What is Mathematics is a masterpiece by the great German mathematician R Courand. Introduce in an easy-to-understand way.

This book is written for beginners and experts, students and teachers, philosophers and engineers. It is a world-famous popular mathematics reading. This book gives a clear introduction to the whole mainstream mathematics knowledge system and a detailed explanation of the most important concepts in mainstream mathematics. I think it can solve the first and second problems mentioned by the landlord.

What is mathematics? Douban link /subject/ 1320282/

Mathematics: Its Content, Method and Significance is a masterpiece written by famous mathematicians in the former Soviet Union to popularize mathematical knowledge. The book has 3 volumes. This book introduces the content, historical development and application of modern mathematics in natural science and engineering technology in extremely popular language. This can just solve the three problems mentioned by the landlord.

Mathematics: its content, method and significance Douban link /subject/ 1230328/

The two famous books mentioned above, written by a German and a Soviet, have different styles. Reading them will help broaden your horizons.

Of course, in the process of building a mathematical knowledge system, it is very important to read some books on the history of mathematics and understand how the basic mathematical concepts you have learned come from. In this respect, I admire Klein's Thoughts on Ancient and Modern Mathematics (volume 1-4) most, and another masterpiece comparable to it is Bell's Master of Mathematics: From Zhi Nuo to Poincare, which is a biography.

Douban link of ancient and modern mathematical thoughts/subject/1277169/

Master of Mathematics: Link from Zhi Nuo to Poincare Douban /subject/ 1428309/

Among the books written by China people, I highly admire Qi Youmin's Revisiting Calculus, but I suggest that you study calculus before reading it. Reorganizing your knowledge system will give you a brand-new feeling. Speaking of Qi, he has also translated many famous mathematical works, some of which are professional, but one book called Mathematics in the Modern World is a relatively easy-to-understand model, because it comes from a series of mathematical collections of Scientific American, a high-end popular science magazine, in the forties and sixties. The authors are all big names and the content is very complicated. But it is aimed at the general public, so it is very easy to read.

Mathematics Douban Link in Modern World /subject/2298747/

Review the links/topics of calculus douban/123979 1/

Zhang Dianzhou's Mathematics in the 20th Century mainly focuses on mathematics in the 20th century, which is too abstract. Just flip through it as a novel. Not very recommended.

Douban Link 20th Century Mathematics Jingwei /subject/ 1625008/

On the history of mathematics, I have also read a book, A Tutorial for Genius, which is very suitable for high school students. If you are still stuck in the stage of reciting mathematical concepts and formulas, I can guarantee that after reading this book for the first time, you will feel extremely shocked and amazed. In terms of easy understanding, it may surpass all previous works. The only drawback is that the Chinese version is somewhat poor in typesetting.

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Now many people admire Wu Jun's book The Beauty of Mathematics. In fact, the book Beauty of Mathematics only talks about the applied knowledge of statistics and information theory, not the beauty of mathematics, but the beauty of statistical application. Can't compare with the works of Klein and Courant.

The beauty of mathematics douban link/subject/10750155/