2
$\begingroup$

I have been self-studying mathematics for many years now and I've noticed that you don't really find mathematics books which have solutions to the exercises, and sometimes they don't have exercises at all. I think that if I could do exercises and compare my answers to the solutions, it would give me much stronger understanding of the subjects.

So I was wondering if there is a book that would contain problems from different subjects in mathematics with solutions. I know there are some such books but they're usually concentrated on only one or two subjects. It would be convenient if all the exercises were in one book.

I'm looking for a book in the undergraduate level which would cover as wide range of fields in pure mathematics. Areas I'm interested in are analysis, algebra, topology and number theory. I'm excluding fields such as geometry, elementary algebra and other fields that are a subject of competition mathematics (IMO) because there are already a lot of resources for those.

If such a book existed, it would be a very valuable resource for self-study. Thanks!


Edit:

This question was put on hold as too broad. The reason, why I think it's better not to restrict this question too much, is because I know there aren't many such books, that I've described above, if any. This way the people answering have more freedom to suggest anything close to what I'm looking for. And because there aren't many such books, there won't be a problem of having too many possible answers.

Also, when I don't restrict it too much, I think more people could benefit from the question and answers.

According to help center: "if your question - - has many valid answers (but no way to determine which - if any - are correct), then it is probably too broad" I don't think that this is the case with my question since the correct answer is the book with questions from as many fields as possible (and I did restrict it to fields mentioned above...).

$\endgroup$

closed as too broad by Hans Lundmark, Martin Sleziak, JMP, Ethan Bolker, Robert Soupe Jul 1 '18 at 19:38

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • 4
    $\begingroup$ mathematics is like infinity.You should mention the topic atleast ! $\endgroup$ – laura Jun 29 '18 at 7:26
  • 3
    $\begingroup$ In Introduction to Smooth Manifolds, Lee says "I have deliberately not provided written solutions to any of the problems, either in the back of the book or on the Internet. In my experience, if written solutions to problems are available, even the most conscientious students find it very hard to resist the temptation to look at the solutions as soon as they get stuck. ... " $\endgroup$ – Jo Be Jun 29 '18 at 7:27
  • 3
    $\begingroup$ " ... But it is exactly at that stage of being stuck that students learn most effectively, by struggling to get unstuck and eventually finding a path through the thicket. Reading someone else’s solution too early can give one a comforting, but ultimately misleading, sense of understanding. [...] Even if someone else gives you a suggestion that turns out to be the key to getting unstuck, you will still learn much more from absorbing the suggestion and working out the details on your own than you would from reading someone else’s polished proof. " $\endgroup$ – Jo Be Jun 29 '18 at 7:28
  • $\begingroup$ @Jo Yeah, I get that. But the problem is that I'm not always sure if my solution is correct or efficient. I don't have a teacher who could check my answers or give help... $\endgroup$ – Miksu Jun 29 '18 at 9:53
  • 1
    $\begingroup$ @JoBe I do not think it is unreasonable to want a book with solutions - especially when self-studying, when there is no one to present problems or correct your work. Working problems without getting any kind of feedback on your solution could lead to an overestimate of your mastery of the material. $\endgroup$ – Jair Taylor Jun 29 '18 at 20:54
3
$\begingroup$

Miksu, hello!

I'm not able to recommend a single book covering both algebra and analysis, at least in English. Also, from your question it appears you're at a level where you're still becoming accustomed to rigorous math, and what does or doesn't constitute a proof. Therefore the books I'm going to suggest are at a level generally somewhat below that of, say, Rudin's Principles of Mathematical Analysis.

  1. The solutions manual to Spivak's Calculus. (The problem statements are in the textbook.)

  2. Demidovich. Problems in Mathematical Analysis.

  3. Halmos. Linear Algebra Problem Book.

  4. Faddeev, Sominsky. Problems in Higher Algebra.

The last two books have a separate "Hints" section that comes before the answers.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.