Applied Mathematics & Statistics - Courses
AMS 003: Precalculus for Science and Engineering. F,W
Includes real and complex numbers, inequalities, linear and quadratic equations, functions, graphs, exponential and logarithmic functions, trigonometry, and analytic geometry, with applications in science and engineering. Students cannot receive credit for both this course and Mathematics 2AB or 3. Mathematics 3 can substitute for course 3. Prerequisite(s): score of 20 or higher on Mathematics Placement Exam or Mathematics 2. (General Education Code(s): Q.) The Staff
AMS 005: Statistics. F,W,S
Introduction to statistical methods/reasoning, including descriptive methods, data-gathering (experimental design and sample surveys), probability, interval estimation, significance tests, one- and two-sample problems, categorical data analysis, correlation and regression. Emphasis on applications to the natural and social sciences. Students cannot receive credit for this course if they have already received credit for course 7. (General Education Code(s): IN, Q.) H. Lee, A. Kottas, B. Sanso
AMS 007: Statistical Methods for the Biological, Environmental, and Health Sciences. F,W
Case-study-based introduction to statistical methods as practiced in the biological, environmental, and health sciences. Descriptive methods, experimental design, probability, interval estimation, hypothesis testing, one- and two-sample problems, power and sample size calculations, simple correlation and simple linear regression, one-way analysis of variance, categorical data analysis. (Formerly Statistical Methods for the Biological and Environmental Sciences. ) Prerequisite(s): score of 31 or higher on mathematics placement exam, course 3, 11A, Mathematics 3, 11A, 19A or by permission of instructor. Concurrent enrollment in course 7L is required. (General Education Code(s): IN, Q.) H. Lee, R. Prado, D. Draper
AMS 007L: Statistical Methods for the Biological, Environmental, and Health Sciences Laboratory (2 credits).F,W
Computer-based laboratory course in which students gain hands-on experience in analysis of data sets arising from statistical problem-solving in the biological, environmental, and health sciences. Descriptive methods, interval estimation, hypothesis testing, one-and two-sample problems, correlation and regression, one-way analysis of variance, categorical data analysis. (Formerly Statistical Methods for the Biological and Environmental Sciences Laboratory. ) Prerequisite(s): score of 31 or higher on mathematics placement exam, course 3, 11A, Mathematics 3, 11A, 19A, or by permission of instructor. Concurrent enrollment in course 7 is required. H. Lee, R. Prado, D. Draper
AMS 011A: Mathematical Methods for Economists. F,W,S
An introduction to mathematical tools and reasoning, with applications to economics. Topics are drawn from precalculus and calculus and include functions and graphs, techniques of differentiation, relative extrema, logarithms and exponents, and differentials. Students who have already taken Mathematics 11A and 19A should not take this course. (Also offered as Economics 11A. Students cannot receive credit for both courses.) Prerequisite(s): score of 31 or above on Mathematics Placement Exam. Students who do not place into precalculus should enroll in Math 2. (General Education Code(s): IN, Q.) J. Katznelson
AMS 011B: Mathematical Methods for Economists. F,W,S
Mathematical tools and reasoning, with applications to economics. Topics are drawn from integral calculus, multivariable calculus, and linear algebra and include definite integrals, partial derivatives, Lagrange multipliers, matrix algebra, and solving systems of linear equations. (Also offered as Economics 11B. Students cannot receive credit for both courses.) Prerequisite(s): course 11A or Economics 11A. (General Education Code(s): IN, Q.) J. Katznelson
AMS 027: Mathematical Methods for Engineers. F,S
This course provides the mathematical background for several engineering courses. The content includes linear algebra, ordinary differential equations, and Laplace Transform methods. Students cannot receive credit for this course and Mathematics 24 or 27. Prerequisite(s): Mathematics 19B or 22 or 23A or 26 or permission of instructor. Concurrent enrollment in course 27L is required. H. Wang, J. Cortes, The Staff
AMS 027L: Mathematical Methods for Engineers Laboratory (2 credits).F,S
