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Dynamical Systems
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This book addresses the following topics: Iterations and fixed points; bifurcations; conjugacy; space and time averages; the contraction fixed point theorem; Hutchinson's theorem and fractal images; hyperbolicity; and symbolic dynamics. 151 page pdf file.

Material Type:
Textbook
Provider:
Harvard University
Provider Set:
Harvard University Mathematics Department
Author:
Shlomo Sternberg
Lie Algebras
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This book addresses the following topics: The Campbell Baker Hausdor formula; sl(2) and its Representations; classical simple algebras; Engel-Lie-Cartan-Weyl; conjugacy of Cartan subalgebras; simple finite dimensional algebras; cyclic highest weight modules; Serre's theorem; Clifford algebras and spin representations; The Kostant Dirac operator; The center of U(g); and Chevalley's theorem.

Subject:
Algebra
Material Type:
Textbook
Provider:
Harvard University
Provider Set:
Harvard University Mathematics Department
Author:
Shlomo Sternberg
Semi-Riemann Geometry and General Relativity
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This book represents course notes for a one semester course at the undergraduate level giving an introduction to Riemannian geometry and its principal physical application, Einstein’s theory of general relativity. The background assumed is a good grounding in linear algebra and in advanced calculus, preferably in the language of differential forms.

This book covers the following topics: The principal curvatures; rules of calculus; Levi-Civita Connections; bundle of frames; connections on principal bundles; Gauss's lemma; special relativity; Die Grundlagen der Physik; submersions; Petrov types; and Star.

Subject:
Calculus
Geometry
Material Type:
Textbook
Provider:
Harvard University
Provider Set:
Harvard University Mathematics Department
Author:
Shlomo Sternberg
Theory of functions of a real variable
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I have taught the beginning graduate course in real variables and functional analysis three times in the last five years, and this book is the result. The course assumes that the student has seen the basics of real variable theory and point set topology. The elements of the topology of metrics spaces are presented (in the nature of a rapid review) in Chapter I. The course itself consists of two parts: 1) measure theory and integration, and 2) Hilbert space theory, especially the spectral theorem and its applications. In Chapter II I do the basics of Hilbert space theory, i.e. what I can do without measure theory or the Lebesgue integral. The hero here (and perhaps for the first half of the course) is the Riesz representation theorem. Included is the spectral theorem for compact self-adjoint operators and applications of this theorem to elliptic partial di erential equations. Chapter III is a rapid presentation of the basics about the Fourier transform. Chapter IV is concerned with measure theory.

Material Type:
Textbook
Provider:
Harvard University
Provider Set:
Harvard University Mathematics Department
Author:
Shlomo Sternberg