Course Syllabus
Fall 2026 Syllabus
Instructor: Prof. Aleksandr Logunov
Email: alogunov@mit.edu
Office: 2-478
Office hours: Monday, 3pm - 4pm, 2-478.
TA Office hours: Tuesday, 4:30-6:00 pm, 2-429
+TBA
Lectures: Mondays and Wednesdays, 1:00-2:30 PM
Room: 4-370
Term: September 9-December 10, 2026
Course website: Canvas
Course Description
The aim of the course is to teach the principal concepts and methods of complex analysis. We will mostly follow the classic textbook of geometrical flavor by L.Ahlfors.
Textbook(required): Lars V. Ahlfors, Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable, 3rd edition, McGraw-Hill, 1979.
Other recommended textbook(optional): Donald Sarason, Complex Function Theory, 2nd edition, AMS, 2007.
The course will cover a substantial portion of the Ahlfors’ textbook up to chapter 6.1.
Topics include holomorphic functions, complex integration, Cauchy formula, residue calculus, series and product developments, harmonic functions, conformal mappings and if time permits additional topics.
Lectures may substantially deviate from the textbook and include different material, examples, applications and proofs that are not in the textbook, and regular attendance is strongly recommended.
Approximate schedule, reading and recommended exercises
https://canvas.mit.edu/courses/39103/pages/reading-and-recommended-exercises
Prerequisites
18.100B (or an equivalent course in real analysis) + Linear Algebra. Students should be comfortable with reading abstract material and writing rigorous mathematical proofs.
Similar Courses that follow Ahlfors (with materials)
• Helgason, MIT 18.112 (Fall 2008)
• McMullen, Harvard Math 113 (Fall 1997)
Homework (10% of the grade)
Homework will be assigned every two weeks, with approximately one week to complete each assignment. Late submissions are not accepted, but the lowest homework score will be dropped.
You are strongly encouraged to make a genuine effort before consulting outside help. Many problems have solutions available online and can also be solved by AI. If you get stuck, ask for a hint rather than reading a full solution. Read only enough to identify the missing idea, then try to complete the problem yourself. Office hours are also a good source of hints and guidance. AI may be used for hints after a genuine attempt, as well as for feedback, alternative approaches, or suggestions for improving presentation. It should not be used to generate or write your solutions. Learning to solve problems and present rigorous arguments clearly and simply requires practice, and relying too heavily on outside help can leave you less prepared for in-class exams and tests.
Collaboration is encouraged: discuss problems and ideas with classmates, but write your own solutions.
MIT resource to find partners in problem solving:
https://psetpartners.mit.edu
Math Learning Center
A free resource to support you in your math courses.
Location: 4-107
Hours: Monday–Thursday, 3:00–5:00 pm and 7:30–9:30 pm
Courses covered: 18.01, 18.02, 18.03, 18.100, 18.112, 18.404, 18.600, 18.615, 18.650, 18.675, 18.700, 18.701, 18.705, 18.725, 18.785, 18.901.
During these hours, MLC tutors are available to help with problem sets, concepts, and general questions in a welcoming environment. You can also check the tutor schedule to see when someone with expertise in your course is available.
Examinations
• In class test 1: Monday, October 5, 2026, during the regular class period.
• In class test 2: Wednesday, November 18, 2026, during the regular class period.
• Final examination: during MIT's December 14-18 final-exam period. The exact date, time, and location will be determined and announced by the MIT Registrar.
Grading
Homework 10%
In-class test 1 (Monday, October 5, 2026) 20%
In-class test 2 (Wednesday, November 18, 2026) 20%
Final examination 50%
Important Dates, Holidays, and Schedule Changes
• Monday, September 7: Labor Day holiday (before classes begin)
• Wednesday, September 9: First 18.112 lecture
• Monday, October 12: Indigenous Peoples Day holiday; no 18.112 lecture
• Tuesday, October 13: MIT follows a Monday schedule; 18.112 meets Tuesday, 1:00-2:30 PM, in place of the October 12 Monday meeting
• Monday, October 5: Test 1 during the regular class period
• Wednesday, November 18: Test 2 during the regular class period
• Wednesday, November 11: Veterans Day holiday; no 18.112 lecture
• Thursday-Friday, November 26-27: Thanksgiving holidays; no change to the Monday/Wednesday 18.112 schedule
• Wednesday, December 9: Last 18.112 lecture
• Thursday, December 10: MIT last day of classes
• Final-examination period: Monday, December 14-Friday, December 18, 2026; exact exam date, time, and location determined by the MIT Registrar
Course Summary:
| Date | Details | Due |
|---|---|---|