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Preface to the Dover Edition Preface to the First Edition 1. Mathematics in General 2. Motion without Movement 3. Short Cuts in the Higher Arithmetic 4. The Language of Sets 5. What is a Function? 6. The Beginnings of Abstract Algebra 7. Symmetry: The Group Concept 8. Axiomatics 9. Counting: Finite and Infinite 10. Topology 11. The Power of Indirect Thinking 12. Topological Invariants 13. Algebraic Topology 14. Into Hyperspace 15. Linear Algebra 16. Real Analysis 17. The Theory of Probability 18. Computers and Their Uses 19. Applications of Modern Mathematics 20. Foundations Appendix Notes Glossary of Symbols Index