Sagher, Y., Chair; Booton, B.O.; Brewer, J.W.;
Ding, M.; Ford, T.J.; Goldwyn, R.M.; Hoffman, F.; Kalies,
W.D.; Kizlik, S.V.; Klingler, L.C.; Lin, Y.; Locke, S.C.;
Magliveras, S.S.; Meyerowitz, A.D.; Milman, M.M.; Mullin,
R.C.; Niederhausen, H.; Peitgen, H.O.; Pina, P.A.; Qian, L.; Radulescu, D.;
Radulovic, D.; Richman, F.; Schmidmeier, M.; Schonbek,
T.P.; Steinwandt, R.; Viola-Prioli, J.E.; Voss, R.F.;
Wang, Y.; Wei, W.; Yiu, P.Y.; Zhang, X.D.
Affiliated Faculty: Belogay, E.; Elishakoff, I.E.; Fitchett,
S.; Lin, Y.K.; Mandell, A.J.; Mech, W.P.; Morris, J.D.; Ronco,
S.; Waterman, D.
Faculty Emeritus: Freeman, J.M.; Schaefer, H.H.;
Schroeck, F.E.
Courses offered by the Department of Mathematical Sciences may require
the use of a calculator or computer software.
Cryptography and Information Security (CIS 4362) 3 credits
Prerequisites: MAS 2103, MAD 2502
Classical cryptology, entropy. Stream and block ciphers.
Public-key versus symmetric cryptography, one-way and trapdoor
functions. Primality and factorization, DLP, Diffie-
Hellman, RSA and ElGamal cryptosystems. Issues of
computer and network security. Secure protocols,
identification, authentication, digital signatures, secret
sharing schemes.
Fundamental Concepts of Mathematics (MGF 1202) 3 credits
Prerequisite: Intermediate or high school algebra
(Gordon Rule-mathematics)
A general education course surveying a variety of mathematical topics.
This course focuses on problem-solving and applications, with attention
given to the history of mathematics.
Note: Not offered currently.
Mathematics for Liberal Arts I (MGF 1106) 3 credits
(Gordon Rule-mathematics)
Prerequisite: MAT 1033 "Intermediate Algebra" or suitable placement score
Systematic counting, probabiliby, statistics, history of mathematics,
geometry, sets, logic, voting techniques, graph theory.
Mathematics for Liberal Arts II (MGF 1107) 3 credits
(Gordon Rule-mathematics)
Prerequisite: MAT 1033 "Intermediate Algebra" or suitable placement score
Financial mathematics, linear and exponential growth, history of mathematics,
elementary number theory.
College Algebra (MAC 1105) 3 credits
(Gordon Rule-mathematics)
Prerequisite: Intermediate Algebra or suitable placement score
Linear and quadratic functions, systems of equations and inequalities,
polynomial functions and equations, complex numbers, rational exponents
and radicals, matrices and determinants, exponential and logarithmic functions.
Trigonometry (MAC 1114) 3 credits
(Gordon Rule-computational)
Prerequisite: MAC 1105 and passing grade on pretest
Theory of trigonometric functions and their inverses, graphs, identities
and conditional equations, solutions of triangles, complex numbers and
polar representation. Additional topics as time permits.
Precalculus Algebra (MAC 1140) 3 credits
(Gordon Rule-computational)
Prerequisite: MAC 1105 and passing grade on pretest. Recommended Corequisite: MAC 1114
Polynomial, rational, and other algebraic functions; exponential and logarithmic
functions; piecewise defined functions. Properties and graphs of functions.
Polynomial and rational inequalities. Conic sections. Matrices and determinants.
Sequences and series. Mathematical induction. Binomial Theorem. Applications.
Precalculus Algebra and Trigonometry (MAC 1147) 4 or 5 credits
(Gordon Rule-computational)
Prerequisite: MAC 1105 or suitable placement score
Polynomial, rational, and other algebraic functions;
trigonometric, inverse trigonometric, exponential and
logarithmic functions; piecewise-defined functions. Properties
and graphs of functions. Polynomial and rational inequalities.
