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: Cantorís Argument
    5. More Proofs of Impossibility
    6. Spernerís 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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