<p>I'm going into senior year now, but I'm beyond the high school math and therefore am taking a math course at a University. I've had AP Calc AB, but my school doesn't have BC.
I went in to take the placement test last week, and I was placed into "Complex/Algebraic Analysis."</p>
<p>Is this class going to be hard?</p>
<p>The course catalog said tha the class covers:</p>
<p>The algebra of complex numbers; fractional powers.
Logarithm and power functions; exponential and trigonometric functions.
Analyticity; Cauchy-Riemann equations.
Integrals and Cauchy's Theorem and Formula
Morera's theorem; maximum modulus theorem; Liouville's theorem; Fundamental Theorem of Algebra.
Taylor series and Laurent series; regions of convergence, absolute and uniform convergence
The calculus of residues: isolated, removable, polar, and essential singularities; behavior of the function near an isolated singularity; calculating residues; evaluation of real integrals
Conformal mappings: fractional linear transformations; the geometric nature of the power, exponential, and logarithmic maps; Riemann Mapping Theorem.
Harmonic functions: Laplacian; relation to analytic functions; conjugate harmonic functions; Dirichlet problem; applications. </p>
<p>...A little but of this is familiar. But the rest of it sounds down right scary. Has anyone taken anything similar to this?</p>
<p>It sounded like precalc until it got to the Cauchy-Riemenn equation. That’s advanced stuff that you probably don’t have the best background ever to do.
And after that, I haven’t heard of any of those things. I Wikipediad “Taylor Series” and it looks really hard.</p>
<p>You are not going to do well. Brace yourself for hell.</p>
<p>All of the theorems and such may sound intimidating, but they’re not. Don’t back out of a class simply because some stuff “sounds scary”! Since you’ve taken AB calc and you were placed into this class, then this class and the material that it covers are likely to be appropriate for you. It also looks like they’ll be reviewing algebra and calculus a bit, so it’s not as if you’ll be thrown into analysis without any preparation whatsoever.</p>
<p>Umm… this is a hard class. Make yourself very, very familiar with epsilon-delta-stuff and proofs (do them yourself…)- people who took this have had at least one “Real Analysis” class. What is taught in Real Analysis is calc, but at a very different level.</p>
<p>Most of this class should be doable with hard work (Taylor series is dirt cheap, though the proof requires a trick), but you will definitively struggle with calculus of residues if you have no experience. Harmonic functions are easy, though. </p>
<p>If you were tested in this, it should be doable (at that university). I for myself would not have taken it at my university (though that might have to do with the professor who teaches it there… genius.) in high school.
Try to do Real Analysis. Should be easier. </p>
<p>(I don’t think they’ll be reviewing algebra and calculus. I think they’ll be reintroducing them with complex numbers.)</p>
<p>it depends on the rigor of your university
if you cover it properly it will be hard,
but some schools don’t really cover it properly at the undergrad level.
do you know what textbook they use?</p>
<p>I’d say that the class is definately a step up from Calc BC. And it’s a real college level course too, not the nice intro way in. If you are best at “doing” mathematics (i.e. the teacher shows you something and you can imitate it) then the class is not for you, however if you are better at “understanding” math (i.e. you learn what the teacher tells you and use it to solve questions that don’t look like anything you’ve see before) then it will be a good challenge.</p>
<p>How did you get into complex analysis? I highly doubt you’re ready for this without Calc II (i.e. the second semester of Calc covered in BC), Multivariable Calculus, Differential Equations, and Linear Algebra, at the very least. But if you placed into it, give it a sporting chance.</p>
LOL Taylor series… only like the easiest thing in calc BC. If you placed into the class, you should be okay imo… post this in college life, they’ll know better than we do (LOL… I am a college student. jeez I need to get off this forum).</p>
<p>youll be fine, i took bc and taylor series is oh so easy, you basically remember a sequence, i hated polar equations but youll be fine, and haha harmonic series are quite the easy stuff. just learn your material well and ask questions if you get stuck.</p>
<p>well, I haven’t taken it yet, but last year a senior at my school tested into honors analysis at uchicago, and found it really hard. This guy was a usamo qualifier.</p>
<p>Honors Analysis is in the top 2 hardest math classes in the country. As a first year, you can only gain entrance by invitation (you have to score in the top 10 schoolwide on the exam). Requires on average 35 hours/week, according to Paul Sally, although in my experience, it was more like 25-30.</p>