I've always gotten a lot out of the expository stuff written by Tao, so you probably can't go wrong with the notes regardless. I've skimmed through parts of Terrence Tao's notes on analysis, and these seem like a good option as well (though I looked at his graduate-level notes, I don't know if this is what you're referring to). Of all the analysis textbooks I've looked at, I feel like I've gained the most from the time I've spent with Stein and Shakarchi's series - these books will expose you to the "bigger picture" that many classical texts ignore (though the "classics" are still worth looking at). Along the way the authors expose you to all kinds of in-depth and enlightening applications (including PDEs, analytic number theory, additive combinatorics, and probability). These books cover introductory Fourier analysis, complex analysis, measure theory, and functional analysis. After that I'd suggest looking at the 'Lectures in Analysis' series written by Elias Stein and Rami Shakarchi (Stein was actually Terrence Tao's advisor). (There's a phrase that gets thrown around a lot: "If you can't solve a problem then there's an easier problem you can't solve find it").īaby/Blue Rudin is a great book for an introduction to the basics of analysis (beyond one-variable "advanced calculus"). Having access to solutions can be helpful, but you don't want to find yourself relying on them. Take a break, try a different problem, maybe wait a few days and try again - you'll gain a lot more from the problem if you struggle and solve it yourself. ![]() ![]() First of all: you shouldn't give up on problems after 30 minutes.
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