Trigonometric identities. Conditional trigonometric equations.
Conic sections. Solutions of triangles. Vector algebra. Parametric
equations. Polar coordinates. Matrices and determinants.
Sequences and series. Mathematical induction. Binomial
theorem. Applications.
Honors Seminar in Mathematics (MAT 1930) 3 credits
(Gordon Rule-writing) (min. 6,000 words)
Special topics course for lower division honors students in which the approach is generally philosophical and/or historical and which focuses on basic questions and issues of enduring importance related to the topic. The course emphasizes improvement of students’ critical thinking and writing skills.
Topics in Mathematics (MAT 1931) 1-4 credits
Prerequisite: Permission of instructor
Topics of interest to lower-division students.
Topics in Mathematics (MAT 1932) 1-3 credits
(Gordon Rule-computational)
Prerequisite: Permission of instructor; Co-requisite: College Algebra
Topics of interest to lower-division students.
Topics in Mathematics for Teachers (MAE
1935) 1-3 credits
Honors Seminar in Statistics (STA 1930) 3 credits
(Gordon Rule - writing, minimum 6,000 words)
Special topics course for lower division honors students in which the
approach is generally philosophical and/or historical and which focuses
on basic questions and issues of enduring importance related to the topic.
The course emphasizes improvement of students’ critical thinking and writing
skills.
Topics in Statistics (STA 1932) 3 credits
(Gordon Rule - mathematics)
Topics of interest to lower division students.
Methods of Calculus (MAC 2233) 3 credits
(Gordon Rule - computational)
Prerequisite: MAC 1105
A descriptive and intuitive introduction to the methods and
applications of differentiation and integration. Primarily for
social science and business administration majors.
Life Science Calculus I (MAC 2241) 3 credits
(Gordon Rule - computational)
Prerequisite: MAC 1105
Introduction to trigonometry, elementary functions,
differential and integral calculus, matrices, elementary
statistics, computer algebra. Examples and other topics of
interest to Biology and Psychology students.
Life Science Calculus II (MAC 2242) 3 credits
Gordon Rule, computational
Prerequisite: MAC 2241
Continuation of the topics listed under Life Science Calculus
I, examples and other topics of interest to Biology and
Psychology students.
Calculus with Analytic Geometry I (MAC 2311) 4 credits
(Gordon Rule - computational)
Prerequisites: MAC 1147, or both MAC 1140 and MAC 1114, and passing grade on pretest
Continuity, differentiability, differential approximation,
optimization and curve sketching of functions and inverse
functions of a single variable, including treatment of
trigonometric functions. Mean value theorem and L’Hopital’s
Rule. Introduction to integration.
Calculus with Analytic Geometry II (MAC 2312) 4 credits
(Gordon Rule - computational)
Prerequisite: MAC 2311
Continuation of MAC 2311. Logarithmic, Exponential,
hyperbolic, and inverse trigonometric functions, techniques
of integration, partial fractions, area, trapezoid and Simpson’s
rules, volume, work; analytic geometry; Taylor
approximations; sequences and series; polar representation
of complex numbers.
Calculus with Analytic Geometry III (MAC 2313) 4 credits
Prerequisite: MAC 2312
Vector space, inner product, length, cross product, curves in
space; functions of several variables: differentiability,
gradient, tangent planes, differential approximation,
surfaces, optimization with constraints, multiple integrals,
theorems of Green, Stokes and Gauss.
Discrete Mathematics (MAD 2104) 3 credits
(Gordon rule - computational)
Prerequisite: MAc 1105 or permission of instructor
A proof-oriented approach to, and applications of, propositional logic,
sets, functions, relations, combinatorics, graphs and trees.
Introduction to Computational Mathematics (MAD 2502) 3 credits
Corequisite: MAC 2311
An introduction to mathematical computation by means of
algorithmically solving a number of mathematical problems.
Introduction to C++. The emphasis will be on the
mathematical algorithms involved with problems from
analysis, number theory, combinatorics, algebra, linear
algebra, numerical analysis and probability.
