#260 overall
Mathematics and its History (Norman Wildberger)
YouTube
2 recommenders · 2 threads · recommended in 2 years, 2019–2020 · score 1.8
A YouTube lecture series by mathematician Norman Wildberger that follows John Stillwell's book 'Mathematics and Its History', covering the development of mathematical ideas such as calculus, polynomials, group theory, and topology from an undergraduate perspective.
Commenters point to it as an intuitive companion to Stillwell's academic book, with one calling the buildup to calculus fascinating and another suggesting it for self-learners with a weak math background.
Mathematicsintermediatefreevideo lectures#history of mathematics#calculus#stillwell#wildberger#self-study
Recommendations by year
20062026
You should probably look up the undergrad math courses of the grad school you want to go to, they will have lectures notes and textbook/chapter reading recommendations so structured and you aren't going through enormous reference books. Search the textbook name on youtube, often there will be some lectures for it sometimes even by the author.
There's an ML math prep book https://mml-book.com/ which is basically a crash course, and a series of lectures here for a background in math for an intro machine learning course at CMU https://www.youtube.com/user/professorgeoff though note they aren't as long as they seem, as these were live lectures so they start late, have breaks between exercises, etc. If you've read the Elements of Statistical Learning 2e you likely know much of this already.
Personally my recommendation is go through a Wilberger course, this set of undergrad lectures is for the Stillwell book 'Mathematics and it's History' https://www.youtube.com/playlist?list=PL55C7C83781CF4316 it will intuitively cover differential geometry, topology, group theory, polynomials etc, to the depth of Stillwell's book and if you see something that interests you or that you forgot, then you can pursue it taking formal courses. I'd recommend his Linear Algebra course too on the same youtube channel he uses clear definitions for everything so when you get to abstract 3D vector spaces it makes sense.
Anybody with a complete shit background in math like I used to have try the Wildberger foundations playlists on the same channel watching how he writes proofs, then pick up some large book written by Knuth and start attempting the exercises as a weekly hobby, which will now be possible to do. This is also how you retain these skills by using them on a regular basis, at least for me anyway.
Initially I heard about Euler's famous Basel problem. Years later I got to solving it for my self (for curiosity and fun). I guess what intrigued me was to think of trigonometric sine as an infinite polynomial...After I worked it out, I had indeed seen the fire in Euler's own eyes...I could see how excited he was at having discovered something amazing...But this got me into hooked into math history. What I really wanted was how people came about discovering the Taylor's series...the intuition behind it. So that is how I came across John Stillwell's book. I have to warn people it is rather academic. But if, you, as a self-learner, is excited about mathematics, I would suggest Norman J Wildberger's youtube lectures on mathematics history. I find the buildup to calculus quite fascinating. J. Stillwell's book was the recommended reference in those lectures...