Math 098 - Introduction to College Math A (4-1-4 additive credits)
Intended for students whose major requires Math 113 or Math 138. Topics include: Elementary Algebra, Introduction to Graphs and Functions, Linear Functions, Equations, Inequalities, Systems of Linear Equations, Radicals and Complex Numbers, Quadratic Equations, Rational Expressions and Rational Functions, Functions and Relations, Exponential and Logarithmic Functions and Equations. Introduction to the logistics of applied calculus. Diverse applications will be emphasized throughout the course. This course may not be used to satisfy degree requirements in any program. Effective From: Fall 2007

Math 099 - Introduction to College Math B (4-1-4 additive credits)
Intended for students whose major requires Math 111. Topics include: Elementary Algebra, Introduction to Graphs and Functions, Linear Functions, Equations, Inequalities, Systems of Linear Equations, Radicals and Complex Numbers, Quadratic Equations, Rational Expressions and Rational Functions, Functions and Relations, Exponential and Logarithmic Functions and Equations. Introduction to the logistics of applied calculus. Diverse applications will be emphasized throughout the course. This course may not be used to satisfy degree requirements in any program. Effective From: Fall 2007

Math 102 - Modern Pre-calculus (6 credits)
This course is an incentive non-traditional approach to pre-calculus employing curriculum innovations for the preparation of students for college calculus. The course infuses calculus techniques into the pre-calculus curriculum. The format includes both regular class and workshop environments with a focus on student problem solving. Course meets on Saturdays in the fall and spring terms and M, T, W, R in the summer, second session. This course is only available to high school students.

Math 103 - University Mathematics I (4-1- 4 additive credits)
Prerequisite: Math 098 with a grade of C or better or placement by performance on standardized entrance examinations. Consists of a series of projects, many of which introduce and use elementary differentiation and/or integration in which the students perform sustained algebraic and trigonometric computations. The projects involve the following topics: polynomials, rational expressions, expressions involving radicals, exponential and logarithmic functions, right triangle trigonometry, and the solution of linear and quadratic equations. This course may not be used to satisfy degree requirements in any program. Effective Until: Summer 2007

Math 104 - University Mathematics II (4-1- 4 additive credits)
Prerequisite: Math 103 with a grade of C or better or placement by performance on standardized entrance examinations. Consists of a series of projects, many of which introduce and use elementary differentiation and/or integration in which the students perform sustained algebraic and trigonometric computations. The projects involve the following topics: radian measure, conic sections, trigonometric functions and identities, law of sines and cosines, logarithmic equations, partial fraction decomposition, systems of linear and nonlinear equations, functions in polar coordinates, and hyperbolic functions. This course may not be used to satisfy degree requirements in any program. Effective Until: Summer 2007

Math 105 - Elementary Probability and Statistics (3-0-3)
Prerequisite: (Intended for students who are not in Science or in Engineering.) Math 107 or Math 109 with a grade of C or better or placement by performance on standardized entrance examinations. Considers notions of probability. Topics include the binomial and normal distributions, expected value, and variance. The notions of sampling, hypothesis testing, and confidence intervals are applied to elementary situations.

Math 106 - University Mathematics I A (4-1-4)
Prerequisites: Phys 105 and Math 108 or Math 109 or Math 110. Corequisite: Math 109 or Math 110. Intended for students whose major requires Math 113 or Math 138. Prerequisite: Math 098 with a grade of C or better or placement by performance on standardized entrance examinations. Consists of a series of projects, many of which introduce and use elementary differentiation and/or integration in which the students perform sustained algebraic and trigonometric computations. The projects involve the following topics: polynomials, rational expressions, expressions involving radicals, exponential and logarithmic functions, right triangle trigonometry, and the solution of linear and quadratic equations. Degree credit awarded for the following majors only: Hist, PTC and STS. Effective From: Fall 2007

Math 107 - University Mathematics II A (4-1-4)
Intended for students whose major requires Math 113 or Math 138. Prerequisite: Math 106 with a grade of C or better. Consists of a series of projects, many of which introduce and use elementary differentiation and/or integration in which the students perform sustained algebraic and trigonometric computations. The projects involve the following topics: radian measure, conic sections, trigonometric functions and identities, laws of sines and cosines, logarithmic equations, partial fraction decomposition, systems of linear and nonlinear equations, functions in polar coordinates, and hyperbolic functions. Degree credit awarded for the following majors only: Hist, PTC and STS. Effective From: Fall 2007

Math 108 - University Mathematics I B (4-1-4)
Intended for students whose major requires Math 111. Prerequisite: Math 099 with a grade of C or better or placement by performance on standardized entrance examinations. Consists of a series of projects, many of which introduce and use elementary differentiation and/or integration in which the students perform sustained algebraic and trigonometric computations. The projects involve the following topics: polynomials, rational expressions, expressions involving radicals, exponential and logarithmic functions, right triangle trigonometry, and the solution of linear and quadratic equations. Degree credit awarded for the following majors only: Hist, PTC and STS. Effective From: Fall 2007

Math 109 - University Mathematics II B (4-1-4)
Intended for students whose major requires Math 111. Prerequisite: Math 108 with a grade of C or better. Consists of a series of projects, many of which introduce and use elementary differentiation and/or integration in which the students perform sustained algebraic and trigonometric computations. The projects involve the following topics: radian measure, conic sections, trigonometric functions and identities, laws of sines and cosines, logarithmic equations, partial fraction decomposition, systems of linear and nonlinear equations, functions in polar coordinates, and hyperbolic functions. Degree credit awarded for the following majors only: Hist, PTC and STS. Effective From: Fall 2007

Math 110 - University Mathematics II - Trigonometry (4-1-4)
Prerequisite: Placement by performance on standardized entrance examinations. This course reviews the trigonometry needed for higher level mathematics courses. The following topics are covered: radian measure, conic sections, trigonometric functions and identities, laws of sines and cosines, logarithmic equations, partial fraction decomposition, systems of linear and nonlinear equations, functions in polar coordinates, and hyperbolic functions. Degree credit awarded for the following majors only: Hist, PTC and STS. Effective From: Fall 2007

Math 111 - Calculus I (4-1-4)
Prerequisite: Math 109 or Math 110 with a grade of C or better or placement by performance on standardized entrance examinations. Topics include limits, differentiation, applications of differentiation, and integration. Effective From: Fall 2007

Math 111H - Honors Calculus I (4-1-4)
Admission to this course is by invitation, based on standardized entrance exams. Topics enhance those of Math 111 and concepts are studied in detail. Emphasizes science and engineering applications.

Math 112 - Calculus II (4-1-4)
Prerequisite: Math 111. Topics include integration, applications of integration, series, exponential and logarithmic functions, transcendental functions, polar coordinates, and conic sections.

Math 112H - Honors Calculus II (4-1-4)
Prerequisite: grade of B or better in Math 111H or grade of A in Math 111. Topics enhance those of Math 112 and concepts are studied in detail. Emphasizes science and engineering applications.

Math 113 - Finite Mathematics and Calculus I (4-0-4)
Prerequisite: (Intended for Architecture students.) Math 107 or Math 110 with a grade of C or better or placement by performance on standardized entrance examinations. An introduction to differential and integral calculus. Applications include area, volumes, curve lengths, surface area, centroids, and moments. Focus is on application throughout the course. Effective From: Fall 2007

Math 114 - Finite Mathematics and Calculus II (4-0-4)
Prerequisite: (Intended for Architecture students.) Math 113. Topics include numerical methods, set theory and counting, series, descriptive statistics and basic probability, matrices, and optimization.

