## Analysis (Honors)

• Time and place: MWF at 11 in MS 5127
• Instructor: Thomas M. Liggett
• Office hours: MWF 1:30-2:30 in MS 7919
• TA: Neel Tiruviluamala. His office hours are M 4-5 and Th 11-12.
• Text: Principles of Mathematical Analysis by W. Rudin
• Prerequisites: Mathematics 131AH (or 131A, in which case you should check with me before enrolling), and 115A. (The main use of 115A will occur toward the end of the quarter, so concurrent enrollment in 115A should be fine.)
• The first discussion section (on January 5) will be devoted to going over the 131AH final exam, and further review of 131AH.
• The midterm will be on Wednesday, Feb. 10. It will cover pp 120-158. Solutions
• The final exam will be on Wednesday, March 17, 11:30-2:30, and will cover Chapters 6,7 and 8. My office hours that week will be Tuesday (1-2 and 3-4) instead of Monday.
• 131ah Midterm and Midterm solutions
• 131ah Final and Final solutions
• The schedule for the week of Jan. 18 is different from normal: (a) Monday is a holiday. (b) Tuesday will be a lecture day with me (in MS 6201). (c) Wednesday will be a discussion day with Neel (in MS 5127). (d) The HW is due Wednesday. (e) My office hours will be on Tuesday instead of Wednesday.
• Final exam solutions

### Homework

• Due Jan. 5: Page 114 #8,11,13.
• Due Jan. 12: Page 115 #15(don't miss the question at the end about vector valued functions), 16,17,19,22,23,26,27.
• Due Jan. 20: Page 138 #1,2,3,5,6,7,8.
• Due Jan. 26: Prove parts b and d of Theorem 6.12. Page 139 #9,10,11,12,13,15.
• Due Feb. 2: Page 141 #17,18; page 165 #1,2,3,4,5; integrate x^2d\alpha from 0 to 1, where \alpha is the Cantor function.
• Due Feb. 9: Page 166 #6,7,9 (also, if the converse is false, is it true under a natural additional assumption?), 10,11,12,13 (on part (b), some printings of the book have an error; it should say "... uniformly on bounded sets.")
• Due Feb. 16: Page 168 #15,16,18,20,25.
• Due Feb. 23: Page 169 #21,22,24; page 196 #1,2,3.
• Due Mar. 2: Page 197 #5(use series, not l'Hospital),6,7,8,9,10,11.
• Due Mar. 9: Page 198 #12,14,15,17(a),19,22.