2001 - 2002
Undergraduate Catalog

Mathematics

College of Liberal Arts and Sciences

INSTRUCTIONAL STAFF 2000-2001

Alladi, K., Chair;Block, L.S., Associate Chair; Bona, M.; Boyland, P.L.; Brechner, B.L.; Brooks, J.K.; Carter, C.; Cenzer, D.S.; Chen, Y.; Crew, R.M.; Dinculeanu, N.; Drake, D.A.; Dranishnikov, A.N.; Edwards, B.H.; Ehrlich, P.E.; Emch, G.G.; Garvan, F.G.; Glover, J.; Groisser, D.J.; Hager, W.W.; Ho, C.Y.; Hueter, I.; Keating, K.P.; Keesling, J.E.; Khuri, R.L.; King, J.L.; Klauder, J.R.; Kutuzova, M.; Larson, J.A.; Levin, N.; Mair, B.A.; Martinez, J.; McCracken, D.L.; McCullough, S.A.; Metzler, D.; Mitchell, W.J.; Moore, T.O.; Moskow, S.; Olson, T.E.; Pilyugin, S., Pop-Stojanovic, Z.R.; Rao, M.K.; Robinson, P.L.; Saxon, S.A.; Shen, L.C.; Sin, P.K.; Smith, J.Y.; Smith, R.; Summers, S.J.; Thompson, J.G.; Tiep, P.H.; Tornwall, S.B.; Townsend, M.D.; Turull, A.; Vince, A.J.; Voelklein, H.K.; Walsh, T.; White, N.L.; Wilson, D.C.; Zapletal, J.

Undergraduate Coordinator: B. Edwards

Actuarial Science Advisers:

Bruce Edwards, 364 Little Hall, 392-0281 ext 281;

Dennis Wackerly, 220 FLO, 392-1941 ext 227;

David Nye, 329 BUS, 392-0153;

Graduate Coordinator: P. Robinson

MAA 4102 Introduction to Advanced Calculus for Engineers and Physical Scientists 1. F, S.
Credits: 3; Prereq: MAC 2313 or MAC 3474 and grade of C or better in MAS 4105 or MAS 3114.
Review of limits, differentiation and integration; calculus of vector functions; line and surface integration; calculus of variations; Fourier series. Material presented with view to applications.

MAA 4103 Introduction to Advanced Calculus for Engineers and Physical Scientists 2. S, SS.
Credits: 3; Prereq: MAA 4102.
A continuation of MAA 4102.

MAA 4211 Advanced Calculus 1. F.
Credits: 3; Prereq: grade of C or better in MAS 4105.
An advanced treatment of limits, differentiation, integration, series; calculus of functions of several variables.

MAA 4212 Advanced Calculus 2. S.
Credits: 3; Prereq: MAA 4211.
A continuation of MAA 4211.

MAA 4226 Introduction to Modern Analysis 1. F.
Credits: 3; Prereq: grade of C or better in MAS 4105.

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.

MAA 4227 Introduction to Modern Analysis 2. S.
Credits: 3; Prereq: MAA 4226.
A continuation of MAA 4226.

MAA 4402 Elements of Complex Variables for Engineers and Physical Scientists. S, SS.
Credits: 3; Prereq: MAC 2313 (or MAC 3474) and MAP 2302.
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. Mathematics: calculus and precalculus.

MAC 1114 Trigonometry.
Credits: 2.
Exponential and logarithmic functions, trigonometry, analytic and additional applications of trigonometry. (M) (See note above) GR-M†

MAC 1140 Precalculus Algebra.
Credits: 3.
College algebra, functions, coordinate geometry, exponential and logarithmic functions. (M) (See note above) GR-M†

MAC 1147 Precalculus: Algebra and Trigonometry.
Credits: 4.
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). (M) (See note above) GR-M†

MAC 2233 Survey of Calculus 1.
Credits: 3; Prereq: Strong background in Precalculus.
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†

MAC 2234 Survey of Calculus 2. F, S.
Credits: 3; Prereq: MAC 2233 or equivalent.
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†

MAC 2311 Analytic Geometry and Calculus 1.
Credits: 4; Prereq: Strong background in precalculus.
Introduction to analytic geometry; limits; continuity; differentiation of algebraic and trigonometric functions, differentials; introduction to integration and the fundamental theorem of calculus. (M) (Credit will be given for at most one of MAC 2311 and MAC 3472.) GR-M†

