## Real Analysis: Math 209A

Fall 2004, TTh 2:10-3:30 p.m. in Olmsted Hall 1132

### Announcements

• The final exam has been graded. If you have not received your grade from me, you are welcome to email me. Also, you can come by on Friday to pick up your exam. Have a good vacation!

### Homework

• Homework 7, due December 2. Note two (!) corrections in Problem 1.
• Homework 6, due November 18.
• Royden, Chapter 5, Problems 3, 8, 10, 13, 15, 20. In problem 3, "maximum" should be "minimum".
• The midterm has been graded.
• Homework 5, due October 28.
• Read Sections 3.5-3.6, Chapter 4.
• Royden, Chapter 3, Problems 19, 20, Chapter 4, Problems 2, 3, 22.
• Homework 4, due October 21.
• Royden, Chapter 3, Problems 24, 25, 26, 28. In problem 28, you can use exercise 16. In problem 26, do not repeat the arguments of the theorems, only prove the new results.
• Homework 3, due October 14.
• Read sections 2.6-2.7, Chapter 3.
• Homework 2, due October 7.
• Royden, Chapter 2, Problems 1, 9, 26, 36, 37.
• Homework 1, due September 30.

### Syllabus

Professor: Michael Anshelevich, 250 Surge Building,
Office hours: TTh 1-2 p.m., W 9-10 a.m.

Text: H.L.Royden, "Real Analysis", 3rd edition, Prentice-Hall, 1988. Recommended text: Richard L. Wheeden, Antoni Zygmund, "Measure and Integral. An Introduction to Real Analysis", Dekker, 1977 (on reserve at the Science library).
Prerequisites: Math 151C or equivalent: abstract approach to calculus, differentiation and integration.
Topics:
• Review of set theory and properties of the real line.
• Lebesgue measure. Measurable sets.
• Measurable functions. Lebesgue integrals.
• Differentiation in measure theory.
• L^p spaces.
Exams: We will have a take-home midterm handed out October 28, due in class November 4. The final exam is on Thursday, December 9, 8-11 a.m. No make-up exams will be given. If you miss the final, you automatically fail the course. On the take-home exam, books and notes are allowed, collaboration is not. The final is closed book, closed notes.
Homework: weekly, due Thursdays in class. No late homework will be accepted; the lowest score will be dropped. You are encouraged to work together, but you must each turn in your own work.
Grading: Homework 30%, midterm 30%, final 40%.

Other important dates: October 8 (last day to add or drop a course), November 5 (last day to withdraw from a course).
Students with disabilities: Please come talk to me no later than the first week of classes.