Gil Posted July 13, 2020 Share Posted July 13, 2020 (edited) Calling all mathy people. I need your help. What are the preliminary topics and skills that one should have before tackling a undergrad level course in Complex Variables? It's one of the UG math courses that I've never taken or studies and my kid is thinking about a course in Complex Variables for Autodidactic Studies. Any advice? Edited July 13, 2020 by Gil Quote Link to comment Share on other sites More sharing options...
Gil Posted July 14, 2020 Author Share Posted July 14, 2020 We've been through a lot of material taught in a UG math program. Over the last 4ish years, I've been teaching a mix of math at the post-highschool/undergraduate level, in various strands and mixed through different courses/resources. But the last several months math has been sporadic as we've given more time for other subjects and what math he's done has been more interest based stuff so the last several months math has been a mixed bag, dipped into irregularly. Now that he wants to do complex variables, I'm trying to determine if there are any particulars he might need to cover or brush up on in particular to be successful. Quote Link to comment Share on other sites More sharing options...
HomeForNow Posted July 14, 2020 Share Posted July 14, 2020 Typically one would have done up to Multivar Cal (Calc 3) first. Series from Calc 2. General familiarity/fluency with Limits, Derivatives, Integrals. I've never taught it (taught all the prereq topics though) and when I took the course many years ago, I thought it was a very nice topic, even though I'm not a calculus-y person. 1 1 Quote Link to comment Share on other sites More sharing options...
Gil Posted July 14, 2020 Author Share Posted July 14, 2020 He's rock solid on and fluent in single and multivariable calculus. Same with trig and differential equations. He's had a couple of cycles with real analysis, some topology. He's done a lot of math for a kid, but he's not mastered everything that he's been exposed to or dabbled in above Diff. Eq/Linear Algebra. (Beyond Calc 3/DE/LA mastery isn't the goal, just good exposure. I am not equipped to take them to mastery above a certain level.) He's most likely going to be using Complex Variables with Applications (Brown) and pairing it with Schaums outlines. I'll have him find a lecture series as well, but he's not a fan of video instruction so I don't know that he'll stick with the lectures all the way through. 1 Quote Link to comment Share on other sites More sharing options...
Brad S Posted July 18, 2020 Share Posted July 18, 2020 In all likelihood, he's more than ready. I would double check what the course description says are the prerequisites and/or the preface to the text. In my decades-old experience, most of the courses I saw just needed a good multivariable calculus course as a prerequisite. Quote Link to comment Share on other sites More sharing options...
lewelma Posted July 18, 2020 Share Posted July 18, 2020 Don't think I can add anything to square's opinions. Have fun! Quote Link to comment Share on other sites More sharing options...
Gil Posted July 18, 2020 Author Share Posted July 18, 2020 (edited) 8 hours ago, lewelma said: Don't think I can add anything to square's opinions. Have fun! Thanks! He's excited and I'm excited for him. Honestly the real issue is how to monitor and support his math education going forward. I picked you to bother because, in particular, you have the experience of supporting an advanced learners math education through math you increasingly don't quite "get" yourself. As well as a lot of experience and insight in supporting and developing the executive functioning skills to enable a boy to be successful at math that is higher and higher over your head. Mathematically, this is pretty much as far as I go. It was always my plan to introduce them to and get them competent in the STEM-core of the mathematics that I learned in college but we're a few years ahead of schedule and I'm running out of the mental bandwidth. What seemed logical and feasible at 20, seems whimsical and unbearable at 30. Currently, I am not in a place where I can co-learn more advanced math with him and to be perfectly clear going forward, I don't want to co-learn more advanced math with him. I'm not willing to study advanced mathematics at this pace or intensity for the next 5+ years with him. I don't want to study advanced mathematics at this pace or intensity for the next 5+ years with him. I won't study advanced mathematics at this pace or intensity for the next 5+ years with him. Of course we'll continue to play with and explore interesting bits of math as a family for as long as we're all enjoying it. But Pal has a real interest in mathematics and is likely to continue to study and explore higher math through graduation (he's planning to home school high-school). Really this is the first--of presumably--many times that Pal will have to self-teach some math-thing that he won't be able to get help with at home. Buddy won't be doing CV this year and so Pal won't even have the company and support of his more studious brother. After this year we're going to have the same problem, with pretty much every math course because; Buddy is his fathers son and is into applied math, but Pal is spawned from an alien and likes pure math. (Honestly, who is this child and where did he come from?) Pal is the one who thinks that he wants to do a PhD (probably in math) and he decided that he wants to study a course in Complex Variables for a part of his Autodidactic Studies course this term. But the issue isn't CV so much as it is his mathematics education going forward. That's why you're the Boardie for this job, @lewelma. Edited July 18, 2020 by Gil Quote Link to comment Share on other sites More sharing options...
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