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

Mark C. Chu-Carroll

  • 出版商: Pragmatic Bookshelf
  • 出版日期: 2013-08-27
  • 定價: $1,225
  • 售價: 9.0$1,103
  • 語言: 英文
  • 頁數: 282
  • 裝訂: Paperback
  • ISBN: 1937785335
  • ISBN-13: 9781937785338
  • 相關分類: 邏輯設計 Logic-design
  • 立即出貨 (庫存 < 3)

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商品描述

Mathematics is beautiful--and it can be fun and exciting as well as practical. Good Math is your guide to some of the most intriguing topics from two thousand years of mathematics: from Egyptian fractions to Turing machines; from the real meaning of numbers to proof trees, group symmetry, and mechanical computation. If you've ever wondered what lay beyond the proofs you struggled to complete in high school geometry, or what limits the capabilities of computer on your desk, this is the book for you.

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.

商品描述(中文翻譯)

數學是美麗的,它不僅可以是有趣和令人興奮的,還可以是實用的。《好數學》是你對兩千年數學中最引人入勝的主題的指南:從埃及分數到圖靈機;從數字的真正含義到證明樹、群對稱和機械計算。如果你曾經想知道在高中幾何中你努力完成的證明之外還有什麼,或者你的桌上電腦的能力有限,那麼這本書就是為你而寫的。

羅馬數字為什麼仍然存在?我們如何知道某些無窮大比其他無窮大更大?我們如何確定一個程序一定會結束?在這本關於現代和非現代數學的快節奏之旅中,計算機科學家馬克·朱-卡羅爾探索了兩千多年數學思想的一些最重大的突破和失望。數學中有喜悅和美麗,在從他受歡迎的“好數學”博客中選出的二十多篇文章中,你會發現一些概念、證明和例子,它們常常令人驚訝、反直覺或者只是奇怪。

馬克從數字的基礎開始,通過有趣的旅程介紹了整數、自然數、有理數、無理數和超越數。旅程繼續探索了數學中一些最奇怪的數字,包括零、黃金比例、虛數、羅馬數字和埃及分數。在深入研究現代邏輯,包括線性邏輯和邏輯精通的Prolog語言之後,旅程以現代集合論的遊覽和現代機械計算的進展和悖論結束。

如果你的高中或大學數學課程讓你對數字背後的內在含義感到困惑,馬克的書將同時娛樂和啟發你。