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MATH 250a: Vector Analysis
3.00 Credits
Yale University
Matt Feiszli. mwf9.25-10.15 QR (32) Calculus of functions of several variables, using vector and matrix methods. Inverse and implicit function theorems. Transformation of multiple integrals. Line and surface integrals of vector fields. Curl and divergence. Differential forms. Theorems of Green, Gauss, and Stokes. After math 120a or b, and 222a orb or 225a orb or equivalent.
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MATH 250a - Vector Analysis
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MATH 251b: stat 251bG,Stochastic Processes
3.00 Credits
Yale University
Staff. For description see under Statistics.
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MATH 251b - stat 251bG,Stochastic Processes
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MATH 260b: amth 260b,Basic Analysis in Function Spaces
3.00 Credits
Yale University
Ronald Coifman. tth1-2.15 QR (26) The standard basic functional analytic tools needed by scientists and users of mathematics. math 260b is a natural continuation of phys 301a.
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MATH 260b - amth 260b,Basic Analysis in Function Spaces
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MATH 270a: Set Theory
3.00 Credits
Yale University
Mara Neusel. mwf 1.30-2.20 QR (36) Algebra of sets; finite, countable, and uncountable sets. Cardinal numbers and cardinal arithmetic. Order types and ordinal numbers. The axiom of choice and the well-ordering theorem. After math 120a or b or equivalent.
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MATH 270a - Set Theory
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MATH 290b: Fractal Geometry:Concepts and Applications
3.00 Credits
Yale University
Douglas Lind. tth11.35-12.50 QR (24) An examination of mathematical patterns repeating on many levels. Mathematical concepts of fractals and chaos, and application of these tools to modeling natural phenomena. Prerequisites: math 120a or b and 222a or b or equivalent.
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MATH 290b - Fractal Geometry:Concepts and Applications
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MATH 300b: Topics in Analysis
3.00 Credits
Yale University
Triet Le. mwf 11.35-12.25 QR (34) An introduction to analysis, with topics chosen from infinite series, the theory of metric spaces, and fixed-point theorems with applications. Students who have taken math 230 should take math 301a in stead of this course. After mat h 250a or with permission of i nstructor
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MATH 300b - Topics in Analysis
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MATH 301a: Introduction to Analysis
3.00 Credits
Yale University
Peter Jones. tth1-2.15 QR (26) Foundations of real analysis, including metric spaces and point set topology, infinite series, and function spaces. After math 230 or equivalent.
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MATH 301a - Introduction to Analysis
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MATH 305b: Real Analysis
3.00 Credits
Yale University
Dapeng Zhan. mwf 11.35-12.25 QR (34) The Lebesgue integral, Fourier series, applications to differential equations. After math 301a or with permissio n of i nstructor math 310a, Introduction to Complex Analysis. Gregory Margulis. tth11.35-12.50 QR (24) An introduction to the theory and applications of functions of a complex variable. Differentiability of complex functions. Complex integration and Cauchy's theorem. Series expansions. Calculus of residues. Conformal mapping. After math 230 or 250a or equivalent.
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MATH 305b - Real Analysis
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MATH 315: bG ,Intermediate Complex Analysis
3.00 Credits
Yale University
Gregory Margulis. mw 2.30-3.45 QR Meets RP (37) Continuation of math 310a. Topics may include argument principle, Rouché's theorem, Hurwitz theorem, Runge's theorem, analytic continuation, Schwarz reflection principle, Jensen's formula, infinite products, Weierstrass theorem. Functions of finite order, Hadamard's theorem, meromorphic functions. Mittag-Leffler's theorem, subharmonic funct ions. After math 3
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MATH 315 - bG ,Intermediate Complex Analysis
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MATH 320: aG ,Measure Theory and Integration
3.00 Credits
Yale University
Howard Garland. tth1-2.15 QR Meets RP (26) Construction and limit theorems for measures and integrals on general spaces; product measures; Lp spaces; integral representation of linear functionals. After math 305b or equivalent.
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MATH 320 - aG ,Measure Theory and Integration
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