DESCRIPTION: This course will cover the history of mathematics from its early beginnings through the medieval period and on to selected developments in the modern period.

PREREQUISITE(S): Math 163.

BASIS FOR GRADING: Exams (2 or 3), attendance, class participation, paper.

THIS COURSE IS GOOD PREPARATION FOR: Students of Mathematics Education.

(1) History of Mathematics, 3^rd ed. by David Burton, McGraw Hill Publ.

(2) Journey Through Genius, 1990 by William Dunham, Penguin Books.

RECOMMENDED:

by Sanderson Smith, Key Curriculum Press.

(2) A History of Pi, 1971 by Petr Beckmann, St. Martin’s Press.

TR 2:00-3:15 Hagstrom

DESCRIPTION: Introduction to dynamic models and their computational analysis. Introduction to, and extensive use of, Mathematica software.

PREREQUISITE(S): One year of calculus.

BASIS FOR GRADING: Homework and projects.

TEXTBOOKS: (1) Mathematica: A Practical Approach, 2^nd ed. by Blachman and

Williams, Prentice-Hall.

Mathematical Association of America.

Section 001 MWF 9:00-9:50 Putkaradze

002 MW 1:00-2:15 Lorenz

DESCRIPTION: Vector algebra, functions, curves, arc length, line integrals, directional derivative and gradient, divergence, curl, Gauss’ and Stokes’ theorems, applications.

PREREQUISITE(S): Math 264 or permission of chairperson.

BASIS FOR GRADING: Homework and tests.

THIS COURSE IS GOOD PREPARATION FOR: Upper division courses in pure/applied math.

TEXTBOOKS: Introduction to Vector Analysis, 7^th ed. by Davis and Snider, Quant

Systems Publ.

(1) Schaum’s Outlines of Vector Analysis, by M. Spiegel, McGraw-Hill.

(2) Div Grad Curl and All That, 3^rd ed. by H.M. Schey, WW Norton & Co.

MWF 1:00-1:50 Ellison

DESCRIPTION: Introduction to the theory and applications of partial differential equations. The solution of some classical partial differential equations, like the heat equation, the wave equation and the potential equation, will be considered. Fourier series and integrals, Bessel functions and Legendre polynomials will be studied in connection with these equations.

PREREQUISITE(S): Math 264 and 316.

BASIS FOR GRADING: Homework and exams.

THIS COURSE IS GOOD PREPARATION FOR: Math 463, 466, 472; and advanced courses in engineering, math, and physics.

TEXTBOOK: Introduction to Partial Differential Equations with Matlab, 1998 by Jeffrey

Cooper, Springer-Verlag: Birkhauser Publ.

Section 001 TR 9:30-10:45 Coutsias

002 MW 1:00- 2:15 Galicki

003 TR 2:00- 3:15 Staff

DESCRIPTION: An introduction to linear systems and matrix algebra. Applications to graphics, population dynamics and differential equations will be discussed.

PREREQUISITE(S): Math 162 and 163.

BASIS FOR GRADING: Homework, quizzes, computer projects, and final exam.

TEXTBOOK: Linear Algebra With Applications, 5^th ed. by S.J. Leon, Prentice-Hall Publ.

Section 001 MWF 10:00-10:50 Embid

002 MW 11:00-11:50 Nitsche

003 MW 1:00- 2:15 Wofsy

004 MW 5:30- 6:45 Staff

DESCRIPTION: Covers first order differential equations, second order linear and special non-linear differential equations, Laplace transforms and discontinuous forcing functions, linear systems of differential equations including a study of eigenvalues and eigenvectors, phase plane analysis and stability of linear systems. Integrated into the course are computer assignments covering numerical approximations to first order, second order, and linear systems of differential equations.

PREREQUISITE(S): Math 163.

BASIS FOR GRADING: Quizzes, exams, computer problems, and final.

THIS COURSE IS GOOD PREPARATION FOR: Mechanics, circuits, vibrating systems, mathematical modeling in all fields of biological, physical, and social sciences.

TEXTBOOKS: Elementary Differential Equations and Boundary Value Problems, 6^th ed.

by Boyce and DiPrima, Wiley and Sons Inc.

