Maurice Klein: Ancient and Modern Mathematical Thoughts
This book consists of three volumes and is a classic in the history of mathematics. His works exceed one million words, expounding the creation and development of mathematics from ancient times to the first few decades of the 20th century, with special emphasis on the work of mainstream mathematics. It is a major feature of this book to quote a large number of first-hand materials and comprehensively mention the contributions of mathematicians in various historical periods, especially famous mathematicians.
Li Daqian, an academician of China Academy of Sciences, commented: "This book highlights the ancient and modern mathematical thoughts and their development context through the introduction of the long and colorful history of mathematics, and grasps the core and soul, which will be of great help to promote and attract readers to approach, taste, understand and love mathematics."
Paulia: How to solve problems: a new method of mathematical thinking.
This is a well-known masterpiece of Paulia, an internationally renowned mathematician, on mathematics teaching methods in middle schools, which has had a far-reaching impact on mathematics education. Paulia believes that the fundamental purpose of middle school mathematics education is to teach young people to think. He regards "solving problems" as a means and way to cultivate students' mathematical talent and teach them to think.
The core of the book is a "how to solve problems" table obtained in the process of solving problems. In the book, according to the questions and suggestions in the table, the author guides students to think about problems and explore ways to solve them, and then gradually grasps the general law of the problem-solving process. There is also a "small dictionary of inquiry method" in the book, which further explains the typical and useful intellectual activities in the process of solving problems.
Aigner & Ziegler: Proof in Mathematical Classics
This book introduces the creative and original proofs of 40 famous mathematical problems. Some of them proved that the idea was not only strange and ingenious, but also perfect on the whole. No wonder some pious mathematicians in the west compare such a masterpiece to the creation of God. This is not a textbook, nor a monograph, but a book to broaden the horizons of mathematics and improve mathematics cultivation.
Simon Singh: Fermat's Last Theorem: A mystery that has puzzled the world's wise men for 358 years.
Vivid stories and fluent language have made Fermat's Last Theorem: a mystery that has puzzled wise people in the world for 358 years from form to spirit. The book is divided into two main lines, one is the efforts of mathematicians in past dynasties to conquer Fermat's Last Theorem, and the other is the growth path of wiles, the prover of Fermat's Last Theorem. In the meantime, it is interspersed with anecdotes of mathematicians, which are brilliant.
Gauss: Arithmetic Exploration
Arithmetic Research is the first masterpiece of Gauss, a great German mathematician known as the "prince of mathematics". The book was officially published in 1797 and 180 1. It is a masterpiece written in Latin and the most classic and authoritative work in number theory.
This book consists of seven chapters, including number congruence, linear congruence equation, power congruence equation and quadratic congruence equation. The content discussed in this book belongs to the study of integers in mathematics, with the purpose of introducing the author's discussion in the field of advanced arithmetic.
The concise and perfect style of this book somewhat slowed down its spread, and finally when talented young people began to study it in depth, they could not buy it because the publishing house went bankrupt. Even Eisenstein, Gauss's favorite student, doesn't have one, and some students have to copy the whole book from beginning to end.