Understanding Mathematics is a book about mathematical ideas and methods. The author guides readers to understand the essence and significance of mathematics through his own experiences and viewpoints. The theme of this book is "Understanding Mathematics", which aims to make readers understand the essence and significance of mathematics through in-depth thinking and exploration, so as to better master and apply mathematics.
At the beginning of this book, a striking question is put forward: "What is mathematics?" The author believes that mathematics is a tool to describe the objective world, a method of reasoning and thinking, and a means to solve problems. The essence of mathematics is the crystallization of human wisdom and an advanced form of thinking.
Next, the author shows the development course of mathematics to readers by combing the history of mathematics. From ancient algebra to modern mathematics, from Euclid to the invention of calculus, the author introduces the history and background of mathematics in detail. Through these contents, readers can understand that mathematics is not only a bunch of numbers and formulas, but also an idea and method.
Another important theme of this book is mathematical thinking. The author thinks that mathematical thinking is a kind of logical reasoning ability and abstract thinking ability. Mathematically, the correctness of the conclusion is proved by logical reasoning, and the essence of the problem is grasped by abstract thinking. Mathematical thinking is an advanced thinking form and an important tool for people to solve problems.
In order to better illustrate mathematical ideas and methods, the author quoted many vivid examples and stories in the book. For example, through the problem of "chickens and rabbits in the same cage", the author shows readers how to solve the problem through mathematical modeling and reasoning; By proving Pythagorean theorem, the author shows readers how to prove the correctness of the conclusion through logical reasoning. These examples and stories make readers better understand the essence and methods of mathematics.
Generally speaking, math comprehension is a good math reading. By reading this book, readers can understand the origin and development of mathematics, master mathematical ideas and methods, and better apply mathematics to solve problems. At the same time, this book also puts forward some valuable thinking questions to guide readers to think deeply and explore the essence and significance of mathematics.
Notes on Mathematical Stories in the Decisive Battle of Cryptography during World War II
The Mathematical Story in the Cryptographic Decisive Battle of World War II is a book about the Cryptographic War of World War II. The author tells the story of the cryptographic war in history, so that readers can understand the important role of mathematics in secure communication and intelligence decoding. The theme of this book is "Mathematics in the Decisive Battle of Cryptography", which aims to let readers know the importance of mathematics in the field of information security by telling the history of cryptographic warfare.
The book begins with an introduction to the background of the crypto-war during World War II. At that time, the password technology was still immature, and the passwords of both parties were easily deciphered by the other party. In this context, the author introduces in detail several important cryptographic wars during World War II, including the German "charade" and the British "bomb" cipher machine. Through these stories, readers can understand the important role of mathematics in password design and decoding.
In the following chapters, the author introduces the basic knowledge and technology of cryptography in detail. Including the basic concept of password, symmetric key and asymmetric key, hash function and digital signature. Through simple language and vivid examples, the author let readers know the basic knowledge and technology of cryptography.
Another important theme of this book is mathematical ideas and methods. The author thinks that mathematical thinking and methods are the key to solve the password problem. In cryptography, we need to design a secure cryptographic algorithm through logical reasoning and abstract thinking, and analyze and evaluate the security of passwords through probability statistics. Mathematical thinking and methods are necessary tools to solve password problems.
In order to better illustrate mathematical ideas and methods, the author quoted many vivid examples and stories in the book. For example, through the design of "bomb" cipher machine, the author shows readers how to design a secure cipher algorithm through mathematical methods and logical reasoning; By deciphering the password of "dancing villain", the author shows readers how to decipher the password through probability statistics and abstract thinking. These examples and stories make readers better understand the importance and role of mathematics in cryptography.
Generally speaking, the mathematical story in the decisive battle of cryptography during World War II is a good popular science book. By reading this book, readers can understand the importance and role of mathematics in the field of information security, master some basic cryptography knowledge and technology, and better apply mathematics to protect communication security. At the same time, this book also puts forward some valuable thinking questions to guide readers to think deeply and explore the application and prospect of mathematics in the field of information security.