= = What is the specific mathematics talking about = =
There is always a trend in mathematics, that is, who invented a brand-new mathematics (structure), and relying on this "new" mathematics, the problems that used to belong to this category can be easily swept away, and their ease can even be completed by computer programs, so we began to learn new mathematics and abandoned all kinds of hacking skills before. Slowly, we will forget that in the wild times, people, the original and most imaginative way ... people became machines. ...
A little exaggerated, but the preface of the book describes the situation of mathematics education in the United States at that time. Knuth and Graham tried to teach students the skills of dealing with practical problems with more specific mathematical problems rather than abstract concepts and theorems. Of course, these practical problems are strictly analyzed and proved in the field of computer algorithm mentioned by Knuth later. Algorithms are the most basic and important part of computer science, so the subtitle of this book is called "Fundamentals of Computer Science". This basis does not refer to the mathematical theoretical basis of the computer, but an algorithm (problem) analysis basis.
"But what exactly is the specific mathematics? It is a mixture of continuous mathematics and discrete mathematics. More specifically, use a set of problem-solving skills to control the mathematical formula of operation. Once the reader learns the content of this book. All you need is a cool head, a big piece of paper, and well-written words in order to calculate the seemingly terrible sum, understand the complex recursive relationship and find subtle patterns in the data. In terms of algebraic skills, you will be so fluent that you will often find it easier to get accurate results than to solve approximate solutions that are established in a limited sense. " The last sentence refers to the numerical calculation in the computer.
The above is the author's definition of the content or goal of this book in the preface. I want to talk further about the necessity of skills:
Skills can reflect a person's amazing insight into problems and various essential patterns, which are not obtained through mechanical reasoning. Skill is an empirical attempt, which encourages you to give full play to your intuition and seek answers exploratively and creatively. This kind of exploration is the most wonderful thinking activity.
= = Why do you want to read this book = =
My reason is simple. 1) I prefer math. Although I am a computer major, I gradually find that abstract thinking of mathematics is an important factor in writing orthogonal, compact and concise programs. In addition, the pure beauty provided by mathematics is no less than anything that can be called "beauty" in the world, and it may be more beautiful. I decided to read TAOCP. This book should be the best practice before class.
What about the general reason?
Mathematically speaking, some people like purely conceptual things, some people like reasoning to prove more points, some people like logic, and some people like to study various skills. If you are the last person, this book is absolutely suitable for you. But if it is pure problem-solving skills, you obviously underestimate the author's level. In the book, you can see how far mathematicians have pushed "skills"!
From the computer point of view, this book will not directly improve your coding skills, but it will prepare a foundation for you to analyze program algorithms (unfortunately, most of us don't need it in the current application product development), so that you can quickly identify and calculate some mathematical problems. As Knuth, one of the authors of this book, said in the preface of the Chinese version, "This book introduces some mathematical skills that I have often used in studying computer science in the past 30 years." With this, the experience of the great god is worth your time to learn.
Finally, in the final analysis, this is a math book, which has the characteristics of any other excellent math book: it is beautifully written, but it really takes some brains to understand, but it is very worthwhile.