The first and second volumes of mathematical analysis are generally completed in three semesters. In order to save costs, many schools' mathematics departments will compile their own textbooks. Although the content is almost the same, the layout of the chapters is different. Originally, many people chose mathematics major because high school loves mathematics. As a result, because of the layout of the chapter, it was very difficult at first, which discouraged many people and eventually failed to learn well. Advanced algebra is also difficult at first, and the skill is higher than mathematical analysis (personal opinion), so the textbook largely determines whether you learn well or not.
Here are two books on mathematical analysis: Mathematical Analysis, revised by Chen Ji (published by Fudan University) and published by East China Normal University (the specific editor forgot); Advanced Algebra recommends two books: one from Peking University Press and the other from Tsinghua. The authors of these two books don't remember them.
Let me introduce mathematical analysis first. For this set of textbooks published by China Normal University, the difficulty is moderate and it is a classic! I use this set of textbooks in my study. The content of the textbook covers most of the classical knowledge points in mathematical analysis, and the difficulty is easy to explain. It is very suitable for junior scholars to study and graduate students to review. There are at least 20 topics in each chapter of the textbook. The difficulty of each topic can exercise our thinking ability, and some topics are very skillful. If you plan to take the postgraduate entrance examination in mathematics, then all the topics in this textbook should be done. Chen Jixiu's version was written by Fudan University. As we all know, the mathematics department of Fudan University is second only to Peking University in China, so it is difficult for textbooks to be produced by China Normal University. Those who plan to enter the mathematics department of Fudan University in Peking University can refer to this book, and the rest can refer to China Normal University Edition. Chen Jixiu himself is also a well-known doctoral supervisor of Fudan University (I admire him very much). This set of teaching materials is rich in knowledge points but not confusing, and the problems are a bit odd (I only read part of it during my college years, but I didn't read it all). Not suitable for beginners, but it is recommended as an auxiliary material for graduate students.
Let's start with two sets of books on advanced algebra. The first is the Tsinghua version. I haven't seen it very much (although it is in the library), but I saw it mentioned on the Internet, so I list it here for reference. Let's focus on the advanced algebra of Peking University. To tell you the truth, this book definitely impressed me. This book is really classic and perfect! ! The content is completely acceptable in difficulty, and there will be 20 to 30 topics after each chapter, each of which is a classic. Even the postgraduate entrance examination questions in many schools will copy the questions in this book (see 20 12 Postgraduate Entrance Examination Questions for Advanced Algebra in East China Normal University, in which there is a polynomial problem exactly the same as that in Peking University Edition), and the solutions in the exercises mostly cover the exercise skills of Advanced Algebra (if in doubt, you can go to the Doctor of Mathematics Forum for consultation, which is much superior). I really appreciate this book. Moreover, this book should have been published for 30 or 40 years, and it is still enduring, which shows its brilliance.