A Mathematician s Apology

Author: G. H. Hardy
Publisher: Cambridge University Press
ISBN: 1107394473
Format: PDF, ePub
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G. H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his idiosyncrasies and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times.

Valuing Useless Knowledge 2nd ed

Author: Robert Bates Graber
Publisher: Truman State Univ Press
ISBN: 1612480748
Format: PDF, Mobi
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With higher education coming under increasing scrutiny in today's economic climate, is a liberal-arts education still a valuable investment? Robert Bates Graber explores the historical, philosophical, and sociological origins and nature of liberal education, and draws on anthropology to show why we do, and why we should, value education that appears impractical. The premise remains as in the original 1995 edition, but the argument is strengthened and the discussion expanded. Graced by a foreword from Truman President Troy Paino, this new edition is even more enlightening, more provocative, and—dare we say—more useful than the original!

Don Juan

Author: George Gordon Lord Byron
Publisher: BoD – Books on Demand
ISBN: 3743711842
Format: PDF, ePub, Docs
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George Gordon Lord Byron: Don Juan Erstdruck: Erster und Zweiter Gesang, London (John Murray) 1819; Dritter bis Fünfter Gesang, London (John Murray) 1821; Sechster bis Vierzehnter Gesang, London (John Hunt) 1823; Fünfzehnter und Sechzehnter Gesang, London (John Hunt) 1824. Hier in der Übers. v. Otto Gildemeister, Berlin: Verlag von G. Reimer, 1877. Neuausgabe mit einer Biographie des Autors. Herausgegeben von Karl-Maria Guth. Berlin 2017. Textgrundlage sind die Ausgaben: Lord Byrons Werke. 6 Bände in dreien, übers. v. Otto Gildemeister, Berlin: Verlag von G. Reimer, 1877. Die Paginierung obiger Ausgaben wird in dieser Neuausgabe als Marginalie zeilengenau mitgeführt. Umschlaggestaltung von Thomas Schultz-Overhage unter Verwendung des Bildes: Franz von Lenbach, Drei Damen in Kostümen des Don Juan Festes, 1902. Gesetzt aus der Minion Pro, 11 pt.

A Course on Integration Theory

Author: Nicolas Lerner
Publisher: Springer
ISBN: 3034806949
Format: PDF, Kindle
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This textbook provides a detailed treatment of abstract integration theory, construction of the Lebesgue measure via the Riesz-Markov Theorem and also via the Carathéodory Theorem. It also includes some elementary properties of Hausdorff measures as well as the basic properties of spaces of integrable functions and standard theorems on integrals depending on a parameter. Integration on a product space, change of variables formulas as well as the construction and study of classical Cantor sets are treated in detail. Classical convolution inequalities, such as Young's inequality and Hardy-Littlewood-Sobolev inequality are proven. The Radon-Nikodym theorem, notions of harmonic analysis, classical inequalities and interpolation theorems, including Marcinkiewicz's theorem, the definition of Lebesgue points and Lebesgue differentiation theorem are further topics included. A detailed appendix provides the reader with various elements of elementary mathematics, such as a discussion around the calculation of antiderivatives or the Gamma function. The appendix also provides more advanced material such as some basic properties of cardinals and ordinals which are useful in the study of measurability.​

Reading Writing and Proving

Author: Ulrich Daepp
Publisher: Springer Science & Business Media
ISBN: 1441994793
Format: PDF, ePub
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This book, which is based on Pólya's method of problem solving, aids students in their transition from calculus (or precalculus) to higher-level mathematics. The book begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics and ends with suggested projects for independent study. Students will follow Pólya's four step approach: analyzing the problem, devising a plan to solve the problem, carrying out that plan, and then determining the implication of the result. In addition to the Pólya approach to proofs, this book places special emphasis on reading proofs carefully and writing them well. The authors have included a wide variety of problems, examples, illustrations and exercises, some with hints and solutions, designed specifically to improve the student's ability to read and write proofs. Historical connections are made throughout the text, and students are encouraged to use the rather extensive bibliography to begin making connections of their own. While standard texts in this area prepare students for future courses in algebra, this book also includes chapters on sequences, convergence, and metric spaces for those wanting to bridge the gap between the standard course in calculus and one in analysis.