MAT334
Complex variables
Winter 2022
Course information
MAT334H1-S
Theory of functions of one complex variable, analytic and meromorphic functions. Cauchy's theorem, residue calculus, conformal mappings, introduction to analytic continuation and harmonic functions.
MAT223H1/MATA23H3/MAT223H5/MAT240H1/MAT240H5, MAT235Y1/MAT235Y5/(MAT232H5, MAT236H5)/(MATB41H3, MATB42H3)/MAT237Y1/(MATB41H3, MATB42H3, MATB43H3)/MAT237Y5/MAT257Y1
Lectures and tutorials are in person, except for the first three weeks of the course which will take place entirely online via Zoom links to be found on the course Quercus page. There are three hours of lectures and one hour of tutorial per week.
Instructors
| name | section | office hour | |
|---|---|---|---|
| Maxence Mayrand | mayrand@math.toronto.edu | LEC0101 | Fri 13:30—14:30 |
| Stefan Dawydiak | stefand@math.utoronto.ca | LEC5101 | Wed 11:00—12:00 |
Email is the preferred method of communication.
Students will find Zoom links for the office hours on the course Quercus page.
Lectures
LEC0101 — Maxence Mayrand
Tuesday12:00—14:00
Thursday12:00—13:00
Tuesday, January 11, 2022
Thursday, April 7, 2022
MP 102
LEC5101 — Stefan Dawydiak
Tuesday18:00—21:00
Tuesday, January 11, 2022
Tuesday, April 5, 2022
MP 202
Teaching assistants
| name | tutorials | office hour | |
|---|---|---|---|
| Chao An | chao.an@mail.utoronto.ca | TUT0301 | Fri 13:00-13:30 |
| Lemonte Alie-Lamarche | lemonte@math.utoronto.ca | TUT0101 TUT0201 | Thu 13:30-14:00 |
| Wenkui Du | wenkui.du@mail.utoronto.ca | Wed 9:00-9:30 | |
| Nathan Gurrin-Smith | nathan.gurrinsmith@mail.utoronto.ca | TUT0401 TUT0501 | Thu 18:00-18:30 |
| Daniel Spivak | daniel.spivak@mail.utoronto.ca | TUT5102 TUT0601 | Fri 16:00-16:30 |
| Oliver Trevett | oliver.trevett@mail.utoronto.ca | TUT5101 TUT5201 | Tue 11:00-11:30 |
Zoom links for office hours are on Quercus.
Tutorials
| sections | time | room | TA |
|---|---|---|---|
| TUT0101 | Tuesday 14:00-15:00 | GB 304 | Alie-Lamarche |
| TUT0201 | Tuesday 15:00-16:00 | SS 1084 | Alie-Lamarche |
| TUT0301 | Tuesday 16:00-17:00 | AB 107 | An |
| TUT0401 | Wednesday 10:00-11:00 | RW 143 | Gurrin-Smith |
| TUT0501 | Wednesday 14:00-15:00 | CR 405 | Gurrin-Smith |
| TUT0601 | Wednesday 15:00-16:00 | SF 2202 | Spivak |
| TUT5101 | Tuesday 17:00-18:00 | HS 108 | Trevett |
| TUT5102 | Tuesday 17:00-18:00 | RW 142 | Spivak |
| TUT5201 | Wednesday 17:00-18:00 | SS 1072 | Trevett |
During the tutorials, TAs will explain solutions to some exercises, answer students questions, and review the relevant course material.
Tutorials start in the second week of the term (Jan 17—Jan 21) and continue every week until the last week of the term (Apr 4—Apr 8), except for the reading week (Feb 21—Feb 25).
Textbook
Fisher, S. D. Complex variables. Second edition. Dover Publications, Inc., Mineola, NY, 1999.
Course content
The plan is to cover chapters 1, 2, and 3 of the textbook.
