Math 113 Spring 2026
My Complex Analysis Course
Last updated June 03, 2026 14:15:54 EDT

General Information HW Assignments Canvas Page


Announcements:


Week of March 30 to April 3
Assignments Made on:
Monday:
  • Homework 0: Before class on Monday, you should download a copy of the text from the "Files" tab on our canvas page and read (or at least skim) sections 1.1 thru 1.4. I'd love some feedback on the usefulness of these sections. Also download homework-0 from the gradescope page and answer the survey questions there. Then upload a PDF file with your answers in gradescope. Part of the point of homework-0 is to make sure everyone is comforable with gradescope and the process of uploading solutions and linking the problems to their respective pages. Also, it's fun to tell your friends that there was an assignment due the first day of class. (Note Homework-0 is simply a survey and can be turned in anytime -- preferably this week. It is not part of your grade.)
  • Solutions: The solutions to (most of) the exercises in Sections 1.1 to 1.3 can be found at the end of the text. These are also fair game for the Typo competition. As we progress through the term, more solutions will be avaliable under the files tab on our canvas page.
  • Do: There is quite a bit in Section 1.4 and we will, quite unfarily, view this a "background material". Since we won't be covering much of it in lecture, it is up to you to be sure you are up to speed. Feel free to discuss this material in office hours. You should work Ex 1.4.1, Ex 1.4.8(a), Ex 1.4.9, Ex 1.4.13.
  • Study: (Not to be turned in.) If you ever might teach this stuff, you should have a look at most of the exercises in Section 1.3 and 1.4. Especially Ex 1.4.3-5.
Wednesday:
  • Read Section 1.5.
  • Do: Ex 1.5.2 and Ex 1.5.8.
  • Study: Ex 1.5.9 and Ex 1.5.10.
Friday:
  • Read Sections 2.1 and 2.2. Update It seems we will only get as far as section 2.1 in lecture. We will make "Homework 1" due on Wednesday. Any work assiged on Monday will be due whenver "Homework 2" is due.
  • Do: Ex 2.1.8, Ex 2.2.3, Ex 2.2.5. (Ex 2.2.5 is really untangling definitions, but it will probably still be tricky for most.)
  • Study: Ex 2.1.4, Ex 2.1.6, Ex 2.2.4, Ex 2.2.7 (This is tricky, but gives another version of Thm 2.6 without the unmotivated step of the proof).


Week of April 6 to 10, 2026
Assignments Made on:
Monday:
  • Typo Competition: Here is the current typo contest tally. (Last modified June 03, 2026)
  • Study: Catch up Day.
  • Do: No new assignment. Note that Homework 1 is due Wednesday.
Wednesday:
  • Study: Read Sections 3.1 and 3.2 through Definition 3.15.
  • Do: EP-1: Suppose that $D$ is a domain and that $0\notin D$. Show that there is a branch of $\log z$ in $D$ if and only if $1/z$ has an antiderivative on $D$. Hint: if $f'(z)=1/z$ for all $z\in D$, consider the function $h(z)=z/\exp(f(z))$ and note that $\exp(z)=a$ has infinitely many solutions if $a\not=0$. (Not to be turned in: observe that this result implis that $f(z)=1/z$ does not have an antiderivative on $\mathbf C\setminus \{0\}$.)
Friday:
  • Study: Read through section 3.3.
  • Do: Ex 3.2.2 and Ex 3.2.5
  • Study: You really should be aware of Ex 3.2.6, Ex 3.2.7, and Ex 3.2.8.


