Good Math
eBook - ePub

Good Math

A Geek's Guide to the Beauty of Numbers, Logic, and Computation

  1. 282 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

Good Math

A Geek's Guide to the Beauty of Numbers, Logic, and Computation

About this book

Why do Roman numerals persist? How do we know that some infinities are larger than others? And how can we know for certain a program will ever finish? In this fast-paced tour of modern and not-so-modern math, computer scientist Mark Chu-Carroll explores some of the greatest breakthroughs and disappointments of more than two thousand years of mathematical thought. There is joy and beauty in mathematics, and in more than two dozen essays drawn from his popular "Good Math" blog, you'll find concepts, proofs, and examples that are often surprising, counterintuitive, or just plain weird.

Mark begins his journey with the basics of numbers, with an entertaining trip through the integers and the natural, rational, irrational, and transcendental numbers. The voyage continues with a look at some of the oddest numbers in mathematics, including zero, the golden ratio, imaginary numbers, Roman numerals, and Egyptian and continuing fractions. After a deep dive into modern logic, including an introduction to linear logic and the logic-savvy Prolog language, the trip concludes with a tour of modern set theory and the advances and paradoxes of modern mechanical computing.

If your high school or college math courses left you grasping for the inner meaning behind the numbers, Mark's book will both entertain and enlighten you.

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Yes, you can access Good Math by Mark C. Chu-Carroll in PDF and/or ePUB format, as well as other popular books in Computer Science & Computer Science General. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Good Math
  2. For the Best Reading Experience...
  3. Table of Contents
  4. Early praise for Good Math
  5. Preface
  6. Part 1: Numbers
  7. 1 Natural Numbers
  8. 2 Integers
  9. 3 Real Numbers
  10. 4 Irrational and Transcendental Numbers
  11. Part 2: Funny Numbers
  12. 5 Zero
  13. 6 e : The Unnatural Natural Number
  14. 7 φ : The Golden Ratio
  15. 8 i : The Imaginary Number
  16. Part 3: Writing Numbers
  17. 9 Roman Numerals
  18. 10 Egyptian Fractions
  19. 11 Continued Fractions
  20. Part 4: Logic
  21. 12 Mr. Spock Is Not Logical
  22. 13 Proofs, Truth, and Trees: Oh My!
  23. 14 Programming with Logic
  24. 15 Temporal Reasoning
  25. Part 5: Sets
  26. 16 Cantor’s Diagonalization: Infinity Isn’t Just Infinity
  27. 17 Axiomatic Set Theory: Keep the Good, Dump the Bad
  28. 18 Models: Using Sets as the LEGOs of the Math World
  29. 19 Transfinite Numbers: Counting and Ordering Infinite Sets
  30. 20 Group Theory: Finding Symmetries with Sets
  31. Part 6: Mechanical Math
  32. 21 Finite State Machines: Simplicity Goes Far
  33. 22 The Turing Machine
  34. 23 Pathology and the Heart of Computing
  35. 24 Calculus: No, Not That Calculus— λ Calculus
  36. 25 Numbers, Booleans, and Recursion
  37. 26 Types, Types, Types: Modeling λ Calculus
  38. 27 The Halting Problem
  39. Bibliography