Why Prove it Again?
Alternative Proofs in Mathematical Practice
Häftad, Engelska, 2016
889 kr
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Produktinformation
- Utgivningsdatum2016-10-22
- Mått155 x 235 x 15 mm
- Vikt336 g
- FormatHäftad
- SpråkEngelska
- Antal sidor204
- FörlagBirkhauser Verlag AG
- ISBN9783319349671
Tillhör följande kategorier
John W. Dawson, Jr., is Professor Emeritus at Penn State York.
- Proofs in Mathematical Practice.- Motives for Finding Alternative Proofs.- Sums of Integers.- Quadratic Surds.- The Pythagorean Theorem.- The Fundamental Theorem of Arithmetic.- The Infinitude of the Primes.- The Fundamental Theorem of Algebra.- Desargues's Theorem.- The Prime Number Theorem.- The Irreducibility of the Cyclotomic Polynomials.- The Compactness of First-Order Languages.- Other Case Studies.
“The book motivates and introduces its topic well and successively argues for the claim that comparative studies or proofs are a worthwhile occupation. All chapters are accessible to a generally informed mathematical audience, most of them to mathematical laymen with a basic knowledge of number theory and geometry.” (Merlin Carl, Mathematical Reviews, April, 2016)“This book addresses the question of why mathematicians prove certain fundamental theorems again and again. … Each chapter is a historical account of how and why these theorems have been reproved several times throughout several centuries. The primary readers of this book will be historians or philosophers of mathematics … .” (M. Bona, Choice, Vol. 53 (6), February, 2016)“This is an impressive book, giving proofs, sketches, or ideas of proofs of a variety of fundamental theorems of mathematics, ranging from Pythagoras’s theorem, through the fundamental theorems of arithmetic and algebra, to the compactness theorem of first-order logic. … because of the many examples given, there should be something to suit everybody’s taste … .” (Jessica Carter, Philosophia Mathematica, February, 2016)
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