Differential Equations I (MAP 2302) 3 credits
(Gordon Rule - computational)
Prerequisite: MAC 2312
An introduction to ordinary differential equations stressing basic techniques
and applications.
Differential Equations II (MAP 4303) 3 credits
Prerequisite: MAP 2302
Further techniques in ordinary differential equations and an introduction
to partial differential equations.
Note: Not currently offered.
Matrix Theory (MAS 2103) 3 credits
Prerequisite: MAC 2311 or MAC 2233
Vectors and vector spaces. Linear transformation and matrices. Rank
and determinants. Systems of linear equations. Diagonalization. Characteristic values.
Linear Algebra II (MAS 4107) 3 credits
Prerequisite: MAS 2103 or Linear Algebra I
Vector spaces, complex numbers, basis and dimension, eigenvalues and eigenvectors, Cayley-Hamilton theorem, Jordan normal form, and other topics.
Mathematics Study Abroad (MAT 2952) 1-4 credits
Prerequisite: Sophomore standing
Credit for enrollment in approved study abroad programs.
Statistics in Practice (STA 2022) 3 credits
Prerequisite: MAC 1105 or MGF 1202 or MGF 1106
Introduction to statistical reasoning through an overview of real-world
applications. Examples of statistical methods in practice will be drawn
from daily life in addition to the areas of government and public policy,
law, business and industry, public health, engineering, and sciences.
Introductory Statistics (STA 2023) 3 credits
(Gordon Rule-mathematics)
Prerequisite: MAC 1105 or MGF 1202 or MGF 1106
An introductory course covering descriptive statistics, probability,
binomial and normal distributions, sampling distributions and hypothesis
tests, and sampling procedures. Laboratory required.
Statistics Study Abroad (STA 2952) 1-4 credits
Prerequisite: Sophomore standing
Credit for enrollment in approved study abroad programs.
Numerical Methods (MAD 3400) 3 credits
Prerequisites: MAC 2312 and some programming experience
(Not available for students with credit for MAD 4401)
An introductory course in computing for engineering and science students
presenting FORTRAN programming as a tool for the solution of numerical
problems. Topics covered include numerical errors, roots of equations,
curve fitting, matrix methods, numerical integration, solution of differential
equations, and graphic output.
Topics in Mathematics for Teachers (MAE 3935)
1-3 credits
Engineering Mathematics I (MAP 3305) 3 credits
Prerequisite: MAC 2313
Complex numbers, matrices, determinants, systems of equations, diagonalization,
first and second order linear differential equations and systems thereof,
including power series solutions.
Note: Not currently offered.
Engineering Mathematics II (MAP 4306) 3 credits
Prerequisites: MAC 2313 and one of MAP 3305 or MAP 2302
Frobenius method, partial differential equations of physics and engineering.
Boundary value, initial value, Sturm-Liouville problems, Laplace transforms.
Actuarial Mathematics I (MAP 4172) 3 credits
Prerequisites: MAC 2311, 2312, 2313, ECO 2013, and STA 4442
The course covers concepts from calculus and probability as they pertain to actuarial sciences. It cover differential equations, parameterized curves, general probability, Bayes’ theorem, and univariate and multivariate probability distributions. Grading: Pass/fail option
Preparation for Actuarial Exam II (MAP 4173) 1 credit
Prerequisites: ECO 2023, RMI 3011
Course includes a review of topics in microeconomics and
macroeconomics, basic interest theory, and finance. The
application of these topics to problems encountered in
actuarial science is emphasized.
Internship in Actuarial Sciences (MAP 4945) 1-6 credits
Prerequisite: Departmental approval
Supervised internships individually assigned to accommodate
students’ professional development in the actuarial field.
May be repeated for a maximum of 6 credits.
Introductory Number Theory (MAS 3203) 3 credits
The basic theory of divisibility and congruences. The theorems of Fermat,
Euler and Wilson. Quadratic residues.
