Exercise books in linear algebra and geometry

Question

I'm studying Brannan's Geometry and Lang's Introduction to Linear Algebra and I was wondering if there are some exercise books (that is, books with solved problems and exercises) that I can use as companions.

The books I'm searching for should be:

full of hard, non-obvious, non-common, and thought-provoking problems;
rich of complete, step by step, rigorous, and enlightening solutions.

Ask for the books of the Schaum's series (Mac Graw - Hill Editors). These books contain hundreds of completely solved exercises plus hundreds of exercises with the solutions only. — Timbuc, Sep 28 '14 at 09:11
For linear algebra, have you looked at Paul Halmos' Linear Algebra Problem Book? http://www.amazon.com/Algebra-Problem-Dolciani-Mathematical-Expositions/dp/0883853221# — , Oct 09 '14 at 16:58
@Timbuc the Schaum's series does indeed have many exercises, but they are not very....hard. They are pretty trivial — Euler_Salter, Jan 15 '17 at 18:35

score 9 · Accepted Answer · edited Jun 12 '20 at 10:38

9

A classic in linear algebra is Paul R. Halmos' Linear Algebra Problem Book.

In fact it's also a great book teaching many aspects of linear algebra and a great book in teaching how to solve problems. The first part contains more than 160 problems, the last part contains detailed solutions. A nice idea is a small chapter in between about 15 pages long, which contains hints for each of the problems.

The reader is encouraged even if he is able to solve a problem to also check the solution, since they may contain additional info in form of interesting comments.

I fully agree with the end of his preface:

I hope you will enjoy trying to solve problems. I hope you will learn something by doing so, and I hope you will have fun.

edited Jun 12 '20 at 10:38

Community

1

answered Oct 09 '14 at 22:02

Markus Scheuer

108,315

Very good suggestion. – Dal Oct 09 '14 at 22:11
@Thanks, you're welcome. In fact I appreciate some of his books. My favorite is Naive Set Theory :-) – Markus Scheuer Oct 09 '14 at 22:19
By the way, do you know some exercise books on geometry to use as a companion to Brannan's? – Dal Oct 09 '14 at 22:21
Sorry, no. I've a lot of different problem books, but none with focus geometry. – Markus Scheuer Oct 09 '14 at 22:26
I see. Would you mind telling me the names of other problem books (in different topics) that you find useful? I'm sure that I can learn a lot from your experience. – Dal Oct 09 '14 at 22:33
This is a great suggestion. I really like this book. – etothepitimesi Oct 09 '14 at 23:00
@Dal: You may have a look at my answer to this question where I recommend problem books in analysis. Other books are presumably too specific. But at least one treasure: When you start studying point set topology the book Counterexamples in Topology is really cool. It's not a problem book per se, but when you are searching for topologies with certain properties, you will find there a solution. – Markus Scheuer Oct 10 '14 at 07:06
Thank you very much for your kindness and your help :) – Dal Oct 10 '14 at 12:02
@Dal: You're welcome! And thank you very much for the bounty! :-) Best regards, – Markus Scheuer Oct 14 '14 at 20:01

score 4 · Answer 2 · answered Oct 09 '14 at 23:28

Let me start by mentioning a series of books on linear algebra, by T. S. Blyth and E. F. Robertson, that I consider to be really enlightening:

Theory + Solved Exercises

Solved Exercises

And now, my secret weapons (more directed towards matrix theory):

Matrix Algebra, by K. Abadir and J. Magnus;
Problems and Solutions in Introductory and Advanced Matrix Calculus, by Willi-Hans Steeb.

Have fun!

Thanks a lot for the suggestions. – Dal Oct 11 '14 at 21:57 — Dal, Oct 11 '14 at 21:57

score 1 · Answer 3 · answered Sep 29 '14 at 01:18

1

I agree with Timbuc, the Schaum's calculus book has helped me with having many solved problems and explanations. I have seen a geometry addition being sold on amazon and ebay for a pretty good price

answered Sep 29 '14 at 01:18

amjh23

25

Any other suggestion? – Dal Sep 30 '14 at 23:25

score 1 · Answer 4 · answered Oct 09 '14 at 23:37

1

I've studied on this. Actually it's in Italian but it's a wonderful text.

answered Oct 09 '14 at 23:37

Ivan Di Liberti

4,881

Exercise books in linear algebra and geometry

4 Answers4

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