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I am an undergraduate engineering physics student since 1 1/2 years back. I've taken classes in real analysis, complex analysis and linear algebra.

When one tries to read about math on Wikipedia the articles talk about mathematical structures, mathematical objects and so on. I'd like to know more about this, the "foundations of mathematics".

I want to know if there are any appropriate books, given my background, that would be possible to use for self-study?

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    What do folks here think of Basic Concepts of Mathematics by Elias Zakon? It's free online: http://www.trillia.com/zakon1.html2012-03-11

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A classic text that used to be (and still may be) a standard undergraduate text for courses in the foundations of mathematics is Introduction to the Foundations of Mathematics by Raymond Louis Wilder. You can find this book in virtually every U.S. college/university library, and apparently (from what I've just read online) Wilder's book is being reprinted by Dover Publications. I think this book would be a very good fit for what you're looking for and your background. (I've had a copy of the 1965 edition for nearly 30 years, so I'm somewhat familiar with it.)

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    I recently discovered that a digital copy of the 1965 edition of Wilder's [**Introduction to the Foundations of Mathematics**](https://archive.org/details/IntroductionToTheFoundationsOfMathematics) is freely available (and apparently legally available) on the internet.2014-10-10