Cooperative Education-Mathematics (MAT 3949) 1-2 credits
Grading: S/U
History of Mathematics (MHF 3404) 3 credits
Prerequisite: MAD 2104
Chronological study of the evolution of mathematical thought from primitive
counting to modern ideas of the 20th century.
Survey of Geometry (MTG 3212) 3 credits
Prerequisite: MAD 2104
Euclidean and non-Euclidean geometries. Introduction to projective geometry
and the geometry of transformations.
Intermediate Statistics (STA 3163) 2 credits
(Gordon Rule-computational)
Prerequisite: STA 2023 or equivalent; Co-requisite: STA 3163L
An introduction to large-sample estimation and tests of hypotheses;
t-tests; chi-square tests; one-way ANOVA; linear and multiple regression;
correlation; experimental designs. Laboratory required.
Intermediate Statistics Laboratory (STA 3163L) 1 credit
Co-requisite: STA 3163 or PSY 3234
Computer organization, computer implementation of basic and intermediate
statistical inferences that include describing data, graphic presentation,
analysis of data. Applications will reflect the descriptive and statistical
inferences appropriate to the discipline under which this course is offered
(e.g., business, education, engineering, mathematics, psychology, etc.).
Cooperative Education - Statistics (STA 3949)
1-2 credits
Modern Analysis (MAA 4200) 3 credits
Prerequisites: MAC 2313 and MAD 2104
Basic properties of real numbers. Functions. Limits and
properties of continuous functions. Differential calculus.
Introductory Complex Analysis (MAA 4402) 3 credits
Prerequisite: MAC 2313
An introduction to complex analysis, analytic functions, Taylor series,
Cauchy’s theorem. Calculus of residues. Recommended for engineering and
science majors.
Graph Theory (MAD 4301) 3 credits
Prerequisites: MAS 2103 and MAD 2104
A first course in theory and applications of graphs including basic
properties; coloration; algebraic and geometric aspects; enumeration; algorithms; network flows.
Introduction to Coding Theory (MAD 4605) 3 credits
Prerequisites: MAS 2103 and STA 4442 or equivalent
Introduction to the theory of Error Correcting Codes. Binary
symmetric channel, probability of error, finite fields, linear
codes, standard array, maximum likelihood decoding, sphere
packing, Plotkin and other bounds, Hamming codes, Perfect
codes, BCH codes, Dual codes, the Krawtchouk polynomials,
and MacWilliams theorem.
Numerical Analysis I (MAD 4401) 3 credits
Prerequisites: MAC 2313, MAP 2302, MAS 2103 and some
programming experience
(Not available for students with credit for MAD 3400.)
Floating point arithmetic, interpolations, approximations, differentiation
and integration, linear and nonlinear systems of equations, differential
equations, eigenvalues and eigenvectors, error analysis and norms. This
course emphasizes theory.
Numerical Analysis II (MAD 4402) 3 credits
Prerequisites: MAC 2313, MAP 2302, MAS 2103, and one of either MAD 4401 or MAD 3400
Continuation of topics introduced in MAD 4401.
Modern Algebra (MAS 4301) 3 credits
Prerequisite: MAD 2104
Elementary number theory. Groups, rings and ideals, polynomials, and
fields.
Directed Independent Study (MAT 4906) 1-4 credits
Prerequisite: Permission of instructor
Study of topics relating to the special needs and interests of individual
students.
Special Topics (MAT 4930) 1-4 credits
Prerequisite: Permission of instructor
Lectures on specialized topics.
Problem-Solving Seminar (MAT 4937) 1 credit
Prerequisite: Permission of instructor
Miscellany of challenging mathematical problems not usually met in the
standard courses.
Mathematics Study Abroad (MAT 4957) 1-4 credits
Prerequisite: Sophomore standing
Credit for enrollment in approved study abroad programs.
Mathematical Methods of Physics (PHS 4113) 3 credits
Prerequisite: MAP 2302
This course, together with PHZ 5115, comprises a course in techniques
of mathematical physics. Among topics covered in this course are: applications
of complex variables, Fourier series, integral transforms, solution of
homogeneous partial differential equations by separation of variables,
eigenfunction expansions and integral transforms. Applications to problems
in physics and engineering will be stressed.
