"There is no branch of mathematics, however abstract, which may not someday be applied to the phenomena of the real world."
- Nicolai Lobachevsky
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"There is no branch of mathematics, however abstract, which may not someday be applied to the phenomena of the real world." - Nicolai Lobachevsky |
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Mathematics |
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NOTE: Syllabi presented here are generic departmental syllabi indicating, primarily, the text and material to be covered. More specific information on grading, the use of technology, and/or the writing intensity of a course is available from individual instructors.
| Math 0098. Elemetary Algebra. (4) | Topics include review of real numbers (order of operations, fractions, decimals, percents, and integers), solving and graphing linear equations and inequalities, operations with polynomials. An introduction to solving systems of linear equations and inequalities, factoring and operations with rationals. Applications will be emphasized. |
| Math 0099. Intermediate Algebra. (4) | A transition from elemetary algebra to college algebra.Topics include operations with radicals, graphing of linear and nonlinear functions, algebra of linear and nonlinear functions, systems of linear equations and inequalities, review of factoring and quadratic functions. Applications will be emphasized. |
| Math
1070. Elementary Statistics. (3) Prerequisite: high school algebra II. |
Descriptive statistics, basic probability and
distribution of random variables, estimation and hypothesis tests for means and
proportions, regression and correlation, analysis of count data. (Formerly Math 107) |
| Math 1090H. Honors Statistics. (3)
Prerequisite: consent of Honors Program director. |
Nondeterministic conceptualizations of phenomena as a foundation for inference. Descriptive and inferential methods of statistics including synopses of real experiments, means, variances, regression and correlation, probability, sampling, hypotheses testing. (Formerly Math 109H) |
| Math 1101. Mathematical
Modeling. (3) Prerequisite: high school algebra II or its equivalent. This course is NOT an appropriate prerequisite for precalculus or calculus courses. |
Mathematical modeling using graphical, numerical, symbolic, and verbal techniques to describe and explore real-world data and phenomena. Emphasis is on the use of elementary functions to investigate and analyze applied problems and questions, on the use of appropriate supporting technology, and on the effective communication of quantitative concepts and results. |
| Math
1111. College Algebra. (3) Prerequisite: high school algebra II. |
Algebraic techniques; coordinate geometry; algebraic and rational functions; relations; linear systems; complex numbers. (Formerly Math 104) |
| Math
1220. Survey of Calculus. (3) Prerequisite: Math 1111. |
Differential and integral calculus of selected real-valued functions of one and several real variables with applications. (Formerly Math 122) |
| Math
1113. Precalculus. (3) Prerequisite: Math 1111, or departmental approval. |
Trigonometric functions, identities, inverses, and equations; vectors; polar coordinates, conic sections. (Formerly Math 126) |
| Math 2030. Principles of Mathematics. (3) (This course will not be accepted as part of the requirements of a major in mathematics.) | Designed for teachers at the elementary and middle school level; topics included are numerical systems, sets and relations, primes and divisors, binary operations and properties, rational numbers and real numbers. (Formerly Math 203) |
| Math
2050. Informal Geometry. (3) Prerequisite: Math 2030. (Not acceptable as part of the requirements for a major in mathematics.) |
Designed for teachers at the elementary and middle school level. Sets; points; lines, including the real number line; space figures; elementary theorems and proofs, congruence and measurement of segments and angles; parallels and parallelograms; areas.(Formerly Math 205) |
| Math
2211. Calculus of One Variable I. (4) Prerequisite: Math 1113 or the equivalent. |
Limits and Continuity, Differentiation, Mean Value Theorem for Derivatives; applications of differentiation; definition of the integral; Fundamental Theorem of Calculus; applications of integration to area. |
| Math
2212. Calculus of One Variable II. (4) Prerequisite: Math 2211 . |
Applications and techniques of integration; transcendental and trigonometric functions; polar coordinates; infinite sequences and series; indeterminate forms; improper Integrals. |
| Math
2215. Multivariate Calculus. (4) Prerequisite: Math 2212. |
Real-valued functions of several variables, limits, continuity, differentials, directional derivatives, partial derivatives, chain rule, multiple integrals, applications. (Formerly Math 215) |
| Math
2420. Discrete Mathematics. (3) Prerequisite: Math 1220 or Math 1113. |
Introduction to discrete structures which are applicable to computer science. Topics include number bases, logic, sets, Boolean algebra, and elementary concepts of graph theory. (Formerly Math 220) |
| Math
3000. Bridge to Higher Mathematics. (3) Prerequisite: Math 2212 |
Topics from set theory, real numbers, analysis and algebra which illustrate a formal approach to the presentation and development of mathematical concepts and proofs. |
| Math
3030. Mathematical Models for Computer Science. (3) Prerequisites: Math 2420 and Math 2215. |
Elements of mathematical modeling including: probability, distributions of random variables, sampling, statistical inference, transforms, operators, vector analysis; elements of linear algebra. |
| Math 3050. Geometry and Spatial
Sense. (3) |
Building on Euclidean geometry this course is designed to develop a more visual understanding of geometry and enhance intuition in two- and three-dimensions. Topics include measurement, two-dimensional geometry, three-dimensional geometry, spherical geometry, symmetry, tesselations, efficient shapes, transformations |
| Math 3070. Introduction to
Probability and Statistics. (3) Prerequisite: Math 2030 or consent of instructor. (Not acceptable as part of the requirements for a major in mathematics.) |
This course is intended to provide an overview of the basics of probability and descriptive statistics. Various forms of technology will be used. |
| Math 3260. Differential Equations.
