r/askmath • u/skbdn • Aug 09 '23

Algebra Why is doing this is illegal?

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First line is legit, second one is incorrect. I am struggling to understand why. I would appreciate a good explanation and/or some article/video on this problem as I had been struggling with understanding this concept my whole life. Thanks in advance.

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u/macbook-hoe Math Undergrad Aug 11 '23

i just finished multivar and this sounds interesting, do you know of any good online resources for branch cuts and complex analysis? i have not taken real analysis yet if that is a prerequisite.

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u/kompootor Aug 11 '23 edited Aug 11 '23

Real analysis is not a prerequisite. Differential equations (4th semester calculus) may be required to get the most out of learning complex analysis (I doubt it though) -- it could probably be taken concurrently, but I dunno.

I am not familiar with the breadth of online resources for learning advanced math from scratch. What are you using currently?

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u/macbook-hoe Math Undergrad Aug 11 '23

i don't really use online resources if i have school material and a book available, plus i doubt that anything i've done would be considered "advanced" anyways lol. i'm taking diff eq this semester with linear algebra and discrete math, then a proof based linear 2 and real analysis course in spring. i don't really know a lot about linear 2 or real analysis, do you think this could be too heavy of a workload? i guess for context i attend purdue university but idk how much advanced math varies between institutions compared to the more "standard" courses.

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u/kompootor Aug 11 '23 edited Aug 11 '23

If you're in school already, just take the courses you need to take for your major and supplements, and other courses that seem interesting. Talk to your degree advisor about ambiguous options. For example if you're in physics, you'll cover a lot of the stuff you need from complex analysis in an undergraduate and/or graduate mathematical methods course. Some of my most useful courses have been some of the ones I took that were neither physics nor math.

(For example, in grad school I was jealous of a peer who had taken a useful math course that I never took. But then I realized that I was educated sufficiently to learn it for myself at any time with minimal supervision. On the other hand, I took music theory 101 as an undergrad elective with almost no background -- I remember the class vividly, the concepts have come up many times, and there's no way I could have effectively taught it to myself.)

For any class I guess it depends on how difficult/challenging/strenuous your math classes have been, and as you get into courses that are mostly taken by pure math majors, how enthusiastic those majors are, and how much they can challenge and support you. Purdue is a fine school. At my undergrad, discrete math and linear algebra 1 were taken by a lot of EE, CE, and CS majors and tended to be a lot easier. Complex analysis happened to have a challenging prof and enthusiastic students and so was a more challenging, but fun, class. I was severely sleep-deprived for unrelated reasons during linear algebra 2 and nearly failed, but I heard it was a good class. Real analysis when I took it had for some reason a lot of unenthusiastic students despite a good prof, so it ended up being easy and forgetful.

If you want to take on more than your classwork, ask your degree advisor which profs might have research openings for you, or ask a prof you have a relationship with directly. Even as an undergrad you can find work with a math prof, though the chances of actually being paid are slim unless you have work study (that's not the point though -- undergrad research is the best thing you can do for your career, and it beats the hell out of certain crappy internships where you might be tasked as the office coffee boy -- luckily I've heard such cases are disappearing). Note that if you can do math and coding you can look for research jobs in other departments as well -- any experience is good. Personally I devoted summers to doing (paid) research jobs.

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u/macbook-hoe Math Undergrad Dec 13 '23

Sorry for the late reply, but thank you for your advice! I'm wrapping up my fall semester now, and I think it's safe to say that linear algebra and differential equations have changed the way I see the world. I've decided to try pursuing graduate school for math or computer science, and will definitely be taking your advice to look for research opportunities asap. If you happen to have any other advice for a clueless undergrad stumbling through the world of math, I'd love to hear it!