Probability and Statistics for Engineers (STA 4032) 3 credits
Prerequisite: MAC 2312
Basic concepts of probability; random variables; discrete and continuous
probability distributions; functions of random variables; estimation theory;
tests of hypotheses.
Computational Statistics I (STA 4102) 3 credits
Prerequisite: STA 4234 or STA 4443
Computer algorithms for evaluation, simulation and visualization, random
number generation, sampling from prescribed distributions. Simulations,
graphics for data display, computation of probabilities and percentiles,
hypothesis testing, simple linear regression and multiple regression.
Computational Statistics II (STA 4103) 3 credits
Prerequisite: STA 4102
Continuation of topics introduced in STA 4102.
Applied Statistics I (STA 4234) 2 credits
Prerequisite: MAC 2312, STA 2023, STA 4442; Co-requisite: STA 4202L
Point and interval estimation, hypothesis tests, nonparametric procedures,
contingency tables. Essential distribution theory. Linear models, including
multiple regression and analysis of variance. Emphasis on data analysis,
statistical graphics, and diagnostics via personal computing.
Applied Statistics II (STA 4203) 3 credits
Prerequisite: STA 4202 (Applied Statistics I)
Multivariate statistical methods, including the multivariate normal
distribution, component analysis, factor analysis, multivariate analysis
of variance and regression, discriminant analysis, and causal modeling.
Students will use SAS and/or SPSS statistical software.
Note: Not currently offered.
Planning Investigations (STA 4222) 3 credits
Prerequisites: STA 4234 and MAC 2312
Basic concepts of experimental design: randomized blocks, Latin squares,
incomplete blocks, factorial designs, fractional factorials, nested designs.
Second part of course covers introduction to design of sample surveys:
simple random, stratified, cluster sampling; complex designs; ratio and
regression estimation; enumerative vs. analytical surveys. Student project
required.
Probability and Statistics I (STA 4442) 3 credits
Prerequisites: Calculus and Analytic Geometry
An introductory course treating combinatorics, probability spaces, laws
of large numbers, and central limit theorem. An introduction to Markov
processes, information theory and applications.
Probability and Statistics II (STA 4443) 3 credits
Prerequisite: STA 4442
Properties of test statistics, estimation and testing, linear models,
contingency tables; topics from nonparametric statistics, design of experiments
or methods of inference.
Linear Programming & Game Theory (STA 4618) 3 credits
Prerequisite: MAS 2103
Dantzig’s simplex method. Duality. Convexity and optimal strategies.
Applications.
Probability and Random Processes (STA 4800) 3 credits
Prerequisite: MAP 4306 or graduate standing
Introductory probability theory, random variables and processes, and
ergodicity. Application to engineering.
Directed Independent Study (STA 4906) 1-4 credits
Prerequisite: Permission of Instructor
Study of topics relating to the special needs and interests of individual
students.
Special Topics (STA 4930 ) 1-4 credits
Prerequisite: Permission of instructor
Topics of interest to upper-division students.
Statistics Study Abroad (STA 4957) 1-4 credits
Prerequisite: Sophomore standing
Credit for enrollment in approved study abroad programs.
Topics in Geometry (MTG 4930 ) 1-4 credits
Prerequisite: Permission of instructor
Topics in geometry chosen from Euclidean geometry, projective geometry,
geometry of the complex plane, hyperbolic geometry, finite geometries,
automorphism groups, Riemannian geometry, fractal geometry, combinatorial geometry,
computational geometry, or other areas of current interest.
Honors Thesis in Mathematics (MAT 4970) 3 credits
Prerequisite: MAA 4200, MAS 4301 and permission of instructor
Supervised research and writing of the honors thesis.
