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[Straight to the Point]

I would really appreciate any suggestions on self-study materials that relate to math, logic, and/or the philosophy of both. Also, any thoughts or suggestions that you may have in regards to organizing such a self-study so that it can be undertaken as "logically" as possible.

You only need to read further if you like giving more specific advice related to where I am personally in my education.

[More information for those that are interested]

I'm working towards an undergraduate in philosophy and mathematics, and currently close to completing Calculus 1. Philosophy is my first and foremost love, but math and logic have become a passion. So as far as background to possibly help you if you'd like to help me with suggestions:

  • Acquainted with formal logic (e.g., at the level of Theodore Sider's "Logic for Philosophy").
  • Formal math education includes Calc 1 (namely, Brigg/Cochran/Gillet "Calculus, 2nd edition;" not very proof-based).
  • Learning basics of number theory (in Ore's "Number Theory and Its History"), set theory, and foundations of mathematics; also tackling--slowly--more advanced texts (e.g., Shapiro's "Foundations without Foundationalism" and Potter's "Set Theory and Its Philosophy").

I'm interested in learning:

  • Pre- and Post-Calculus mathematics (I will be taking Calc 2 shortly). (Preferably something proof-based and explanatory [added philosophical insight is a plus!]; moreover, I say pre-calculus, because I understand that so much interesting mathematics takes place in algebra, etc).
  • Mathematical logic. (Preferably something "intermediate." By that I mean, the text can presuppose a good deal of acquaintance with logical notation, but where I tend to struggle is with understanding the varieties of differences of opinion, and their implications logico-mathematically, of metamathematical items such as, class, set, properties, membership, etc, as found in studies of semantical models, deductive systems, etc.
  • Anything that you, as possibly a more advanced student yourself, wish you had covered more or understood better before advancing.

Any input would be substantially helpful. I love math and want to learn more. Sorry for any misuse of terms (I'm still learning). Any clarification needed, simply ask.

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Book Recommendations: 1. Logic: Mendelson's intro to mathematical logic 2. Algebra: Maclane and Birkhoff's Algebra 3rd ed, and pick up Dummit and Foote for the exercises 3. Analysis: Pugh's Real Mathematical Analysis 2nd ed

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  • $\begingroup$ Wow, great resources! I've overlooked Mendelson in the past simply because I didn't know what was a good resource and what wasn't in the vast literature. And I've seen Birkhoff mentioned here a few times. All of them look wonderful, thank you for taking the time to share! $\endgroup$ – Cody Rudisill Nov 6 '15 at 21:57
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As an addition to the above I would add 'Godel's Proof' by Nagel, Newman with a foreword of Douglas R. Hofstadter. And of course Hofstadter's Godel, Escher, Bach. Note that there is also a (short) MIT OpenCourseWare course specifically about GEB.

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Student Exercise Tasks (for Mathematics, Language Arts, etc.) - autocorrected

raw url: http://www.public-domain-materials.com/folder-student-exercise-tasks-for-mathematics-language-arts-etc---autocorrected.html

(hot link)

In fact, you are free to copy the entire website and alter it to fit your individual needs, if you wish.

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