Maple V Learning Guide, 1996 by Heal/Hansel/Rickland, by Springer-

Verlag: Waterloo Maple.

MWF 9:00-9:50 Buium

DESCRIPTION: Set theory, induction, enumeration theory, arrangements, selections, combinations, permutations, generating functions, and recurrence relations.

PREREQUISITE(S): One year of calculus.

BASIS FOR GRADING: Tests and homework.

THIS COURSE IS GOOD PREPARATION FOR: Math 317, 318, and computer engineering.

TEXTBOOK: Not available.

TR 2:00-3:15 Boyer

DESCRIPTION: This is a standard course in linear algebra with emphasis on geometric content. Efforts will be made to motivate new concepts before their definitions. Topics to be convered: vectors, matrices, vector spaces, linear transformations, orthogonal projections, inner product spaces, determinants, eigenvalues, and eigenvectors.

PREREQUISITE(S): Math 264.

BASIS FOR GRADING: Homework, tests, and final.

THIS COURSE IS GOOD PREPARATION FOR: Most advanced pure and applied mathematics courses.

TEXTBOOKS: Linear Algebra, 3^rd ed. by Larry Smith, Springer-Verlag.

RECOMMENDED:

Interactive Linear Algebra with Maple V, 1998 by Deeba and

Gunawardena, Springer-Verlag.

MWF 10:00-10:50 Nakamaye

DESCRIPTION: Groups, rings, homomorphisms, permutation groups, quotient structure, ideal theory, and fields.

PREREQUISITE(S): Math 264.

TEXTBOOK: Undergraduate Algebra, 2^nd ed. by Serge Lang, Springer-Verlag.

TR 2:00-3:15 Loring

DESCRIPTION: We will begin with an overview of sets, functions, and proofs. Then, we will study recursion, counting methods, combinatorics, and graph theory.

PREREQUISITE(S): One year of calculus.

BASIS FOR GRADING: Homework, midterm, and final.

THIS COURSE IS GOOD PREPARATION FOR: Electrical engineering and computer science.

TEXTBOOK: Discrete Mathematics with Graph Theory, 1998 by Goodaire and

Parmenter, Prentice-Hall Publ.

M 4:00-6:30 Kelly

DESCRIPTION: We discuss secondary mathematics topics from an advanced point of view. I tope to deepen your knowldege of algebra, geometry, trigonometry, analytic geometry, and calculus. The course is open only to students who plan to teach mathematics.

PREREQUISITE(S): One year of calculus.

BASIS FOR GRADING: Problems at the board, homework, and two exams.

THIS COURSE IS GOOD PREPARATION FOR: Teaching math.

TEXTBOOK: Modern Analytic Geometry, 1988 by Wooten et al., Houghton-Mifflin Publ.

Section 001 TR 9:30-10:45 Huzurbazar

002 TR 2:00- 3:15 Koltchinskii

DESCRIPTION: Basic probability, discrete random variables, continuous random variables, independence, joint distributions, expected values, variances and covariances, confidence intervals, correlation, hypothesis testing, and tests for one and two sample problems. Topics from: Markov chains, queues, sums of random variables, systems models, and reliability.

PREREQUISITE(S): One year of calculus.

BASIS FOR GRADING: Quizzes, midterms, and final.

THIS COURSE IS GOOD PREPARATION FOR: Statistics, statistics in engineering, and statistics in biology and geology.

TEXTBOOK: Concepts in Probability and Stochastic Modeling, 1995 by Higgins and

McNutty, ITP: Duxbury Press.

TR 9:30-10:45 Christensen

DESCRIPTION: Statistical tools for scientific research, including parametric and non-parametric methods for ANOVA and group comparisons, simple linear and multiple linear regression, and basic ideas of experimental design and analysis, Emphasis placed on the use of statistical packages such as SAS.

PREREQUISITE(S): An introductory statistics course or permission of instructor.

TEXTBOOKS: Notes are provided in the department.

RECOMMENDED:

Analysis of Variance, Design, and Regression: Applied Statistical

Methods, by Ronald Christensen, CRC Press: Chapman & Hall.

