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Lately, I've been learning a lot of mathematics. But I am having a problem. Although for most part I understand in general as to how a function is derived and not so much as to understanding the proof of a theorem, the problem I am having is not understanding the material "conceptually."

For instance, in my Linear Algebra course, I finished with a top score but I did not understand as to how the material worked. One example is the determinant of a matrix. Although I do know how to compute it, if someone were to ask me what does determinant mean intuitively, I know that I would either botch the answer to a degree where the individual would never ask a math related question again or I would simply say I don't know and stress over it for weeks. The latter is currently the phase I am going through which is very discouraging and a downer.

But I believe there is a solution. I just learned that in my university, a math class is offered for Philosophy majors. So, I was wondering if anyone knew of any good textbook that presents some rigorous mathematical material from philosophical perspective so that the reader can actually understanding as to "how" a formula works.

Also any input and suggestion as to how I can help myself in terms of understanding the material more conceptually would be appreciated.

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closed as too broad by Andres Caicedo, Potato, Ramanujan, Cameron Buie, tetori Nov 2 '13 at 5:50

There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs.If this question can be reworded to fit the rules in the help center, please edit the question.

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Not what you are really asking, but a nice description of what determinants are, at your level, can be found in the article: John Hannah. A Geometric Approach to Determinants, The American Mathematical Monthly, 103 (5), (May, 1996), 401-409. –  Andres Caicedo Nov 2 '13 at 2:57
    
I think you might enjoy Goldblatt's Topoi: The Categorial Analysis of Logic. It has made me question things I took for granted, which I feel is leading me to a better understanding of some of the choices made in the foundations of mathematics. Sorry if I'm completely off. I hope you find an answer to your question; it's an important one. –  Hunan Rostomyan Nov 2 '13 at 3:03
    
Lawvere & Schanuel's "Conceptual Mathematics" is also a nice introduction to using the ideas of category theory to tie things together. Personally, I find the language of categories helps me get over not being able to explain what certain constructions "are" by helping me think about what they do. –  Malice Vidrine Nov 2 '13 at 3:43
    
Nice paper, Andres!! –  Armin Meisterhirn Nov 2 '13 at 13:03