Week of April 13 to 17, 2026
Assignments Made on:
Monday:
  • Study: Read Section 4.1
  • Do: Ex 4.3.1
  • Alert: Starting with Homework 3, the "first question" will be an "Acknowledgement Statement". This can be simply, "I worked by myself", or "I worked with Dick and Jane on problems x and y", or "I used ChatGPT to get started on problems z and w", or whatever honestly describes how you arrived at your solutions. Keep in mind that you always assert that you completely understand any work that you do turn in.
Wednesday:
  • Study: Read Section 4.2 and 4.3
  • Do:
    1. Ex 4.2.1, Ex 4.3.2, Ex 4.3.4, and Ex 4.3.8. The challenge of Ex 4.3.4 is the write up and elegant solution without hand waving.
    2. (EP-2) Complete the proof of Cauchys Theorem for Convex Domains by showing that if $f$ is continuous at $z_0$, then $$ \lim_{z\to z_0}\frac1{z-z_0}\int_{[z_0,z]} \bigl(f(w)-f(z_0)\bigr) \,dw=0.$$
Friday:
  • Study: Read Section 5.1.
  • Do: Ex 5.1.2 and Ex 5.1.3.
  • Study: You should know how to do Ex 5.1.1. Notice that Ex 5.1.4 is supposed to be trivial since the identities hold in the real case and you apply Corollary 5.3. You should at least think about Ex 5.1.5 long enough to realize that it is not an immediate consequence of Theorem 5.2.


Week of April 20 to 24, 2026
Assignments Made on:
Monday:
  • Typo Competition: Here is the current typo contest tally. (Last modified June 03, 2026)
  • Study: Read section 5.2.
  • Do: Ex 5.2.5, Ex 5.2.11, and Ex 5.2.12
  • Be Aware: Ex 5.2.3, Ex 5.2.6, Ex 5.2.8, Ex 5.2.13.
Wednesday:
  • Study: Read sections 5.3 and 5.4. Remember that there is no class Friday. We will meet tomorrow in our x-hour instead.
  • Do: Ex 5.3.6, Ex 5.3.9, Ex 5.3.12, Ex 5.4.1, and 5.4.2. Especially in Ex 5.3.6, you can use the result of Ex 5.3.5 without proof.
  • Be Aware: You should be comfortable with Ex 5.3.5. If fact you should consider it assigned but ungraded. If you like Ex 5.3.12, have a look at Ex 5.3.13.
Thursday (x-hour):
  • Study: Read section 5.5 up to the Open Mapping Theorem.
  • Do: Try Ex 5.4.5. This is sort of a challenge problem and no one should get stressed if they can't do it.
Friday:
  • Study: No class today. Have a great weekend.
  • Do:


Week of April 27 to May 1, 2026
Assignments Made on:
Monday:
  • May: Our schedule in May will be a bit crazy. There will be no class May 15, May 25 (Memorial Day), and May 29. We will make these classes up in our x-hour May 7, May 21, and May 28. This could change, but I will make assouncements in class in any case.
  • Study: We'll finish section 5.5 today and perhaps start section 6.1.
  • Do: Ex 5.5.2, Ex 5.5.3, and Ex 5.5.4. (You can use Ex 2.2.4 without proof if you read the solution.)
Wednesday:
  • Study: Read Section 6.1
  • Do: Ex 5.5.6
Friday:
  • Study: Finish Section 6.1 and start Section 6.2.
  • Do:
    1. In Homework 4, some folks wanted to use L'Hospital's Rule. We haven't proved any such result, nor do the proofs from calculus work in our setting of analytic functions. So I created a few problems, four actually, to see what we can recover. The assignment can be found under the Files -> Homework Solutions tab on our canvas page. The file is lhospital.pdf.
    2. (EP-3) Verify the claim made in lecture during the proof of the general Cauchy Theorem: suppose $D$ is a domain and that $g$ is continous on $D\times D$. If $z_n \to z$ in $D$ and if $K\subset D$ is compact, show that $f_n(\cdot) =g(z_n ,\cdot)$ converges uniformly on $K$ to $f(\cdot)=g(z,\cdot)$. (Hint: there are lots of ways to approach this problem. I used the fact that a continuous function on a compact metric space is necessarily uniformly continuous -- a reference is Theorem 4.19 in Rudin's Principles of Mathematical Analysis or Theorem 1.33 of Foland's Advanced Calculus.)


