美丽的数学：我们如何生活、工作和沟通的数字革命背后令人惊讶的简单想法

English | September 17th, 2024 | ISBN: 0262549778 | 240 pages | True EPUB | 3.65 MB

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.

英文| 2024年9月17日|国际标准图书编号：0262549778 | 240页|真正的EPUB | 3.65 MB 来自畅销书《量子计算为每个人》的作者，这是一种简洁、易懂、优雅的数学方法，不仅说明了概念，还传达了数字信息时代的惊人本质。 我们大多数人都知道20世纪初改变我们对宇宙看法的伟大物理学理论：量子力学和广义相对论。但我们对构成数字革命支柱的辉煌理论知之甚少。在《美丽的数学》一书中，Chris Bernhardt探讨了信息时代的核心数学。他会问这样的问题：什么是信息？数字信息比模拟信息有什么优势？我们如何将模拟信号转换为数字信号？什么是算法？什么是通用计算机？机器如何学习？ 美丽数学的四大主题是信息、交流、计算和学习。Bernhardt通常从一个重要概念的简单数学模型开始，然后揭示一个深层次的潜在结构，将最初看似无关的领域的概念联系起来。他的目标是用最少的数学来呈现概念，但没有什么是过于简单的。在此过程中，伯恩哈特还讨论了字母表、电报和模拟革命；信息论；冗余和压缩；误差和噪声；加密；模拟信息如何转换为数字信息；算法；最后是神经网络。其中包括历史轶事，以了解当时的技术、其影响以及需要解决的问题。 无论读者的数学背景如何，Beautiful math都是一个引人入胜的旅程，通过数学思想来巩固我们日常的数字互动。

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