Tentative schedule
| week | textbook sections | evaluation | note |
|---|---|---|---|
| Jan 10—Jan 16 | 1 | ||
| Jan 17—Jan 23 | 1 | Test 1 | First tutotrial |
| Jan 24—Jan 30 | 1 | Test 2 | |
| Jan 31—Feb 06 | 1, 2 | Test 3 | First in-person lectures and tutorials |
| Feb 07—Feb 13 | 2 | Test 4 | |
| Feb 14—Feb 20 | 2 | Test 5 | |
| Feb 21—Feb 27 | Reading week: no lecture and no tutorial | ||
| Feb 28—Mar 06 | 2 | Test 6 | |
| Mar 07—Mar 13 | 2 | Test 7 | Test 7 is in-person |
| Mar 14—Mar 20 | 3 | Test 8 | |
| Mar 21—Mar 27 | 3 | Test 9 | Test 9 is in-person |
| Mar 28—Apr 03 | 3 | Test 10 | Test 10 is in-person |
| Apr 04—Apr 10 | 3 | Test 11 | Last tutorial |
Marking scheme
There will be 11 weekly tests, the lowest of which will be dropped. The remaining 10 tests will each count for 10% of the final grade. There are no problem sets or term tests, and there is no final exam.
Three tests will be administered in-class, the remainder will be administered asynchronously online and submitted via Crowdmark. Online tests will be available to be opened for 24 hours, and must be completed within two hours of opening. The test dates are as follows:
| Test number | Online/in-person | Times available | Duration |
|---|---|---|---|
| Test 1 | Online | 00:01-23:59 Monday, January 17 | 2 hours |
| Test 2 | Online | 00:01-23:59 Monday, January 24 | 2 hours |
| Test 3 | Online | 00:01-23:59 Monday, January 31 | 2 hours |
| Test 4 | Online | 00:01-23:59 Monday, February 7 | 2 hours |
| Test 5 | Online | 00:01-23:59 Monday, February 14 | 2 hours |
| Test 6 | Online | 00:01-23:59 Monday, February 28 | 2 hours |
| Test 7 | In-person | Tuesday, March 8, in class | 1 hour |
| Test 8 | Online | 00:01-23:59 Monday, March 14 | 2 hours |
| Test 9 | In-person | Tuesday, March 22, in class | 1 hour |
| Test 10 | In-person | Tuesday, March 29, in class | 1 hour |
| Test 11 | Online | 00:01-23:59 Monday, April 4 | 2 hours |
The online tests will be sent to you via Crowdmark.
No other submission method for the online tests will be accepted.
The easiest way to upload your test is to use a scanner, but if you don't have access to one, you can also use a scanner app on your phone. Make sure that your work is legible before submitting it; otherwise, it will not be accepted.
The in-person, in-class tests will be written on paper and collected after the test.
There will be no make-up tests. For students who missed a test because of illness or any other approved legitimate reason, its weight will be transferred evenly to the remaining tests.
Written solutions are not provided, but some of them will be discussed in tutorials. You are encouraged to consult with TAs, your fellow students, and the instructors to identify shortcomings in your grasp of the material.
You may not collaborate with other students on any of the tests. Your submissions must be your own work, written independently, in your own words. Otherwise, it will be considered an offence under the University of Toronto's Code of Behaviour on Academic Matters (see section B.I.) and serious sanctions will be applied.
Discussion forum
We will use Piazza, which is a discussion forum where you can ask as many questions as you like, and will receive answers from other students, the TAs, or the instructor.
To join the forum, go to piazza.com and search for MAT334. You will also get an email invitation at the beginning of the course. Alternatively, you can sign up using by cliking here.
Practice problems
1—6, 9, 11, 17
1—18, 22—26, 33, 34
1—15
1—24, 31—40
1—30
1—12, 15, 16
1—11, 16—18, 20, 22
1, 3, 5, 7, 9, 11, 13, 15, 17, 19
1—12
1—17
1—6, 7—15, 22
1—19
1, 3, 5, 7, 8, 10, 13, 15, 18, 20
1, 2, 3
Tests coverage
1.1, 1.2
1.3
1.4, 1.5
1.6
1.6
2.1, 2.2
2.3
2.4 and 2.5 excluding Laurent series (i.e. up to page 141)
Laurent series and 2.6 up to (and including) the subsection "Integrals of Rational Functions"
2.6
3.1 and 3.2 except for the subsection titled "Mean Value"