Week of May 4 to 8, 2026
Assignments Made on:
Monday:
  • May: Lots of schedule adjustments in May. In particular, we are meeting in our x-hour this week as well as our usual MWF meetings. There will be no class May 15, May 25 (Memorial Day), and May 29. We will make these classes up in our x-hour May 7, May 21, and May 28. This could change, but I will make assouncements in class in any case.
  • Typo Competition: Here is the current typo contest tally. (Last modified June 03, 2026)
  • Study: Finish Section 6.2 and start Section 7.1.
  • Do: Ex 6.2.2, Ex 6.2.4, Ex 6.2.6.
Wednesday:
  • Study: Finish Section 7.1 and start Section 7.2
  • Do: Ex 7.1.3 (Compare with Ex 5.4.5)
Thursday (x-hour):
  • Study: Finish Section 7.2 and start Section 7.3
  • Do: Ex 7.2.2.
Friday:
  • Study: Finish Section 7.3 and start Section 7.4
  • Do:
    1. (EP-4) This is just Ex 7.4.2.


Week of May 11 to 15, 2026
Assignments Made on:
Monday:
  • May: Remember this is no lecture on Friday (May 15) this week. We will also have no lecture on Monday May 25 (Memorial Day), and Friday May 29. We will make these classes up in our x-hour May 21 and May 28. This could change, but I will make assouncements in class in any case.
  • Typo Competition: Here is the current typo contest tally. (Last modified June 03, 2026) The flow has slowed down. I know that the typos haven't.
  • Study: Finish Section 7.4 and start Section 10.1
  • Do: Ex 7.4.3, Ex 7.4.4, and Ex 7.4.5. You can consider Ex 7.4.5 another challenge problem.
Wednesday:
  • Study: Finish Section 10.1 and start Section 10.2.
  • Do: Ex 10.1.2, and Ex 10.1.3.
Friday:
  • Study: No lecture today.
  • Do:


Week of May 18 to 22, 2026
Assignments Made on:
Monday:
  • This Week: Our schedule is a bit uncertain this week. I will probably update it lecture by lecture rather than planning out the whole week. I still plan to meet Thursday, but will confirm on Wednesday. We will definitely meet Thursday next week (May 28) but will not meet Monday and Friday that week. I am still behind in grading homework, so the due date from these assignments will be announced later.
  • Study: Read Section 9.1 and start Section 9.2. Note that the exposition in Section 9.1 differs considerably from that in lecture.
  • Do: Ex 9.1.1.
Wednesday:
  • Study: Finish section 9.2 and start section 9.3.
  • Do: Ex 9.2.2, Ex 9.2.3, Ex 9.2.5, Ex 9.3.5
  • Observe I might be worth checking out (but do not turn in) Ex 9.3.7 to compare with the methods in section 9.2. Also, I think Ex 9.2.6 is amusing.
Thursday (x-hour):
  • Study: No lecture today.
  • Do:
Friday:
  • Study: I hope to get thru Prop 9.28. As noted in lecture, all the remaining problems (starting with Chapter 9) will be due on the last day of class -- Wednesday, June 3rd.
  • Do: Ex 10.1.1, Ex 9.3.10, Ex 9.3.11, Ex 9.3.12.
  • Observe Ex 9.3.8 and/or Ex 9.3.9 might be fun, but the algebra is challenging.


Week of 25 to 29, 2026, 2026
Assignments Made on:
Monday :
  • Study: Memorial Day (All classes canceled)
  • Do:
Wednesday:
  • Study: Finish section 9.3 up to but not including the "Key Hole Path" subsection. (We won't cover that in lecture.)
  • Do: Ex 9.3.14. (There is a typo in Ex 9.3.14. It should read $f(z)=(z^2-a^2)^{-1}$.)
Thursday (x-hour):
  • Study: Read Section 11.1
  • Do: Ex 11.1.3. (This is the last problem that will be graded.)
Friday:
  • Study: No Lecture Today
  • Do:


Week of June 1 to 3, 2026
Assignments Made on:
Monday:
  • Study: We finished section 11.2 and the course. While the last homework is due on Wednesday (at 2pm), Gradescope will accept it until Friday at 2pm. Let me know if you still need an extension.
  • Do:
Wednesday:
  • Typo Competition: Here is the current typo contest tally. (Last modified June 03, 2026) It seems that Ali nudged out Ben at the finish line. I will happily (well sort of) accept more contributions via the canvas page, but I will probably not continue posting the score.
  • Study: We finished Monday.
  • Do:
Friday:
  • Study:
  • Do:


Dana P. Williams
Last updated June 03, 2026 14:15:54 EDT