11–20 of 180 posts
It's "just" calculus... but it's also everything else leading up to it.
It's a wonderful book, written in a very engaging style, and it shows you how mathematicians think and how they play. It shows you why we have proofs, why things go wrong, and all that had to happen before we came up with a definition of derivatives and integrals that we're happy with (and of course, all of the things we can do with our newfound definitions).
I know you asked for books, but I have to mention the videos of Grant Sanderson (3Blue1Brown) [1]. His explanations of mathematics are the only ones I can think of that have given me the same sort of piercing clarity and insight that one gets from reading Feynman on physics. [1]: https://www.youtube.com/c/3blue1brown
Prelude to Mathematics by W.W. Sawyer was written to give students an overview of modern math concepts beyond algebra. Topics include non-euclidian geometry, linear algebra, projective geometry and group theory. Again, for someone with an understanding of algebra. I enjoyed it and think it's in the spirit of what you're looking for. Edit: Introduction to Graph Theory by Trudeau is another that I really liked. Very li…
If you have a grasp of algebra and sets this book is an easy read for the curious or mathematically immature.
Edit WhatIsDukkha is correct and their suggestion better reflects what I intended to say.
Not really a book that has lectures but it's a great book that covers all popular topics in Mathematics (fun to read).
(Link: https://mirtitles.org/2015/12/07/mathematics-can-be-fun-yako...)
Spivak's Calculus. It's "just" calculus... but it's also everything else leading up to it. It's a wonderful book, written in a very engaging style, and it shows you how mathematicians think and how they play. It shows you why we have proofs, why things go wrong, and all that had to happen before we came up with a definition of derivatives and integrals that we're happy with (and of course, all of the things we can do…
Spivak's Calculus. It's "just" calculus... but it's also everything else leading up to it. It's a wonderful book, written in a very engaging style, and it shows you how mathematicians think and how they play. It shows you why we have proofs, why things go wrong, and all that had to happen before we came up with a definition of derivatives and integrals that we're happy with (and of course, all of the things we can do…
But then I tried to solve some final exams from previous years, and realized the feeling is false. These books gave me great intuition - but they made all the math look deceivingly simple, and as a result it is hard to develop the actual problem solving skills and intuition.
I know my experience is not unique - in fact, everyone I know who tried to learn exclusively from Feynman had the same experience.
>This isn't a popular suggestion (and by that I don't mean to say it's rejected or people don't like it, I just haven't heard it suggested before in this context) but at university for electronic engineering we used K.A. Stroud's Engineering Mathematics. This book is surprisingly little focused on actual applications to engineering, it takes you through calculus by introducing the derivative, for example, and then some linear algebra stuff. But what surprises people is that it starts off with the properties of addition and multiplication - it's that simple. It's a book that starts from zero and takes you very, very far. It won't take you to a mathematician's 100 but it'll take you to any serious engineering undergrad's 100.