Math 138 - General Calculus I (3-0-3)
Intended for students who are not in Science or in Engineering. Prerequisite: Math 107 or Math 110 with a grade of C or better or placement by performance on standardized entrance examinations. An introduction to differential and integral calculus of a single variable. Effective From: Fall 2007

Math 211 - Calculus III A (3-0-3)
Prerequisite: Math 112. Topics include vectors, curvature, partial derivatives, multiple integrals, line integrals, and Green's theorem. Students who are considering a major in Mathematical Sciences or who are undecided about their major should take Math 213.

Math 211H - Honors Calculus IIIA (3-0-3)
Prerequisite: Grade of B or better in Math 112H or grade of A in Math 112. Topics enhance those of Math 211 and concepts are studied in detail. Effective From: Fall 2008

Math 213 - Calculus III B (4-0-4)
Prerequisite: Math 112. Topics include vectors, curvature, partial derivatives, multiple integrals, line integrals, and Green's, divergence, and Stokes' theorems.

Math 213H - Honors Calculus III (4-0-4)
Prerequisite: grade of B or better in Math 112H or grade of A in Math 112. Topics enhance those of Math 213 and concepts are studied in detail. Emphasizes science and engineering applications.

Math 222 - Differential Equations (4-0-4)
Prerequisite: Math 211 or Math 213. Methods for solving ordinary differential equations are studied together with physical applications, Laplace transforms, numerical solutions, and series solutions.

Math 222H - Honors Differential Equations (4-0-4)
Prerequisite: grade of B or better in Math 213H or grade of A in Math 211 or Math 213. Topics enhance those of Math 222 and concepts are studied in detail. Emphasizes science and engineering applications.

Math 225 - Survey of Probability and Statistics (1-0-1)
Prerequisite: Math 112. Topics include descriptive statistics, elements of probability, random variables and distributions; mean and variance; introduction to estimation and inference. This course satisfies the Mathematics GUR in probability and statistics. However, degree credit will not be granted for both Math 225 and any other upper level course in probability and/or statistics. Effective Until: Fall 2007

Math 225A - Survey of Probability and Statistics (1-0-1)
For Chemical Engineering students only. Prerequisite: Math 112. Topics include descriptive statistics, elements of probability, random variables and distributions; mean and variance; introduction to estimation and inference. This course satisfies the Mathematics GUR in probability and statistics. However, degree credit will not be granted for both Math 225 and any other upper level course in probability and/or statistics.

Math 226 - Discrete Analysis (4-0-4)
Prerequisite: Math 112. An introduction to discrete mathematics. Topics include elementary set theory, logic, combinatorics, relations, graphs and trees, algebraic systems.

Math 226H - Honors Discrete Analysis (4-0-4)
Prerequisite: grade of "B"or better in Math 112H or grade of "A" in Math 112. An introduction to discrete mathematics. Topics enhance those of Math 226 and concepts are studied in detail. Emphasizes science and engineering applications.

Math 238 - General Calculus II (3-0-3)
Prerequisite: (Intended for students who are not in Science or in Engineering.) Math 138. A continuation of Math 138. Topics include applications of integral calculus and an introduction to ordinary differential equations.

Math 240 - Numerical Mathematics Laboratory (3-0-3)
Prerequisite: Math 112, and CIS 113 or knowledge of FORTRAN, C, or C++. Introduction to basic concepts and processes of numerical mathematics with emphasis on practical issues of implementation, use of numerical algorithms and software, and interpretation of numerical data. Weekly projects involving writing computer programs, presenting numerical results in tables and graphs, evaluation and approximation of standard numerical functions, round-off errors and loss of significance, basic iterative processes, matrix arithmetic, random number generation, and Monte Carlo methods. Students gain experience using a programming language, such as C, and mathematical software, such as MATLAB.

Math 244 - Introduction to Probability Theory (3-0-3)
Prerequisite: Math 112. Topics include basic probability theory in discrete and continuous sample space, conditional probability and independence, Bayes' theorem and event trees, random variables and their distributions, joint distribution and notion of dependence, expected values and variance, moment generating functions, useful parametric families of distributions including binomial, geometric, hypergeometric, negative binomial, exponential, gamma, normal and their applications, simple case of central limit theorem and its uses.

Math 245 - Multivariate Probability and Stochastic Processes (3-0-3)
Prerequisite: Math 244 or Math 333. Topics include discrete and continuous multivariate distributions and their moments, multivariate normal distributions, order statistics, discrete and continuous Markov chains, Poisson processes, and Brownian motion processes.

Math 246 - Introduction to Financial Mathematics ((3-0-3))
An introduction to the basics of simple interest and discount, compound interest and discount, and simple annuities. This course is primarily intended for students whose major only requires Calculus I. It cannot be used for credit towards major or minor degrees offered by the Department of Mathematical Sciences. Effective From: Fall 2005

Math 279 - Statistics and Probability for Engineers (2-0-2)
Prerequisite: Math 112. This course introduces methods of summarizing and analyzing engineering data and the importance of observing processes over time such as control charts. Descriptive statistics, plots and diagrams are then used to summarize the data. Elements of probability and random variables with their distributions along with mean and variance are taught. All this knowledge is then used as a platform towards covering how to do basic estimation and inference, including confidence intervals and hypothesis testing based on a single sample. Students taking this course cannot receive degree credit for Math 225, 244, or 333. Effective From: Spring 2008

Math 305 - Statistics for Technology (3-0-3)
Prerequisite: (Intended for students in Engineering Technology.) Math 111, 138 or Unified Calculus. An introduction to the modern concepts of statistics needed by engineering technologists. Topics include organization of data, descriptive statistics, discrete and continuous probability distributions, sampling distribution and designs, estimation -- one and two populations, tests of hypotheses.

Math 309 - Mathematical Analysis for Technology (4-0-4)
Prerequisites: (Intended for students in Engineering Technology.) Calculus I or Unified Calculus. Emphasis on integration techniques; applications such as related rates, curve sketching, maximum and minimum, area, moments, centroids, volumes, approximate methods, partial derivatives, vector calculus, parametric equations, and infinite series.

Math 310 - Co-op Work Experience I ( 3 Credits)
Prerequisites: Completion of the sophomore year, departmental approval, and permission of the Office of Cooperative Education and Internships. Students gain major-related work experience and reinforcement of their academic program. Work assignments facilitated and approved by the co-op office. Mandatory participation in seminars and completion of a report.

Math 321 - Introduction to the Finite Element Method (3-0-3)
Prerequisite: Math 222. An elementary introduction to the theory and practice of the finite element method (FEM) is given. The mathematical underpinnings covered in this course include the basics of Sobolev spaces, Galerkin's method and various other weak formulations. Mathematical modeling of different physical problems and their solution techniques are also discussed. Existing finite element programs will be introduced through a course project. Effective From: Spring 2009

Math 322 - Differential Equations for Technology (3-0-3)
Prerequisite: (Intended for students in Engineering Technology.) Math 309. An applied science study using differential equations as the vehicle for comprehension of the unknown. Introduction to first-order differential equations and their applications to motion, cooling and electromechanical systems followed by higher order differential equations and their solutions. Study of methods of undetermined coefficients, variation of parameters, and many series and numerical methods. Includes Laplace transforms, matrix methods, and eigenvalue problems.

