[Turkmath:7753] Re: Steven G. Krantz Yeni Kitabına erisım

31 Mayıs 2011 Sal 10:32:56 EEST

Cahit,
Tebrikler.  Ispatının  bu kitapta  bahsedilmesi,  tanınmasına  yardımcı
olacaktır.
Kitabın icindekilerine baktım. Her amator ve profesyonel matematikcinin
elinde bulunması, karistirmasi,   yer yer okumaktan zevk alacagini
dusunuyorum.

tesekkur ederim
Akgul

The Proof is in the Pudding

ISBN 9780387489087

Preface

Contents

     Acknowledgments

1 What Is a Proof and Why?

     1.1 What Is a Mathematician?

     1.2 The Concept of Proof

     1.3 How Do Mathematicians Work?

     1.4 The Foundations of Logic

          1.4.1 The Law of the Excluded Middle

          1.4.2 Modus Ponendo Ponens and Friends

     1.5 What Does a Proof Consist Of?

     1.6 The Purpose of Proof

     1.7 The Logical Basis for Mathematics

     1.8 Platonism versus Kantianism

     1.9 The Experimental Nature of Mathematics

     1.10 The Role of Conjectures

          1.10.1 Applied Mathematics

     1.11 Mathematical Uncertainty

     1.12 The Publication and Dissemination of Mathematics

     1.13 Closing Thoughts

2 The Ancients

     2.1 Eudoxus and the Concept of Theorem

     2.2 Euclid the Geometer

          2.2.1 Euclid the Number Theorist

     2.3 Pythagoras

3 The Middle Ages and An Emphasison Calculation

     3.1 The Islamic Influence on Mathematics

     3.2 The Development of Algebra

          3.2.1 Al-Khwarizmi and the Basics of Algebra

     3.3 Investigations of Zero

     3.4 The Idea of Infinity

4 The Dawn of the Modern Age

     4.1 Euler and the Profundity of Intuition

     4.2 Dirichlet and the Heuristic Basis for Rigorous Proof

          4.2.1 The Pigeonhole Principle

     4.3 The Golden Age of the Nineteenth Century

5 Hilbert and the Twentieth Century

     5.1 David Hilbert

     5.2 G.D. Birkhoff, Norbert Wiener, and the Development of American
Mathematics

     5.3 L.E.J. Brouwer and Proof by Contradiction

     5.4 The Generalized Ham Sandwich Theorem

          5.4.1 Classical Ham Sandwiches

          5.4.2 Generalized Ham Sandwiches

     5.5 Much Ado about Proofs by Contradiction

     5.6 Errett Bishop and Constructive Analysis

     5.7 Nicolas Bourbaki

     5.8 Srinivasa Ramanujan and a New View of Proof

     5.9 The Legend of Paul Erdos

     5.10 Homage to Paul Halmos

     5.11 Perplexities and Paradoxes

          5.11.1 Bertrand's Paradox

          5.11.2 The Banach-Tarski Paradox

          5.11.3 The Monte Hall Problem

          5.11.4 The Axiom of Choice

6 The Tantalizing Four-Color Theorem

     6.1 Humble Beginnings

7 Computer-Generated Proofs

     7.1 A Brief History of Computing

     7.2 The Difference between Mathematics and Computer Science

     7.3 Theorem Proving vs. Program Verification

     7.4 How a Computer Can Search a Set of Axioms for the Statement and
Proof of a New Theorem

     7.5 How the Computer Generates the Proof of a New Result

8 The Computer as an Aid to Teaching and a Substitute for Proof

     8.1 Geometer's Sketchpad

     8.2 Computer Algebra Systems

     8.3 Numerical Analysis

     8.4 Computer Imaging and the Visualization of Proofs

     8.5 Mathematical Communication

9 Aspects of Modern Mathematical Life

     9.1 The World We Live In

     9.2 Mathematics Institutes

     9.3 Mathematical Communication

10 Beyond Computers: The Sociology of Mathematical Proof

     10.1 The Classification of the Finite Simple Groups

     10.2 Louis de Branges's Proof of the Bieberbach Conjecture

     10.3 Wu-Yi Hsiang's Solution of the Kepler Sphere-Packing Problem

     10.4 Thurston's Geometrization Program

     10.5 Grisha Perelman's Attack on the Poincar´e Conjecture and the
Geometrization Program

11 A Legacy of Elusive Proofs

     11.1 The Riemann Hypothesis

     11.2 The Goldbach Conjecture

     11.3 The Twin-Prime Conjecture

     11.4 Stephen Wolfram and A New Kind of Science

     11.5 Benoît Mandelbrot and Fractals

     11.6 Roger Penrose and The Emperor's New Mind

     11.7 The P/NP Problem

          11.7.1 The Complexity of a Problem

          11.7.2 Comparing Polynomial and Exponential Complexity

          11.7.3 Polynomial Complexity

          11.7.4 Assertions That Can Be Verified in Polynomial Time

          11.7.5 Nondeterministic Turing Machines

          11.7.6 Foundations of NP-Completeness

          11.7.7 Polynomial Equivalence

          11.7.8 Definition of NP-Completeness

     11.8 Andrew Wiles and Fermat's Last Theorem

     11.9 The Wily Infinitesimal

     11.10 A Miscellany of Misunderstood Proofs

          11.10.1 Frustration and Misunderstanding

12 John Horgan and "The Death of Proof?"

     12.1 Horgan's Thesis

     12.2 Will "Proof" Remain the Benchmark for Mathematical Progress?

13 Closing Thoughts

     13.1 Why Proofs Are Important

     13.2 Why It Is Important for Our Notion of Proof to Evolve and Change

     13.3 What Will Be Considered a Proof in 100 Years?

Index of Names

References

Index

2011/5/31 Ibrahim Arkut <icahit at ebim.com.tr>

> Kitap Google booktan kismen
>
>
> http://books.google.com.tr/books?id=mMZBtxVZiQoC&pg=PA242&lpg=PA242&dq=%22four+color+theorem%22+Cahit&source=bl&ots=VyflGXQ-ea&sig=A7D8IO_gi4W8-e4STWwCypNORxU&hl=en&ei=LovkTY3tGsfDswbXwtD6BQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBYQ6AEwADiOAg
>
> veya asagıdaki linkten tumu indirilebilir
>
>
> http://library.nu/docs/2FI36BKYRP/The%20Proof%20is%20in%20the%20Pudding%3A%20The%20Changing%20Nature%20of%20Mathematical%20Proof
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