MAC 2312 Analytic Geometry and Calculus 2.
Credits: 4; Prereq: MAC 2311 or MAC 3472.
Techniques of integration; applications of integration; differentiation and integration of inverse trigonometric, exponential and logarithmic functions; sequences and series. (M) (Credit will be given for at most one of MAC 2312, MAC 3512, and MAC 3473.) GR-M†

MAC 2313 Analytic Geometry and Calculus 3.
Credits: 4; Prereq: MAC 2312 or MAC 3512 or MAC 3473.
Solid analytic geometry; vectors; partial derivatives; multiple integrals. (M) (Credit will be given for at most one of MAC 2313 and MAC 3474.) GR-M†

MAC 3472 Honors Calculus 1. F.
Credits: 4; Prereq: Strong background in precalculus
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) (Credit will be given for at most one of MAC 2311 and MAC 3472.) GR-M†

MAC 3473 Honors Calculus 2. F, S.
Credits: 4; Prereq: MAC 3472.
A continuation of MAC 3472. (M) (Credit will be given for at most one of MAC 2312, MAC 3512, and MAC 3473.) GR-M†

MAC 3474 Honors Calculus 3. F, S.
Credits: 4; Prereq: MAC 3473.
A continuation of MAC 3473. (M) (Credit will be given for at most one of MAC 2313 and MAC 3474.) GR-M†

MAC 3512 Calculus 2 for Advanced Placement Students. F.
Credits: 4; Prereq: Advancement Placement credit for MAC 2311.
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) (Credit will be given for at most one of MAC 2312, MAC 3512, and MAC 3473.) GR-M†

MAD 4203 Introduction to Combinatorics 1. F.
Credits: 3; Prereq: MAC 2312 or MAC 3512 or MAC 3473.
Permutations and combinations, binomial coefficients, inclusion-exclusion, recurrence relations, Fibonacci sequences, generating functions, graph theory. (M) GR-M†

MAD 4204 Introduction to Combinatorics 2. S.
Credits: 3; Prereq: MAC 2312 or MAC 3512 or MAC 3473.
Matching theory, block designs, finite projective planes and error-correcting codes. This course can be taken without taking MAD 4203.

MAD 4401 Introduction to Numerical Analysis. F, S.
Credits: 3; Prereq: MAS 4105 or MAS 3114 and a scientific programming language.
Numeric integration, nonlinear equations, linear and non-linear systems of equations, differential equations and interpolation.

MAD 4504 Theory of Computing. S.
Credits: 3; Prereq: COP 3530.
Finite and infinite state machines; Turing machines, formal languages and their recognition automata; recursive functions; decidability and unsolvability; halting problem; space-time tradeoff. (M)

MAE 3811 Mathematics for Elementary School Teachers 2.
Credits: 3; Prereq: A passing score on the Arithmetic Competency Examination.
Properties and operations of rational numbers, ratio, proportion, percent, an introduction to real numbers, elementary algebra, informal geometry and measurement, and an introduction to probability and descriptive statistics.

MAP 2302 Elementary Differential Equations.
Credits: 3; Prereq: MAC 2312 or MAC 3512 or MAC 3473.
First order differential equations, theory of linear differential equations, solution of linear equations with constant coefficients, the Laplace transform, solution of equation by the Laplace transform. (M) GR-M†

MAP 3170 Introduction to Actuarial Mathematics. F.
Credits: 3; Prereq: MAC 2312 or MAC 3512 or MAC 3473.
Amount function, simple and compound interest, present value, dollar-weighted and time-weighted rates, force of interest, discrete and continuos annuities bonds, amortization, capitalization and applications.

MAP 4101 Probability Theory and Stochastic 1.
Credits: 3.

MAP 4102 Probability Theory and Stochastic Processes 2. S.
Credits: 3; Prereq: STA 4321.
Random walks and Poisson processes, martingales, Markov chains, Brownian motion, stochastic integrals and Ito’s formula.

MAP 4305 Introduction to Differential Equations for Engineers and Physical Scientists.
Credits: 3; Prereq: MAP 2302.
Series solutions of differential equations, Sturm-Liouville Systems.

MAP 4341 Elements of Partial Differential Equations. S.
Credits: 3; Prereq: MAC 2313 (or MAC 3474) and MAP 2302; MAP 4305 recommended.
Origin and solution of partial differential equations by various methods including Lagrange linear equations; elementary partial equations of mathematical physics.

MAP 4403 Mathematical Methods for Engineers.
Credits: 3; Prereq: MAC 2313, MAP 2302.
Complex variables, including derivatives and integrals, singularities, Taylor/Laurent series and residues; Linear Algebra, including Gaussian elimination, determinants, inversion, linear independence, QR decomposition, eigenvalues and eigenvectors, systems of differential equations; (time permitting) Numerical methods, including roots of equations, numerical integration and numerical optimization.