Math 326 - Discrete Analysis for Computer Engineers (3-0-3)
Prerequisite: Math 112. An introduction to mathematical logic, Boolean algebra, and Karnaugh maps. Other topics include functions, equivalence relations and partially ordered sets, counting, graph theory and finite state machines. The emphasis is on computation but proofs will be addressed. Students cannot receive credit for both Math 226 and Math 326.

Math 328 - Mathematical Methods for Scientists and Engineers (3-0-3)
Prerequisites: Math 211, Math 213. Corequisite: Math 222. The course exposes students to concepts of mathematics encountered throughout the physical science and engineering disciplines. Topics include matrix algebra, vector analysis, complex numbers, and boundary value problems in partial differential equations. Effective From: Spring 2008

Math 331 - Introduction to Partial Differential Equations (3-0-3)
Prerequisite: Math 222. Partial differential equations in science and engineering. Topics include initial- and boundary-value problems for parabolic, hyperbolic, and elliptic second-order equations. Emphasis is placed on separation of variables, special functions, transform methods, and numerical techniques.

Math 331H - Honors Introduction to Partial Differential Equations (3-0-3)
Prerequisite: grade of "B" or better in Math 222H or grade of "A" in Math 222. Topics enhance those of Math 331 and concepts are studied in detail. Emphasizes science and engineering applications.

Math 332 - Introduction to Functions of a Complex Variable (3-0-3)
Prerequisite: Math 222. Functions of a complex variable: Cauchy-Riemann equations, Cauchy-Goursat theorem, integration, series, residues, poles, geometrical aspects. Emphasis on techniques.

Math 332H - Honors Introduction to Functions of a Complex Variable (3-0-3)
Prerequisite: grade of "B" or better in Math 222H or grade of "A" in Math 222. Topics enhance those of Math 332 and concepts are studied in detail. Emphasizes science and engineering applications.

Math 333 - Probability and Statistics (3-0-3)
Prerequisite: Math 112. Descriptive statistics and statistical inference. Topics include discrete and continuous distributions of random variables, statistical inference for the mean and variance of populations, and graphical analysis of data.

Math 333H - Honors Probability and Statistics (3-0-3)
Prerequisite: grade of "B" or better in Math 112H or grade of "A" in Math 112. Topics enhance those of Math 333 and concepts are studied in detail. Emphasizes science and engineering applications.

Math 334 - Operations Research (3-0-3)
Prerequisite: Math 244 or Math 333. Considers mathematical methods found especially in contemporary fields such as operations research and reliability engineering. Topics include linear programming, graph theory, finite mathematics, differential equations, matrices, and determinants.

Math 335 - Vector Analysis (3-0-3)
Prerequisite: Math 211 or Math 213. Algebra and calculus of vectors. Topics include the theorems of Gauss, Green, and Stokes, and curvilinear coordinates.

Math 336 - Applied Abstract Algebra (3-0-3)
Prerequisite: Math 112 or departmental approval. Classical algebra from a modern and constructive viewpoint. Emphasis is on the development of algorithmic and computational skills. Topics include rings, fields, and groups and their applications to science and engineering.

Math 337 - Linear Algebra (3-0-3)
Prerequisite: Math 112 or departmental approval. Matrices, determinants, systems of linear equations, vector spaces, linear transformations, eigenvalues, eigenvectors, and related topics.

Math 337H - Honors Linear Algebra (3-0-3)
Prerequisite: grade of "B" or better in Math 112H or grade of "A" in Math 112. Topics enhance those of Math 337 and concepts are studied in detail. Emphasizes science and engineering applications.

Math 340 - Applied Numerical Methods (3-0-3)
Prerequisites: Math 211 or Math 213, and CIS 101 or CIS 113 or Math 240. Introduction to numerical methods with emphasis on mathematical models. Implements and investigates numerical techniques for the solution of linear and nonlinear systems of equations, eigenvalue problems, interpolation and approximation, techniques of optimization, Monte Carlo methods, and applications to ordinary differential equations and integration.

Math 340H - Honors Applied Numerical Methods (3-0-3)
Prerequisites: CIS 101 or CIS 113. Grade of "B" or better in Math 213H or grade of "A" in Math 211 or Math 213. Topics enhance those of Math 240 and concepts are studied in detail. Emphasizes science and engineering applications.

Math 341 - Introduction to Statistics (3-0-3)
Prerequisite: Math 244 or Math 333. Covers the theory and applications of classical statistical inference. Topics include sampling distributions, point and interval estimation, criteria of good estimators, maximum likelihood estimators and their large sample properties, statistical hypotheses and tests, including most powerful and uniformly most powerful tests and likelihood ratio tests, classical tests of parametric hypotheses about means and variances of normal populations, tests for proportion, chi-square tests of homogeneity, independence, goodness-of-fit, sign test and Wilcoxon test.

Math 344 - Regression Analysis (3-0-3)
Prerequisite: Math 333 or Math 341. An introduction to statistical data analysis using regression techniques. Topics include least squares estimation, hypothesis testing, prediction, regression diagnostics, residual analysis, variance stabilizing transformations, regression using indicator variables, variable selection, and model building.

Math 345 - Multivariate Distributions (3-0-3)
Prerequisites: Math 244 or Math 333. Topics include discrete and continuous multivariate distributions and their moments, multivariate distributions including multivariate normal and multinominal distributions, order statistics, conditional probability and the use of conditioning, discrete time Markov chains and their examples, discrete time branching processes, homogeneous and nonhomogeneous Poisson processes. Effective From: Spring 2008

Math 346 - Mathematics of Finance I (3-0-3)
Prerequisite: Math 112. The main topics include basic problems in interest, annuities, certain amortization and sinking funds, bonds and related securities. Effective From: Spring 2005

Math 347 - Mathematics of Finance II (3-0-3)
Prerequisites: Math 346 and Math 244 or Math 333 and Math 211 or Math 213. This course introduces mathematical models of bond and stock prices, which lead to arbitrage pricing of options and other derivative securities, and portfolio management. These areas of mathematical finance have a great impact on the way financial markets function. Topics include risk-free, and risky assets, portfolio management, futures, and options. Effective From: Spring 2005

Math 371 - Physiology and Medicine (3-0-3)
Prerequisite: Math 222. (No biology requirement.) Mathematical models of organs and organ systems: the heart and circulation, gas exchange in the lungs, electrical properties of excitable membranes, neuro-biological clocks, the renal countercurrent mechanism, muscle mechanics. The biology is introduced with each topic. Emphasis is on quantitative problem solving, model building, and numerical simulation. Effective From: Fall 2008

Math 372 - Population Biology (3-0-3)
Prerequisite: Math 222. (No biology requirement.) Introduction to the mathematics of populations: Malthus' model of geometric population growth, Euler's renewal equations, age structure in human populations, predator satiation, chaos, mathematical models of inheritance, and the theory of epidemics. The ability to weave back and forth between physical concepts and mathematical notation is emphasized as well as the relationships between random and non-random models of similar phenomena. Effective From: Fall 2008

Math 373 - Introduction to Mathematical Biology (3-0-3)
Prerequisites: Math 211 or 213 or 213H and Math 337. This course provides an introduction to the use of mathematical techniques applied to problems in biology. Discrete and continuous models of biological phenomena will be discussed. Biological topics discussed range from the subcellular molecular systems and cellular behavior to physiological problems, population biology and developmental biology. Techniques of phase plane analysis for differential equations are introduced in the course. No prior background in biology is necessary. Effective From: Spring 2005

Math 388 - Introduction to Chaos Theory (3-0-3)
Prerequisite: Math 211 or Math 213. An elementary treatment of chaos theory and its applications concentrating on discrete dynamical systems. Uses theory and applications illustrated by computer experiments to develop such topics as bifurcation, attractors, the logistic map, period-doubling routes to chaos, symbolic dynamics, Sarkovskii's theorem, fractals, and Julia and Mandelbrot sets for complex dynamics.

