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Course Criteria
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3.00 Credits
Ideas and techniques in representation theory of finite groups and Lie groups.
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3.00 Credits
A calculus-based introduction to the mathematical theory of probability at the advanced undergraduate level. Topics include the computational basics of probability theory, combinatorial methods, conditional probability including Bayes' theorem, random variables and distributions, expectations and moments, the classical distributions, and the central limit theorem. Prerequisite: Math 318 or 308, or permission of the instructor.
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3.00 Credits
Theory of estimation, minimum variance and unbiased estimators, maximum likelihood theory, Bayesian estimation, prior and posterior distributions, confidence intervals for general estimators, standard estimators and distributions such as the student-t and F-distribution from a more advanced viewpoint, hypothesis testing, the Neymann-Pearson Lemma (about best possible tests), linear models, and other topics as time permits. Prerequisite: Math 493 or permission of the instructor.
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3.00 Credits
Content varies with each offering of the course. Past offerings have included such topics as random walks, Markov chains, Gaussian processes, empirical processes, Markov jump processes, and a short introduction to martingales, Brownian motion and stochastic integrals. Prerequisites: Math 318 and 493, or permission of instructor.
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3.00 Credits
Topic varies with each offering.
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3.00 Credits
Topic varies with each offering.
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3.00 Credits
Prerequisites: junior or senior standing, eligibility for honors work in mathematics and permission of the department's Director of Undergraduate Studies.
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3.00 Credits
A consideration of three primary areas of research in cognitive science: attention, memory, and language. These topics are used to illustrate the techniques by which mental abilities are investigated and explained in psychology and neuroscience: the focus, in particular, is on the use of reaction time studies, brain imaging, and cell recordings to isolate the basic components that make up complex functions. In addition to the central concepts and theories in each areas, the course addresses philosophical implications of this research concerning how the mind and brain are related, how the mind-brain encodes or represents information, and the nature of consciousness. And there is an emphasis on applying these findings to important problems, such as Alzheimer's disease and deficits due to brain damage. The class is taught by three members of the faculty from different disciplines and combines a whole-group lecture with small discussion classes. The goal is to give students a good understanding of the interdisciplinary nature of cognitive science and to help them develop the ability to think and write critically about scientific research into the mind-brain. Prerequisite: admission to the Mind, Brain, and Behavior program.
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3.00 Credits
In this course, participants in the Mind, Brain, and Behavior Program continue their exploration of cognitive science. We explore different frameworks for thinking about how the different branches of cognitive science relate to each other. The course contains an introduction to relevant topics in the philosophy of science and the philosophy of mind. Prerequisite: MBB/PNP 120.
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1.00 - 3.00 Credits
An introduction to research for students in the Mind, Brain, and Behavior program. Students work under the supervision of a mentor. Prerequisite: admission to the Mind, Brain, and Behavior program, completion of MBB/PNP 122, and permission of the mentor.
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