Real Analysis, Lecture 1: Constructing the Rational Numbers

One of my favorite video series on YouTube is Francis Su's _Real Analysis_. ▶ this video He walks through the basics of constructing the real numbers, defines metric spaces and proves some topological properties, defines continuous functions, and goes into differentiable functions. The video quality isn't great but his teaching style is phenomenal - he's really great about engaging the class and getting them to walk through the reasoning for each of the theorems.

I highly recommend Francis Su's Real Analysis Youtube lectures, on Youtube [1]. He is an amazing teacher. I first started trying to learn Real Analysis from Baby Rudin, but I couldn't understand the point behind the ideas introduced there. Then I started watching these lectures, which are based on Baby Rudin and mostly follow it, and it helped a lot (together with reading the main text itself - a crucial step). The only bad thing is that only half of Rudin is covered - the other half is covered in Real Analysis 2, which is unfortunately not online as far as I can tell. [1] ▶ this video

This series of courses from Francis Su. It is not mentioned a lot but I think it succeeded in creating an intuition on Real Analysis for me. I think it could help people joining this ▶ this video

John Baez (physicist / category theorist / smort dude) has a list of books to learn math and physics. Is an interesting source to crib from. link Gerhard t'Hooft has a page on how to become of a good physicist. link Not math though. I'm not necessarily suggesting that a mountain of books is the best way to go about it. I think I respond best to video lectures. I'm not sure where you're starting from or how applied/pure you want. Here's a quick mind dump some of my favorites and some that I haven't watched. Roughly in order of how much I liked them. Gilbert Strang's Computational Methods for engineers was life changing for me. It is a two part MIT opencourse. link A Stanford course on the Fourier transform link Bartosz Milewski's Category theory for programmer's link Stephen Boyd's courses are online. link Linear Systems, convex optimization. Useful stuff. Francis Su's Real Analysis is very good ▶ this video Indian universities have an astounding collection of videos link I have a tough time with the accents, which is a bummer. UCCS MathOnline has quite a haul link I've been enjoying this Visual Group Theory course lately link Math Doctor Bob link Wildberger has some interesting takes on elementary and non elementary topics link link Perimeter scholars lectures. Physics not math. Good stuff. Federico Ardila has a number of combinatorics courses. link Nonlinear algebra course link Also of course there is Coursera and edX stuff. Godspeed.

I've watched a series of lectures on the subject by Harvey Mudd college, on youtube [1]. It helped me a lot, tho, I'd have to say these are introductory level, not really a deep dive, but more useful as an introduction. [1] ▶ this video