Math 391 - Numerical Linear Algebra (3-0-3)
Prerequisites: Math 337 and CS 113 or CS 115 or CS 101. This course provides an introduction to computational linear algebra. Topics include direct solution of linear systems, iterative methods for linear systems, fast Fourier transforms, least squares problems, singular value decomposition and eigenvalue/eigenvector problems. Effective From: Fall 2008

Math 401 - Undergraduate Research Seminar (1-1-1)
Research seminar intended for students who participate in year-long research projects. Methodologies and techniques needed for summer research projects are discussed. Presentations of current research topics are made by various faculty. Effective From: Spring 2008

Math 410 - Co-op Work Experience II (3 credits)
Prerequisites: Math 310, departmental approval, and permission of the Office of Cooperative Education and Internships. Provides major-related work experience. Mandatory participation in seminars and completion of requirements that include a report and/or project.

Math 426 - Advanced Discrete Analysis (3-0-3)
Prerequisite: Math 226 or Math 326. Topics include graphs, trees and their applications, grammars, finite state machines, Turing machines and Petri nets, applied combinatorics -- Stirling, Catalan, and Ramsey numbers, Polya-Burnside counting methods, finite Markov chains and coding theory.

Math 430 - Analytical and Computational Neuroscience (3-1-3)
Prerequisites: Math 211 or Math 213, Phys 121, and CIS 101 or CIS 113. A mathematical and computational introduction to the biophysical mechanisms that underlie physiological functions of single neurons and synapses. Topics include voltage-dependent channel gating mechanisms, the Hodgkin-Huxley model for membrane excitability, repetitive and burst firing, nerve impulse propagation in axons and dendrites, single- and multi-compartmental modeling, synaptic transmission, calcium handling dynamics and calcium dependent currents and processes.

Math 431 - Systems Computational Neuroscience (3-1-3)
Prerequisites: Math 211 and 100 level CS GUR, or instructor's approval. This course provides a mathematical and computational introduction to operations of neuronal systems and networks. Topics covered include central pattern generators, neuroethology of sensory systems, sensory-motor transformations, models of various brain regions, models of visual processes, large networks modeling, models of learning and memory, neural coding and mathematics of neural networks. Effective From: Fall 2007

Math 432 - Mathematics of Financial Derivatives I (3-0-3)
Prerequisites: Math 222 and Math 346. Mathematical analysis of models encountered in the area of finacial derivatives. Topics include modeling and analysis of futures markets, determination of future prices, hedging strategies, swaps, option markets, stock options and their trading strategies. Effective From: Fall 2007

Math 433 - Mathematics of Financial Derivatives II (3-0-3)
Prerequisites: Math 340 and Math 432. Mathematical analysis of models encountered in the area of financial derivatives with emphasis on numerical methods. Topics include: Binomial Trees, Black Scholes Models, Finite Difference Methods. Effective From: Fall 2007

Math 440 - Advanced Applied Numerical Methods (3-0-3)
Prerequisites: Math 331 and Math 340. A survey of numerical methods for solving ordinary and partial differential equations. Includes initial-value and boundary-value problems for ordinary differential equations and for elliptic, hyperbolic, and parabolic partial differential equations.

Math 440H - Honors Advanced Applied Numerical Methods (3-0-3)
Prerequisites: grade of "B" or better in Math 331 or Math 331H and Math 340 or Math 340H. Topics enhance those of Math 440 and concepts are studied in detail. Emphasizes science and engineering applications.

Math 441 - Actuarial Mathematics I (3-0-3)
Prerequisite: Math 346. Topics include the economics of insurance, individual risk models for a short term, survival distributions and life tables, life insurance per year, life annuities, and net premiums.

Math 442 - Actuarial Mathematics II (3-0-3)
Prerequisite: Math 441. Topics include net premium reserves, insurance models including expenses, nonforfeiture benefits, and dividends.

Math 443 - Statistical Methods (3-0-3)
Prerequisite: Math 341. Topics include complete sufficient statistics and uniformly minimum variance estimators, general linear hypotheses and related topics, nonparametric inference including rank and order statistics, permutation methods, U-statistics, and Pitman efficiency.

Math 444 - Applied Sampling Methods and Quality Control (3-0-3)
Prerequisite: Math 333, or Math 244 and Math 341. An introduction to sample survey and statistical quality control. Topics include sampling from a finite population and different sampling techniques, more detailed study of random sampling and stratification, control charts and acceptance sampling plans in statistical quality control.

Math 445 - Introduction to Experimental Design ( 3-0-3)
Prerequisite: Math 333, or Math 244 and Math 341. Basic concepts and principles of designs are covered. Topics include randomized blocks, Latin squares, factorial designs.

Math 446 - Topics in Applied Statistics (3-0-3)
Prerequisite: Math 341 or Math 333. Topics may include biostatistics, environmental statistics, statistical consulting.

Math 447 - Applied Time Series Analysis (3-0-3)
Prerequisite: Math 341 or Math 333. An introduction to applied univariate time series analysis. Topics include regression techniques for modeling trends, smoothing techniques (moving average smoothing, exponential smoothing), autocorrelation, partial auto-correlation, moving average, and autoregressive representation of series, Box-Jenkins models, forecasting, model selection, estimation, and diagnostic checking, Fourier analysis, and spectral theory for stationary processes.

Math 448 - Stochastic Simulation (3-0-3)
Prerequisite: Math 333 and Math 340. An introduction in the use of computer simulation to study stochastic models. Topics include the generation of samples of continuous and discrete random variables and processes with applications to stochastic models, statistical analysis of the results, and variance reduction techniques. Effective From: Fall 2005

Math 450H - Methods of Applied Mathematics I (Capstone I) (3-0-3)
Prerequisites: Math 331, Math 337, and Math 340. Combines mathematical modeling with physical and computational experiments conducted in the Undergraduate Mathematics Computing Laboratory.

Math 451H - Methods of Applied Mathematics II (Capstone II) ( 3-0-3)
Prerequisite: Math 450H. Small teams of students conduct research projects under the guidance of faculty members who perform applied research.

Math 453 - High-Performance Numerical Computing (3-0-3)
Prerequisites: Math 391 and Math 440. The course covers state-of-the-art numerical algorithms for solving large-scale problems accurately and efficiently. Topics include iterative methods for linear systems and eigenvalue computations, introduction to parallel program and parallel numerical algorithms and spectral methods. An instructor-selected advanced topic will be included in the course. Effective From: Spring 2009

Math 460 - Differential Geometry of Curves and Surfaces (3 credits)
Prerequisites: Math 222. Curves in the plane and Euclidean space, moving frames, surfaces in Euclidean space, orientability of surfaces, Gaussian and mean curvatures, surfaces of revolution, ruled surfaces, minimal surfaces, special curves on surfaces, Theorema Egregium, the intrinsic geometry of surfaces.

