[__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.