
Self-contained and suitable for undergraduate students, this text offers a working knowledge of calculus and statistics. It assumes only a familiarity with basic analytic geometry, presenting a coordinated study that develops the interrelationships between calculus, probability, and statistics. Starting with the basic concepts of function and probability, the text addresses some specific probabilities and proceeds to surveys of random variables and graphs, the derivative, applications of the derivative, sequences and series, and integration. Additional topics include the integral and continuous variates, some basic discrete distributions, as well as other important distributions, hypothesis testing, functions of several variables, and regression and correlation. The text concludes with an appendix, answers to selected exercises, a general index, and an index of symbols.
1) Calculus: Basic Concepts for High Schools by Lev Tarasov. Soviet-era book written as a dialogue between the author and reader. Absolutely fantastic (also see his other books on Probability etc.) - https://mirtitles.org/2018/09/04/calculus-basic-concepts-for...
2) Calculus: An Intuitive and Physical Approach by Morris Kline. A classic; any book by Morris Kline is a must-have - https://store.doverpublications.com/products/9780486404530
3) Calculus: The Princess of Mathematics by H.C.Verma et al. A two-vol must-have affordable set. The author is a well-known Indian Physics professor and this is written specifically for students to "understand" calculus i.e. it is not a typical textbook. - https://garudalife.in/calculus-the-princess-of-mathematics-v...
4) How to Think about Analysis by Lara Alcock. Provides conceptual insight like the Tarasov book above. Checkout the author's other books too. - https://global.oup.com/academic/product/how-to-think-about-a...
I believe we need to study Calculus alongside Probability/Statistics nowadays due to their pervasive use in ML/AI/etc. To that end;
a) Methods of Mathematics Applied to Calculus, Probability, and Statistics by Richard Hamming. It is by Hamming so one of the best. - https://store.doverpublications.com/products/9780486439457?_...
b) Calculus and Statistics by Michael Gemignani. Similar to the above - https://store.doverpublications.com/products/9780486449937
For distributed systems I'd read Lynch's book on Distributed Algorithms.
For stats Michael Freedman's book, Statistics, is a good simple introduction. Someone mentioned Calculus and Statistics (http://www.amazon.com/Calculus-Statistics-Dover-Books-Mathem...) here on HN a couple of weeks ago. I had looked it when it came out and re-reviewed it with that thread -- I really like it a fair bit more than I remember and a better text for those looking for a more rigorous treatment than Freedman -- although probably still too simple if you're reading Foundations of Statistical NLP.
There's also Scott's book on Programming Languages, which is worth reading.