Computer demonstrations of solutions of differential equations. Numerical simulations of differential equations using the supplied Matlab programs with graphics user interfaces. Elementary programming in Matlab language to solve equations and to visualize solutions. Prerequisite(s): Mathematics 19B or 22 or 23A or 26 or permission of instructor. Concurrent enrollment in course 27 is required. H. Wang, J. Cortes, The Staff
AMS 107: Introduction to Fluid Dynamics. *
Fundamental topics in fluid dynamics. Euler and Lagrange descriptions of continuum dynamics. Conservation laws for inviscid and viscous flows. Potential flows. Exact solutions of the Navier-Stokes equation. Boundary layer theory. Gravity waves. Students cannot receive credit for this course and Applied Mathematics and Statistics 217. (Also offered as Physics 107. Students cannot receive credit for both courses.) Prerequisite(s): course 27, or Physics 116 A-B-C or equivalent. N. Brummell
AMS 113: Managerial Statistics. *
Practical methods for analyzing data relevant to the management sciences, with particular emphasis on information systems management. Reviews basic topics in probability and statistics, including correlation and simple linear regression and multiple regression. Experience using statistical software package. Case studies drawn from business problems. Students cannot receive credit for this course and Economics 113. Prerequisite(s): course 11B or Economics 11B or Mathematics 11B or 19B. (General Education Code(s): Q.) H. Lee
AMS 131: Introduction to Probability Theory. S
Introduction to probability theory and its applications. Combinatorial analysis, axioms of probability and independence, random variables (discrete and continuous), joint probability distributions, properties of expectation, Central Limit Theorem, Law of Large Numbers, Markov chains. Students cannot receive credit for this course and Computer Engineering 107. Prerequisite(s): course 11B or Economics 11B or Mathematics 11B or 19B. (General Education Code(s): Q.) R. Prado, M. Mangel
AMS 132: Statistical Inference. F
Introduction to statistical inference at a calculus-based level: maximum likelihood estimation, sufficient statistics, distributions of estimators, confidence intervals, hypothesis testing, and Bayesian inference. Prerequisite(s): course 131 or Computer Engineering 107. The Staff
AMS 146: Introduction to Dynamical Systems. W
Linear difference equations and the calculus of differences. Nonlinear difference equations and maps. Fixed points, stability, bifurcations, and cycles. The logistic map and the period-doubling cascade to chaos. Strange attractors and measures of chaos. Students cannot receive credit for this course and Mathematics 145. Prerequisite(s): course 27 or Mathematics 27 or Mathematics 21 and 24. P. Garaud, J. Cortes
AMS 147: Computational Methods and Applications. W
Applications of computational methods to solving mathematical problems using Matlab. Solution of nonlinear equations, linear systems, differential equations, sparse matrix solver, and eigenvalue problems. Some prior experience with Matlab is helpful but not required. Knowledge of differential equations is recommended (course 27 or Mathematics 24). Prerequisite(s): course 27 or Mathematics 21. H. Wang
AMS 162: Design and Analysis of Computer Simulation Experiments. *
Methods for the design and analysis of computer simulation experiments: random number generation; estimation of sample size necessary to achieve desired precision goals; antithetic variables and other devices for increasing simulation efficiency; analysis of the output of large "deterministic" computer programs, exploring the sensitivity of outputs to changes in the inputs. Applications drawn mainly from engineering and environmental sciences. Prerequisite(s): course 5 or 7 or 113 or 131 or Computer Engineering 107 or permission of instructor. (General Education Code(s): Q.) The Staff, H. Lee
AMS 198: Independent Study or Research. F,W,S
Students submit petition to sponsoring agency. May be repeated for credit. The Staff
AMS 198F: Independent Study or Research (2 credits).F,W,S
Students submit petition to sponsoring agency. May be repeated for credit. The Staff
AMS 205: Mathematical Statistics. F
Graduate introduction to topics in probability and mathematical statistics from the frequentist point of view: sufficiency, exponential families, maximum likelihood estimation, optimality theory for estimation, confidence intervals and significance testing, decision theory, convergence in probability and in law, central limit theorems, and efficiency and asymptotic normality. Enrollment restricted to graduate students. B. Sanso
