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Rudin's text was the first modern English text on classical real analysis, and its organization of topics has been frequently imitated. [1] In Chapter 1, he constructs the real and complex numbers and outlines their properties. (In the third edition, the Dedekind cut construction is sent to an appendix for pedagogical reasons.)
Walter Rudin (May 2, 1921 – May 20, 2010 [2]) was an Austrian-American mathematician and professor of mathematics at the University of Wisconsin–Madison. [3]In addition to his contributions to complex and harmonic analysis, Rudin was known for his mathematical analysis textbooks: Principles of Mathematical Analysis, [4] Real and Complex Analysis, [5] and Functional Analysis. [6]
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Rudin's conjecture is a mathematical conjecture in additive combinatorics and elementary number theory about an upper bound for the number of squares in finite arithmetic progressions. The conjecture, which has applications in the theory of trigonometric series , was first stated by Walter Rudin in his 1960 paper Trigonometric series with gaps .
Mary Ellen Rudin (December 7, 1924 – March 18, 2013) [1] was an American mathematician known for her work in set-theoretic topology. [2] In 2013, Elsevier established the Mary Ellen Rudin Young Researcher Award , which is awarded annually to a young researcher, mainly in fields adjacent to general topology .
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The Shapiro polynomials P n (z) may be constructed from the Golay–Rudin–Shapiro sequence a n, which equals 1 if the number of pairs of consecutive ones in the binary expansion of n is even, and −1 otherwise. Thus a 0 = 1, a 1 = 1, a 2 = 1, a 3 = −1, etc.