[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.