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Putnam and Beyond
Răzvan Gelca, Titu Andreescu (Taschenbuch, Englisch)
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Beschreibung
This book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Preliminary material provides an overview of common methods of proof: argument… by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. Each chapter systematically presents a single subject within which problems are clustered in each section according to the specific topic. The exposition is driven by nearly 1300 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors. The source, author, and historical background are cited whenever possible. Complete solutions to all problems are given at the end of the book. This second edition includes new sections on quad ratic polynomials, curves in the plane, quadratic fields, combinatorics of numbers, and graph theory, and added problems or theoretical expansion of sections on polynomials, matrices, abstract algebra, limits of sequences and functions, derivatives and their applications, Stokes' theorem, analytical geometry, combinatorial geometry, and counting strategies. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research. This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. Putnam and Beyond is organized for independent study by undergraduate and gradu ate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
03.10.2017
Sprache
Englisch
EAN
9783319589862
Herausgeber
Springer International Publishing
Sonderedition
Nein
Autor
Răzvan Gelca, Titu Andreescu
Seitenanzahl
850
Auflage
2
Einbandart
Taschenbuch
Schlagwörter
Putnam mathematics competition, mathematical induction, pigeonhole principle, Cauchy-Schwarz Inequality, one-variable polynomials, Chebyshev polynomials, linear algebra, Perron-Frobenius theorem, Cayley-Hamilton theorem, definite integrals, Taylor series, Fourier series, combinatorics
Thema-Inhalt
PBF - Algebra
PBK - Mathematische Analysis, allgemein
PBM - Geometrie
PBH - Zahlentheorie
PBD - Diskrete Mathematik
Höhe
254 mm
Breite
17.8 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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