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Course Criteria
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4.00 Credits
An introduction to abstract algebraic structures. Some of the topics covered are groups, normal subgroups, homomorphisms, permutation groups, rings, cosets, rings of polynomials and fields. Proofs will be an essential part of the course. Prerequisite: Courses 210 and 226. Offered every third semester. B. Baird, K. McKeon
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4.00 Credits
A study of topics selected from algebra, real analysis, geometry, number theory, combinatorics, statistics, applied mathematics or other fields. Topics vary from year to year and may include topology, chaos and dynamical systems, numerical analysis, or statistical computing. Computer software may be used for research and experimentation. May be repeated for credit. Permission from the instructor. Staff
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4.00 Credits
Study of the algebraic and geometric structure of the complex number system. Development of the theory of differentiation and integration of functions of a complex variable. Other topics include series representation of analytic functions, study of residues, and conformal mappings. Prerequisite: Course 301; or 212 and either 225 or 226; or permission of the instructor. C. Hammond, P. Susskind
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4.00 Credits
Structure and properties of graphs and their applications. Topics include traversability, trees, connectivity, network flow, graph coloring, chromatic number and planarity. Discussion of the application of graph theory to computer science, transportation, scheduling, communication, chemistry and a variety of other fields. Prerequisite: Course 210. K. McKeon
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4.00 Credits
Topics important in both advanced mathematics and the sciences, principally physics. These may include complex functions and power series; multiple integration; change of variables; the Jacobian; elementary Fourier analysis; series solutions of differential equations; orthogonal bases, e.g., Legendre polynomials, and special functions; partial differential equations, e.g. Laplace's, Poisson's, diffusion orheat flow equations; integral transforms; and physical examples. Prerequisite: Course 225 and one of Course 226 or Course 212, or permission of the instructor. P. Susskind
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4.00 Credits
An introduction to the classical and contemporary theory of computation, including abstract automata theory, formal languages, computability by Turing machines and recursive functions, computability and decidability, and computational complexity. Prerequisite: Course 210. P. Susskind
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4.00 Credits
A study of Euclidean and one or more non-Euclidean geometries. The geometric theory, its historical setting, its physical and philosophical implications will all be treated. The purpose of the course will be to clarify the role of Euclidean geometry in mathematics, to introduce the ideas of axiom systems and their central role in mathematics, and to shed further light on the nature of mathematics. Prerequisite: Course 113 or Course 226, and permission of the instructor. P. Susskind
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4.00 Credits
A study of the theory needed for problems involving randomness or uncertainty. Discrete and continuous distributions, the Law of Large Numbers, the Central Limit Theorem and applications will be treated, with emphasis on preparation for Course 317. Prerequisite: Courses 113 and 210; or Course 212; or permission of the instructor. Offered every third semester. G. Chandler, K. McKeon
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4.00 Credits
Methods of statistical inference with emphasis on the mathematics which underlies these methods. Topics include estimation, hypothesis testing, regression, analysis of variance and nonparametric methods. Prerequisite: Course 316. G. Chandler
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4.00 Credits
Individual Study
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