So you want to study mathematics
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So you want to study mathematics
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Re: So you want to study mathematics
#2I've been on a Math journey since I retired a couple of years ago and I agree with all the books mentioned that I know and look forward to picking up some of the one I do not know. I agree baby Rudin is essential, but I find it tough going.
Some books I liked for self study because they have answers:
Introduction to Analysis, Mattock.
Elementary Differential Geometry, Pressley.
There is also recently Needham's Visual Differential Geometry and Forms, which is great.
Edit: I should also mention Topology without Tears (free, online, very good) https://www.topologywithouttears.net/
Re: So you want to study mathematics
#3I've been on a Math journey since I retired a couple of years ago and I agree with all the books mentioned that I know and look forward to picking up some of the one I do not know. I agree baby Rudin is essential, but I find it tough going. Some books I liked for self study because they have answers: Introduction to Analysis, Mattock. Elementary Differential Geometry, Pressley. There is also recently Needham's Visual…
I think learning Real Analysis from baby Rudin is like learning Probability Theory from Wikipedia. It's so encyclopedic that if it's your first look at real analysis, it will be too dense to understand, but if it's your second or third look, you will find beauty in its brevity.
Re: So you want to study mathematics
#4I've been on a Math journey since I retired a couple of years ago and I agree with all the books mentioned that I know and look forward to picking up some of the one I do not know. I agree baby Rudin is essential, but I find it tough going. Some books I liked for self study because they have answers: Introduction to Analysis, Mattock. Elementary Differential Geometry, Pressley. There is also recently Needham's Visual…
Agree that Baby Rudin is VERY difficult to study on its own. I recommend only studying it alongside the other two books I listed: Abbott's Understanding Analysis and Spivak's Calculus (which has a solutions manual). Abbott in particular is very straightforward (at least in comparison with baby Rudin haha)
Re: So you want to study mathematics
#5I've been on a Math journey since I retired a couple of years ago and I agree with all the books mentioned that I know and look forward to picking up some of the one I do not know. I agree baby Rudin is essential, but I find it tough going. Some books I liked for self study because they have answers: Introduction to Analysis, Mattock. Elementary Differential Geometry, Pressley. There is also recently Needham's Visual…
Consider Analysis 1/2 by Terence Tao for introduction to analysis.
Re: So you want to study mathematics
#6Going from Strang to D&F seems like a steep jump. The former is an applied textbook for non-mathematicians and the latter is a proof-based text for advanced undergraduate / graduate-level math students.
I would suggest working through a proof-based linear algebra book in between to ease the transition. Axler's is a good one. Alternatives include Hoffman and Kunze and the more modern Friedberg, Insel, and Spence.
Re: So you want to study mathematics
#7Going from Strang to D&F seems like a steep jump. The former is an applied textbook for non-mathematicians and the latter is a proof-based text for advanced undergraduate / graduate-level math students. I would suggest working through a proof-based linear algebra book in between to ease the transition. Axler's is a good one. Alternatives include Hoffman and Kunze and the more modern Friedberg, Insel, and Spence.
Both Strang and D&F are extra-relevant for cryptography (I was struck by how much the earliest parts of D&F --- which I haven't gotten much further beyond --- read like the mathematics background chapter of a cryptography book), and I've been in study groups for both of them with non-mathematicians that went OK. But the D&F study group fell apart for logistical reasons, so maybe it would have hit a wall after a couple more months.
Re: So you want to study mathematics
#8I loved last year being able to take university courses online. I knocked out analysis, topology, and quantum mechanics as a non matriculated student. I'd had those books for years but never could get through them alone. (The main thing being, you really don't have anything to gague whether you know it well enough or not).
I really wish there was more opportunity for that. I'd love to take a few more classes, mostly in pure math, but there's simply nothing on offer for remote study past the 200ish level. (There are some remote masters programs in applied math, but nothing for pure).
I don't think I'd enjoy doing a PhD full-time. One or two classes per semester while working seems just about right. But the closest university is an hour away, so in-person isn't a realistic option.
Re: So you want to study mathematics
#9Going from Strang to D&F seems like a steep jump. The former is an applied textbook for non-mathematicians and the latter is a proof-based text for advanced undergraduate / graduate-level math students. I would suggest working through a proof-based linear algebra book in between to ease the transition. Axler's is a good one. Alternatives include Hoffman and Kunze and the more modern Friedberg, Insel, and Spence.
Second Axler. "Linear Algebra Done Right" is probably the pure mathematics textbook I've most enjoyed reading ever (but be warned you will learn very little about applied methods from it if that's what you care about).
Also enjoyed Artin's Algebra.
Re: So you want to study mathematics
#10I never got beyond algebra/geometry in High school. I think I had to take one 100 level math class in college, but it was basically a review of HS math. Oh, and I had to take a stats class for non-technical people in graduate school. That was my worst graduate class by far. But, I would like to learn some more math, like calculus. I’m hoping to get to it when I retire in a decade or so.