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Course Criteria
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3.00 Credits
The study of topological spaces from algebraic properties, including the essentials of homology and the fundamental group. The Brouwer fixed point theorem. The homology of surfaces. Covering spaces. Prerequisites: MATH V21010, MATH W4041, MATH W4051 Not offered in 2009-2010. 3 points
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3.00 Credits
Real numbers, metric spaces, elements of general topology. Continuous and differential functions. Implicit functions. Integration; change of variables. Function spaces. Prerequisites: The second term of this course may not be taken without the first. Prerequisites: MATH V1202 or the equivalent and V2010. General Education Requirement: Quantitative and Deductive Reasoning (QUA). 3 points
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3.00 Credits
A theoretical introduction to analytic functions. Holomorphic functions, harmonic functions, power series, Cauchy-Riemann equations, Cauchy's integral formula, poles, Laurent series, residue theorem. Other topics as time permits: elliptic functions, the gamma and zeta function, the Riemann mapping theorem, Riemann surfaces, Nevanlinna theory. Prerequisites: MATH V1207 and Math V1208 or MATH W4061. 3 points
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3.00 Credits
The mathematics of finance, principally the problem of pricing of derivative securities, developed using only calculus and basic probability. Topics include mathematical models for financial instruments, Brownian motion, normal and lognormal distributions, the Black Scholes formula, and binomial models. Prerequisites: MATH V1202, V3027, STAT W4150, SEIO W4150, or their equivalents. General Education Requirement: Quantitative and Deductive Reasoning (QUA). 3 points
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3.00 Credits
The implicit function theorem. Concept of a differentiable manifold. Tangent space and tangent bundle, vector fields, differentiable forms. Stoke's theorem, tensors. Introduction to Lie groups. - O. Savin Prerequisites: MATH W4051 or W4061 and V2010. 3 points
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3.00 Credits
Material from topology and differential geometry with illustrations of their use in electrodynamics, general relativity, and Yang-Mills theory. In particular topological and differential manifolds, tensors, vector bundles, connections, and Lie groups are covered. Prerequisites: MATH V1202 or the equivalent and V2010. Not offered in 2009-2010. 3 points
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3.00 Credits
This course will focus on quantum mechanics, paying attention to both the underlying mathematical structures as well as their physical motivations and consequences. It is meant for undergraduates with no previous formal training in quantum theory. The measurement problem and issues of non-locality will be stressed. Prerequisites: Math V1202 or the equivalent and Math V2010. 3 points
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1.00 Credits
Intended as an enrichment to the mathematics curriculum of the first two years, this course introduces a variety of mathematical topics (such as three dimensional geometry, probability, number theory) that are often not discussed until later, and explains some current applications of mathematics in the sciences, technology and economics. Prerequisites: Some calculus or permission of the instructor. 1 point
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3.00 Credits
Honors-level introductory course in enumerative combinatorics. Pigeonhole principle, binomial coefficients, permutations and combinations. Polya enumeration, inclusion-exclusion principle, generating functions and recurrence relations. Corequisites: MATH V2010 is helpful as corequisite, not required. Not offered in 2009-2010. 3 points
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4.00 Credits
H. Dabashi 4 points
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