Lower Division Courses
AMS 2: Pre-Statistics
Reviews and introduces mathematical methods useful in the elementary study of statistics, including logic, real numbers, inequalities, linear and quadratic equations, functions, graphs, exponential and logarithmic functions, and summation notation.
AMS 3: Precalculus for Science and Engineering
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 5: Statistics
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 7: Statistical Methods for the Biological, Environmental, and Health Sciences
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 7L: Statistical Methods for the Biological, Environmental, and Health Sciences Laboratory
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 10: Mathematical Methods for Engineers I
Applications-oriented course on complex numbers and linear algebra integrating MATLAB as a computational support tool. Introduction to complex algebra. Vectors, basis and transformations. Matrix algebra. Solutions of linear systems, inverse and determinants. Eigenvalues and eigenvectors. Geometric transformations. Students cannot receive credit for this course and for course 27L or Mathematics 21. (Formerly course 27, Mathematical Methods for Engineers.)
AMS 10A: Basic Mathematical Methods for Engineers I
Applications-oriented course on complex numbers and linear algebra integrating MATLAB as a computational support tool. Introduction to complex algebra. Vectors, basis and transformations. Matrix algebra. Solutions of linear systems, inverse and determinants. Students cannot receive credit for this course and course 10 or course 27L or Mathematics 21.
AMS 11A: Mathematical Methods for Economists
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 11B: Mathematical Methods for Economists
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 20: Mathematical Methods for Engineers II
Applications-oriented class on ordinary differential equations (ODEs) and systems of ODEs using Matlab as a computational support tool. Linear ODEs and systems of linear ODEs. Nonlinear ODEs using substitution and Laplace transforms. Phase-plane analysis. Introduction to numerical methods. Students cannot receive credit for this course and for course 27L or Mathematics 24.
AMS 20A: Basic Mathematical Methods for Engineers II
Applications-oriented class on ordinary differential equations (ODEs) and systems of ODEs integrating Matlab as a computational support tool. Linear ODEs and systems of linear ODEs. Nonlinear ODEs using substitution and Laplace transforms. Students cannot receive credit this course and for courses 20 or 27L or Mathematics 24.
AMS 27: Mathematical Methods for Engineers
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 27L: Matlab for Engineers Laboratory
Introduction to Matlab; elementary programming. Visualization of functions and data. Linear algebra and numerical solutions of differential equations using the supplied Matlab programs. Previous knowledge of linear algebra and differential equation is expected. (Formerly Mathematical Methods for Engineers Laboratory.)
AMS 80A: Gambling and Gaming
Games of chance and strategy motivated early developments in probability, statistics, and decision theory. Course uses popular games to introduce students to these concepts, which underpin recent scientific developments in economics, genetics, ecology, and physics.
Upper Division Courses
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 114: Introduction to Dynamical Systems
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 115: Stochastic Modeling in Biology
Application of differential equations, probability, and stochastic processes to problems in cell, organismal, and population biology. Topics include life-history theory, behavioral ecology, and population biology. Students may not receive credit for this course and course 215.
AMS 131: Introduction to Probability Theory
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
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
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.
AMS 147: Computational Methods & Applications
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 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
Graduate Courses
AMS 202: Linear Models in SAS
Case study-based course teaches statistical linear modeling using the SAS software package. Teaches generalized linear models; linear regression; analysis of variance/covariance; analysis of data with random effects and repeated measures.
AMS 205A: Mathematical Statistics
Graduate introduction to topics in probability and mathematical statistics. Probabilities, random variables, common families of distributions; expectation and higher moments; multivariate distributions, marginals and conditionals; point estimation, methods and properties; interval estimation, methods and properties; and hypothesis testing, methods and properties. (Formerly course 205.)
AMS 205B: Statistical Inference
Statistical inference from a frequentist point of view. Properties of random samples; convergence concepts applied to point estimators; principles of statistical inference; obtaining and evaluating point estimators with particular attention to maximum likelihood estimates and their properties; obtaining and evaluating interval estimators; and hypothesis testing methods and their properties.
AMS 206: Bayesian Statistics
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 course 132 or permission of instructor. Enrollment restricted to juniors, seniors, and graduate students. H. Lee
AMS 207: Intermediate Bayesian Statistical Modeling
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 211: Foundations of Applied Mathematics
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
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
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
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 Dynamical Systems
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
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
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
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
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
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
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
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: Seminar on Applied Math and Statistics
Weekly seminar series covering topics of current research in applied mathematics and statistics. Permission of instructor required. Enrollment restricted to graduate students. (Formerly Seminar on Applied Mathematics and Statistics.) May be repeated for credit. The Staff
AMS 285: Seminar in Career Skills
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: Advanced Topics in Mathematical & 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 Numerical Solution of PDEs
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 291: Advanced Topics in Bayesian Statistics
Advanced study of research topics in the theory, methods, or applications of Bayesian statistics. The specific subject depends on the instructor. Enrollment restricted to graduate students and by permission of indstructor.