3 ms·

"Approachability" might vary somewhat but you might find the following useful; * For an introduction (and a reference) to various areas of Modern Mathematics t

"Approachability" might vary somewhat but you might find the following useful; * For an introduction (and a reference) to various areas of Modern Mathematics that one didn't even know existed, The Princeton Companion to Mathematics and The Princeton Companion to Applied Mathematics are a must. * All the Math You Missed: (But Need to Know for Graduate School) by Thomas Garrity - A survey and a good adjunct to a textbook. * Mathematics: Its Content, Methods and Meaning by Kolmogorov et al. - Classic text from the great Russian Mathematicians. * Methods of Mathematics Applied to Calculus, Probability, and Statistics by Richard Hamming - Unique text from the great Richard Hamming (also checkout his other books). There is plenty more of course, specifically; checkout "Dover Publications" texts, many of which are classics and affordable.

__rito__ 3y ago
Yeah, thanks for the recommendation. I already know the basics, and I want to learn more. I cam handle hard, but the textbooks need to be written in a manner that doesn't require the help of a teacher or a classroom.
- rramadass 3y ago
  None of the above are "basics", they range from undergraduate to research level topics, in particular; the two Princeton Companions are a must have. https://press.princeton.edu/books/hardcover/9780691118802/the-princeton-companion-to-mathematics https://press.princeton.edu/books/hardcover/9780691118802/th... https://press.princeton.edu/books/hardcover/9780691150390/the-princeton-companion-to-applied-mathematics https://press.princeton.edu/books/hardcover/9780691150390/th... PS: In an earlier HN thread, somebody had highly recommended the 4-vol Foundations of Applied Mathematics developed for Brigham Young University’s Applied and Computational Mathematics degree program for beginning graduate and advanced undergraduate students. I have not browsed/read them yet but they are on my "future acquisition and study" list. They seem great and well worth looking into - https://foundations-of-applied-mathematics.github.io/ https://foundations-of-applied-mathematics.github.io/
  - __rito__ 3y ago
    Thanks for the original recommendations, and these two. I have heard about the Princeton Review books. I have not read them yet. Among your original recommendations, I have heard about "All the Maths you Missed". And I have read several chapters of the one by Kolmogorov et al. It's a fantastic book. It lays the landscape really well, discusses things, and covers the breadth of the field rather than the depth of any particular field. I find the writing style really good. It could be seen as a reference book for people who already know the stuff, or are looking to know about new stuff, but want to have ideas about what those stuff might be.

__rito__ 3y ago

Yeah, thanks for the recommendation. I already know the basics, and I want to learn more. I cam handle hard, but the textbooks need to be written in a manner that doesn't require the help of a teacher or a classroom.

rramadass 3y ago
None of the above are "basics", they range from undergraduate to research level topics, in particular; the two Princeton Companions are a must have. https://press.princeton.edu/books/hardcover/9780691118802/the-princeton-companion-to-mathematics https://press.princeton.edu/books/hardcover/9780691118802/th... https://press.princeton.edu/books/hardcover/9780691150390/the-princeton-companion-to-applied-mathematics https://press.princeton.edu/books/hardcover/9780691150390/th... PS: In an earlier HN thread, somebody had highly recommended the 4-vol Foundations of Applied Mathematics developed for Brigham Young University’s Applied and Computational Mathematics degree program for beginning graduate and advanced undergraduate students. I have not browsed/read them yet but they are on my "future acquisition and study" list. They seem great and well worth looking into - https://foundations-of-applied-mathematics.github.io/ https://foundations-of-applied-mathematics.github.io/
- __rito__ 3y ago
  Thanks for the original recommendations, and these two. I have heard about the Princeton Review books. I have not read them yet. Among your original recommendations, I have heard about "All the Maths you Missed". And I have read several chapters of the one by Kolmogorov et al. It's a fantastic book. It lays the landscape really well, discusses things, and covers the breadth of the field rather than the depth of any particular field. I find the writing style really good. It could be seen as a reference book for people who already know the stuff, or are looking to know about new stuff, but want to have ideas about what those stuff might be.