Math 473 - Intermediate Differential Equations (3-0-3)
Prerequisites: Math 222 and Math 337. Topics in the qualitative behavior of solutions of ordinary differential equations with applications to engineering problems. Includes phase plane analysis, stability, dynamical systems, and chaos.

Math 475 - Intermediate Partial Differential Equations ( 3-0-3)
Prerequisites: Math 331 and Math 337. A survey of methods, beyond separation of variables, for analyzing and solving the fundamental partial differential equations of mathematical physics. Considers first-order equations, Laplace's equation, the wave equation, the heat equation, and linear hyperbolic systems. Emphasizes using methods of calculus to solve canonical initial- and boundary-value problems.

Math 475H - Honors Intermediate Partial Differential Equations (3-0-3)
Prerequisites: Grade of "B" or better in Math 331H and Math 337H or Grade of "A" in Math 331 and Math 337. Topics enhance those of Math 475 and concepts are studied in detail. Emphasizes science and engineering applications.

Math 477 - Stochastic Processes (3-0-3)
Prerequisites: Math 244 or Math 333 and Math 337. This course introduces the theory and applications of random processes needed in various disciplines such as mathematical biology, finance, and engineering. Topics include discrete and continuous Markov chains, Poisson processes, as well as topics selected from Brownian motion, renewal theory, and simulation. Effective From: Fall 2006

Math 480 - Introductory Mathematical Analysis (3-0-3)
Prerequisite: Math 211 or Math 213. Builds on principles taught in basic calculus courses. Topics discussed include continuity, differentiation, integration, and the limit process of sequences and series.

Math 481 - Advanced Calculus (3-0-3)
Prerequisite: Math 213 and Math 480. Systematic development of partial differentiation, multiple and improper integrals, transformations, inverse and implicit function theorems, and integrals over curves and surfaces.

Math 491 - Independent Study in Mathematics (3-0-3)
Prerequisites: Senior standing and departmental approval. Each student works under the direct supervision of a member of the Department of Mathematical Sciences. The work consists primarily of a project applying the student's mathematical skills to an engineering- or science-oriented project.

Math 493 - Seminar in Actuarial Science (1-0-1)
Prerequisite: Departmental approval. A series of lectures by practicing actuaries on topics of technical and/or current practices. Subjects announced at the time of registration. Progress is evaluated through projects and term papers. A comprehensive report summarizing some aspect of special interest to the student is required.

Math 495 - Topics in Applied Mathematics (3-0-3)
Prerequisites: Math 331, Math 332, and Math 340, or departmental approval. A survey of selected areas of applied mathematics. Case histories of problems in applied mathematics from an industrial background.

Math 545 - Introductory Mathematical Analysis (3 credits)
Prerequisite: Math 211 or Math 213, and departmental approval. Rigorous treatment of the calculus of real-valued functions of one real variable: the real number system, epsilon-delta theory of limit, continuity, derivative, and the Riemann integral. The fundamental theory of calculus. Series and sequences including Taylor series and uniform convergence. The inverse and implicit function theorems.

Math 546 - Advanced Calculus (3 credits)
Prerequisite: Math 545 or Math 480. Rigorous treatment of the calculus of real-valued functions of several real variables: the geometry and algebra of n-dimensional Euclidean space, limit, continuity, derivative, and the Riemann integral of functions of several variables, the inverse and implicit function theorems, series, including Taylor series, optimization problems, integration on curves and surfaces, the divergence and related theorems.

Math 573 - Intermediate Differential Equations (3 credits)
Prerequisites: Math 222, Math 337, or departmental approval. Methods and applications for systems of ordinary differential equations: existence and uniqueness for solutions of ODEs, linear systems, stability analysis, phase plane and geometrical methods, Sturm-Liouville eigenvalue problems.

Math 590 - Graduate Co-op Work Experience I (3 additive credits)
Prerequisites: Graduate status, departmental approval, and permission of the Division of Career Development Services. Cooperative education/internship providing on-the-job complement to academic programs in mathematics. Work assignments and projects are developed by the Co-op Office in consultation with the Department of Mathematical Sciences.

Math 591 - Graduate Co-op Work Experience II (3 additive credits)
Prerequisites: Graduate status, departmental approval, and permission of the Division of Career Development Services.

Math 592 - Graduate Co-op Work Experience III (3 additive credits)
Prerequisites: Graduate status, departmental approval, and permission of the Division of Career Development Services.

Math 593 - Graduate Co-op Work Experience IV (0 credits)
Prerequisites: One immediately prior 3-credit registration for graduate co-op work experience with the same employer. Requires approval of departmental co-op advisor and the Division of Career Development Services. Must have accompanying registration in a minimum of 3 credits of course work. Effective From: Fall 2006

Math 599 - Teaching in Mathematics (3 credits)
Required of all master's and doctoral students in Mathematical Sciences who are receiving departmental or research-based awards. Provides students with the skills needed to communicate effectively and to perform their teaching and related duties. Students are exposed to strategies and methods for communicating and for teaching undergraduate mathematics, and they are required to practice and demonstrate these techniques. Not counted for degree credit.

Math 611 - Numerical Methods for Computation (3 credits)
Prerequisites: (This course is not intended for students in the Master's in Applied Mathematics program or in the doctoral program in Mathematical Sciences.) Math 222, Math 337, and proficiency in a computer language (FORTRAN, C, or C++), or departmental approval. A practical introduction to the numerical methods of science and engineering. Numerical solution of linear systems. Interpolation and quadrature. Iterative solution of nonlinear systems. Computation of eigenvalues and eigenvectors. Numerical solution of initial- and boundary-value problems for ODEs. Introduction to numerical solution of PDEs. Includes examples requiring student use of a computer with some use of software packages.

Math 613 - Advanced Applied Mathematics I: Modeling (3 credits)
Prerequisites: Math 331 and Math 337, or departmental approval. Concepts and strategies of mathematical modeling are developed by investigation of case studies in a selection of areas. Consistency of a model, nondimensionalization and scaling, regular and singular effects are discussed. Possible topics include continuum mechanics (heat and mass transfer, fluid dynamics, elasticity), vibrating strings, population dynamics, traffic flow, and the Sommerfeld problem.

Math 614 - Numerical Methods I (3 credits)
Prerequisites: Math 222, Math 337, Math 340, and proficiency in a computer language (FORTRAN, C, or C++), or departmental approval. Theory and techniques of scientific computation, with more emphasis on accuracy and rigor than Math 611. Machine arithmetic. Numerical solution of a linear system and pivoting. Interpolation and quadrature. Iterative solution of nonlinear systems. Computation of eigenvalues and eigenvectors. Numerical solution of initial- and boundary-value problems for systems of ODEs. Applications. The class includes examples requiring student use of a computer.

Math 630 - Linear Algebra and Applications (3 credits)
Prerequisites: (This course is not intended for students in the Master's in Applied Mathematics program or in the doctoral program in Mathematical Sciences.) Math 211 or Math 213, and Math 222. Development of the concepts needed to study applications of linear algebra and matrix theory to science and engineering. Topics include linear systems of equations, matrix algebra, orthogonality, eigenvalues and eigenvectors, diagonalization, and matrix decomposition.

