This course introduces methods in data science, including exploring problems, developing and implementing possible data analytic solutions and interpreting findings. Statistical programming and computational reasoning are emphasized. Topics include data visualization, data manipulation, data analysis and presentation. Reproducible research methods are explored and case studies are emphasized.

A fundamental fact of science is that repeated measurements exhibit variability. The course presents ways to design experiments that will reveal systematic patterns while 'controlling' the effects of variability and methods for the statistical analysis of data from well-designed experiments. Topics include completely randomized, randomized complete block, Latin Square and factorial designs, and their analysis of variance. The course emphasizes applications, with examples drawn principally from biology, psychology, and medicine.

This course provides an overview of statistical methods, their conceptual underpinnings, and their use in various settings taken from current news, as well as from the physical, biological, and social sciences. Topics will include exploring distributions and relationships, planning for data production, sampling distributions, basic ideas of inference (confidence intervals and hypothesis tests), inference for distributions, and inference for relationships, including chi-square methods for two-way tables and regression.

A stochastic process is a collection of random variables. For example, the daily prices of a particular stock are a stochastic process. Topics of this course will include Markov chains, queueing theory, the Poisson process, and Brownian motion. In addition to theory, the course will investigate applications of stochastic processes, including models of call centers and models of stock prices. Simulations of stochastic processes will also be used to compare with the theory.

This course provides an overview of statistical methods, their conceptual underpinnings, and their use in various settings taken from current news, as well as from the physical, biological, and social sciences. Topics will include exploring distributions and relationships, planning for data production, sampling distributions, basic ideas of inference (confidence intervals and hypothesis tests), inference for distributions, and inference for relationships, including chi-square methods for two-way tables and regression.

This course provides an overview of statistical methods, their conceptual underpinnings, and their use in various settings taken from current news, as well as from the physical, biological, and social sciences. Topics will include exploring distributions and relationships, planning for data production, sampling distributions, basic ideas of inference (confidence intervals and hypothesis tests), inference for distributions, and inference for relationships, including chi-square methods for two-way tables and regression.

This is an introduction to differential equations for students in the mathematical or other sciences. Topics include first-order equations, second-order linear equations, qualitative study of dynamical systems, and first- and second-order linear partial differential equations.

Topics include algebraic structures: groups, rings (including some elementary number theory), fields, and vector spaces.

Topics include the real number system, convergence of sequences and series, power series, uniform convergence, compactness and connectedness, continuity, abstract treatment of differential and integral calculus, metric spaces, and point-set topology.

A selection of projects with a goal of discovery of properties and patterns in mathematical structures. The choice of projects varies from year to year and is drawn from algebra, analysis, discrete mathematics, geometry, applied mathematics, and statistics.