(3) Prerequisite: Math 2215. |
First-order equations, linear differential equations with special emphasis on constant coefficient and Euler equations, systems of equations, applications. (Formerly Math 360) |
| Math 3420. Applied
Combinatorics. (3) Prerequisite: Math 2212 |
Counting principles; topics include combinations, permutations, generating functions, recurrence relations, principle of inclusion and exclusion, and Polya's theory of counting. |
| Math 3435. Introductory Linear
Algebra. (3) Prerequisites: Math 2215 and Math 3000. |
Theory and applications of matrix algebra and linear transformations. Topics include linear equations, vector spaces, matrices, subspaces, and bases. (Formerly Math 335) |
| Math 3450. Elements of Number
Theory. (3) Prerequiste: Math 2211. |
The mathematical study of the integersa and their generalizations. Topics to include prime and composite numbers, factoring, congruences and modular arithmetic, GCDs and relatively prime integers, applications of number theory. |
| Math 3510. Introduction to
Probability and Its Applications. (3) Corequisite: Math 2212. |
Basic probability, theory, combinatorial problems, random variables, laws of large numbers, random walks, Markov chains; applications drawn from decision and stochastic processes. (Formerly Math 351) |
| Math 3690H. Honors Readings. (1-3)
Prerequisites: consent of Honors Program director. |
Discussion and readings on selected topics. (Formerly Math 369H) |
| Math 3820. Historical and Cultural Development of Mathematics I. (3) | Exploration of the historical and cultural development of mathematics between ~3000 B.C. and ~A.D. 1600. Mathematics topics to include the development of arithmetic, geometry (practical, deductive, and axiomatic), number theory, trigonometry, syncopated and symbolic algebra, probability and statistics. |
| Math 3821. Historical and
Cultural Development of Mathematics II. (3) Prerequisite: Math 2211. |
Exploration of the historical and cultural development of mathematics from ~A.D. 1600. Mathematics topics to include the development of algebraic geometry, logarithms, calculus, non-Euclidean geometry, abstract algebra, probability, and analysis. |
| Math 4211. Optimization. (3) Prerequisite: Math 2215. |
Lagrange multipliers, gradient methods (steepest descent), search techniques, variational methods and control problems; and other topics such as dynamic and nonlinear programming. (Formerly Math 411) |
| Math 4250. Complex Analysis. (3)
Prerequisite: Math 3000. |
Complex numbers, analytic functions, complex series, Cauchy theory, residue calculus, conformal mapping. (Formerly Math 425) |
| Math 4253. Introduction to
Operations Research. (3) Prerequisite: Math 3435 or Math 3030. |
Linear programming, the simplex method, network theory, game theory, Markov analysis, and other topics such as inventory analysis, queuing theory, integer programming. (Formerly Math 453) |
| Math 4258. Vector Calculus. (3) (Equivalent to Physics 4510) Prerequisite: Math 2215. |
Vector algebra, curvilinear motion, vector fields, gradient, divergence, Laplacian, line and surface integrals, integral theorems. (Formerly Math 458) |
| Math 4265. Partial Differential
Equations. (3) (Equivalent to Physics 4520) Prerequisite: Math 3260. |
First-order equations, classification of linear second-order equations, separation of variables, Fourier series, orthogonal functions, Green's functions.(Formerly Math 465) |
| Math 4301. Transformational
Geometry. (3) Prerequisite: Math 3000. |
For middle and secondary teachers, emphasizing an algebraic approach to geometry using vectors and transformations. (Formerly Math 401) |
| Math 4371. Modern Geometry. (3) Prerequisite: Math 3000. |
Euclidean and non-Euclidean geometry, including incidence, order, and the parallel postulate. (Formerly Math 471) |
| Math 4391. Introduction to Differential Geometry and its Applications. (3) (Same as Phys 4391) | The theory of curves and surfaces in parametric and implicit form. Curvature and torsion of a curve. The shape operator and the total and mean curvature of a surface. The Gauss-Weingarten equations. The Egregium Theorem. Surfaces of constant curvature and non-Euclidean geometry. Minimal surfaces. The Gauss Bonnet Theorem. Submanifolds in Euclidian spaces, vector fields, differential forms and the theorems of Frobenius and Stokes. Applications to Physics. |
| Math 4420. Graph Theory. (3) Prerequisite: Math 3000. |
Introduction to graph theory; topics include structure of graphs, trees, connectivity, Eulerian and Hamiltonian graphs, planar graphs, graph colorings, matchings, independence, and domination. Additional topics may include symmetry of graphs, directed graphs, extremal graph theory and Ramsey theory, graph embeddings, and probabilistic methods in graph theory. |
