Math 120A (Fall 2023)
Summary
Math 120A is an introduction to complex analysis. We will cover everything from the basic properties of the complex numbers, through to the Residue Theorem on line integrals. See below for a full list of topics.
Unlike the 140ABC and 142AB real analysis courses, we will be more concerned with all the surprising and useful things that are true about complex-valued functions, and what we can do with them, than with supplying complete rigorous proofs of everything. In particular this class is designed to be approachable to someone who has not taken one of the upper-division real analysis sequences (though we will need some basic real analysis). Equally, the course is meant to hold interest for those who have taken these classes, because complex analysis has a different flavor.
There is no required textbook for this course. However, Complex Analysis by T. Gamelin is available online through UCSD and is a recommended optional textbook.
Contacts
The instructor is Freddie Manners (email fmanners); my office is AP&M 7343. The TA is Christopher Xue (email cxue).
Class and office hours
Lectures are held on Mondays, Wednesdays and Fridays, 09:00am–09:50am. Lectures will be held in-person in PETER 102. Attendance is "mandatory but not enforced": if you choose not to attend, you will not lose points, but I also do not guarantee you will learn things.
Note there is no class on Wednesday November 22 (because of Thanksgiving).
Section will take place in-person at the advertized times and places.
The Google calendar below has times and locations for all class events.
Exams
There will be two (in-person, evening) midterms, on Monday October 23 (Week 4) at 7:00pm–8:20pm, in CENTR 212, and Tuesday November 14 (Week 7) at 7:00pm–8:20pm in WLH 2204.
The final exam is on Wednesday December 13, at 08:00am–11:00am. It is also in-person (location TBD).
You should ensure at the start of the quarter that you can attend these exams. In general, alternative modalities, dates or times (in particular, remote exams) will not be offered.
Homework
Homework will be set every week, due by 2359 each Wednesday night (with the exception of Week 7 when it becomes Thursday to accommodate the midterm). The first homework deadline is on Wednesday October 11 (Week 2); the last on Wednesday December 6 (Week 10). There will be some optional homework in week 10 as exam practice.
Midterm weeks and Thanksgiving Week will have reduced homework loads and in some cases altered deadlines, but still some homework.
Please note: while discussing homework problems in groups is permitted (and encouraged), your final written-up solutions must be written by you, by yourself, in your own words. If your homework appears to have been copied directly from another student (or another source) that is very likely to constitute an academic integrity issue. You also may not post homework questions or solicit answers on the internet.
Grading
Your combined grade for the course is calculated as follows. First, your lowest homework score is dropped. Then, take 25% homework + 20% midterm 1 + 20% midterm 2 + 35% final exam.
The letter grade cut-offs will be at least as generous as the following table (but may be more generous). Separately, exam scores may be curved to adjust for difficulty.
| A+ | A | A- | B+ | B | B- | C+ | C | C- | F |
|---|---|---|---|---|---|---|---|---|---|
| 97 | 93 | 90 | 87 | 83 | 80 | 77 | 73 | 70 | < 70 |
Resources
In addition to this website, the course has a Canvas page, a Gradescope page and a Piazza site. The sign-up codes for Gradescope and Piazza are listed on the Canvas home page.
Provisional schedule
A rough schedule of topics is given below. Note it is very much subject to change and offered as a guideline only.
| Week | Mon | Wed | Fri | Topic |
|---|---|---|---|---|
| 0 | L1 | Introduction | ||
| 1 | L2 | L3 | L4 | The complex numbers and basic properties. The complex exponential and related functions. |
| 2 | L5 | L6 | L7 | A crash course in topology. The Riemann sphere, stereographic projection. Roots and logarithms. |
| 3 | L8 | L9 | L10 | Review of real analysis. Power series. |
| 4 | Review | L11 | L12 | Differentiability. The Cauchy--Riemann equations. |
| 5 | L13 | L14 | L15 | Conformal maps. Line integrals. Cauchy's Theorem. |
| 6 | L15 | L16 | XXX | Cauchy's Integral formula. Louisville's Theorem. |
| 7 | Review | L17 | L18 | Power series and differentiability at infinity. |
| 8 | L18 | XXX | XXX | Zeros of holomorphic functions. |
| 9 | L21 | L22 | L23 | Laurent series. The Residue Theorem. |
| 10 | L24 | L25 | Review | Further topics and examples (if time). |
Office hours
Regular office hours and locations are listed in the table below. However, please check the calendar below for any one-off changes or cancellations.
| Instructor / TA | Location | Regular hours |
|---|---|---|
| Freddie Manners | APM 7343 | Mondays 3:00–4:00pm, Wednesdays 11:30am–12:30pm |
| Christopher Xue | HSS 4012 | Tuesdays 1:00pm–3:00pm, Wednesdays 1:00pm–2:00pm |
Course calendar
A link to add this calendar is available on the course's Canvas page.