# Books with a summary at the end.

Are there any textbooks in linear algebra, analysis, or algebra which provide a summary of the ideas presented in the chapter? A similar question has been asked earlier List books with end of chapter summaries

The image is taken from the NCERT 12th standard maths book.

My purpose of asking this question is the following:

It will be helpful if someone wants to review a subject before appearing for some entrance exam or an interview.

A good short note will also be helpful.

• Ah, if only Grothendieck had done that in his Elements de Geometrie Algebrique. Dec 7 '19 at 19:01
• Why not you make it in yourself ? By doing this not only you can increase the depth of your own knowledge in various fields, but also you grow your experience. Believe me, it will be very conducive to your future study too. Dec 8 '19 at 9:52

Here is a list of textbooks for linear algebra I used in completing my undergraduate degree in mathematics and physics. Unfortunately, all the analysis and algebra books I used did not summarize the key points at the end of each chapter. Like mentioned in the comments: that is a good exercise, as most students dread to hear, left to the reader; but alas, here is my list.

$$\bullet$$ $$3000$$ Solved Problems in linear algebra, By Seymour Lipschutz

This book contains 3000 Solved Problems that can not only help students to understand abstract concepts of linear algebra, but they are also, an excellent complement for any course of Linear Algebra. Solved problems cover from simple problems to proofs of theorems, which help you to organize the thought processes and give you a better concept and intuition of the material.

The book is very clear and complete, and the range of material covered is more than you will find in the lower undergraduate class. If you take the time to work through this book, you will be a master of the topic with a much wider foundation and with many different approaches to same problem. It will also help you catch up on the little "details" which you might have absorbed for the duration that you thought you would be tested on it, but after such time the information vanished into the void of forgotten math.

$$\bullet$$ Theory and Problems of Linear Algebra, By Seymour Lipschutz

Each chapter begins with clear statements of pertinent definitions, principles and theorems together with illustrative and other descriptive material. It’s easy-to-follow and all topics are well organized. It provides hundreds of examples, solved problems, and practice exercises to test the student’s skills.

The solved problems serve to illustrate and amplify the theory, bring into sharp focus those fine points without which the student continually feels himself on unsafe ground, and provide the repetition of basic principles so vital to effective learning. Numerous proofs of theorems are included among the solved problems. Supplementary problems serve as a complete review of the material of each chapter.

This next book is written by Gilbert Strang. While it does not have direct summaries at the end of each chapter, his new videos on youtube "A New Way to Start Linear Algebra" act as great chapter reviews for this text - even though this was written before the videos were recorded (thats how great he is)!

$$\bullet$$ Linear Algebra and its applications, By Gilbert Strang

This book is an excellent and accessible intro to the subject, where the author begins with a brief and enthusiastic explanation of the nature of linear algebra.

The book is written in a very colloquial and natural way, using an informal and personal style, and emphasizing on understanding instead on proofs; nevertheless it does not flow as easily as the author’s lectures. The proposed problems, give you the opportunity to practice the theoretical as well as computational algebraic skills.

The author tries, in all moment, to demonstrate that linear algebra is a fascinating subject by showing both, its beauty and value. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics. He explains concepts, rather than deduces.

• I hope this was helpful my friend! I will edit my answer in the future if I find any good analysis and algebra books that fit this criteria. @sarthakgupta Jul 24 '20 at 2:07