5 ms·
Same here. For me the best flow comes from a simple information dense book, like any famous tome from Springer Graduate Texts in Mathematics. In relation to th
by nextos 5y ago
Same here. For me the best flow comes from a simple information dense book, like any famous tome from Springer Graduate Texts in Mathematics.
In relation to this, IMHO the best way to learn the foundations of mathematics is to teach yourself either:
* Linear algebra and real analysis (if your end goal is ML or statistics)
* Logic and type theory (if your end goal is formal methods or PLT)
For the first option, a typical sequence (like the one taught at Harvard Math 55) is Halmos (or Axler) plus Rudin (and a good companion like Gelbaum & Olmsted). A more practical bottom-up approach is to use a good matrix analysis book such as Meyer, plus a more practical calculus (vs analysis) textbook like Hubbard & Hubbard.
For the second option, a good theoretical logic book (Ben Ari and Schoening are my favorites) paired along with Girard. A more practical option would use Huth & Ryan as a logic volume along with Pierce's TAPL.
- bluechair 5y agoCould you provide the full titles/authors of these books?
- nextos 5y agoFull titles, authors and ISBNs should be available via Goodreads: * Halmos: https://www.goodreads.com/book/show/692030 https://www.goodreads.com/book/show/692030 * Axler: https://www.goodreads.com/book/show/309768 https://www.goodreads.com/book/show/309768 * Rudin: https://www.goodreads.com/book/show/292079 https://www.goodreads.com/book/show/292079 * Gelbaum & Olmsted: https://www.goodreads.com/book/show/818070 https://www.goodreads.com/book/show/818070 * Meyer: https://www.goodreads.com/book/show/1002449 https://www.goodreads.com/book/show/1002449 * Hubbard (5th edition available): https://www.goodreads.com/book/show/631871 https://www.goodreads.com/book/show/631871 * Ben Ari: https://www.goodreads.com/book/show/115121 https://www.goodreads.com/book/show/115121 * Schoening: https://www.goodreads.com/book/show/4993214 https://www.goodreads.com/book/show/4993214 * Girard: https://www.goodreads.com/book/show/3400118 https://www.goodreads.com/book/show/3400118 * Huth & Ryan: https://www.goodreads.com/book/show/151847 https://www.goodreads.com/book/show/151847 * Pierce: https://www.goodreads.com/book/show/112252 https://www.goodreads.com/book/show/112252
- bluechair 5y agoAmazing. Thank you.
- trenchgun 5y agoI have been gravitating towards this. Feel like I only got very shallow learning from my CS courses. Bought physical books now to grok the subject better (for now theory of computation, algorithms etc). Feel like especially my math foundation is lacking, so thanks a lot for these recommendations!