> I can't tell if the author has done a real analysis course before, but if they haven't that's the one they should choose next... I don't see the utility of re-doing calculus or linear algebra if the author is already strong in both.
having (somehow) completed many of these requirements for my 18c degree, i would say that analysis is not necessary if your interest is actually applied math. There's a great line in rudin's preface that says that his approach is ~"pedagogically sound at the expense of being logically incorrect," and recommending analysis for somebody that's not looking to mainline a pure math degree to me feels "pedagogically unsound (but logically correct)"[0].
I took analysis and i appreciated it, but i really loved the applied classes in my degree: 18.310, 18.311, 18.781 (theory of numbers) along with algebra 18.701/702. If you haven't taken a higher-level algebra class, it will let you know if analysis is right for you because you'll brush up against the edges of it without (what i consider to be, at least) its hallmark punishing density.
There are other great electives in math at mit, shop around the 18.4* classes and dial in by interest, most of them only require a prereq of 18.02/18.03/18.06 and you can sort of figure the rest out along the way.
Something to be aware of is that for a while 18.310 didn't have a dedicated instructor, so it really was all over the place. 18.311 was also somewhat hastily structured the semester i took it, but it is actually pretty good material.
You may find that after you've done all these classes that you are actually interested in pure math and at that point i would suggest looking at 18.100b (analysis), 18.700 (linear algebra), 18.100c(real analysis), 18.901(topology) and the rest of the "hard math classes," but i really do think that you'll find that the rationale for those classes doesn't click if you haven't taken a few classes like 310 or 701 first.
just my two cents! good luck, have fun!
[0]: this is the actual quote, it's in the preface rudin's principles of mathematical analysis 3rd ed. which is the 'textbook' for 100b.
> i would say that analysis is not necessary if your interest is actually applied math
If you start reading research papers in applied math, there’s a ton of measure theory and functional analysis there.
More generally, both introductory real analysis and introductory complex analysis are assumed basic foundational background for pretty much any kind of research mathematics, applied or otherwise.
I’m also not sure I would recommend trying to self-study them though. Some expert guidance/feedback is pretty helpful for someone starting out.
having (somehow) completed many of these requirements for my 18c degree, i would say that analysis is not necessary if your interest is actually applied math. There's a great line in rudin's preface that says that his approach is ~"pedagogically sound at the expense of being logically incorrect," and recommending analysis for somebody that's not looking to mainline a pure math degree to me feels "pedagogically unsound (but logically correct)"[0].
I took analysis and i appreciated it, but i really loved the applied classes in my degree: 18.310, 18.311, 18.781 (theory of numbers) along with algebra 18.701/702. If you haven't taken a higher-level algebra class, it will let you know if analysis is right for you because you'll brush up against the edges of it without (what i consider to be, at least) its hallmark punishing density.
There are other great electives in math at mit, shop around the 18.4* classes and dial in by interest, most of them only require a prereq of 18.02/18.03/18.06 and you can sort of figure the rest out along the way.
Something to be aware of is that for a while 18.310 didn't have a dedicated instructor, so it really was all over the place. 18.311 was also somewhat hastily structured the semester i took it, but it is actually pretty good material.
You may find that after you've done all these classes that you are actually interested in pure math and at that point i would suggest looking at 18.100b (analysis), 18.700 (linear algebra), 18.100c(real analysis), 18.901(topology) and the rest of the "hard math classes," but i really do think that you'll find that the rationale for those classes doesn't click if you haven't taken a few classes like 310 or 701 first.
just my two cents! good luck, have fun!
[0]: this is the actual quote, it's in the preface rudin's principles of mathematical analysis 3rd ed. which is the 'textbook' for 100b.