AMS 206: Bayesian Statistics. W
Introduction to Bayesian statistical methods for inference and prediction; exchangeability; prior, likelihood, posterior, and predictive distributions; coherence and calibration; conjugate analysis; Markov Chain Monte Carlo methods for simulation-based computation; hierarchical modeling; Bayesian model diagnostics, model selection, and sensitivity analysis. Prerequisite(s): graduate standing or permission of instructor. H. Lee
AMS 207: Intermediate Bayesian Statistical Modeling. S
Hierarchical modeling, linear models (regression and analysis of variance) from the Bayesian point of view, intermediate Markov chain Monte Carlo methods, generalized linear models, multivariate models, mixture models, hidden Markov models. Prerequisite(s): graduate standing or permission of instructor. R. Prado, B. Sanso
AMS 210: Mathematical Models. *
Serves a dual purpose: provides an introduction to the ideas underlying the mathematical modeling of physical phenomena; and in discussing the various phenomena, this course either reviews or introduces mathematical concepts and techniques. Models described chosen from diverse topics such as population dynamics, chemical reactions, fluid and solid mechanics, quantum theory, and probability. Mathematical techniques covered include advanced theory of ordinary and partial differential equations, eigenvalue problems, and linear stability theory. Enrollment restricted to graduate students or permission of instructor. The Staff
AMS 211: Foundations of Applied Mathematics. F
Accelerated class on applied mathematical methods for all sciences. Topics include: multivariate calculus, linear algebra, Fourier series, ordinary differential equations, complex analysis, and integral transforms. Enrollment restricted to graduate students. The Staff
AMS 212A: Applied Mathematical Methods I. F
Focuses on the analytical and numerical methods for solving differential equations. Topics include well-posed problems, Fourier transform, separation of variables, Green's functions, Huygen's principle, calculus of variation, numerical discretization, local truncation error, global error, error estimation, numerical stability, multigrid method. (Formerly course 211.) Enrollment restricted to graduate students. Undergraduates are encouraged to take this class with permission of instructor. H. Wang, P. Garaud, N. Brummell
AMS 212B: Applied Mathematical Methods II. W
Covers pertubation methods: asymptotic series, stationary phase and expansion of integrals, matched asymptotic expansions, multiple scales and the WKB method, Padé approximants and improvements of series. (Formerly course 212.) Prerequisite(s): course 212A. H. Wang, P. Garaud, N. Brummell
AMS 213: Numerical Solutions of Differential Equations. W
Focuses on numerical solutions of differential equations. Topics include Runge-Kutta methods; error estimation and error control; consistency, stability, and convergence; conjugate gradient method; multigrid method; CFL condition; and high-resolution methods for conservation laws. Enrollment restricted to graduate students or permission of instructor. H. Wang, P. Garaud, N. Brummell
AMS 214: Applied Dynamic Sys. S
Introduction to applied dynamical systems and the qualitative study of differential equations. Topics include: Lyapunov stability, invariant manifolds, periodic orbits, Lagrangian and Hamiltonian equations, center manifold theory, bifurcations, and perturbation theory, and averaging. Special emphasis on motivation behind new concepts and their application to problems in science and engineering. Examples drawn from astronomy, biology, engineering, and robotics. Prerequisite(s): AMS 146 or permission of the instructor. Enrollment restricted to graduate students. Undergraduates are encouraged to enroll with permission of the instructor. Enrollment limited to 15. H. Wang, M. Mangel, P. Garaud, J. Cortes, The Staff
AMS 215: Stochastic Modeling in Biology. *
Application of differential equations and probability and stochastic processes to problems in cell, organismal, and population biology. Topics include life history theory, ecology, and population biology. Enrollment restricted to graduate students or permission of instructor. M. Mangel
