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So, here is my intent and situation.

I am OK at solving novel problems. I've been through general University calculus, and have always gotten mainly A's and B's in my maths courses. But I've mainly achieved this through picking up patterns, etc. and I always skip steps in my head which leads to problems when I get to tougher problems down the line. I find myself weak on the fundamentals, so I cannot solve higher level problems. I am taking discrete maths right now as a part of my Computer Science degree, but I find that the kids coming from math backgrounds are running circles around me.

As a result of all this, I'm not as good at solving novel problems that have new situations and contexts that I have no seen before as I would like to be. I don't intend on trying to become a mathematician by any means, but I believe that learning how to properly approach problems in maths will help me learn to approach other problems, both in Computer Science and life in general.

I am really trying to take a more math centric approach to solving the problems I come across in Computer Science and, right now, discrete maths. But I would like to maybe go backwards a little bit in my free time and work on bettering my fundamentals and learn how to better problem solve with topics that are more easily tractable.

Can anyone recommend me a good book that would fit this description? Or am I looking for something that doesn't really exist?

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I think these two books should be (very!) good references:

Good luck!

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  • $\begingroup$ This is exactly what I am looking for, thank you! $\endgroup$
    – Adam Thompson
    Commented Oct 5, 2015 at 19:22
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See if the following book fits your desire/intention:

The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics

http://store.doverpublications.com/0486277097.html

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I second Kolmin's recommendations especially "The Art and Craft of Problem Solving" by Paul Zeitz. It is a fantastic book. Another book on problem solving, focusing more on ways to think, for solving tough problems, is written by the greatest of them all, namely George Polya.

Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving, Volumes I and II By George Polya

I highly recommend this book. Information in the II volume is priceless and there are hardly any other books which have given information as useful as in this book. This information may not transform anyone instantaneously into a problem solving genius but atleast, it mentions the kind of though process that is necessary for solving tough problems. This, I think, in turn helps to gain mathematical maturity at a much higher rate than otherwise. I can attest to the fact that this book made a tremendous difference in the way I thought about problem solving.

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