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MANCHU A: Elementary Manchu
4.00 Credits
Harvard University
Introduction to Manchu grammar with elementary readings in Manchu script.
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MANCHU A - Elementary Manchu
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MANCHU B: Elementary Manchu
4.00 Credits
Harvard University
Readings in a variety of historical and literary texts with emphasis on Manchu documentary sources, with and without diacritical marks.
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MANCHU B - Elementary Manchu
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MATH 101: Sets, Groups and Topology
4.00 Credits
Harvard University
An introduction to rigorous mathematics, axioms, and proofs, via topics such as set theory, symmetry groups, and low-dimensional topology.
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MATH 101 - Sets, Groups and Topology
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MATH 110: Vector Space Methods for Differential Equations
4.00 Credits
Harvard University
Develops the theory of inner product spaces, both finite-dimensional and infinite-dimensional, and applies it to a variety of ordinary and partial differential equations. Topics: existence and uniqueness theorems, Sturm-Liouville systems, orthogonal polynomials, Fourier series, Fourier and Laplace transforms, eigenvalue problems, and solutions of Laplace's equation and the wave equation in the various coordinate systems.
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MATH 110 - Vector Space Methods for Differential Equations
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MATH 112: Introductory Real Analysis
4.00 Credits
Harvard University
An introduction to mathematical analysis and the theory behind calculus. An emphasis on learning to understand and construct proofs. Covers limits and continuity in metric spaces, uniform convergence and spaces of functions, the Riemann integral.
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MATH 112 - Introductory Real Analysis
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MATH 113: Analysis I: Complex Function Theory
4.00 Credits
Harvard University
Analytic functions of one complex variable: power series expansions, contour integrals, Cauchy's theorem, Laurent series and the residue theorem. Some applications to real analysis, including the evaluation of indefinite integrals. An introduction to some special functions.
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MATH 113 - Analysis I: Complex Function Theory
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MATH 114: Analysis II: Measure, Integration and Banach Spaces
4.00 Credits
Harvard University
Lebesgue measure and integration; general topology; introduction to L p spaces, Banach and Hilbert spaces, and duality.
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MATH 114 - Analysis II: Measure, Integration and Banach Spaces
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MATH 115: Methods of Analysis
4.00 Credits
Harvard University
Complex functions; Fourier analysis; Hilbert spaces and operators; Laplace's equations; Bessel and Legendre functions; symmetries; Sturm-Liouville theory.
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MATH 115 - Methods of Analysis
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MATH 116: Convexity and Optimization with Applications
4.00 Credits
Harvard University
Develops the theory of convex sets, normed infinite-dimensional vector spaces, and convex functionals and applies it as a unifying principle to a variety of optimization problems such as resource allocation, production planning, and optimal control. Topics include Hilbert space, dual spaces, the Hahn-Banach theorem, the Riesz representation theorem, calculus of variations, and Fenchel duality. Students will be expected to understand and invent proofs of theorems in real and functional analysis.
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MATH 116 - Convexity and Optimization with Applications
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MATH 118r: Dynamical Systems
4.00 Credits
Harvard University
Introduction to dynamical systems theory with a view toward applications. Topics include existence and uniqueness theorems for flows, qualitative study of equilibria and attractors, iterated maps, and bifurcation theory.
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MATH 118r - Dynamical Systems
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