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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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closed as too broad by user223391, Tim Raczkowski, user91500, user99914, SchrodingersCat Nov 16 '15 at 5:06

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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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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