Mathematics

Dennis Wackerly, 220 FLO, 392-1941 ext 227; David Nye, 329 BUS, 392-0153; Graduate Coordinator: P. Robinson

Theory of real numbers, functions of one variable, sequences, limits, continuity, and differentiation; continuity and differentiability of functions of several variables. MAA 4102 is not recommended for students who plan to do graduate work in mathematics; these students should take MAA 4211. (Note: credit will be given for at most one of MAA 4102, MAA 4211, and MAA 5104.)

A continuation of MAA 4102. Theory of integration, transcendental functions, and infinite series. MAA 4102 is not recommended for students who plan to do graduate work in mathematics; these students should take MAA 4212. (Note: credit will be given for at most one of MAA 4103, MAA 4212, and MAA 5105.)

An advanced treatment of limits, differentiation, integration, series; calculus of functions of several variables. (Note: credit will be given for at most one of MAA 4211, MAA 4102, and MAA 5104.)

A continuation of MAA 4211. (Note: credit will be given for at most one of MAA 4212, MAA 4103, and MAA 5105.)

Topology of metric spaces, numerical sequences and series, continuity, differentiation, the Riemann-Stielties integral, sequences and series of functions, the Stone-Weierstrass, theorem, functions of several variable, Stokes’ theorem, the Lebesgue theory. (Note: credit will be given for at most one of MAA 4226 and MAA 5228.)

A continuation of MAA 4226. (Note: credit will be given for at most on of MAA 4227 and MAA 5229.)

Complex numbers, analytic functions, Cauchy-Riemann equations, harmonic functions, elementary functions, integration, Cauchy-Goursat theorem, Cauchy integral formula, infinite series, residues and poles, conformal mapping. (Note: credit will be given for at most one of MAA 4402 and MAA 5404.)

Exponential and logarithmic functions, trigonometry, analytic and additional applications of trigonometry. (M) GR-M†(See note above)

College algebra, functions, coordinate geometry, exponential and logarithmic functions. (M) GR-M† (See note above)

College algebra, functions, coordinate geometry, exponential and logarithmic functions, and trigonometry. This fast-paced course is designed as a review of algebra and trigonometry to prepare the student for calculus. This course assumes prior knowledge of intermediate algebra (Algebra II) and trigonometry. (M) GR-M† (See note above)

A geometric and heuristic approach to calculus; differentiation and integration of simple algebraic and exponential functions; applications to graphing, marginal analysis, optimization, areas and volumes. (M) GR-M† (See note above)

Sequences, geometric and Taylor series; systems of linear equations, Gaussian elimination, matrices, determinants and vectors; partial differentiation, multiple integrals; applications to marginal analysis, least-squares and Lagrange multipliers. (M) GR-M†

Introduction to analytic geometry; limits; continuity; differentiation of algebraic and trigonometric functions; differentials; introduction to integration; and the fundamental theorem of calculus. (M) GR-M† (Credit will be given for at most one of MAC 2233, MAC 2311, and MAC 3472.)

Techniques of integration; applications of integration; differentiation and integration of inverse trigonometric, exponential and logarithmic functions; sequences and series. (M) GR-M† (Credit will be given for at most one of MAC 2312, MAC 3512, and MAC 3473.)

Solid analytic geometry; vectors; partial derivatives; multiple integrals. (M) GR-M† (Credit will be given for at most one of MAC 2313 and MAC 3474.)

A first course in calculus for students who enjoy and have a sound background in mathematics. The topics covered in the sequences MAC 3472-3-4 closely parallel those covered in MAC 2311-2-3 but are treated in greater depth. (M) GR-M† (Credit will be given for at most one of MAC 2311 and MAC 3472.)

A continuation of MAC 3472. (M) GR-M† (Credit will be given for at most one of MAC 2312, MAC 3512, and MAC 3473.)

A continuation of MAC 3473. (M) GR-M† (Credit will be given for at most one of MAC 2313 and MAC 3474.)

A calculus course for entering freshmen who have Advanced Placement credit for MAC 2311. The content of MAC 2311 and 2312 is covered: limits, continuity, differentiation, applications of differentiation, integration, logarithms and exponential functions, applications of integration, techniques to integration, sequences, series, conic sections and parametric equations. The content of the AP syllabus is reviewed during the first half of the semester, and there is a special emphasis on topics not in the AP Calculus AB syllabus, such as infinite series. (M) GR-M† (Credit will be given for at most one of MAC 2312, MAC 3512, and MAC 3473.)

Logic, sets, functions. Algorithms and complexity; integers and algorithms. Mathematical reasoning and induction. Counting principles; permutations and combinations; discrete probability. Advanced counting techniques, inclusion-exclusion.

Permutations and combinations, binomial coefficients, inclusion-exclusion, recurrence relations, Fibonacci sequences, generating functions, graph theory. (M)

Matching theory, block designs, finite projective planes and error-correcting codes. This course may be taken without taking MAD 4203.

Numerical integration, nonlinear equations, linear and non-linear systems of equations, differential equations, and interpolation.

Properties of and operations with rational numbers; ratio; proportion; percentages; an introduction to real numbers; elementary algebra; informal geometry and measurement; and an introduction to probability and descriptive statistics.

First-order ordinary differential equations, theory of linear ordinary differential equations, solution of linear ordinary differential equations with constant coefficients, the Laplace transform and its application to solving linear ordinary differential equations. (M) GR-M†

Amount function, simple and compound interest, present value, dollar-weighted and time-weighted rates, force of interest, discrete and continuous annuities, bonds, amortization, capitalization, and applications.

