Mathematics and Logic

Mark Kac and Stanislaw M. Ulam

Contents

Introduction

CHAPTER

1. Examples
   1. The Infinity of Primes
   2. Irrationality of sqrt(2)
   3. Approximation by Rational Numbers
   4. Transcendental Numbers: Cantor’s Argument
   5. More Proofs of Impossibility
   6. Sperner’s Lemma
   7. The Art and Science of Counting
   8. Digression on the Number System and on Functions
   9. Elementary Probability and Independence
   10. Measure
   11. Probability Revisited
   12. Groups and Transformations
   13. Homology Groups
   14. Vectors, Matrices and Geometry
   15. Special Theory of Relativity as an Example of the Geometric View in Physics
   16. Transformations, Flows and Ergodicity
   17. More on Iteration and Composition of Transformations
   18. Proving the Obvious
2. Themes, Trends, and Syntheses
3. Relations to Other Disciplines
4. Summary and Outlook

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