Math 113 Analysis I: Complex Function Theory

Welcome to Math 113 Analysis I: Complex Function Theory! In this course, you will learn to admire the great integral theorems of Augustin-Louis Cauchy, flanked above by two representations of the exponential function.

Class meets in Science Center 222 on TR, 2:30-4pm.

Note: Every semester, I try to pick up one new html trick to incorporate into my website. This semester's trick is collapsable lists! Clicking on the headers below will expand the subject, often revealing new collapsable lists. This allows me to include a lot of detail and justification on course policies, etc., without cluttering everything to the point of unreadability. The announcements, reading assignments, and problem sets are always displayed, but I encourage you to explore the rest of the material as well.


  • The course policies are described throughout this webpage. They are also outlined in the syllabus.
  • The most important thing is that you respect your fellow classmates and yourselves in all interactions. We've all taken different paths to get here, but we've come together for the shared goal of learning complex analysis.
  • Homework: 50%
  • Midterm: 20%
  • Final: 30%

  • Email:
  • Office: Science Center 238

    My office is kind of hard to find the first time, so here's a map. If you come out of the main elevators on the second floor, take a u-turn to your left and go all the way to the end of the hallway. Go through the door at the end to enter a cluster of math department offices. If you keep walking back in that direction, you'll find my office.
  • Office hours:
    • Tuesday 4-5pm
    • Wednesday 10-11am
    • Friday 12-1pm
    Office hours are a great time to come and ask questions about course material and/or homework. Note that my office hours are not right before homework is due. This is by design, to encourage you to start looking at the homework early.

  • Email:
  • Office Hours: M 8-10pm, Leverett Dining Hall (Math Night)
  • Problem Session: Friday 1-2pm, SC 110

Assignment .pdf .tex Due Date
Week 1 PS1 PS1 Jan. 30
Week 2 PS2 PS2 Feb. 6
Week 3 PS3 PS3 Feb. 13
Week 4 PS4 PS4 Feb. 20
Week 5 PS5 PS5 Feb. 27
Week 6 PS6 PS6 Mar. 8
Week 7 Cancelled due to midterm.
Week 8 PS8 PS8 Apr. 3
Week 9 PS9 PS9 Apr. 10
Week 10 PS10 PS10 Apr. 17
Week 11 PS11 PS11 Apr. 24

  • Actively engaging with the material is the best way to learn math. I want to give you as much opportunity to do so as possible, so we will have weekly problem sets due Tuesday. In particular, you can turn in problem sets either in class or via email to Vaughan. Either way, the problem sets are due by the end of class.
  • Math is a team sport and the best way to learn is to find classmates and friends to work on problem sets with. I really encourage you to work with people in this class both on completing the problem sets and gaining a better understanding of the material in general.
  • Math Night is a great place to meet up with people in your class and in the larger department. Note that the homework is cleverly scheduled to be due the class after Math Night each week.
  • To really drive home that I'm serious about collaboration and to help you find people to work with, for the first three assignments, I will be assigning you groups to work with. I'll send out emails to groups around the same time that I post assignments. These aren't the only people you can work with, but I'd like you to try working in these groups for at least an hour. If you do, then your group will get 10 bonus points on the assignment. Make sure everyone writes at the top of their homework that y'all worked together so the grader's know.

    If you run into problems meeting up with your group (some group members don't want to meet, but others do; there's no time that works for everyone; etc.), let me know and I'll help resolve the problem.
  • LaTeX or TeX is a typesetting program that allows you to easily type the mathematical symbols that you'll need to use on your homework.
  • Here is a template on Overleaf that will let you dive right in. There will be a LaTeX how-to seminar hosted by our course assistant.

    Another useful tool is DeTeXify is another useful tool that allows you to draw the symbol you want, and it will help you find the right code. I often use the DeTeXify app on my phone when trying to use new symbols.
  • TeXing your homework is a valuable skill to learn in math, and helps greatly streamline the process of grading and resubmitting. In this class, there's a scaling requirement of TeXing your homework: you should TeX at least 2*(week number) problems on each assignment (so 2 for PS1, 4 for PS2, etc.) until Spring Break. After Spring Break, you are required to TeX your entire problem set.
  • We all make mistakes, and the best thing to do is to learn from these mistakes. Thus, if you get back a problem set that you wish you had done better on, you can resubmit up to one week after the problem sets are returned. You're eligible for up to half of the points missed. Also, to avoid gaming of this combined with no late homework, you can only resubmit problems that you actually submitted in the first place.
  • The homework is designed to help you check, solidify, and deepen your understanding of the material. Since this course builds on itself (as most do), this is less helpful if you delay it. Thus, late homework is not accepted.
  • Homework should be turned in by the end of class, either a hard copy or an email.
  • I understand that things come up, and so you are given two 'grace' assignments throughout the semester. These are assignments that you can turn in up to one week late. If something comes up outside of the scope of these two grace assignments, please discuss it with me individually.

Week Reading from Marsden and Hoffman
Week 0 1.1
Week 1 1.1-1.4
I would like you review the Week 0 reading before the first day of class; it covers some of the basics of complex numbers. Then complete the rest of the Week 1 reading as we progress through the week.
Week 2 1.4-1.6, 2.1
Week 3 2.1-2.3
Week 4 2.4-2.5
Week 5 Chapter 3

  • It's important to do the reading for class. This will give you some initial exposure to the material prior to coming to class.
  • Come to class with questions from the reading! I don't expect you to obtain a perfect understanding of the material from reading, and you should use class time as an opportunity to clear up any confusion from the reading.
  • You should aim to complete the reading prior to the start of the week. Typically, we class will progress through the text as written, but sometimes things will be covered in a different order. Additionally, there are a few problem set problems written with this schedule in mind.
  • Keep in mind that you will be responsible both for the material covered in class and in the readings!

  • The midterm will be given as a take home exam over the weekend March 23-25 (the weekend after Spring Break. You are allowed to work on them during a (contiguous) three hour window of your choice. Choose your time and location carefully because there is no 'pausing' of the time. You should record your starting and ending time on the exam, and return the completed exam to my office by noon on the following Monday.

    Late exams will not be accepted. YOu can also email your exam to me, but all work including TeXing must be complete in the three hour window.

  • The midterms will be taken home exams. You are not permitted to discuss the exam with anyone until all exams have been turned in. You are also not permitted to consult any resources (books, notes, the internet, etc.) except yourself and a single page of notes as outlined below.

    The only outside resource allowed is a single side of an 8 1/2 by 11 piece of paper of notes on the exam. This sheet must be prepared prior to the exam period begining and must be emailed to me before the start of the exam window. You should use a hard copy of the sheet and not use any sort of magnification to help you read.
  • We will have a three-hour in class final exam during the time scheduled by the registrar. It will be comprehensive.
  • The exam is scheduled for May 10 at 2pm.

  • I'm happy to accommodate any modifications suggested by the Accessible Education Office (AEO). Please be sure to provide me with the introductory letter as soon as possible.
  • I expect students at all time to follow Harvard's Honor Code and practice academic integrity. I understand that the line between collaboration and plagiarism can be murky on problem sets, but the following is a good (and oft quoted) rule of thumb: working together is fantastic, but you should always be able to separate and right up your solutions individually. If you have any questions, please don't hesitate to ask.

If you have any questions, please feel free to contact me at
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