MAP 4413 Fourier Series and Transforms 1. S.
Credits: 3; Prereq: MAC 2313 (or MAC 3474) and MAP 2302; MAP 4305 recommended.
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 process, their autocorrelation functions, and problems of interpolation, extrapolation, filtering and smoothing or second order stationary processes.

MAS 3114 Computational Linear Algebra.
Credits: 3; Prereq: MAC 2312 (or MAC 3512 or MAC 3473) and a scientific programming language.
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†

MAS 3300 Numbers and Polynomials.
Credits: 3; Prereq: MAC 2312 or MAC 3512 or MAC 3473.
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. This course is particularly useful for prospective secondary school mathematics teachers. (M) GR-M†

MAS 4105 Linear Algebra 1.
Credits: 4; Prereq: MAC 2313 or MAC 3474; MAS 3300 recommended.
Linear equations, matrices, vector spaces, linear transformations, determinants, eigenvalues, inner product spaces. This course is more proof-oriented than MAS 3114.

MAS 4107 Linear Algebra 2. S.
Credits: 3; Prereq: MAS 4105.
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 as well as develop computational skills. The course serves both as a transition for the math majors from a study of techniques into more conceptual math and as a coherent foundation in linear algebra for engineering and science majors. GR-M†

MAS 4124 Introduction to Numerical Linear Algebra. F.
Credits: 3; Prereq: MAS 4105 or MAS 3114 and a scientific programming language.
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 of linear systems and eigensystems.

MAS 4156 Introduction to Vector Analysis. S.
Credits: 3; Prereq: MAC 2313 or MAC 3474.
Review of vector algebra, lines, planes and space curves; vector fields, their divergence and curl; line surface and volume integrals including the Divergence Theorem and Stokes’ Theorem.

MAS 4203 Introduction to Number Theory. S, SS.
Credits: 3; Prereq: MAC 2312 or MAC 3512 or MAC 3473; MAS 3300 recommended.
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)

MAS 4301 Abstract Algebra 1.
Credits: 3; Prereq: grade of C or better in MAS 4105.
Sets and mappings, groups and subgroups, homomorphisms and isomorphisms, permutations, rings and domains, arithmetic properties of domains, fields. The course involves learning to prove theorems.

MAS 4302 Abstract Algebra 2. S.
Credits: 3; Prereq: MAS 4301.
Further topics in abstract algebra.

MAT 4905 Individual Work.
Credits: 1 to 3; Maximum of 10 credits; Prereq: MAC 2313 and permission of departmental undergraduate coordinator. May be repeated for credit.
For special topics not obtainable in the regular course offerings. GR-M†

MAT 4930 Special Topics in Mathematics.
Credits: 1 to 3; Prereq: Permission of a departmental adviser. May be repeated for credit. Maximum of 16 credits.

MGF 1106 Mathematics for Liberal Arts Majors.
Credits: 3. Students who have received credit for MGF 1202 will not receive credit for MGF 1106.
A general education course which includes an introduction to logic and set theory, algebra, probability and statistics, an elementary introduction to linear programming and game theory, and a review of geometry and measurement. (M) GR-M†

MGF 1107 Math for Liberal Arts II.
Credits: 3.
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.(M) GR-M†

MHF 3202 Sets and Logic. F.
Credits: 3; Prereq: MAC 2312 or MAC 3512 or MAC 3473.
Examples of sets, operations on sets, set algebra, Venn diagrams, truth tables, tautologies, applications to mathematical arguments and mathematical induction. (M) GR-M†

MHF 4102 Elements of Set Theory. F.
Credits: 3; Prereq: MAS 4105.
The basic axioms and concepts of set theory. Students present proofs.

MHF 4203 Foundations of Mathematics. S.
Credits: 3; Prereq: MAS 4105.
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. (M)

MHF 4404 History of Mathematics. SS.
Credits: 3; Prereq: MAC 2312 or MAC 3512 or MAC 3473.
An introduction of mathematics. The course includes a historical discussion of selected mathematical topics. (M)(GR-M†)

MTG 3212 Geometry. S.
Credits: 3; Prereq: MAC 2312 or MAC 3512 or MAC 3473.
A systematic study of the axiomatic structure of 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†

MTG 4302 Elements of Topology 1. F.
Credits: 3; Prereq: MAS 4105.
The basic concepts of general topology.

MTG 4303 Elements of Topology 2. S.
Credits: 3; Prereq: MTG 4302.
Continuation of MTG 4302.