Random walks and Poisson processes, martingales, Markov chains, Brownian motion, stochastic integrals and Ito’s formula.

This is a second course in differential equations. Topics covered are: systems of linear differential equations, stability theory and phase plane analysis, power series solutions of differential equations, Sturm-Liouville boundary-value problems, and special functions. (Note: credit will be given for at most one of MAP 4305 and MAP 5304.)

Topics covered are: introduction to second-order linear partial differential equations (Heat, Wave, and Laplace equations), separation of variables in PDEs, Sturm-Liouville eigenvalue problems, method of eigenfunction expansions (Fourier analysis), Green’s functions. Introduction to first-order PDEs and the method of characteristics may be included at the preference of the instructor. (Note: credit will be given for at more one of MAP 4341 and MAP 5345.)

Complex variables, including derivatives and integrals, singularities, Taylor/Laurent series and residues; Linear Algebra, including Gaussian elimination, determinants, inversion, linear independence, eigenvalues and eigenvectors, and (time permitting) QR decomposition, systems of differential equations; (time permitting) Numerical methods, including roots of equations, numerical integration, and numerical optimization.

Introduction to linear systems and transforms; Laplace, Fourier and Z transforms and their mutual relationship; convolutions. Operational calculus; computational methods including the fast Fourier transform; second-order stationary processes and their autocorrelation functions; and problems of interpolation, extrapolation, filtering and smoothing of second-order stationary processes.

Linear equations, matrices and determinants. Vector spaces and linear transformations. Inner products and eigenvalues. This course emphasizes computational aspects of linear algebra. (M) GR-M†

This course emphasizes theorems and proofs. Topics include a algebraic and order properties of the real numbers, introduction to number theory, rational numbers and their decimal expansions, uncountability of the real numbers, complex numbers, irreducible polynomials over the integral, rational, real and complex numbers, elementary theory of equations. Taking one (but not both) of MAS 3300 and MH 3202 is very useful in preparing students for a major in mathematics. This course is also particularly useful for prospective secondary-school mathematics teachers. (M) GR-M†

Linear equations, matrices, vector spaces, linear transformations, determinants, eigenvalues, inner product spaces. This course includes both theory and computational skills. The student is expected to develop the ability to reason through, and coherently write up, proofs of theorems. For math majors, this course serves as a transition from a study of techniques into more conceptual math; for engineering and science majors, it serves also as a coherent foundation in linear algebra.

Further topics in linear algebra. GR-M†

Topics in linear algebra most useful in applications with emphasis on the numerical methods involved: direct and iterative solutions to systems of linear equations; matrix norms; Householder transformations; singular value decomposition; least squares and the generalized inverse; QR method for computing eigenvalues; condition number of linear systems and eigensystems.

Review of vector algebra, lines, planes and space curves; vector fields, their divergence and curl; line, surface, and volume integrals, the Divergence Theorem and Stokes’ Theorem. (Note: credit will be given for at most one of MAS 4156 and MAS 5157.)

An introduction to elementary number theory and its applications to computer science and cryptology. Divisibility, primes, Euclidean Algorithm, congruences, Chinese Remainder Theorem, Euler-Fermat Theorem, primitive roots. Selected applications to decimal fractions, continued fractions, computer file storage and hashing functions, and public-key cryptography. (M)

Sets and mappings, groups and subgroups, homomorphisms and isomorphisms, permutations, rings and domains, arithmetic properties of domains, fields. This course requires facility in writing proofs.

Further topics in abstract algebra.

For special topics not obtainable in the regular course offerings.

Qualified undergraduates will take part in seminars or classes on special topics.

This course is designed for non-science and non-business majors who need to fulfill their Gordon Rule and General Education math requirements. The course includes an introduction to set theory, logic, number theory, probability, statistics, graphing, and linear programming. (M) GR-M†

A general education course that demonstrates the beauty and utility of mathematics. Topics include financial management, linear and exponential growth, mathematics in the arts, and discrete mathematics. This course may be taken without MGF 1106. (M) GR-M†

Examples of sets, operations on sets, set algebra, Venn diagrams, truth tables, tautologies, applications to mathematical arguments and mathematical induction. Taking one (but not both) of MAS 3300 and MHF 3202 is also very useful in preparing students for a major in mathematics. This course can also be very useful for prospective and in-service-school teachers and middle-school teachers. (M) GR-M†

The basic axioms and concepts of set theory. Students present proofs. (Note: credit will be given for at most one of MHF 4102 and MHF 5107.)

Models and proofs. Foundations of the real and natural numbers, algorithms, Turing machines, undecidability and independence. Examples and applications in algebra, analysis, geometry and topology. (Note: credit will be given for at most one of MHF 4203 and MHF 5207.)

An introduction to the history of mathematics. The course includes a historical discussion of selected mathematical topics. (M) GR-M†

A systematic study of the axiomatic structure of Euclidean and non-Euclidean geometry, including a comparison of the metric (Birkhoff) and synthetic (Hilbert) developments of absolute geometry; parallelism, similarity, area, lines and planes in space, solid mensuration. This course is particularly useful for prospective secondary school mathematics teachers. (M) GR-M†

Axiomatic structure of Euclidean geometry: congruence, parallelism, area, similarity, circles, polygons, medians, constructions, solid geometry, spherical and hyperbolic geometry.

The basic concepts of general topology. (Note: credit will be given for at most one of MTG 4302 and MTG 5316.)

Continuation of MTG 4302. (Note: credit will be given at most one of MTG 4303 and MTG 5317.)