ADVANCED UNDERGRADUATE AND GRADUATE COURSES
Introductory Analysis I (MAA 5228) 3 credits
Introductory Analysis II (MAA 5229) 3 credits
Prerequisite: MAA 4200 or permission of instructor
A sequence of two courses intended for mathematically mature students
contemplating graduate work in mathematics. These are the same courses offered a few years ago as MAA 5226, 5227.
The real and
complex numbers, metric spaces, sequences and series,
continuity, differentiation and integration of functions of
one or several real variables.
Real Analysis I (MAA 6306) 3 credits
Real Analysis II (MAA 6307) 3 credits
Prerequisite: MAA 5227
Abstract measure theory, the Lebesgue and other related integrals, the theorems of
Lebesgue, Radon-Nikodym, and Fubini, and the Lp-spaces.
Complex Analysis I (MAA 6406) 3 credits
Complex Analysis II (MAA 6561) 3 credits
Prerequisite: MAA 5227
The complex plane and its geometry, stereographic projection and linear fractional
transformations, analytic and harmonic functions, contour integration, Cauchy's theorem
and the calculus of residues, and special functions and conformal mapping.
Topics in Real and Complex Analysis (MAA 6416) 1-4 credits
Prerequisite: Permission of instructor
Advanced treatment of topics such as theory of distribution, Fourier analysis, and special
functions. May be repeated for credit.
Topics in Functional Analysis (MAA 6506) 1-4 credits
Prerequisite: Permission of instructor
An advanced treatment of topics such as theory of normed linear spaces, Banach algebras,
and Hilbert spaces; Gelfand theory and spectral theorem for normal operators, applications
to integral equations, and other topics. May be repeated for credit.
Introductory Combinatorics (MAD 5202) 3 credits
Prerequisites: MAC 2313 and MAD 2104 or permission of instructor
This course is intended for the mathematically mature
student contemplating graduate work in mathematics.
A second course in discrete mathematics: graphs and networks, enumeration, lattices, designs, codes, applications,
and proof techniques.
Combinatorics I (MAD 6206) 3 credits
Combinatorics II (MAD 6207) 3 credits
Prerequisite: MAD 5202
A survey of combinatorial theory including methods of enumeration, theorems on
choice, existence and construction of designs, and graphs and networks.
Topics in Combinatorics (MAD 6209) 1-4 credits
Prerequisite: Permission of instructor
Advanced treatment of topics such as block designs, coding theory, enumeration, graph
theory, matroid theory, and umbral calculus. May be repeated for credit.
Prerequisites: Permission of instructor
Shannon theory. One-way, trapdoor functions, entropy.
Symmetric and public-key cryptography. Stream and block
ciphers. Diffie-Hellman, RSA, EIGamal systems and attacks.
Elliptic curve systems. Hash functions and data integrity.
Identification, digital signatures.
Prerequisites: MAD 6477 or equivalent
Entropy, probabilistic attacks. Passive and active attacks.
Ciphertext-only, known-plaintext, chosen-plaintext, chosenciphertext
attacks, adaptive attacks. Types of security. Know attacks
on computationally-secure systems. Meet in the middle attacks.
Differential and linear cryptanalysis. Random number generators,
tests, analysis and weakness.
Prerequisites: MAS 4301 or permission of instructor
Channels, intro to information theory, Shannon's capacity
theorem. Linear codes. Hamming, cyclic codes, BCH codes,
sphere packings, the Golay codes, weight enumerators.
MacWiliams' equation.
