Courses: Mathematics (MATH)

1300: Fundamentals of Mathematics
Cr. 3. (3-0). A survey of pre-college 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.

1310: College Algebra
Cr. 3. (3-0). Prerequisite: satisfactory score on placement examination. Students with credit in MATH 1330 or 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.

1312: Introduction to Mathematics (formerly MATH 1308)
Cr. 3. (3-0). Prerequisite: credit for or placement out of MATH 1310. May not apply toward a degree from College of Natural Sciences and Mathematics. Ideas in mathematics central to its historical development and its use in contemporary life; critical thinking and problem solving. Topics may include logic, algorithms, numbers, geometry, and topics in the history of mathematics.

1313: Finite Mathematics with Applications
Cr. 3. (3-0). Prerequisite: credit for or placement out of MATH 1310. Students with prior credit for MATH 2431 or INDE 2331 will not receive credit for MATH 1313. 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.

1314: Elements of Calculus
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.

1315: College Mathematics
Cr. 3. (3-0). Prerequisite: Two credits of high school algebra, one credit of geometry, and a satisfactory score on the placement examination. May not apply toward a major or minor in Mathematics. Students may not receive credit for both MATH 1315 and MATH 1313. Functions, graphs, differences and rates of change, mathematical models, mathematics of finance, optimization, and the mathematics of decision-making.

1330: Elementary Functions
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.

1397: Topics in Mathematics
Cr. 3. (3-0). Prerequisite: consent of instructor. Restricted to nonadvanced undergraduates. May be repeated with approval of chair.

1431: Calculus I
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, numerical integration.

1432: Calculus II
Cr. 4. (4-0). Prerequisite: MATH 1431. Calculus of transcendental functions: additional techniques and applications of integration, indeterminate forms, improper integrals, Taylor's formula, infinite series.

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 1330. Credit may not be received for both MATH 1450 and 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.

2303: Elements of Mathematics
Cr. 3. (3-0). Prerequisites: MATH 1310 and 1313. May not apply toward a major or minor in mathematics. Principles of logical reasoning, elementary set theory, number systems, fundamentals of Euclidean geometry, introduction to number theory.

2311: Introduction to Probability and Statistics
Cr. 3. (3-0). Prerequisite: MATH 1310 or MATH 1315 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 2311. Probability, correct probabilistic reasoning, distributions, graphical and descriptive methods, sampling, estimation, hypotheses, statistical inference.

2431: Linear Algebra
Cr. 4. (3-0). Prerequisite: credit for or concurrent enrollment in MATH 1432 and in a laboratory section. Solutions of systems of linear questions and of systems of linear differential equations; matrices, linear transformations, eigen values, and similarity; phase plane portraits.

2433: Calculus III
Cr. 4. (4-0). Prerequisite: MATH 1432. Calculus of functions of several variables: calculus of vector-valued functions, partial differentiation, multiple integrals.

3303: Elements of Algebra and Number Theory
Cr. 3. (3-0). Prerequisites: MATH 1310 and either 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. Topics in number theory and abstract algebra.

3304: Elements of Mathematical Analysis
Cr. 3. (3-0). Prerequisites: MATH 1310 and either 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.

3305: Formal and Informal Geometry
Cr. 3. (3-0). Prerequisites: MATH 1310 and either 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.

3306: Problem Solving in Mathematics
Cr. 3. (3-0). Prerequisites: MATH 1310 and either 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. Strategies for solving problems in mathematics: reduction to smaller problems; analogy in mathematics; conjecture and proof; the processes of abstraction, generalization, and specialization.

3310: History of Mathematics
Cr. 3. (3-0). Prerequisite: MATH 1431. 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 focusing on the development of the real number system and its relation to the Euclidean line.

3321: Engineering Mathematics
Cr. 3. (3-0). Prerequisites: MATH 1432. 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. Students may not receive credit for both MATH 3321 and MATH 3431 .

3330: Abstract Algebra
Cr. 3. (3-0). Prerequisite: MATH 2431. Introduction to groups, rings, and fields.

3333: Intermediate Analysis
Cr. 3. (3-0). Prerequisite: MATH 2433. Properties of real number system, properties of continuous functions, and sequences of functions.

3334: Advanced Multivariable Calculus
Cr. 3. (3-0). Prerequisite: MATH 2433. 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.