Math 631 - Linear Algebra (3 credits)
Prerequisites: Math 222 and Math 337, or departmental approval. Similar in aim and content to Math 630 but with more emphasis on mathematical rigor. Linear systems of equations, matrix algebra, linear spaces, orthogonality, eigenvalues and eigenvectors, diagonalization, and matrix decomposition. Applications.

Math 635 - Analytical Computational Neuroscience (3 credits)
Prerequisites: Math 211 or 213, Math 337, and CIS 113 or Math 240, or departmental approval. This course will provide an intermediate-level mathematical and computational modeling background for small neuronal systems. Models of biophysical mechanisms of single and small networks of neurons are discussed. Topics include voltage-dependent channel gating mechanisms, the Hodgkin-Huxley model for membrane excitability, repetitive and burst firing, single- and multi-compartmental modeling, synaptic transmission, mathematical treatment of 2-cell inhibitory or excitatory networks. In this course, the students will be required to build computer models of neurons and networks and analyze these models using geometric singular-perturbation analysis and dynamical systems techniques.

Math 636 - Systems Computational Neuroscience (3 credits)
Prerequisites: Math 635. This course covers mathematical and computational modeling of neuronal networks. Topics covered include central pattern generators, models of visual processes, models of learning and memory, neural coding and mathematics of neural networks, models of oscillations in sensory, thalamic and thalamo-cortical networks, neuronal wave propagation.

Math 637 - Foundations of Mathematical Biology (3 credits)
Prerequisites: Math 222 and Math 337, or departmental approval. This course provides an introduction to the use of mathematical techniques applied to solve problems in biology. Models discussed fall into 3 categories: discrete, continuous, and spatially distributed. Biological topics discussed range from the subcellular molecular systems and cellular behavior to physiological problems, population biology and developmental biology.

Math 639 - Mathematical Modeling II (3-0-3)
Continuation of Math 613 (Advanced Applied Mathematics I, Modeling). Concepts and strategies of Mathematical modeling are developed by case studies in a selection of areas. Topics will be complementary to those presented in Math 613, and include for example, the mathematical theory of elasticity and electromagnetism. Effective From: Fall 2006

Math 644 - Regression Analysis Methods (3 credits)
Prerequisite: Math 661. Regression models and the least squares criterion. Simple and multiple linear regression. Regression diagnostics. Confidence intervals and tests of parameters, regression and analysis of variance. Variable selection and model building. Dummy variables and transformations, growth models. Other regression models such as logistic regression. Using statistical software for regression analysis.

Math 645 - Analysis I (3 credits)
Prerequisite: Math 546 or departmental approval. Review and extension of the fundamental concepts of advanced calculus: the real number system, limit, continuity, differentiation, the Riemann integral, sequences and series. Point set topology in metric spaces. Uniform convergence and its applications.

Math 646 - Time Series Analysis (3 credits)
Prerequisite: Math 661 or departmental approval. Time series models, smoothing, trend and removal of seasonality. Naive forecasting models, stationarity and ARMA models. Estimation and forecasting for ARMA models. Estimation, model selection, and forecasting of nonseasonal and seasonal ARIMA models.

Math 647 - Time Series Analysis II (3 credits)
Prerequisite: Math 646. Continuation of Math 646. Covers methods of time series analysis useful in engineering, the sciences, economics, and modern financial analysis. Topics include spectral analysis, transfer functions, multivariate models, state space models and Kalman filtering. Selected applications from topics such as intervention analysis, neural networks, process control, financial volatility analysis.

Math 651 - Methods of Applied Mathematics I (3 credits)
Prerequisite: Math 222 or departmental approval. A survey of mathematical methods for the solution of problems in the applied sciences and engineering. Topics include: ordinary differential equations and elementary partial differential equations. Fourier series, Fourier and Laplace transforms, and eigenfunction expansions.

Math 652 - Methods of Applied Mathematics II (3 credits)
Prerequisite: (This course is not intended for students in a graduate program in Mathematical Sciences.) Math 651. Continuation of Math 651. Topics include: partial differential equations, functions of a complex variable, and the calculus of variations.

Math 654 - Clinical Trials Design and Analysis (3 credits)
Prerequisites: Math 665 or equivalent with Departmental approval. Statistical methods and issues in the design of clinical trials and analysis of their data. Topic include clinical trial designs for phases 1-4, randomization principle and procedures, analysis of pharmacokinetic data for bioequivalence, multi-center trials, categorical data analysis, survival analysis, longitudinal data analysis, interim analysis, estimation of sample size and power, adjustment for multiplicity, evaluation of adverse events, and regulatory overview. Effective From: Fall 2007

Math 656 - Complex Variables I (3 credits)
Prerequisite: Math 545 or Math 645 or departmental approval. The theory and applications of analytic functions of one complex variable: elementary properties of complex numbers, analytic functions, elementary complex functions, conformal mapping, Cauchy integral formula, maximum modulus principle, Laurent series, classification of isolated singularities, residue theorem, and applications.

Math 659 - Survival Analysis (3 credits)
Prerequisites: Math 665 or equivalent with Departmental approval. Introduction to statistical methods for modeling time-to-event data in the presence of censoring and truncation, with emphasis on applications to the health sciences. Topics include survival and hazard functions, censoring and truncation, parametric and nonparametric models for survival data, competing-risks, regression models including Cox proportional hazards model and time-dependent covariates, one and two sample tests, and use of appropriate statistical software for computations. Effective From: Fall 2007

Math 661 - Applied Statistics (3 credits)
Prerequisite: Math 112. Role and purpose of applied statistics. Data visualization and use of statistical software used in course. Descriptive statistics, summary measures for quantitative and qualitative data, data displays. Modeling random behavior: elementary probability and some simple probability distribution models. Normal distribution. Computational statistical inference: confidence intervals and tests for means, variances, and proportions. Linear regression analysis and inference. Control charts for statistical quality control. Introduction to design of experiments and ANOVA, simple factorial design and their analysis.

Math 662 - Probability Distributions (3 credits)
Prerequisite: Math 341 or Math 333, and departmental approval. Probability, conditional probability, random variables and distributions, independence, expectation, moment generating functions, useful parametric families of distributions, transformation of random variables, order statistics, sampling distributions under normality, the central limit theorem, convergence concepts and illustrative applications.

Math 663 - Introduction to Biostatistics (3-0-3)
Prerequisites: Undergraduate Calculus. Introduction to statistical techniques with emphasis on applications in health related sciences. This course will be accompanied by examples from biological, medical and clinical applications. Summarizing and displaying data; basic probability and inference; Bayes' theorem and its application in diagonostic testing; estimation, confidence intervals, and hypothesis testing for means and proportions; contingency tables; regression and analysis of variance; logistic regression and survival analysis; basic epidemiologic tools; use of statistical software. Effective From: Spring 2005

Math 664 - Methods for Statistical Consulting (3 credits)
Prerequisite: Math 661 or departmental approval. Communicating with scientists in other disciplines. Statistical tools for consulting. Using statistical software such as JMP, SAS, and S-plus. Case studies which illustrate using statistical methodology and tools are presented by the instructor and guest speakers from academia and industry. Assignments based on case studies with use of statistical software is required.