MW 1:00-2:45 Staff

DESCRIPTION: This is a first course in logical theory. Its primary goal is to study the notion of logical entailment and related concepts, such as consistency and contingency. Formal systems are developed to analyze these notions rigorously.

NOTE: This course is cross-listed as PHIL 356. Please see Philosophy Department for other information regarding this course.

M 11:00-11:50 and TR 11:00-12:15 Loring

DESCRIPTION: We will carefully examine the concepts of limit, continuity, and derivative, and then study Riemann integration.

PREREQUISITE(S): Math 264.

BASIS FOR GRADING: Midterm, homework, and final.

THIS COURSE IS GOOD PREPARATION FOR: Graduate study.

TEXTBOOK: The Way of Analysis, 1995 by R.S. Strichartz, Jones & Bartlett.

TR 9:30-10:45 Hagstrom

DESCRIPTION: Introduction to basic problems in real number computation: linear algebra, integration, and differentiation. Emphasizes the use of MATLAB.

PREREQUISITE(S): Math 163 and some ability in Fortran or C programming.

BASIS FOR GRADING: Homework and projects.

THIS COURSE IS GOOD PREPARATION FOR: All work in scientific and engineering computation.

TEXTBOOK: Introduction to Scientific Computing: A Matrix-Vector Approach Using

MATLAB, 2^nd ed. by C. van Loan, Prentice-Hall Publishing.

MWF 10:00-10:50 Nakamaye

DESCRIPTION: Groups, rings, homomorphisms, permutation groups, quotient structure, ideal theory, and fields.

PREREQUISITE(S): Math 264.

TEXTBOOK: Undergraduate Algebra, 2^nd ed. by Serge Lang, Springer-Verlag.

TR 9:30-10:45 Boyer

DESCRIPTION: Metric spaces, topological spaces, continuity, and algebraic topology.

PREREQUISITE(S): Math 361.

TEXTBOOKS: Introduction to Topology, by Gamelin and Greene, Saunders College.

Topological Spaces, 1997 by Buskes and Van Rooij, Springer-Verlag.

TR 12:30-1:45 Bedrick

DESCRIPTION: This is a beginning course, but suitable for students who wish a systematic development of probability. The course covers the standard discrete and continuous distributions, moments, expectation, conditional probability, joint distributions, independence, laws of large numbers, and the central limit theorem.

PREREQUISITE(S): Math 264 or equivalent (3 semesters of calculus).

BASIS FOR GRADING: Regular homework plus a midterm and final.

THIS COURSE IS GOOD PREPARATION FOR: Future coursework in probability, statistics, applied math, and other scientific areas.

TEXTBOOK: A First Course in Probability, 5^th ed. by S. Ross, Prentice-Hall Publishing.

MW 2:30-3:45 Wofsy

DESCRIPTION: Regression analysis deals with making inferences from data, concerning the dependence of one variable on one or more other variables. We will cover simple linear regression, multiple regression, diagnostics, and model selection, and introduce logistic regression and nonlinear regression.

PREREQUISITE(S): Math 345 or 347, or consent of instructor.

BASIS FOR GRADING: Homework and exams.

THIS COURSE IS GOOD PREPARATION FOR: Stat 545 and other graduate courses in statistics.

TEXTBOOK: Analysis of Variance, Design, and Regression, by Ronald Christensen,

CRC Press: Chapman and Hall.

TR 2:00-3:15 Christensen

M 11:00-11:50 and TR 11:00-12:15 Loring

DESCRIPTION: We will carefully examine the concepts of limit, continuity, and derivative, and then study Riemann integration.

PREREQUISITE(S): Math 264.

BASIS FOR GRADING: Midterm, homework, and final.

THIS COURSE IS GOOD PREPARATION FOR: Graduate study.

TEXTBOOK: The Way of Analysis, 1995 by R.S. Strichartz, Jones & Bartlett.

MWF 12:00-12:50 Embid

DESCRIPTION: Local existence and uniqueness theorem, flows, linearized stability analysis for critical points and the stable manifold theorem. Gradient and Hamiltonian systems. Global existence theorems, limit sets and attractors, periodic orbits and Floquet theory, the Poincaire map. Introduction to structural stability and bifurcation theory. Hopf’s theorem for periodic solutions. Introduction to multi-scale perturbation theory.