Topics in Mathematics for Teachers (MAE 5935) 1-4 credits Teaching Probability and Statistics (MAE 6137) 3 credits Dynamical Systems I (MAP 6208) 3 credits Dynamical Systems II (MAP 6209) 3 credits Topics in Applied Mathematics II (MAP 6436) 1-4 credits Introductory Abstract Algebra I (MAS 5312) 3 credits Introductory Abstract Algebra II (MAS 5313) 3 credits Algebraic Number Theory(MAS 6215) 3 credits Number Theory and Cryptography (MAS 6217) 3 credits Abstract Algebra I (MAS 6311) 3 credits Abstract Algebra II (MAS 6312) 3 credits Topics in Algebra (MAS 6396) 1-4 credits Special Topics (MAT 5932) 1-4 credits Directed Independent Study (MAT 6907) 1-4 credits Special Topics (MAT 6933) 1-4 credits Master's Thesis (MAT 6971) 1-6 credits Dissertation (MAT 7980) 1-12 credits Set Theory (MHF 5206) 3 credits
Prerequisite: MAS 4301 or permission of instructor
The Zermelo-Frankel axioms for set theory,
ordinal and cardinal numbers, and the Axiom of Choice and Zorn’s Lemma. Topics in the History of Mathematics (MHF 6405) 3 credits
General Topology I (MTG 6316) 3 credits General Topology II (MTG 6317) 3 credits Topics in Topology (MTG 6346) 1-4 credits Mathematical Statistics (STA 6326) 3 credits Mathematical Probability (STA 6444) 3 credits Topics in Probability and Statistics (STA 6446) 1-4 credits Directed Independent Study (STA 6907) 1-4 credits
An introduction to probability and statistics with attention to pedagogical
considerations. Topics such as descriptive statistics, probability, probability
distributions, sampling, techniques, and estimation are treated.
Prerequisite: Engineering Mathematics II
Scalar autonomous equations, elementary bifurcations, scalar maps, one-dimensional
chaos, scalar nonautonomous equations, bifurcations of periodic equations, equations on
tori and circle maps, planar autonomous systems.
Prerequisite: Dynamical Systems I
Linear planar systems, planar systems near equilibria, Lyapunov functions, zero and
purely imaginary eigenvalues, periodic orbits, conservative and gradient systems, planar
maps, two-dimensional chaos, and dynamics of higher dimensional systems.
Prerequisite: Permission of instructor
Advanced treatment of topics including ordinary and partial differential equations,
potential theory, the calculus of variations, and optimal control theory. May be repeated
for credit.
Prerequisite: MAS 4301 or permission of instructor
Basic structures of abstract and linear algebra: groups, rings and ideals,
polynomials and factorization, vector spaces and modules, linear transformations, and the
classical Galois theory of fields.
The structure of the ring of integers in an akgebraic number field; extensions of primes and decomposition into products of prime ideals, action of the Galois group on these decompositions, bounds on the size of the ideal class group and the structure of the group of units.
Elementary number theory with applications to cryptography, including: congruences and
modular arithmetic, finite fields, public key cryptography (RSA), primality testing and
factoring.
Prerequisite: MAS 5303
A second course in abstract algebra, covering groups, rings, fields, and linear and
multilinear algebra.
Prerequisite: Permission of instructor
Advanced treatment of topics such as field theory and Galois theory, finite groups,
abelian groups, ring theory, commutative rings, cohomology of algebraic systems and
ordered algebraic structures. May be repeated for credit.
Prerequisite: Permission of instructor
Lectures on advanced specialized topics. May be repeated for credit.
Prerequisite: Permission of instructor
Advanced topics relating to the special needs and interests of individual students.
Prerequisite: Permission of instructor
Topics will vary. May be repeated for credit.
Prerequisite: Admission to doctoral candidacy
Studies of English translations of various mathematical classics from ancient to
modern times, covering a wide range of various mathematical ideas relevant to the teaching
of mathematics at the high school level.
Prerequisite: MHF 5206
Topological spaces, continuous mappings, and homeomorphisms, separation axioms,
metric spaces and metrization, compact and connected spaces, product spaces and uniform
spaces.
Prerequisite: Permission of instructor
Advanced topics such as homotopy, homology, cohomology theories, combinatorial
topology, and spectral sequences. May be repeated for credit.
Prerequisite: STA 6444
Theory of inference, regression, ANOVA, robust procedures, or other selected topics.
Prerequisite: STA 4443
Theory of random variables, stochastic processes, Brownian motion, renewal processes,
martingales, or other selected topics and applications.
Advanced treatment of topics from stochastic processes, limit laws, decision theory, and
sequential methods. May be repeated for credit.
Study of topics relating to the special needs and interests of individual students.