Textbooks to use as reference for standard calculus and probability topics - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T07:39:21Z http://mathoverflow.net/feeds/question/63458 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/63458/textbooks-to-use-as-reference-for-standard-calculus-and-probability-topics Textbooks to use as reference for standard calculus and probability topics Max1 2011-04-29T18:43:49Z 2011-09-12T02:49:59Z <p>I am currently working on a paper to be submitted to a US journal (addressed primarily to non-mathematiciansâ€™ audience) where I use </p> <p>(1) some standard calculus stuff (e.g. limits, Taylor expansions, integration by parts) and (2) some standard probability theory facts (e.g. Central Limit Theorem, Chebyshevâ€™s inequality). </p> <p>What textbooks would you advise me to list as references for these topics so that the readers could find these topics covered there? I am looking for books that are well known in the US (and not hard to access), contain full proofs but are not too hard for non-mathematicians to comprehend? Thank you.</p> http://mathoverflow.net/questions/63458/textbooks-to-use-as-reference-for-standard-calculus-and-probability-topics/63468#63468 Answer by Julien Puydt for Textbooks to use as reference for standard calculus and probability topics Julien Puydt 2011-04-29T20:21:28Z 2011-04-29T20:21:28Z <p>For standard calculus stuff, "A course of pure mathematics" by Hardy seems to fit what you want pretty well.</p> http://mathoverflow.net/questions/63458/textbooks-to-use-as-reference-for-standard-calculus-and-probability-topics/66278#66278 Answer by Mark Kim for Textbooks to use as reference for standard calculus and probability topics Mark Kim 2011-05-28T13:26:21Z 2011-05-28T13:26:21Z <p>Tom Apostol's <em>Calculus</em> is a "calculus" textbook with proofs and contains two chapters on probability. But then again, such isn't exactly a textbook for "non-mathematicians". Even though the text is suitable for students with good high-school mathematics background, it seems unlikely that anyone without a serious interest in mathematics would be willing to sit through over thousand pages of...well, proofs. It is my understanding that probability textbooks "with proofs" tend to assume, at the very least, multivariable calculus as a prerequisite.</p> <p>Also, I am not sure if there are calculus textbooks "with proofs" in the current market that <em>aren't</em> written for serious students of mathematics.</p> http://mathoverflow.net/questions/63458/textbooks-to-use-as-reference-for-standard-calculus-and-probability-topics/67517#67517 Answer by S.V. for Textbooks to use as reference for standard calculus and probability topics S.V. 2011-06-11T15:51:16Z 2011-06-11T15:51:16Z <p>For probability you can use "Probability and Measure", by Patrick Billingsley. Another option is "A Course in Probability Theory" by Kai Lai Chung.</p> http://mathoverflow.net/questions/63458/textbooks-to-use-as-reference-for-standard-calculus-and-probability-topics/67544#67544 Answer by Andrew L for Textbooks to use as reference for standard calculus and probability topics Andrew L 2011-06-11T21:48:50Z 2011-06-11T21:48:50Z <p>I think Gilbert Strang's <em>Calculus</em> not only has all the calculus and probability the average (and not so average) beginner needs-done carefully but highly intuitively with lots of pictures-but best of all,it's available online for free. </p> <p>Can't get better then that for any recommendation for a beginning calculus student. </p>