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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.
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    $\begingroup$ 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. $\endgroup$ – Timbuc Sep 28 '14 at 9:11
  • $\begingroup$ @Timbuc Any other suggestion? $\endgroup$ – Dal Sep 30 '14 at 23:25
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    $\begingroup$ For linear algebra, have you looked at Paul Halmos' Linear Algebra Problem Book? amazon.com/Algebra-Problem-Dolciani-Mathematical-Expositions/dp/… $\endgroup$ – Bungo Oct 9 '14 at 16:58
  • $\begingroup$ @Timbuc the Schaum's series does indeed have many exercises, but they are not very....hard. They are pretty trivial $\endgroup$ – Euler_Salter Jan 15 '17 at 18:35
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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.

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  • $\begingroup$ Very good suggestion. $\endgroup$ – Dal Oct 9 '14 at 22:11
  • $\begingroup$ @Thanks, you're welcome. In fact I appreciate some of his books. My favorite is Naive Set Theory :-) $\endgroup$ – Markus Scheuer Oct 9 '14 at 22:19
  • $\begingroup$ By the way, do you know some exercise books on geometry to use as a companion to Brannan's? $\endgroup$ – Dal Oct 9 '14 at 22:21
  • $\begingroup$ Sorry, no. I've a lot of different problem books, but none with focus geometry. $\endgroup$ – Markus Scheuer Oct 9 '14 at 22:26
  • $\begingroup$ 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. $\endgroup$ – Dal Oct 9 '14 at 22:33
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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):

Have fun!

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  • $\begingroup$ Thanks a lot for the suggestions. $\endgroup$ – Dal Oct 11 '14 at 21:57
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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

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  • $\begingroup$ Any other suggestion? $\endgroup$ – Dal Sep 30 '14 at 23:25
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I've studied on this. Actually it's in Italian but it's a wonderful text.

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