A Course of Pure Mathematics
by G.H. Hardy
Publisher: Cambridge University Press 1921
Number of pages: 476
This classic book has inspired successive generations of budding mathematicians at the beginning of their undergraduate courses. Hardy combines the enthusiasm of the missionary with the rigor of the purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit.
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by Brian S. Thomson - ClassicalRealAnalysis.info
This text is intended as a treatise for a rigorous course introducing the elements of integration theory on the real line. All of the important features of the Riemann integral, the Lebesgue integral, and the Henstock-Kurzweil integral are covered.
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The topology of metric spaces, Hilbert spaces and compact operators, the Fourier transform, measure theory, the Lebesgue integral, the Daniell integral, Wiener measure, Brownian motion and white noise, Haar measure, Banach algebras, etc.
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Set of notes suitable for an introduction to the basic ideas in analysis: the number system, sequences and limits, series, functions and continuity, differentiation, the Riemann integral, further treatment of limits, and uniform convergence.
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Nearly every Ph.D. student in mathematics needs to take a preliminary or qualifying examination in real analysis. This book provides the necessary tools to pass such an examination. The author presents the material in as clear a fashion as possible.