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| Mathematics ---- Analysis
Advanced Calculus, Real Analysis, Complex Analysis, Measure Theory, Functional Analysis, Fourier Analysis, C*-Algebras.
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| 1) Real Analysis, Lee Larson (lecture notes)
(Topics) Axioms for the Real Numbers, sequences, point-set topology, connectedness and compactness, limits, continuity and uniform continuity, differentiation, applications of the Mean Value Theorem.
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| 2) Advanced Calculus and Analysis, Ian Craw (lecture notes)
(Topics) Sequences, monotone convergence, limits and continuity, differentiability, infinite series, power series. Functions of several variables: partial derivatives, tangent planes, integration, Fubini's theorem, change of variables.
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| 3) Interactive Real Analysis, Bert G. Wachsmuth (online resouce)
(Topics) Sets and relations, induction, sequences, convergence, point-set topology, limits and differentiation, Riemann and Lebesgue intergration.
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| 4) An Introduction to C*-Algebras, Pierre de la Harpe & Vaughan Jones (lecture notes)
(Topics) Bounded operators on Hilbert spaces, algebras of operators, compact and Hilbert-Schmidt operators, abstract C*-algebras and functional calculus, AF-algebras and reduced C*-group-algebras, states and the GNS construction, the algebra of canonical anticommutation relations, quasi-free states on the car algebra, unitary projective representations of groups.
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| 5) An Introduction to Fourier Theory, Forrest Hoffman (downloadable notes)
(Topics) Brief introduction to the Fourier transform and transform properties. Definitions of Discrete and Fast Fourier Transformations.
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| 6) A Brief Introduction to Measure Theory and Integration by Richard Bass (lecture notes)
(Topics) Measures, outer measures and Caratheodory's Theorem, Lebesgue-Stieltjes measure, integration, monotone convergence theorem, Fatou's lemma, dominated convergence theorem, product measures and Fubini's theorem, Radon-Nikodym theorem, differentiation, functions of bounded variation, Lp spaces, Holder and Minkowski inequalities.
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| 7) Functional Analysis by T.B. Ward (lecture notes)
(Topics) Normed linear spaces, Banach spaces, linear operators, the Hahn-Banach theorem, Lebesgue measure, Fubini's Theorem, Hilbert spaces, Fourier Analysis.
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| 8) Complex Analysis, George Cain (downloadable text)
(Topics) Complex numbers, complex functions, elementary functions, integration, Cauchy's Theorem, Cauchy's integral formula, harmonic series, Taylor and Laurent series, residues and poles, Rouche's Theorem.
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| 9) Measure Theory by V. Liskevich (lecture notes)
(Topics) Riemann and Lebesgue integration, measures, outer measures and Caratheodory's Theorem, Lebesgue measure, measurable functions, monotone converge theorem, Fatou's lemma, dominated convergence theorem, Lp spaces, Holder and Minkowski inequalities.
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