2. Advanced Algebra is an exercise of advanced algebra in Peking University, and there is an answer.
3. Modern algebra can be selected directly, and exercises can refer to the problem set written by Yang Zixu.
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Here are some references:
Mathematical analysis:
Introduction or basic course:
1, Mathematical Analysis, Chen Fudan University Press, etc. Textbooks of mathematics departments in most schools have been compiled.
PS: Mathematical analysis of Nankai University, a new lecture on mathematical analysis of Peking University, and mathematical analysis of Xiamen University are also quite good.
2. Course of Mathematical Analysis, edited by Chang Gengzhe and Shi Jihuai, published by Advanced Mathematics Publishing House and Shanghai Science and Technology Publishing House, which is out of print. The exercises in this book are very difficult, which is also a feature of the Mathematics Department of the Chinese University of Science and Technology. If you can do all the exercises, I believe it will be a challenge to yourself and a leap in math ability.
Improve the curriculum:
3. Rudin, Principles of Mathematical Analysis is one of Rudin's basic classic works. This book is characterized by a high starting point and a low starting point. Some traditional concepts in modern times are analyzed, and the concepts of real variable function and functional are introduced, which is very helpful for subsequent learning.
4. The Course of Microcomputer Analysis is a classic, with two volumes and four volumes, covering all aspects of mathematical analysis, which can be described as an encyclopedia of mathematical analysis. Many mathematicians of the older generation benefited from this book.
Auxiliary class:
5. "Eight Lectures on Mathematical Analysis" (Qin Xin) This book tells the relevant important concepts of mathematical analysis in a special way. Strong knowledge, strong interest, can have a deep understanding of some concepts of mathematical analysis.
6. Item 51 Basic Mathematics Lecture Item 51 This is a series, including analysis, algebra, geometry, number theory and other branches.
Exercise:
Jimmy Dovich's Mathematical Analysis Problem Set
Typical problems and methods in Pei's mathematical analysis
Advanced Algebra, edited by Peking University Algebra Department and published by Higher Education Press, is a textbook for mathematics departments in most schools.
In addition, Fudan University and Nankai University have also compiled a set of advanced mathematics textbooks. Advanced Algebra by Zhang of Beijing Normal University and Linear Algebra by China University of Science and Technology are also good choices.