<p>This is a weird fusion class. Some pre-calc topics, some BC topics, some common MV topics, some linear algebra topics, and some junk I’ve never heard of. </p>
<p>I’m sure you’ll do fine. Like Cauchy-Schwarz may sound intimidating, but it’s actually pretty straightforward. This seems like a natural progression from calculus. So if you’ve taken that, you’re probably prepared (plus the fact you placed into it).</p>
<p>It has some differential equations in there too.</p>
<p>Easy peasy</p>
<p>???</p>
<p>There are no MV, LA, or ODE problems here. It’s Complex Analysis. Pure Complex Analysis. Also, the Cauchy-Riemann equations aren’t anything terribly important or sophisticated, and they’re not something to be solved (they’re derived). They just provide necessary and sufficient conditions for when a function is holomorphic (i.e., analytic).</p>
<p>I think it’s actually a stupid course setup. Exposing students to complex analysis without real analysis is incredibly misleading, in my opinion. The two cases should be considered separately, with the easier first. Yes, it’s true that many results of real analysis can be generalized to complex analysis. But it’s also true that the complex field is extremely different from the field of real numbers, and I can see how it could be extremely confusing to beginners.</p>
<p>On the other hand, no objections here for skipping MVC, LA, and ODEs. They’re not terribly important if you’re not an engineer. If you’re a pure mathematician, becoming familiar with the key results of set theory and analysis are probably the most important for building a strong foundation.</p>
<p>^I don’t know what complex analysis is but I’m pretty sure that Cauchy-Schwarz is linear algebra and there will probably be some use of double (or triple) integrals or sums, hence the MV. If you were to take MV or LA alone I’m sure there would be some similar problems or methods. I’ll trust you that this is complex analysis. But, at least from the syllabus the OP presented, there are some LA and (likely) MV concepts in there. </p>
<p>Unless your MV and LA were different. Because mine definitely had some of the things the OP mentioned. And it was a textbook course. No teacher just fusing some complex analysis in whenever he chose.</p>
<p>Edit: Actually, turns out Cauchy-Schwarz was never mentioned. Just Cauchy-Riemann and Cauchy’s theorem. I don’t know what the latter is referring to, so maybe there isn’t LA in here. My b.</p>
<p>I have come to the conclusion that CCers will never tell anyone that their classes are too difficult. I swear if there was a thread saying someone placed into a graduate-level physics thesis course [college] freshman year you guys would be like, “It’s not too bad, you have an entire year to write only like 100 pages…which is less than 1 page per day.”</p>
<p>The next post would be, “Oh, my friend did that and it wasn’t too bad.”</p>
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<p>Seriously? You do realize that most people in lower-division math classes want to do something practical like engineering, right? Multivar and LA are really important for lots of fields.</p>