and treat any Calculus they learn as "found money." But assuming you remember at least a little algebra and really want to learn Calculus, I think he's one of the best at teaching it. TBH, I think a person who wanted to learn the equivalent of high-school algebra could just about doing it by watching his Calc I series. So he does a very thorough job of explaining all of the subtle algebraic manipulations that go on as he works through derivatives, integrals, etc. He points out that most students who struggle with Calculus struggle because they (never mastered | forgot | whatever) their basic Algebra. And in particular because he is very detailed in his explanations. I consider him one of the best lecturers in math education, at least for these subjects. ![]() > Does anyone know any other good resources for learning calculus at home? Even though I understand how NSA works, I'd prefer to use any of those. ![]() Many approaches to Calculus do not require assertions about the existence of sets that we cannot construct, even in principle. And therefore NSA can prove anything about Calculus that I care about without needing any axiom beyond ZF.īut in the end this is using a mathematical sledgehammer to drive in a thumb tack. That which we can actually calculate in any useful way can all be calculated on a computer. And we know that it is true without any additional axioms beyond ZF! So take any calculation we can talk about that can be approximated on a computer. (Note, they must be statable in PA, but not necessarily provable there.) But PA can encode any statement we can make about computation. How is this possible? From Shoenfield's absoluteness theorem, you can prove that all statements that an be made in the Peano Axioms that can be proven in ZFC, are also true in ZF. But for all cases I care about, I can already prove it with NSA without ANY additional axioms! I find it a mildly interesting intellectual exercise that you can do NSA with weaker axioms than choice. The axiom of choice is necessary to prove the existence of non-principal ultrafilters in (choice-free) set theory, but the existence of non-principal ultrafilters is not sufficient to prove the axiom of choice. Essentially, the set of properties satisfied by a fixed nonstandard hypernatural gives rise to a non-principal ultrafilter over the naturals. The three axioms of Hrbacek and Katz presented in the article "Infinitesimal analysis without the Axiom of Choice" are the best recent example: these axioms allow you to do everything that is done in Keisler's book and more (including defining the derivative), and you never need to invoke the axiom of choice to justify them. However, there are axioms for nonstandard analysis which are conservative over the usual choice-free set theory ZF. Only model-theoretic approaches, which justify the infinitesimal methods by constructing a hyperreal field, require (a weak form of) the axiom of choice. Pages: 200 Language: English Pages: 200.You write, "we shouldn't need the axiom of choice to define the derivative." Sewing binding for longer life, where the book block is actually sewn (smythe sewn/section sewn) with thread before binding which results in a more durable type of binding. IF YOU WISH TO ORDER PARTICULAR VOLUME OR ALL THE VOLUMES YOU CAN CONTACT US. If the original book was published in multiple volumes then this reprint is of only one volume, not the whole set. Fold-outs, if any, are not part of the book. As this print on demand book is reprinted from a very old book, there could be some missing or flawed pages, but we always try to make the book as complete as possible. ![]() Each page is checked manually before printing. Illustrations, Index, if any, are included in black and white. ![]() This is NOT a retyped or an ocr'd reprint. NO changes have been made to the original text. Bound in genuine leather with Satin ribbon page markers and Spine with raised gilt bands. Leather Binding on Spine and Corners with Golden leaf printing on spine. Hope you will like it and give your comments and suggestions. We found this book important for the readers who want to know more about our old treasure so we brought it back to the shelves. We expect that you will understand our compulsion in these books. If it is multi volume set, then it is only single volume, if you wish to order a specific or all the volumes you may contact us. As these are old books, we processed each page manually and make them readable but in some cases some pages which are blur or missing or black spots. This book is Printed in black & white, Hardcover, sewing binding for longer life with Matt laminated multi-Colour Dust Cover, Printed on high quality Paper, re-sized as per Current standards, professionally processed without changing its contents. Reprinted in 2020 with the help of original edition published long back. Lang: - English, Pages 196, Print on Demand.
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