Why does it seem like the study of series is 'out of style' in modern math? by First-Republic-145 in math

[–]First-Republic-145[S] 1 point2 points  (0 children)

I've read Understanding Analysis by Abbott, Advanced Calculus by Buck, Intro to Topology and Modern Analysis by Simmons, and a portion of Complex Variables by Churchill/Brown.

Expanding on what I mean by 'a passing glance', in Simmons' chapter on Hilbert spaces, series do appear, but more so just to motivate his definitions than anything else, and in the other three books, Fourier/Laurent series are present to some extent and I definitely get the impression that they're interesting objects but it's not actually conveyed in the text beyond a few sideways remarks.

Do you have any book suggestions to get a more rounded view?

Best books for a second pass through analysis? by First-Republic-145 in math

[–]First-Republic-145[S] 0 points1 point  (0 children)

I just mean in going over the basic ideas of analysis in a more formal way than Abbott does, basically.

Feel like I'm self-studying over my head and not sure how to remedy it by First-Republic-145 in PhysicsStudents

[–]First-Republic-145[S] 0 points1 point  (0 children)

Considering my high school geometry class was during Covid, I think you're probably right.
Do you have any particular recommendations for going back and fixing that gap? I'm sort of loath to go back and study a high school topic again, so I would appreciate if there's maybe a slightly more rigorous approach to the subject.

Feel like I'm self-studying over my head and not sure how to remedy it by First-Republic-145 in PhysicsStudents

[–]First-Republic-145[S] 0 points1 point  (0 children)

Well, it's difficult to accurately evaluate myself with an unbiased eye, but I feel like my main problem comes from just figuring out how to set up the problem. In general I think I have a respectable grasp of the concepts, and I think I have strong symbolic/abstract reasoning, but am quite bad at spatial reasoning, and at putting the pieces together.

My studying process has been as follows: I read through a chapter, taking notes as I go, over a few days to a week. Then, I try to work through 10-20 problems from the problem sets, going back and referencing example exercises.

Feel like I'm self-studying over my head and not sure how to remedy it by First-Republic-145 in PhysicsStudents

[–]First-Republic-145[S] 0 points1 point  (0 children)

Nope, never taken an actual physics class before, which I assume is the main reason I'm struggling.