MATH704 Analysis II Spring 2022

Course Information

Instructor Dr. Changhui Tan
Lectures T Th 1:15pm - 2:30pm, at Coliseum 3007
Office Coliseum 2026N
Office Hours M 11:00am - 12:00pm (via Blackboard), Th 11:30am - 12:30pm (in office), or by appointment
Textbooks Terence Tao, An Introduction to Measure Theory, American Mathematical Society, 2011. (ISBN: 978-1-4704-6640-4)
Syllabus Click Here


Course Description

  • The official course description for the MATH 703/704 sequence:
  • Compactness, completeness, continuous functions. Outer measures, measurable sets, extension theorem and Lebesgue-Stieltjes measure. Integration and convergence theorems. Product measures and Fubini’s theorem. Differentiation theory. Theorems of Egorov and Lusin. \(L^p\) spaces. Analytic functions: Cauchy-Riemann equations, elementary special functions. Conformal mappings. Cauchy’s integral theorem and formula. Classification of singularities, Laurent series, the Argument Principle. Residue theorem, evaluation of integrals and series.
  • List of Topics (for MATH 704):


Homework Assignments

  • Homework assignments will be assigned and collected each week. The tentative due date is on Tuesday in class.
  • The homework is not pledged. You are encouraged to discuss the problems. However, each student is responsible for the final preparation of his/her own homework papers.
  • Last update: 4/21, Homework 9 is available, submission is not required.
  •  Download Homework Assignments.



  • There will be two 75 minutes in-class midterm exams. The tentative dates are February 22nd and April 12th. There will be a 150 minutes cumulative final exam.
  • Exams are under the honor code. Be sure and hand in all the work you do on each problem. Good luck! 
  • Last update: 4/19, midterm 2 is available.
  •  Download the Exams.



  • Your grade are distributed as below:
  • Homework » 30%
    Midterms » 20% each
    Final exam » 30%
  • You can monitor your grades via Blackboard.


Contact Information

  • Contact me at This email address is being protected from spambots. You need JavaScript enabled to view it. if you have any questions.