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.


closed as too broad by Andrés E. Caicedo, Potato, Shobhit, Cameron Buie, Hanul Jeon Nov 2 '13 at 5:50

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    $\begingroup$ 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. $\endgroup$ – Andrés E. Caicedo Nov 2 '13 at 2:57
  • $\begingroup$ 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. $\endgroup$ – Hunan Rostomyan Nov 2 '13 at 3:03
  • $\begingroup$ 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. $\endgroup$ – Malice Vidrine Nov 2 '13 at 3:43
  • $\begingroup$ Nice paper, Andres!! $\endgroup$ – Armin Meisterhirn Nov 2 '13 at 13:03