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):
- Lebesgue theory of Measure and Integration:
- Outer measure, measurable sets, measure spaces, complete and regular measures.
- Integration, Fatou’s lemma and convergence theorems.
- Extension theorem, product measure and Fubini’s theorem, Lebesgue-Stieltjes integral.
- Absolute continuity, Vitali’s lemma, differentiation theory for monotone functions and integrals, functions of bounded variation.
- Egorov and Lusin Theorems.
- Definition of \(L^p\), Holder and Minkowski inequalities, completeness of \(L^p\), approximation by step and continuous functions.
- Lebesgue theory of Measure and Integration:
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.
Exams
- 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.
Grades
- Your grade are distributed as below:
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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.