Math 665 - Statistical Inference (3 credits)
Prerequisite: Math 662 or departmental approval. Review of sampling distributions. Data reduction principles: sufficiency and likelihood. Theory and methods of point estimation and hypothesis testing, interval estimation, nonparametric tests, introduction to linear models. Effective From: Fall 2007

Math 668 - Probability Theory (3 credits)
Prerequisite: Math 545 and Math 662, or departmental approval. Introduction to measure theory and integration, axiomatic probability, random variables, distribution function, expectation, independence, modes of convergence, characteristic functions, Laplace-Stieltjes transforms, sums of identically distributed random variables, conditional expectation, martingales.

Math 671 - Asymptotic Methods I (3 credits)
Prerequisite: Math 645 or Math 545, and Math 656, or departmental approval. Asymptotic sequences and series. Use of asymptotic series. Regular and singular perturbation methods. Asymptotic methods for the solution of ODEs, including: boundary layer methods and asymptotic matching, multiple scales, the method of averaging, and simple WKB theory. Asymptotic expansion of integrals, including: Watson's lemma, stationary phase, Laplace's method, and the method of steepest descent.

Math 672 - Biomathematics I: Biological Waves and Oscillations (3 credits)
Prerequisites: Math 222, Math 331, and Math 337, or departmental approval. Models of wave propagation and oscillatory phenomena in nerve, muscle, and arteries: Hodgkin-Huxley theory of nerve conduction, synchronization of the cardiac pacemaker, conduction and rhythm abnormalities of the heart, excitation-contraction coupling, and calcium induced waves, wave propagation in elastic arteries, models of periodic human locomotion.

Math 673 - Biomathematics II: Pattern Formation in Biological Systems (3 credits)
Prerequisites: Math 222, Math 331, and Math 337, or departmental approval. Emergence of spatial and temporal order in biological and ecological systems: Hopf and Turing bifurcation in reaction-diffusion systems, how do zebras get their stripes, patterns on snake skins and butterfly wings, spatial organization in the visual cortex, symmetry breaking in hormonal interactions, how do the ovaries count. Basic techniques of mathematics are introduced and applied to significant biological phenomena that cannot be fully understood without their use.

Math 675 - Partial Differential Equations (3 credits)
Prerequisite: Math 690 or departmental approval. A survey of the mathematical theory of partial differential equations: first-order equations, classification of second-order equations, the Cauchy-Kovalevsky theorem, properties of harmonic functions, the Dirichlet principle. Initial- and boundary-value problems for hyperbolic, elliptic, and parabolic equations. Systems of equations.

Math 676 - Advanced Ordinary Differential Equations (3 credits)
Prerequisites: Math 222, Math 337, and Math 545 or Math 645. A rigorous treatment of the theory of systems of differential equations: existence and uniqueness of solutions, dependence on initial conditions and parameters. Linear systems, stability, and asymptotic behavior of solutions. Nonlinear systems, perturbation of periodic solutions, and geometric theory of systems of ODEs.

Math 677 - Calculus of Variations (3 credits)
Prerequisite: Math 545 or Math 645 or departmental approval. Necessary conditions for existence of extrema. Variation of a functional, Euler's equation, constrained extrema, first integrals, Hamilton-Jacobi equation, quadratic functionals. Sufficient conditions for the existence of extrema. Applications to mechanics.

Math 685 - Combinatorics (3 credits)
Prerequisite: Math 545 or Math 645. Generating functions, principle of inclusion-exclusion, pigeonhole principle, partitions. Polya's theory of counting, graph theory, and applications.

Math 687 - Quantitative Analysis for Environmental Design Research (3 credits)
Prerequisites: Math 333 and departmental approval. Fundamental concepts in the theory of probability and statistics including descriptive data analysis, inferential statistics, sampling theory, linear regression and correlation, and analysis of variance. Also includes an introduction to linear programming and nonlinear models concluding with some discussion of optimization theory.

Math 688 - Mathematical and Statistical Methods in Materials Science (3 credits)
More emphasis on analytical methods and statistics. Course will be required for Ph.D. students in Materials Science. Effective From: Fall 2006

Math 689 - Advanced Applied Mathematics II: Ordinary Differential Equations (3 credits)
Prerequisites: Math 545 or Math 645, Math 613, and Math 631. A practical and theoretical treatment of boundary-value problems for ordinary differential equations: generalized functions, Green's functions, spectral theory, variational principles, and allied numerical procedures. Examples will be drawn from applications in science and engineering.

Math 690 - Advanced Applied Mathematics III: Partial Differential Equations (3 credits)
Prerequisite: Math 689. A practical and theoretical treatment of initial- and boundary-value problems for partial differential equations: Green's functions, spectral theory, variational principles, transform methods, and allied numerical procedures. Examples will be drawn from applications in science and engineering.

Math 691 - Stochastic Processes with Applications (3 credits)
Prerequisite: Math 662. Renewal theory, renewal reward processes and applications. Homogeneous, non-homogeneous, and compound Poisson processes with illustrative applications. Introduction to Markov chains in discrete and continuous time with selected applications.

Math 698 - Sampling Theory (3 credits)
Prerequisite: Math 662. Role of sample surveys. Sampling from finite populations. Sampling designs, the Horowitz-Thompson estimator of the population mean. Different sampling methods, simple random sampling, stratified sampling, ratio and regression estimates, cluster sampling, systematic sampling.

Math 699 - Design and Analysis of Experiments (3 credits)
Prerequisite: Math 662. Statistically designed experiments and their importance in data analysis, industrial experiments. Role of randomization. Fixed and random effect models and ANOVA, block design, latin square design, factorial and fractional factorial designs and their analysis. Effective From: Spring 2006

Math 700 - Master's Project (3 credits)
Prerequisites: Matriculation for the Master of Science in Applied Mathematics or in Applied Statistics and departmental approval. Work must be initiated with the approval of a faculty member, who will be the student's project advisor. Work of sufficient quality may qualify for extension into a master's thesis, see Math 701.

Math 701 - Master's Thesis (6 credits)
Prerequisite: Matriculation for the master's degree and departmental approval. Students must register for a minimum of 3 credits per semester until completion. The work is carried out under the supervision of a designated member of the faculty.

Math 707 - Advanced Applied Mathematics IV: Special Topics (3 credits)
Prerequisite: Departmental approval. A current research topic of interest to departmental faculty. Typical topics include: computational fluid dynamics, theoretical fluid dynamics, acoustics, wave propagation, dynamical systems, theoretical and numerical aspects of combustion, mathematical biology, and various topics in statistics.

Math 710 - Graduate Research Methods (3 credits)
Prerequisite: Math 614, Math 671, and Math 690. Acquaints second-year graduate students with the techniques and vocabulary of a field in applied mathematics. Each student contacts a designated faculty member and is given several basic papers or books on a research topic of current interest. The student prepares two lectures on his/her topic to be given at the end of the semester. A sample list of active fields of research includes acoustics, electromagnetic theory, elasticity, fluid dynamics, combustion, and mathematical biology.

Math 712 - Numerical Methods II (3 credits)
Prerequisites: Math 614, Math 331 or departmental approval, and proficiency in a computer programming language (FORTRAN, C, or C++). Numerical methods for the solution of initial- and boundary-value problems for partial differential equations, with emphasis on finite difference methods. Consistency, stability, convergence, and implementation are considered.

