MATH 240B: Real Analyais, Winter quarter 2020
Class Web Page

Solution to Midterm Exam Problems

Final Exam

Solution to Final Exam Problems

Course Description Basics of normed vector spaces and Hilbert spaces, bounded linear operators and functionals, Lp spaces, fundamental theorems for Banach spaces and bounded lienar functionals, weak convergence. topological spaces, locally compact Hausdorff spaces, compactness theorems, topological vector spaces, Radon measures, regularity and approximations, Riesz representation theorem, the dual of Cc(X) and the dual of C0(X).
Prerequisites Math 140 ABC and Math 240A, or equivalent.
Textbook Gerald B. Folland, Real Analysis: Modern Techniques and Applications, 2nd edition, Wiley, 1999. We will cover part of Chapters 4 - 7.
Topics of lectures
  • Lectures 1 and 2: 5.1 (add some examples) and 5.2 (only the beginning part)
  • Lectures 3 and 4: 6.1 (add approximation via mollifiers)
  • Lectures 5-7: 6.2-6.4 (skip 6.5: Interpolation of Lp spaces)
  • Lectures 8 and 9: 5.2 (add weak convergence and Mazur's theorem)
  • Lectures 10 and 11: 5.3 (add examples of application of the PUB)
  • Lecture 12 and 13: 5.5
  • Lectures 14-21: 4.1-4.6 (skip 4.7 or the proof of Stone-Weierstrass Theorem)
  • Lecture 22: 5.4
  • Lectures 23-27: 7.1-7.3
Lectures 10:00 am - 10:50 am, Mondays, Wednesdays, and Fridays, AP&M 5402.
Instructor Professor Bo Li. Office: AP&M 5723. Phone: (858) 534-6932. Email: Office hours: 11:00 am - 12:00 noon, Mondays, and 1:00 pm - 1:30 pm, Wednesdays.
Grader Yunyi Zhang. Office: 1256. Email:
Homework Homework is assigned, collected, and partially graded regularly. Each homework assingment is due at the beginning of class of the due date.
    Note: Please print your names and student ID nubmers on your homework. Please stable together your homework pages.
    Note: no late homework will be accepted unless a written verification of a valid excuse (such as hospitalization, family emergency, religious observance, court appearance, etc.) is provided.
Homework assignment 1. Due Monday, January 13, 2020. (Solution)
Homework assignment 2. Due Wednesday, January 22, 2020. (Solution)
Homework assignment 3. Due Wednesday, January 29, 2020. (Solution)
Homework assignment 4. Due Friday, February 7, 2020. (Solution)
Homework assignment 5. Due Wednesday, February 19, 2020. (Solution)
Homework assignment 6. Due Wednesday, February 26, 2020. (Solution)
Homework assignment 7. Due Wednesday, March 4, 2020. (Solution)
Homework assignment 8. Due Friday, March 13, 2020. (Solution)
Exams There will be one midterm and one final, close-book and close-note exams. The final exam will be cumulative.
      Midterm exam: 10:00 am - 10:50 am, Friday, February 13, 2020, AP&M 5402.
      Final exam: 8:00 am - 10:59 am, Friday, March 20, 2020. Place: To be announced.
    Note: neither rescheduled nor make-up exams will be allowed unless a written verification of a valid excuse (such as hospitalization, family emergency, religious observance, court appearance, etc.) is provided.
Grading The final course grade will be determined based on the homework and exams with the weights: homework - 30%, midterm exam - 30%, and final exam - 40%.

Last updated by Bo Li on January 7, 2020.