AMS 216: Stochastic Differential Equations. *
Introduction to stochastic differential equations and diffusion processes with applications to biology, biomolecular engineering, and chemical kinetics. Topics include Brownian motion and white noise, gambler's ruin, backward and forward equations, and the theory of boundary conditions. Enrollment restricted to graduate students or consent of instructor. M. Mangel
AMS 217: Introduction to Fluid Dynamics. *
Fundamental topics in fluid dynamics. Euler and Lagrange descriptions of continuum dynamics. Conservation laws for inviscid and viscous flows. Potential flows. Exact solutions of the Navier-Stokes equation. Boundary layer theory. Gravity waves. Students cannot receive credit for this course and course 107. Enrollment restricted to graduate students. N. Brummell
AMS 221: Bayesian Decision Theory. *
Explores conceptual and theoretical bases of statistical decision making under uncertainty. Focuses on axiomatic foundations of expected utility, elicitation of subjective probabilities and utilities, and the value of information and modern computational methods for decision problems. Prerequisite(s): course 206. Enrollment restricted to graduate students. B. Sanso
AMS 223: Time Series Analysis. F
Graduate level introductory course on time series data and models in the time and frequency domains: descriptive time series methods; the periodogram; basic theory of stationary processes; linear filters; spectral analysis; time series analysis for repeated measurements; ARIMA models; introduction to Bayesian spectral analysis; Bayesian learning, forecasting, and smoothing; introduction to Bayesian Dynamic Linear Models (DLMs); DLM mathematical structure; DLMs for trends and seasonal patterns; and autoregression and time series regression models. Prerequisite: course 206. Enrollment restricted to graduate students. R. Prado
AMS 231: Nonlinear Control Theory. W
Covers analysis and design of nonlinear control systems using Lyapunov theory and geometric methods. Includes properties of solutions of nonlinear systems, Lyapunov stability analysis, effects of perturbations, controllability, observability, feedback linearization, and nonlinear control design tools for stabilization. Prerequisite(s): basic knowledge of mathematical analysis and ordinary differential equations is assumed. Enrollment restricted to graduate students or permission of instructor. The Staff
AMS 236: Motion Coordination of Robotic Networks. *
Comprehensive introduction to motion coordination algorithms for robotic networks. Emphasis on mathematical tools to model, analyze, and design cooperative strategies for control, robotics, and sensing tasks. Topics include: continuous and discrete-time evolution models, proximity graphs, performance measures, invariance principles, and coordination algorithms for rendezvous, deployment, flocking, and consensus. Techniques and methodologies are introduced through application setups from multi-agent robotic systems, cooperative control, and mobile sensor networks. Enrollment restricted to graduate students. Enrollment limited to 15. J. Cortes
AMS 241: Bayesian Nonparametric Methods. *
Theory, methods, and applications of Bayesian nonparametric modeling. Prior probability models for spaces of functions. Dirichlet processes. Pólya trees. Nonparametric mixtures. Models for regression, survival analysis, categorical data analysis, and spatial statistics. Examples drawn from social, engineering, and life sciences. Prerequisite(s): course 207. Enrollment restricted to graduate students. A. Kottas
AMS 245: Spatial Statistics. *
Introduction to the analysis of spatial data: theory of correlation structures and variograms; kriging and Gaussian processes; Markov random fields; fitting models to data; computational techniques; frequentist and Bayesian approaches. Prerequisite(s): course 207. Enrollment restricted to graduate students. H. Lee
AMS 256: Linear Statistical Models. W
Theory, methods, and applications of linear statistical models. Review of simple correlation and simple linear regression. Multiple and partial correlation and multiple linear regression. Analysis of variance and covariance. Linear model diagnostics and model selection. Case studies drawn from natural, social, and medical sciences. Course 205 strongly recommended as a prerequisite. Undergraduates are encouraged to take this class with permission of instructor. Prerequisite(s): course 205 or permission of instructor. Enrollment restricted to graduate students. R. Prado, B. Sanso