PREREQUISITE(S): Math 316, 314 or 321, 361, or permission of instructor.

BASIS FOR GRADING: Homework.

THIS COURSE IS GOOD PREPARATION FOR: Study of dynamical systems in math, physics, and engineering.

TEXTBOOKS: (1) Qualitative Theory of Ordinary Differential Equations, 1994 by Brauer

and Nohel, Dover Publ.

(2) Lectures on Ordinary Differential Equations, 1990 by Hurewitz,

Dover Publ.

TR 2:00-3:15 Coutsias

DESCRIPTION: Determinants; theory of linear equations; matrix analysis of differential equations; eigenvalues, eigenvectors, and canonical forms; variational principles; generalized inverses.

PREREQUISITE(S): Math 314 or 321 or permission of instructor.

TEXTBOOK: Linear Algebra and Its Applications, 3^rd ed. by G. Strang, Saunders

This course is cross-listed as CS 471.

MW 3:00-3:50 and MW 4:00-5:15 Steinberg

DESCRIPTION: Introduction to scientific computing fundamentals, exposure to high performance programming language and scientific computing tools, and case studies of scientific problem solving techniques.

PREREQUISITE(S): Math 312, and 314 or 321, or permission of instructor.

TEXTBOOKS: Designing and Building Parallel Programs, by Ian Foster, Addison-

MWF 10:00-10:50 Lorenz

DESCRIPTION: This course covers implementation and analysis of basic numerical methods for a variety of problems. The main emphasis is the numerical approximation of differential equations. Other topics are: numerical interpolation, differentiation, and integration; iterative solution of nonlinear systems; splines; and fast Fourier transform.

PREREQUISITE(S): Math 316 or 361 or equivalent, and some knowledge of programming.

THIS COURSE IS GOOD PREPARATION FOR: The course will meet basic needs for engineers, scientists, and applied mathematician who are interested in obtaining quantitative approximations for analytical problems.

TEXTBOOKS: (1) Numerical Mathematics, by K. Hoffmann, Springer-Verlag Publ.

(2) Numerical Analysis of Differential Equations, by A. Iserles,

MWF 1:00-1:50 Kapitula

DESCRIPTION: Real number system, basic set theory, point-set topology, sequences, series, integration, and differentiation.

PREREQUISITE(S): Math 321 and 361.

BASIS FOR GRADING: Homework and final.

THIS COURSE IS GOOD PREPARATION FOR: The course lays the necessary foundation to get an advanced degree in pure and applied mathematics.

TEXTBOOK: Mathematical Analysis: An Introduction, 1996 by Andrew Browder,

MWF 12:00-12:50 Embid

DESCRIPTION: Local existence and uniqueness theorem, flows, linearized stability analysis for critical points and the stable manifold theorem. Gradient and Hamiltonian systems. Global existence theorems, limit sets and attractors, periodic orbits and Floquet theory, the Poincaire map. Introduction to structural stability and bifurcation theory. Hopf’s theorem for periodic solutions. Introduction to multi-scale perturbation theory.

PREREQUISITE(S): Math 316, 314 or 321, 361, or permission of instructor.

BASIS FOR GRADING: Homework.

THIS COURSE IS GOOD PREPARATION FOR: Study of dynamical systems in math, physics, and engineering.

TEXTBOOKS: (1) Qualitative Theory of Ordinary Differential Equations, 1994 by Brauer

TR 2:00-3:15 Coutsias

DESCRIPTION: Determinants; theory of linear equations; matrix analysis of differential equations; eigenvalues, eigenvectors, and canonical forms; variational principles; generalized inverses.

PREREQUISITE(S): Math 314 or 321 or permission of instructor.

TEXTBOOK: Linear Algebra and Its Applications, 3^rd ed. by G. Strang, Saunders

MWF 12:00-12:50 Nakamaye

DESCRIPTION: Theory of groups, permutation groups, Sylow theorems. Introduction to ring theory, polynomial rings. Principal ideal domains.

PREREQUISITE(S): Math 264.

TEXTBOOKS: Algebra, 3^rd ed. by S. Lang, Addison-Wesley Publ.