| Math 4435. Linear Algebra. (3) Prerequisite: Math 3435. |
Theory and applications of matrix algebra, vector spaces and linear transformations; topics include characteristic values, the spectral theorem, and orthogonality. (Formerly Math 435) |
| Math 4441. Modern Algebra I. (3)
Prerequisite: Math 3000. |
Integers; rational, real and complex numbers; group theory. (Formerly Math 441) |
| Math 4442. Modern Algebra II. (3)
Prerequisite: Math 4441. |
Rings, integral domains, and fields; polynomials over a field, matrices over a field, algebraic numbers and ideals. (Formerly Math 442) |
| Math 4450. Theory of Numbers. (3)
Prerequisite: Math 3000. |
Properties of integers, divisibility, congruence of numbers, Lagrange's theorem, residues, diophantine problems. (Formerly Math 450) |
| Math 4544. Biostatistics. (3)
(Same as Bio 4744) Prerequisites: Bio 1410, 1420, and Math 2211. Degree credit will not be given for both Math 4544 and 4547. |
Principles and methods of statistics as applied to biology and medicine. (Formerly Math 444) |
| Math 4547. Introduction to
Statistical Methods. (3) Prerequisite: a course in calculus. Degree credit will not be given for both Math 4544 and 4547. |
Data analysis, sampling, and probability; standard methods of statistical inference, including t-tests, chi-square tests, and nonparametric methods. Applications include use of a statistical computer package. (Formerly Math 447) |
| Math 4548. Methods of Regression and
Analysis of Variance. (3) Prerequisites: a course in calculus and a course covering methods of statistical inference. |
Simple and multiple regression, model selection procedures, analysis of variance, simultaneous inference, design and analysis of experiments. applications include use of a statistical computer package. (Formerly Math 448) |
| Math 4610. Numerical Analysis
I. (3) Prerequisites: Math 2215 and the ability to program in a high level language. Same as CSc 4610. |
Nature of error; iteration; techniques for nonlinear systems; zeros of functions; interpolation; numerical differentiation; Newton-Cotes formulae for definite integrals; computer implementation of algorithms. |
| Math 4620. Numerical Analysis
II. (3) Prerequisites: Math/CSc 4610, Math 3435 or 3030. |
Gaussian elimination for linear systems; least squeares; Taylor, predictor-corrector and Runge-Kutta methods for solving ordinary differential equations; boundary value problems; partial differential equations. |
| Math 4661. Advanced Calculus I. (3)
Prerequisite: Math 4435. |
Functions of several variables; elements of point set theory, numerical sequences and series, limits, continuity, differentiation. (Formerly Math 461) |
| Math 4662. Advanced Calculus II. (3)
Prerequisite: Math 4661. |
Functions of several variables; sequences and series of functions; integration theory. (Formerly Math 462) |
| Math 4751. Mathematical Statistics
I. (3) Prerequisite: Math 2215. |
Probability, random variables and their distributions, mathematical expectation, moment generating functions, sampling distributions. (Formerly Math 451) |
| Math 4752. Mathematical Statistics
II. (3) Prerequisite: Math 4751. |
Theory of estimation and hypothesis testing, applications of statistical inference, introduction to regression and correlation. (Formerly Math 452) |
| Math 4767. Statistical Computing.
(3) Prerequisites: Math 4752 or 4548, and Math 3435 and the ability to program in a high-level language |
Computational implementation of statistical methods such as descriptive statistics, one and two sample t tests, regression, correlation, ANOVA methods of estimation, and Monte Carlo techniques. Standard statistical packages will be used as well as user-written programs. (Formerly Math 467) |
| Math 4982. Undergraduate Research in
Mathematics. (3) Prerequisites: at least 12 upper-division hours in mathematics. Authorization Required. |
Independent investigation of topics of common interest to student and instructor. (Formerly Math 482) |
| Math 4987H. Honors Thesis. (3) Prerequisites: consent of instructor and Honors Program Director. |
Readings or research preparatory to Honors thesis or project. (Formerly Math 487H) |
| Math 4988H. Honors Thesis. (3) Prerequisites: Math 4987H and consent of Honors Program Director. |
Writing or production of Honors thesis or project. (Formerly Math 488H) |
| Math 4998. Selected Topics. (1-3)
Prerequisite: consent of instructor.
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May be repeated if topics are different. No more than six credit hours may be applied toward the major.(Formerly Math 498) |
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