Mathematics & Statistics

• CAS MA 566: Geometric Methods in Mechanics
  Modern geometric theories applied to motion of physical objects. Differential forms. Symplectic manifolds. Lie groups and their Lie algebras. Hamiltonian and Lagrangian systems; Liouville's theorem. Poincaré’s return theorem, Noether's theorem. Additional topics according to instructor.
• CAS MA 568: Statistical Analysis of Point Process Data
  Introduces the theory of point processes and develops practical problem-solving skills to construct models, assess goodness-of-fit, and perform estimation from point process data. Applications to neural data, earthquake analysis, financial modeling, and queuing theory.
• CAS MA 569: Optimization Methods of Operations Research
  Optimization of linear functions: linear programming, simplex method; transportation, assignment, and network problems. Optimization of non-linear functions: unconstrained optima, constrained optima and Lagrange multipliers, Kuhn-Tucker conditions, calculus of variations, and Euler's equation.
• CAS MA 573: Qualitative Theory of Ordinary Differential Equations
  Eigenvalues, eigenvectors, Jordan normal forms. Linear systems of differential equations, Phase portrait, Hamiltonian systems, stability theory. Applications to systems arising in mechanics, economics, ecology, electrical circuit theory, etc.
• CAS MA 575: Linear Models
  Post-introductory course in linear models, with focus on both principles and practice. Simple and multiple linear regression, weighted and generalized least squares, polynomials and factors, transformations, regression diagnostics, variable selection, and a selection from topics on extensions of linear models.
• CAS MA 576: Generalized Linear Models
  Covers topics in linear models beyond MA 575: generalized linear models, analysis of binary and polytomous data, log-linear models, multivariate response models, non-linear models, graphical models, and relevant model selection techniques. Additional topics in modern regression as time allows.
• CAS MA 577: Mathematics of Financial Derivatives
  Develops the probabilistic tools used in finance and presents the methodologies that are used in the pricing of financial derivatives. No previous knowledge of finance is required.
• CAS MA 578: Bayesian Statistics
  The principles and methods of Bayesian statistics. Subjective probability, Bayes rule, posterior distributions, predictive distributions. Computationally based inference using Monte Carlo integration, Markov chain simulation. Hierarchical models, mixture models, model checking, and methods for Bayesian model selection.
• CAS MA 579: Numerical Methods for Biological Sciences
  Introduction to the use of numerical methods for studying mathematical models of biological systems. Emphasis on the development of these methods; understanding their accuracy, performance, and stability; and their application to the study of biological systems.
• CAS MA 581: Probability
  Basic probability, conditional probability, independence. Discrete and continuous random variables, mean and variance, functions of random variables, moment generating function. Jointly distributed random variables, conditional distributions, independent random variables. Methods of transformations, law of large numbers, central limit theorem. Cannot be taken for credit in addition to CAS MA 381.
• CAS MA 582: Mathematical Statistics
  Point estimation including unbiasedness, efficiency, consistency, sufficiency, minimum variance unbiased estimator, Rao-Blackwell theorem, and Rao-Cramer inequality. Maximum likelihood and method of moment estimations; interval estimation; tests of hypothesis, uniformly most powerful tests, uniformly most powerful unbiased tests, likelihood ratio test, and chi-square test.
• CAS MA 583: Introduction to Stochastic Processes
  Basic concepts and techniques of stochastic process as they are most often used to construct models for a variety of problems of practical interest. Topics include Markov chains, Poisson process, birth and death processes, queuing theory, renewal processes, and reliability.
• CAS MA 584: Multivariate Statistical Analysis
  Presents statistical concepts and methods, and their application for the exploration, regression, testing, visualization, and clustering of multivariate data. Both classical and modern techniques are developed, including methods for analysis of high dimensional and non-euclidean data.
• CAS MA 585: Time Series and Forecasting
  Autocorrelation and partial autocorrelation functions; stationary and nonstationary processes; ARIMA and Seasonal ARIMA model identification, estimation, diagnostics, and forecasting. Modeling financial data via ARCH and GARCH models. Volatility estimation; additional topics, including long-range dependence and state-space models.
• CAS MA 586: The Design of Experiments
  Randomized blocks, Latin and Graeco-Latin squares, factorial arrangements with confounding and fractional replication, split-plot, crossover, and response surface designs. Treatment of missing data, group sizes, relative efficiency, relationship between design and analysis.
• CAS MA 587: Sampling Design: Theory and Methods
  Stratified, cluster, systematic, multistage, double, and inverse sampling; optimum sample size, relative efficiency, sampling with unequal probabilities, types of estimators (ratio and regression) and their properties. Measurement error nonresponse and randomized response models.
• CAS MA 588: Nonparametric Statistics
  The theory and logic in the development of nonparametric techniques including order statistics, tests based on runs, goodness of fit, rank-order (for location and scale), measures of association, analysis of variance, asymptotic relative efficiency.
• CAS MA 590: Introduction to Probability Theory
  Combinatorics. Conditional Probability. Independence. Discrete and continuous random variables. Sigma algebras. Joint, marginal, and conditional distributions. Conditional and unconditional expectations and variance. Derived distributions. Characteristic functions. Convergence of random variables. Limit theorems. Unbiased estimates of mean and variance. Cochran's Theorem. (Cannot be taken for credit in addition to MA 381 or MA 581.)
• CAS MA 614: Statistical Methods II
  Second course in statistics, embodying basic statistical methods used in educational and social science research. Reviews all basic concepts covered in a first statistics course (e.g., CAS MA 613) and presents, in detail, more advanced topics such as analysis of variance, covariance, experimental design, correlation, regression, and selected nonparametric techniques. A problem-solving course; students carry out analysis of data taken from educational and other social science sources.
• CAS MA 671: Chaotic Dynamical Systems
  This course is not open to CAS students. For graduate students in disciplines outside of mathematics. Iterations of functions of one or several variables. Periodicity, stability, chaos, fractals, bifurcations. Julia sets and the Mandelbrot set. Students are required to perform several experiments on personal computers.

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