Math 713 - Advanced Scientific Computing: Multi-Dimensional Finite-Difference Schemes and Spectral Methods (3 credits)
Prerequisite: Math 712 and proficiency in a computer programming language (FORTRAN, C, or C++). Derivation and analysis of finite difference schemes for systems of partial differential equations in two and three spatial dimensions and time. Issues pertaining to efficient implementation of algorithms and to stability of physical and numerical boundary conditions. Pseudo-spectral and spectral methods to solve partial differential equations. Approximation properties of Fourier and Chebyshev series and techniques based on the Fast Fourier Transform (FFT) and on matrix multiplication to numerically compute partial derivatives. Time-discretization techniques suitable for use with pseudo-spectral and spectral methods. Model systems arising in wave propagation, fluid dynamics, and mathematical biology will be considered.

Math 715 - Mathematical Fluid Dynamics I (3-0-3)
Introduction to the basic ideas of fluid dynamics, with an emphasis on rigorous treatment of fundamentals and the mathematical developments and issues. The course focuses on the background and motivation for recent mathematical and numerical work on the Euler and Navier-Stokes equations, and presents a mathematically intensive investigation of various model equations of fluid dynamics (e.g., the Korteweg-de-Vries equations). Effective From: Fall 2005

Math 716 - Mathematical Fluid Dynamics II (3-0-3)
Continuation of Math 715. Further development of the ideas of fluid dynamics, with an emphasis on mathematical developments and issues. A selection of topics will be developed in some detail, for example: Stokes flow and low-Reynolds-number hydrodynamics; flow at high Reynolds number and boundary layers; shock waves and hyperbolic systems; dynamics of interfacial flows; hydrodynamic stability; rotating fluids. Effective From: Fall 2005

Math 717 - Inverse Problems and Global Optimization (3-0-3)
Introduction to inverse problems and global optimization. Linear, quasi-linear, and nonlinear inverse problems are studied with emphasis on regularization techniques. Bayesian statistical approaches and Monte Carlo methods are introduced and discussed in the context of inverse problems. The mathematical foundations of simulated annealing, genetic algorithms, and TABU are presented. Effective From: Fall 2006

Math 720 - Tensor Analysis (3 credits)
Prerequisite: Math 613 and Math 631, or departmental approval. Review of vector analysis in general curvilinear coordinates. Algebra and differential calculus of tensors. Applications to differential geometry, analytical mechanics, and mechanics of continuous media. The choice of applications will be determined by the interests of the class.

Math 722 - Wave Propagation (3-0-3)
Derivation of linear wave equations describing acoustic, electromagnetic, elastodynamic and hydrodynamic phenomena. Fundamental solutions and their application to initial value problems. Applications and solution of boundary value problems using Green's functions, image and spectral methods. Related time harmonic problems, including radiation, scattering, diffraction and transmission phenomena. Dispersive waves and the method of stationary phase. Linear waves in anisotropic media. Effective From: Fall 2006

Math 745 - Analysis II (3 credits)
Prerequisite: Math 645. Lebesgue measure and integration, including the Lebesgue dominated convergence theorem and Riesz-Fischer theorem. Elements of Hilbert spaces and Lp-spaces. Fourier series and harmonic analysis. Multivariate calculus.

Math 756 - Complex Variables II (3 credits)
Prerequisite: Math 656. Selected topics from: conformal mapping and applications of the Schwarz-Christoffel transformation, applications of calculus of residues, singularities, principle of the argument, Rouche's theorem, Mittag-Leffler's theorem, Casorati-Weierstrass theorem, analytic continuation, and applications, Schwarz reflection principle, monodromy theorem, Wiener-Hopf technique, asymptotic expansion of integrals; integral transform techniques, special functions.

Math 761 - Statistical Reliability Theory and Applications (3 credits)
Prerequisite: Math 662 or departmental approval. Survival distributions, failure rate and hazard functions, residual life. Common parametric families used in modeling life data. Introduction to nonparametric aging classes. Coherent structures, fault tree analysis, redundancy and standby systems, system availability, repairable systems, selected applications such as software reliability.

Math 762 - Statistical Inference (3 credits)
Prerequisite: Math 662 or departmental approval. Review of sampling distributions. Data reduction principles: sufficiency and likelihood. Theory and methods of point estimation and hypothesis testing, interval estimation, nonparametric tests, introduction to linear models. Effective Until: Spring 2007

Math 767 - Fast Numerical Algorithms (3-0-3)
The course covers state-of-the-art, analysis-based, fast numerical algorithms for computing discrete summations/transforms and for solving differential/integral equations. In particular, this course presents fast multipole methods and their descendants, including fast Fourier transform for nonequispaced data, fast Gauss transform, fast iterative solver and direct solver for elliptic boundary vallue praoblems. Effective From: Fall 2008

Math 771 - Asymptotic Methods II (3 credits)
Prerequisite: Math 671. Continuation of Math 671. Asymptotic methods for the solution of PDEs, including: matched asymptotic expansions, multiple scales, the WKB method or geometrical optics, and near-field far-field expansions. Applications to elliptic, parabolic, and hyperbolic problems. Further topics in the asymptotic expansion of integrals and the WKB method. Emphasis on examples drawn from applications in science and engineering.

Math 786 - Large Sample Theory and Inference (3 credits )
Prerequisites: Math 762 and Math 668. Limit theorems, central limit theorem, asymptotic expansions and large deviations, limit theorems in martingales and semi-martingales and stochastic differential equations, asymptotic expansions of functions of statistics, linear parametric estimation, asymptotic efficiency, martingale approach to inference: test for homogeneity and goodness of fit, decomposable statistics, inference for counting processes and censored data, inference in nonlinear regression, existence and consistency of least squares estimator (LSE), asymptotic properties of LSE, Von Mises functionals, estimation of parameters of stable laws, empirical characteristics function for inference, generalized least squares for linear models.

Math 787 - Non-Parametric Statistics (3 credits )
Prerequisite: Math 662. Wilcoxon signed-ranks test, Mann-Whitney U test, binomial sign test for single sample and two dependent samples, McNemar's test, Cochran Q test, Wilcoxon matched-pairs signed-ranks test, Kruskal-Wallis one-way analysis of variance, Friedman two-way analysis of variance, Siegel-Tukey test for equal variability, chi-squared goodness-of-fit test, test for homogeneity and independence, single-sample runs test and other tests of randomness, correlation tests: Spearman's rank-order correlation, coefficient and Kendall's tau, Kendall's coefficient of concordance, and Goodman and Kruskal's gamma, comparing power efficiency.

Math 790 - Doctoral Dissertation (Credits as designated)
Prerequisite: Excellent performance on the doctoral qualifying examination. A minimum of 36 credits is required of all candidates for the Ph.D. degree. Candidates must register for 6 to12 credits per semester, to be determined by a designated dissertation advisor. After reaching 36 credits, students must continue to register for 3 credits each semester until degree completion.

Math 791 - Graduate Seminar (0 credit)
All master's and doctoral students receiving departmental or research-based awards must register for this course each semester. Effective From: Fall 2006

Math 792 - Pre-Doctoral Research (3 credits)
Prerequisite: Departmental approval. For students admitted to the Ph.D. program in the Mathematical Sciences. Research is performed under the supervision of a designated faculty member. If the work culminates in doctoral research in the same area, up to 6 credits may be counted toward Math 790. See Math 790.