RECOMMENDED: Algebra, 1974 by Hungerford, Springer-Verlag Publ.

TR 9:30-10:45 Boyer

DESCRIPTION: Introduction to homology and cohomology theories, Homotopy theory, and CW complexes.

PREREQUISITE(S): Math 431 and 521, or permission of instructor.

TEXTBOOKS: Topology and Geometry, 1993 by G.E. Bredon, Springer-Verlag.

RECOMMENDED:

1. Algebraic Topology: An Intuitive Approach, 1999 by H. Soto,

American Mathematical Society.

2. Intuitive Topology, 1994 by V.V. Prasolov, American Mathematical

4:00-5:15 Galicki

DESCRIPTION: Topics include: topological manifolds, local and global theory of smooth manifolds, vector fields flows and foliations, Lie groups, exterior algebra of p-forms, integration and Stoke’s theorem, cohomology, symplectic and Riemannian manifolds.

PREREQUISITE(S): Math 510 and 511.

BASIS FOR GRADING: Homework.

THIS COURSE IS GOOD PREPARATION FOR: Starting a Ph.D. project in differential geometry.

TEXTBOOKS: Differentiable Manifolds – A First Course, 1993 by Lawrence Conlon,

RECOMMENDED:

1. Fundamentals of Differential Geometry, 1998 by S. Lang, Springer-Verlag.
2. Differential Geometry, 1997 by R.W. Sharpe, Springer-Verlag.

TR 12:30-1:45 Huzurbazar

DESCRIPTION: Theory of linear models discussed in STAT 440/540 and 445/545. Linear spaces, matrices, projections. Multivariate normal distribution and theory of quadratic forms. Non-full rank models and estimability. Gauss-Markov theorem. Distribution theory for normality assumptions. Hypothesis testing and confidence regions.

PREREQUISITE(S): STAT 553, STAT 545, and linear algebra or instructor’s permission.

TEXTBOOK: Plane Answers to Complex Questions, 2^nd ed. by Ronald Christensen,

TR 2:00-3:15 Christensen

DESCRIPTION: Basic methods of survey sampling, simple random sampling, stratified sampling, cluster sampling, systematic sampling and general sampling schemes. Estimation based on auxiliary information. Design of complex samples and case studies.

PREREQUISITE(S): STAT 345 or instructor’s permission.

TEXTBOOK: Sampling: Design and Analysis, by S. Lohr, ITP: Duxbury Press.

ARRANGED WITH VARIOUS PROFESSORS.

TR 11:00-12:15 Koltchinskii

DESCRIPTION: Time series models, spectral representations and spectral analysis, filtering and prediction problems, multivariate time series and their spectral analysis, and state-space models and Kalman filtering.

PREREQUISITE(S): Math 441.

BASIS FOR GRADING: Midterm exams and final exam.

THIS COURSE IS GOOD PREPARATION FOR: Advanced classes in statistics, image and signal analysis, and econometrics.

TEXTBOOK: Time Series: Theory and Methods, 1996 by Brockwell and Davis,

Springer-Verlag Publ.

This course is cross-listed as Biomed 588.

T 9:30-11:30 and R 9:30-11:00 Bedrick

PREREQUISITE(S): Math 121 or permission of instructor.

BASIS FOR GRADING: Homework plus exams.

THIS COURSE IS GOOD PREPARATION FOR: Coursework in epidemiology and biostatistics.

TEXTBOOKS: (1) Fundamental of Biostatistics, 4^th ed. by Bernard Rosner, ITP:

(2) JMP Start Statistics (software), by Sall and Lehman, ITP: Duxbury.

MWF 1:00-1:50 Efromovich

DESCRIPTION: The course covers all modern topics of nonparametric curve estimation including density estimation, nonparametric regression, nonparametric time series, and estimation of multivariate functions. Modern tools, including wavelets, are discussed. My own software, available on WWW, will be used to analyze a broad spectrum of simulated and real data sets.

PREREQUISITE(S): Permission of instructor.

BASIS FOR GRADING: Homework, quizzes, and computer projects.

THIS COURSE IS GOOD PREPARATION FOR: Making a Ph.D.