AMS 261: Probability Theory with Markov Chains. S
Introduction to probability theory: probability spaces, expectation as Lebesgue integral, characteristic functions, modes of convergence, conditional probability and expectation, discrete-state Markov chains, stationary distributions, limit theorems, ergodic theorem, continuous-state Markov chains, applications to Markov chain Monte Carlo methods. Prerequisite(s): course 205. Enrollment restricted to graduate students. A. Kottas
AMS 263: Stochastic Processes. S
Includes probabilistic and statistical analysis of random processes, continuous-time Markov chains, hidden Markov models, point processes, Markov random fields, spatial and spatio-temporal processes, and statistical modeling and inference in stochastic processes. Applications to a variety of fields. Prerequisite(s): course 205 or 261 or permission of instructor. The Staff, A. Kottas
AMS 274: Generalized Linear Models. W
Theory, methods, and applications of generalized linear statistical models; review of linear models; binomial models for binary responses (including logistical regression and probit models); log-linear models for categorical data analysis; and Poisson models for count data. Case studies drawn from social, engineering, and life sciences. Prerequisite(s): course 205 or 256. Enrollment restricted to graduate students. A. Kottas
AMS 280A: Seminar in Mathematical and Computational Biology (2 credits).*
Weekly seminar on mathematical and computational biology. Participants present research findings in organized and critical fashion, framed in context of current literature. Students present own research on a regular basis. Enrollment restricted to graduate students. Enrollment limited to 20. May be repeated for credit. M. Mangel
AMS 280B: Seminars in Statistical and Applied Mathematical Modeling (2 credits).F,W,S
Weekly seminar series covering topics of current research in applied mathematics and statistics. Permission of instructor required. Enrollment restricted to graduate students. (FormerlySeminar in Applied Mathematics and Statistics.) May be repeated for credit. The Staff
AMS 285: Seminar in Career Skills (2 credits).F
Seminar in career skills for applied mathematicians and statisticians. Learn about professional activities such as the publication process, grant proposals, and the job market. Enrollment restricted to graduate students, typically within two years of their expected Ph.D. completion date. The Staff
AMS 290A: Topics in Mathematical and Computational Biology. *
Focuses on applications of mathematical and computational methods with particular emphasis on advanced methods applying to organismal biology or resource management. Students read current literature, prepare critiques, and conduct projects. Enrollment restricted to graduate students. Enrollment limited to 20. May be repeated for credit. M. Mangel
AMS 290B: Advanced Topics in the Numerical Solution of PDEs. W
Modern practical methods for the numerical solution of partial differential equations. Methods considered depend on the expertise of the instructor, but are covered in-depth and up to the cutting-edge of practical contemporary implementation. Content could be method-based (e.g., spectral methods, finite-element methods) or topic-based (e.g., simulations of turbulence). Some programming and numerical analysis (e.g., course 213) highly recommended. Enrollment restricted to graduate students and undergraduates with permission of the instructor. Enrollment restricted to graduate students and undergraduates with permission of the instructor. H. Wang, P. Garaud, N. Brummell
AMS 296: Masters Project (2 credits).F,W,S
Independent completion of a masters project under faculty supervision. Students submit petition to sponsoring agency. Enrollment restricted to graduate students. May be repeated for credit. The Staff
AMS 297: Independent Study or Research. F,W,S
Independent study or research under faculty supervision. Students submit petition to sponsoring agency. Enrollment restricted to graduate students. The Staff
AMS 297F: Independent Study (2 credits).F,W,S
Independent study or research under faculty supervision. Students submit petition to sponsoring agency. Enrollment restricted to graduate students. May be repeated for credit. The Staff* - Not currently offered.