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Course Criteria
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3.00 Credits
Full course for one semester. A brief introduction to field structures, followed by presentation of the algebraic theory of finite dimensional vector spaces. Geometry of inner product spaces is examined in the setting of real and complex fields. Prerequisite: Mathematics 112 and 211 or consent of the instructor. Lecture-conference.
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3.00 Credits
Full course for one semester. An elementary treatment of the algebraic structure of groups, rings, fields, and/or algebras. Prerequisite: Mathematics 331. Lecture-conference.
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3.00 Credits
Full course for one semester. Topics in geometry selected by the instructor. Possible topics include the theory of plane ornaments, coordinatization of affine and projective planes, curves and surfaces, differential geometry, algebraic geometry, and non-Euclidean geometry. Prerequisite: Mathematics 331 or consent of the instructor. Lecture-conference. Offered in alternate years. Not offered 2009-10.
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3.00 Credits
Full course for one semester. This course will be concerned with one or more of the following areas of mathematics: recursive function theory, model theory, computability theory, and general theory of formal systems. Prerequisite: two years of college mathematics. Lecture-conference. Offered in alternate years.
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3.00 Credits
Full course for one semester. A study of integers, including topics such as divisibility, theory of prime numbers, congruences, and solutions of equations in the integers. Prerequisite: Mathematics 331 or consent of the instructor. Mathematics 332 is recommended. Lecture-conference. Offered in alternate years. Not offered 2009-10.
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3.00 Credits
Full course for one semester. Emphasis is on enumerative combinatorics including such topics as the principle of inclusion-exclusion, formal power series and generating functions, and permutation groups and Pólya theory. Selected other topics such as Ramsey theory, inversion formulae, the theory of graphs, and the theory of designs will be treated as time permits. Prerequisite: Mathematics 211. Lecture-conference. Offered in alternate years.
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3.00 Credits
Full course for one semester. An introduction to computer science covering the design and analysis of algorithms. The course will focus on various abstract data types and associated algorithms. The course will include implementation of some of these ideas on a computer. Prerequisites: Mathematics 121 and Mathematics 211 or consent of the instructor. Lecture-conference.
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3.00 Credits
Full course for one semester. A study of the organization and structure of modern programming languages. This course will survey key programming language paradigms including functional, object-oriented, and logic- and constraint-based languages. A formal approach will be taken to understanding the fundamental concepts underlying these paradigms, including their syntax, semantics, and type systems. The course will cover selected topics in the implementation of language systems such as parsers, interpreters, and compilers, and of run-time support for high-level languages. Prerequisite: Mathematics 121. Lecture-conference. Offered in alternate years.
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3.00 Credits
Full course for one semester. A development of probability theory in terms of random variables defined on discrete sample spaces. Special topics may include Markov chains, Stochastic processes, and measure-theoretic development of probability theory. Prerequisite: Mathematics 212. Lecture-conference.
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3.00 Credits
Full course for one semester. Theories of statistical inference, including maximum likelihood estimation and Bayesian inference. Topics may be drawn from the following: large sample properties of estimates, linear models, multivariate analysis, empirical Bayes estimation, and statistical computing. Prerequisite: Mathematics 391 or consent of the instructor. Lecture-conference. Offered in alternate years.
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