
Good Math
A Geek's Guide to the Beauty of Numbers, Logic, and Computation
- 282 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
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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Information
Table of contents
- Good Math
- For the Best Reading Experience...
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- Table of Contents
- Early praise for Good Math
- Preface
- Part 1: Numbers
- 1 Natural Numbers
- 2 Integers
- 3 Real Numbers
- 4 Irrational and Transcendental Numbers
- Part 2: Funny Numbers
- 5 Zero
- 6 e : The Unnatural Natural Number
- 7 φ : The Golden Ratio
- 8 i : The Imaginary Number
- Part 3: Writing Numbers
- 9 Roman Numerals
- 10 Egyptian Fractions
- 11 Continued Fractions
- Part 4: Logic
- 12 Mr. Spock Is Not Logical
- 13 Proofs, Truth, and Trees: Oh My!
- 14 Programming with Logic
- 15 Temporal Reasoning
- Part 5: Sets
- 16 Cantor’s Diagonalization: Infinity Isn’t Just Infinity
- 17 Axiomatic Set Theory: Keep the Good, Dump the Bad
- 18 Models: Using Sets as the LEGOs of the Math World
- 19 Transfinite Numbers: Counting and Ordering Infinite Sets
- 20 Group Theory: Finding Symmetries with Sets
- Part 6: Mechanical Math
- 21 Finite State Machines: Simplicity Goes Far
- 22 The Turing Machine
- 23 Pathology and the Heart of Computing
- 24 Calculus: No, Not That Calculus— λ Calculus
- 25 Numbers, Booleans, and Recursion
- 26 Types, Types, Types: Modeling λ Calculus
- 27 The Halting Problem
- Bibliography