3335: Vector Analysis
Cr. 3. (3-0). Prerequisite: MATH 2433 or approval of chair. Algebra and calculus of vectors, vector differential operators, Green's and Stokes' theorems, curvilinear coordinates, tensors.

3336: Discrete Mathematics
Cr. 3. (3-0). Prerequisite: MATH 2431 or equivalent. Topics selected from logic, set theory, combinatorics, and graph theory.

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.

3339: Statistics
Cr. 3. (3-0). Prerequisite: MATH 3338. Sampling; estimation and hypothesis testing; regression; analysis of variance; exploratory techniques.

3363: Introduction to Partial Differential Equations
Cr. 3. (3-0). Prerequisites: MATH 2433 and either MATH 3321 or MATH 3331. Partial differential equations and boundary value problems, Fourier series, the heat equation, vibrations of continuous systems, the potential equation, spectral methods.

3364: Introduction to Complex Analysis
Cr. 3. (3-0). Prerequisite: MATH 3331. The complex number system, analytic functions, Cauchy integral theory, series representation, residue theory, and conformal mapping.

3379: Introduction to Higher Geometry
Cr. 3. (3-0). Prerequisite: MATH 1432 or approval of chair. Synthetic and algebraic geometry; harmonic division, cross ratio; groups of projective transformations.

3396-4396: Senior Research Project
Cr. 3. per semester. Prerequisite: approval of chair. Directed research project culminating in a departmentally approved report.

3397: Selected Topics in Mathematics
Cr. 3. (3-0). Prerequisite: consent of instructor. May be repeated with approval of chair.

3399-4399: Senior Honors Thesis
Cr. 3 per semester. Prerequisite: approval of chair.

3431: Differential Equations
Cr. 4. (3-0). Prerequisites: MATH 2433 and MATH 2431. Systems of ordinary differential equations and topics in linear algebra. Existence, uniqueness, and stability of solutions; initial value problems; elementary bifurcation theory; Jordan normal form; higher order equations and Laplace transforms. Concurrent enrollment in computer laboratory section is required.

4198:4298: 4398:4498: Special Problems
Cr. 1-4 per semester or more by concurrent enrollment. Prerequisite: approval of chair.

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.

4331;4332: Introduction to Real Analysis
Cr. 3 per semester. (3-0). Prerequisite: MATH 3333 or 3334. Properties of continuous functions, partial differentiation, line integrals, improper integrals, infinite series, and Stieltjes integrals.

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.

4335;4336: Partial Differential Equations
Cr. 3 per semester. (3-0). Prerequisite: MATH 3431. Existence and uniqueness for Cauchy and Dirichlet problems; classification of equations; potential-theoretic methods; other topics at the discretion of the instructor.

4337: Point Set Theory
Cr. 3. (3-0). Prerequisite: MATH 3333 or 3334 or consent of instructor.

4340: Nonlinear Dynamics and Chaos
Cr. 3. (3-0). Prerequisite: MATH 3431 or consent of instructor. Dynamical systems associated with one-dimensional maps of the interval and the circle; elementary bifurcation theory; modeling of real phenomena.

4350;4351: Differential Geometry
Cr. 3 per semester. (3-0). Prerequisites: MATH 2433, 2431 or equivalent. Frenet frames, metric tensors, Christoffel symbols, Gaussian curvature, differential forms, moving frames, Euler characteristics, the Gauss-Bonnet theorem and Euler-Poincare index theorem.

4360: Integral Equations
Cr. 3. (3-0). Prerequisites: MATH 3431 and 3334. Relation to differential equations; Fredholm, Hilbert-Schmidt, and Volterra type equations; special devices and approximation methods.

4362: Theory of Ordinary Differential Equations
Cr. 3. (3-0). Prerequisites: MATH 3431 and 3334. Existence, uniqueness, and continuity of solutions of single equations and systems of equations; other topics at the discretion of the instructor.

4364;4365: Numerical Analysis
Cr. 3 per semester. (3-0). Prerequisites: MATH 2431, 3431; COSC 1301 or 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.

4377;4378: Advanced Linear Algebra
Cr. 3 per semester. (3-0). Prerequisites: MATH 2431 and a minimum of three semester hours of 3000-level mathematics. Matrices, eigenvalues, and canonical forms.

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.

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.

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.

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 chair.