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

Author: Mark C. Chu-Carroll

ISBN-13:
978-1937785338
ISBN-10:
1937785335

Note: This write-up is "in process" and will continue to be updated as I progress. Please review the actual book's table of contents for a full listing of the material that is covered.

"Mark Chu-Carroll is one of the premier math bloggers in the world, able to guide readers through complicated concepts with delightful casualness. If you have ever been curious about the golden Ratio or Turing Machines or why pi never runs out of numbers, this is the book for you."

Carl Zimmer, author of "Matter," a weekly science column in The New York Times (from back of book)

Summary

I am reading this book out of curiosity on what I'd forgotten since school and to maybe pick up a few new bits of information. The author mixes interesting stories with the facts behind the concepts, giving it a fresh approach to describing typically very drab topics. He covers a broad set of topics, ranging from "integers" and "the golden ratio" to "turing machines" and "lambda calculus."

This is a book I will pick up and read when it piques my interest. I will keep this page up to date with the things I have learned along the way.

Chapter Overview

Part 1: Numbers

Chapter 1: Natural Numbers

This chapter talks about what numbers "are"? The short version is that numbers can have one of two meanings depending on the context in which they are used: ordinal and cardinal.

  1. When you are using a number to refer to how many of something are in a group, you are using it as an ordinal number.
  2. When you are counting where a specific object is within a group, you are using it as a cardinal number.

Chu-Carroll goes on to explain natural numbers axiomatically (defining the behaviors of numbers), defining addition, and via a proof (using Peano Induction).

An "in English" definition of natural numbers is this:

They're numbers greater than or equal to zero, where each number has a successor and on which you can use that successor relationship to do induction. [page 8]

I really like the final statement summarizing this chapter:

That's what a number is: something that is constructed from a notion of either quantity or position.

[page 8]

The question to ask about a program is not whether it is right or wrong, but whether it is fixable.

[page 23]

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