[rramadass]

"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__]

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]

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/th...

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/

[__rito__]

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.