MATH 630 Real Analysis
Exam Schedule
- First Exam:
- Friday, 30 September 2005
- Second Exam:
- Friday, 28 October 2005
- Third Exam:
- Friday 2 December 2005
- Final Exam:
- Monday, 19 December 2005, 8:00 - 10:00.
Grading Policy
Grades will be based on three hour exams counting 100 points each,
homework and quizzes worth 100 points,
and a final examination that is worth 200 points.
Class Schedule
The class meets according to the following schedule:
- Monday, Wednesday, and Friday, 9:00-9:50
- MTH 0407.
Topics
Lebesgue measure and the Lebesgue integral on R, differentiation of functions of
bounded variation, absolute continuity and fundamental theorem of calculus, Lp
spaces on R, Riesz-Fischer theorem, bounded linear functionals on Lp, measure
and outer measure, Fubini's theorem.
- PREREQUISITES MATH 411 or equivalent.
- TOPICS
- II. Review of Basic Material
- 4. lim sup and lim inf
- 5. Open and Closed sets
- 6. Continuous functions
- 7. Borel Sets
- III. Lebesgue Measure
- 1. Outer Measure
- 2. Measurable Sets and Lebesgue Measure
- 3. A Non-measurable Set
- 4. Measurable Functions
- 5. Littlewood's Three Principles
- IV. Lebesgue Integral
- 1. The Riemann Integral
- 2. The Lebesgue Integral of a bounded function
- 3. The integral of a nonnegative function
- 4. The general Lebesgue Integral
- 5. Convergence in Measure
- V. Differentiation and Integration
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Topics in Royden, (ISBN 0-02-404151-3)
We wil cover Chapters 1-6, 11, 12 of Royden.
Math 630: (Very) Provisional Schedule
Chapters are from Real Analysis, 3rd edition by Royden.
| WEEK | Monday | Wednesday | Friday |
|---|
| Aug 29-Sep 2 | No Class | 2.4 | 2.5 |
| Sep 5 - Sep 9 | Labor Day Holiday | 2.6 | 2.7 |
| Sep 12-Sep 16 | 3.1-2 | 3.2-3 | 3.3 |
| Sep 19-Sep 23 | 3.3 | 3.4 | 3.5 |
| Sep 26-Sep 30 | 3.5 | 3.6 | EXAM #1 |
| Oct 3- Oct 7 | 4.1-2 | 4.3 | 4.4 |
| Oct 10-Oct 14 | 4.5 | 4.5 | 4.8 |
| Oct 17-Oct 21 | 5.1 | 5.2 | 5.2 |
| Oct 24-Oct 28 | 5.3 | 5.4 | 6.1 |
| OCt 31-Nov 4 | 6.2 | 6.2 | 6.3 |
| Nov 7- Nov 11 | 6.4 | 6.4 | 6.5 |
| Nov 14- Nov 18 | 11.1 | EXAM #2 | 11.2-3 |
| Nov 21- Nov 25 | 12.1 | 12.2 | Holiday |
| Nov 28- Dec 2 | 12.3 | 12.4 | Cancelled |
| Dec 5- Dec 9 | 12.5 | 12.5-Review | EXAM #3 |
| Dec 12- Dec 16 | Review | Exam Study Day | |
Homework Problems
List of Suggested Problems
These are problems you should try to work. Some may eventually be assigned,
and others may show up on quizzes.
- Page
- Suggested Problems
- p. 38:
- #7, 8, 9, 11, 12, 13, 14, 15, 16, 17,
- p. 46:
- #24, 25, 28,29,30,34,36
- p. 49:
- #40, 41, 42, 43, 44, 45,47,49,50
- p. 53:
- #52, 53, 54
- p. 55:
- #1, 2, 3, 4
- p. 58:
- #5, 6, 7, 8
- p. 64:
- #9, 10, 11, 12, 13
- p. 66:
- #15, 16, 17
- p. 70:
- #18, 19, 20, 22, 24, 25, 26, 28
- p. 73:
- #30, 31
- p. 76:
- #1
- p. 85:
- #2
- p. 88:
- #3-8
- p. 93:
- #10-17
- p. 96:
- #20-25
- p.101:
- #1, 2, 3, 5
- p.104:
- #7, 8, 11
- p.111:
- #12-15, 17, 18