TEXTBOOK: Nonparametric Curve Estimation: Methods, Theory, and Appications,

MWF 2:00-2:50 Buchner

DESCRIPTION: Analytic functions, power series in one complex variable, Cauchy-Riemann equations, Cauchy’s integral formula, conformal mapping, residues, and applications.

PREREQUISITE(S): Math 362, 311, or permission of instructor.

BASIS FOR GRADING: Homework, midterm and final.

THIS COURSE IS GOOD PREPARATION FOR: Pure and applied mathematics, theoretical physics, and engineering.

TEXTBOOKS: Functions of One Complex Variable Vol. 1., by J. Conway, Springer-

RECOMMENDED:

Classical Topics in Complex Function Theory, by R. Remmert, Springer-

MWF 9:00-9:50 Pereyra

DESCRIPTION: Measure theory extends familiar notions of length, volume, and integration to more general settings. First, we will introduce measurable functions, measures, and measure spaces (in particular, Lebesque measure). Next, we develop integration theory and prove basic convergence theorems. We will also study Lebesque spaces and basic inequalities, modes of convergence, decomposition of measures, and product measures. Many examples will be taken from probability theory.

PREREQUISITE(S): Math 510 (or 361).

BASIS FOR GRADING: Homework and one project.

THIS COURSE IS GOOD PREPARATION FOR: Probability (Math 541), Functional Analysis (Math 581), and any advanced course in Analysis, Partial Differential Equations, etc.

TEXTBOOKS: The Elements of Integration and Lebesque Measure, 1995 by R. Bottle,

1. Real Analysis: Modern Techniques and Their Applications, 2^nd ed. by

G. Folland, Wiley and Sons Inc.

2. Real Analysis – With an Introduction to Wavelet Theory, 1998 by S.

Igari, American Mathematical Society.

3. Measure Theory, 1994 by J.L. Doob, Springer-Verlag Publ.

MWF 11:00-11:50 Ellison

PREREQUISITE(S): A working knowledge of differential equations and some background in either analysis or elementary (non-measure theoretic) probability.

BASIS FOR GRADING: Homework and/or projects.

TEXTBOOKS: Stochastic Differential Equations: An Introduction with Applications, 5^th

1. Handbook of Stochastic Methods for Physics, Chemistry, and the

Natural Sciences, 2^nd ed. by C.W. Gardiner, Springer-Verlag.

2. Random Perturbations of Dynamical Systems, 2^nd ed. by Freidlin and

TR 9:30-10:45 Sulsky

DESCRIPTION: Comprehensive coverage of basic issues such as stability and convergence of solutions for partial differential equations of the elliptic, hyperbolic and parabolic type. Finite difference, finite element, and spectral methods will be discussed.

PREREQUISITE(S): Math 463, 504, and 505.

BASIS FOR GRADING: Computer projects and homework.

THIS COURSE IS GOOD PREPARATION FOR: Advanced work in applied mathematics or other engineering and science fields.

RECOMMENDED:

MW 4:00-5:15 Gibson

DESCRIPTION: A study of Hilbert spaces and other complete metric spaces, approximation in Hilbert spaces, basic operator theory, integral equations, the Fredholm alternative, introduction to distribution theory, Green’s functions, and differential operators.

PREREQUISITE(S): Math 312, 314 or 321, 316, 361 or equivalent.

BASIS FOR GRADING: Homework and exams.

THIS COURSE IS GOOD PREPARATION FOR: Most graduate level applied mathematics or physics.

TEXTBOOK: Principles of Applied Mathematics, 1988 by James Keener, Addison-

MATH 598. PRACTICUM. ARRANGED.

MATH 639. SEMINAR IN GEOMETRY AND TOPOLOGY. ARRANGED.

MATH 650. SEMINAR IN READING AND RESEARCH. ARRANGED.

MATH 669. SEMINAR IN ANALYSIS. ARRANGED.

MATH 679. SEMINAR IN APPLIED MATHEMATICS. ARRANGED.

MATH 689. SEMINAR IN FUNCTIONAL ANALYSIS. ARRANGED.

MATH 699. DISSERTATION. ARRANGED.