 3 per semester. (3-0). Prerequisites: MATH 4350, 2433 and 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 3321. 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.

**MATH 4360: Integral Equations **

Cr. 3. (3-0). Prerequisites: MATH 3331 and 3334. 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 3334. Existence, uniqueness, and continuity of solutions of single equations and systems of equations; other topics at the discretion of the instructor.

**MATH 4364: 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 4365: Numerical Analysis **

Cr. 3 per semester. (3-0). Prerequisites: MATH 4364, 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 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.

**MATH 4378: Advanced Linear Algebra II**

Cr. 3. (3-0). Prerequisite: MATH 4377. 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 3338. Arbitrage-free pricing, stock price dynamics, call-put parity, Black-Scholes formula, hedging, pricing of European and American options.

**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: 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 4386: Mathematical Statistics**

Cr. 3 per semester. (3-0). Prerequisite: MATH 4385 and MATH 3339 or equivalent. Linear models-estimation, testing and application to designs of experiments, nonparametric statistical models.

**MATH 4388: History of Mathematics to Modern Times**

Cr. 3. (3-0). Prerequisite: MATH 3333 or consent of instructor. The history of mathematics and its impact on civilization from the ancient world to modern times, critical events in the development of mathematics, notable mathematicians and the importance of their discoveries.

**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). Prerequisites: MATH 3321 or 3331 and six additional advanced hours in Mathematics. A team approach to a case study of a real world problem; emphasis on mathematical modeling, analysis on written and oral communication; completion of a technical report.

**MATH 4396: Senior Research Project**

Cr. 3. per semester. Prerequisites: MATH 3396 and approval of department chair. Directed research project culminating in a departmentally approved report. MATH 3396 and MATH 4396 must be satisfied in order for any to apply to a degree.

**MATH 4397: Selected Topics in Mathematics**

Cr. 3. (3-0). Prerequisites: consent of instructor and MATH 3333, 3334, or 3330. May be repeated with approval of department chair.

**MATH 4398: Independent Study**

Cr. 3 per semester or more by concurrent enrollment. Prerequisite: approval of department chair

**MATH 4498: Independent Study**

Cr. 4 per semester or more by concurrent enrollment. Prerequisite: approval of department chair.

Catalog Publish Date: August 22, 2012

This Page Last Updated: April 30, 2013