Real Analysis: Math 209C
Spring 2004, TTh 8:10-9:30 in Surge 268
Announcements
- The exam has been graded; let me know if you have not received your grade by email.
Homework
- Homework 6, due May 27.
- Chapter 12: 52, 55 (note: has misprints).
- Chapter 13: 5, 6, 13.
- Homework 5, due May 20.
- Chapter 12: 19, 24, 30, 36, 37, 38.
- Homework 4, due May 13.
- Chapter 12: 1, 10, 13, 17, 21.
- The midterm has been graded.
- Homework 3, due April 29.
- Chapter 7: 47, 48 (take X=R), 50.
- Chapter 9: 42, 43, 44, 46.
- Homework 2, due April 22.
- Chapter 10: 2, 13, 14, 17, 22, 23.
- Homework 1, due April 15.
- Chapter 7: 31, 34, 35, 36, 38.
- Chapter 10: 7, 26, 29.
Syllabus
Professor: Michael Anshelevich, 250 Surge Building.
Office hours: TTh 9:30-10:30 am, W 9-10 am.
Text: H.L.Royden, "Real Analysis," 3rd edition, Prentice-Hall, 1988.
Prerequisites: Math 209AB.
Topics:
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Operators in Banach spaces. Three basic principles of functional analysis (Chapter 10, sections 1-4, also 7.8).
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Two theorems about function spaces: Arzela-Askoli, Stone-Weierstrass (7.10, 9.9).
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Outer measures. Extension of measures. Caratheodory construction (Chapter 12).
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Product measures. Fubini theorem (Chapter 12).
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Time permitting: measures as functionals. Riesz representation theorem (Chapters 12, 13).
Exams: We will have a take-home midterm handed out April 29, due May 6. The final exam is on Monday, June 7, 3:00-6:00 pm. 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: April 9 (last day to add or drop a course), May 7 (last day to withdraw from a course).
Students with disabilities: Please come talk to me no later than the first week of classes.