MATH UN3007

The first six chapters of the textbook of Fundamentals of Complex Analysis (3rd edition) by E.B. Saff and A.D. Snider.

Expect to spend something like 6-8 hours on the weekly problem sets; maybe 4 or 5 hours memorizing stuff you dont have to understand for the midterms; and an indeterminite amount of time studying confusedly in vain for a final you could never adequately prepare for in a million years.

Weekly problem sets, which while collected, didn't seem to be graded very carefully. Midterm and final, both of which, while not exactly easy, were very doable and fair.

Fundamentals of complex analysis. Cauchy Riemann formulas and integrals and applications.

In short: Gallagher is clearly brilliant, but the course has some serious flaws. The course packets (handed out each lecture) are elegant, concise, and make complicated proofs seem simple, but the exercises assigned (which are very time consuming!) aren't designed to help you learn the material. Rather, the homeworks often introduce new stuff and that doesn't really enrich your understanding of the old. The midterms literally asked you to spit back definitions and theorems you have memorized -- they require absolutely no understanding whatsoever, and are graded somewhat harshly (two missed words like 'convexity' is a B-range grade). Then out of nowhere the true/false final exam asks you to apply the theory in the lecture packets in ways you've never seen before and that require a very deep understanding of the material in the packets, an understanding you were never encouraged to develop in the joke midterms and somewhat orthogonal homeworks. In short, having gotten what most likely will be an A or A- in this class, I don't really understand complex analysis.

Basically a good professor. Understands all of the basic concepts quite well. Usually her lectures were fairly understandable, although occasionally she did go a bit fast. The material for this course is relatively difficult, but quite interesting (if you find math interesting). I was able to understand the material and do well having previously taken no course higher than linear algebra. She is open to questions during class and during office hours. On the down side, she was never on time, typically five to ten minutes late. More significantly, she often chose not to do long or complicated algebraic manipulations in class, saying "and you can work it out at home." The steps that she skipped were not really essential, but sometimes I would have liked to have seen them anyway.

I learned about fundamental concepts in Complex Analysis, and I believe that I also improved my mathematical skills more broadly (writing proofs, understanding theorems, etc).

Occasional homework that is collected and not graded. Two doable midterms and a 25 question true-false final with a range of question difficulties.

Very complete introduction to complex analysis.

Taken Spring 2004: Gallagher is a great professor as the other reviews have said, but he is getting older, so he's referring to his notes more frequently and will be slower to grade things- he returned our second midterm which was taken on March 31 on the last day of classes May 3. That said, I think Gallagher's teaching method, doing all the important proofs in class and not requiring you to reproduce them on exams, is the gentlest way to study pure math, but I'm not sure that it's the most effective.