Mathematics is beautiful and it can be fun and exciting as well as fact. Good math is your guide to some of the most compelling themes from two thousand years of Mathematics: from the Egyptian fractions to Turing machines, from the real meaning of the figures to plant the evidence, symmetry groups, and mechanical calculations. If you've ever wondered what lies beyond the proof of you struggling to finish in the middle school, or what limits the ability of the computer on your desk, this is the book for you.
Table of Contents
Part I: Numbers Chapter 1. Natural Numbers Chapter 2. Integers Chapter 3. Real Numbers Chapter 4. Irrational and Transcendental Numbers
Part II: Funny Numbers Chapter 5. Zero Chapter 6. e: The Unnatural Natural Number Chapter 7. φ: The Golden Ratio Chapter 8. i: The Imaginary Number Chapter 9. Roman Numerals Chapter 10. Egyptian Fractions Chapter 11. Continued Fractions
Part IV: Logic Chapter 12. Mr. Spock Is Not Logical Chapter 13. Proofs, Truth, and Trees: Oh My! Chapter 14. Programming with Logic Chapter 15. Temporal Reasoning
Part V: Sets Chapter 16. Cantor’s Diagonalization: Infinity Isn’t Just Infinity Chapter 17. Axiomatic Set Theory: Keep the Good, Dump the Bad Chapter 18. Models: Using Sets as the LEGOs of the Math World Chapter 19. Transfinite Numbers: Counting and Ordering Infinite Sets Chapter 20. Group Theory: Finding Symmetries with Sets
Part VI: Mechanical Math Chapter 21. Finite State Machines: Simplicity Goes Far Chapter 22. The Turing Machine Chapter 23. Pathology and the Heart of Computing Chapter 24. Calculus: No, Not That Calculus—λ Calculus Chapter 25. Numbers, Booleans, and Recursion Chapter 26. Types, Types, Types: Modeling λ Calculus Chapter 27. The Halting Problem
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