Beautiful Math: The Surprisingly Simple Ideas Behind the Digital Revolution in How We Live, Work, and Communicate

Bernhardt, Chris

  • 出版商: MIT
  • 出版日期: 2024-09-17
  • 售價: $1,180
  • 貴賓價: 9.5$1,121
  • 語言: 英文
  • 頁數: 240
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 0262549778
  • ISBN-13: 9780262549776
  • 海外代購書籍(需單獨結帳)

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商品描述

From the bestselling author of Quantum Computing for Everyone, a concise, accessible, and elegant approach to mathematics that not only illustrates concepts but also conveys the surprising nature of the digital information age.

Most of us know something about the grand theories of physics that transformed our views of the universe at the start of the twentieth century: quantum mechanics and general relativity. But we are much less familiar with the brilliant theories that make up the backbone of the digital revolution. In Beautiful Math, Chris Bernhardt explores the mathematics at the very heart of the information age. He asks questions such as: What is information? What advantages does digital information have over analog? How do we convert analog signals into digital ones? What is an algorithm? What is a universal computer? And how can a machine learn?

The four major themes of Beautiful Math are information, communication, computation, and learning. Bernhardt typically starts with a simple mathematical model of an important concept, then reveals a deep underlying structure connecting concepts from what, at first, appear to be unrelated areas. His goal is to present the concepts using the least amount of mathematics, but nothing is oversimplified. Along the way, Bernhardt also discusses alphabets, the telegraph, and the analog revolution; information theory; redundancy and compression; errors and noise; encryption; how analog information is converted into digital information; algorithms; and finally, neural networks. Historical anecdotes are included to give a sense of the technology at that time, its impact, and the problems that needed to be solved.

Taking its readers by the hand, regardless of their math background, Beautiful Math is a fascinating journey through the mathematical ideas that undergird our everyday digital interactions.

商品描述(中文翻譯)

來自暢銷書《量子計算入門》的作者,這本書提供了一種簡潔、易懂且優雅的數學方法,不僅闡明了概念,還傳達了數位資訊時代的驚人特性。

我們大多數人對於二十世紀初改變我們宇宙觀的偉大物理理論有所了解:量子力學和廣義相對論。然而,我們對於構成數位革命基礎的卓越理論則不太熟悉。在《美麗的數學》中,Chris Bernhardt 探索了資訊時代核心的數學。他提出了以下問題:什麼是資訊?數位資訊相較於類比資訊有什麼優勢?我們如何將類比信號轉換為數位信號?什麼是演算法?什麼是「通用」計算機?機器又如何學習?

《美麗的數學》的四個主要主題是資訊、通信、計算和學習。Bernhardt 通常從一個重要概念的簡單數學模型開始,然後揭示出一個深層的結構,將看似無關的概念聯繫起來。他的目標是用最少的數學來呈現這些概念,但沒有任何內容被過度簡化。在這個過程中,Bernhardt 也討論了字母表、電報和類比革命;資訊理論;冗餘和壓縮;錯誤和噪音;加密;類比資訊如何轉換為數位資訊;演算法;以及最後的神經網絡。書中還包含歷史轶事,以便讓讀者了解當時的技術、其影響以及需要解決的問題。

《美麗的數學》引導讀者,無論其數學背景如何,都是一段迷人的旅程,探索支撐我們日常數位互動的數學思想。

作者簡介

Chris Bernhardt was a professor of mathematics at Fairfield University for over thirty years before he retired. His books include Turing's Vision: The Birth of Computer Science and Quantum Computing for Everyone, both published by the MIT Press.

作者簡介(中文翻譯)

克里斯·伯恩哈特(Chris Bernhardt)在費爾菲爾德大學擔任數學教授超過三十年,直到退休。他的著作包括《圖靈的視野:計算機科學的誕生》(Turing's Vision: The Birth of Computer Science)和《量子計算入門》(Quantum Computing for Everyone),兩本書均由麻省理工學院出版社(MIT Press)出版。