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Math 407: An Introduction to Differential Geometry
3.00 Credits
Washington University in St Louis
A study of properties of curves and surfaces in 3-dimensional Euclidean space. The course is essentially a modern recounting of a seminal paper of Gauss. Prerequisites: Math 233 and Math 309.
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Math 407 - An Introduction to Differential Geometry
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Math 408: Nonparametric Statistics
3.00 Credits
Washington University in St Louis
Statistical methods that make few or no assumptions about the data distribution. Permutation tests of different types; nonparametric confidence intervals and correlation coefficients; jackknife and bootstrap resampling; nonparametric regressions. If there is time, topics chosen from density estimation and kernel regression. Short computer programs are written in a language such as R or C. Prerequisites: Math 3200 and Math 493, or permission of instructor.
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Math 408 - Nonparametric Statistics
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Math 410: Introduction to Fourier Series and Integrals
3.00 Credits
Washington University in St Louis
The basic theory of Fourier series and Fourier integrals including different types of convergence. Applications to certain differential equations. Prerequisites: Math 233 and 309.
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Math 410 - Introduction to Fourier Series and Integrals
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Math 4111: Introduction to Analysis
3.00 Credits
Washington University in St Louis
The real number system and the least upper-bound property; metric spaces (completeness, compactness, and connectedness); continuous functions (in R^n; on compact spaces; on connected spaces); C(X) (pointwise and uniform convergence; Weierstrass approximation theorem); differentiation (mean value theorem; Taylor's theorem); the contraction mapping theorem; the inverse and implicit function theorems. Prerequisite: Math 310 or permission or instructor.
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Math 4111 - Introduction to Analysis
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Math 4121: Introduction to Lebesgue Integration
3.00 Credits
Washington University in St Louis
Riemann integration; measurable functions; measures; Lebesgue measure; the Lebesgue integral; integrable functions; L^p spaces; modes of convergence; decomposition of measures; product measures. Prerequisite: Math 4111 or permission of the instructor.
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Math 4121 - Introduction to Lebesgue Integration
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Math 415: Partial Differential Equations
3.00 Credits
Washington University in St Louis
Introduction to the theory of PDE's with applications to selected classical problems in physics and engineering. Linear and quasilinear first-order equations, derivation of some of the classical PDE's of physics, and standard solution techniques for boundary and initial value problems. Preliminary topics such as orthogonal functions, Fourier series, and variational methods introduced as needed. Prerequisites: Math 217 and 309, or permission of instructor.
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Math 415 - Partial Differential Equations
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Math 416: Complex Variables
3.00 Credits
Washington University in St Louis
Analytic functions, elementary functions and their properties, line integrals, the Cauchy integral formula, power series, residues, poles, conformal mapping, and applications. Prerequisites: Math 318, Math 308, or ESE 317, or permission of instructor.
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Math 416 - Complex Variables
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Math 417: Introduction to Topology and Modern Analysis I
3.00 Credits
Washington University in St Louis
An introduction to set theory, metric spaces, and general topology. Connections to analysis are made as appropriate. Prerequisite: Math 4111.
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Math 417 - Introduction to Topology and Modern Analysis I
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Math 418: Introduction to Topology and Modern Analysis II
3.00 Credits
Washington University in St Louis
Continuation of Math 417. May include some algebraic topology (depending on material covered in 417). Prerequisite: Math 417.
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Math 418 - Introduction to Topology and Modern Analysis II
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Math 420: Experimental Design
3.00 Credits
Washington University in St Louis
A first course in the design and analysis of experiments, from the point of view of regression. Factorial, randomized block, split-plot, Latin square, and similar design. Prerequisite: Math 3200 or permission of instructor.
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Math 420 - Experimental Design
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