The goal of this course is to give you working knowledge of basic concepts of Real Analysis and of the elements of the Functional Analysis. ``Working knowledge'' means that you should be able to apply principles and methods that you learn to solving concrete problems. I will assign problems on a regular basis. Homework assignments and the dates when they are due will be posted on the web site. Every week Tom LaGatta will conduct a one-hour discussion session, TBA.
In the Fall, there will be one mid-semester test on Wednesday, October 17, and the final exam on Friday, December 14, from 8:00 to 10:00. Final grades will be assigned based on the results of these exams. No formal point system will be used. The grade ``W'' will be awarded to any student who requests this grade before or on October 12. The grade of ``I'' can be awarded only in an exceptional case to a student who has a valid reason for not completing the course in time (illness, solid family reasons), and who has shown a passing performance in class.
In the Spring, there will be one mid-semester test on Wednesday, March 12, and a take-home final exam. The problems for the final exam will be posted on Wednesday, May 7, and the solutions will be due on Wednesday, May 14, at noon. The grading policy and the "I" policy are the same as in the Fall semester; the "W" deadline is Tuesday, March 11.
In the Fall semester, I intend to cover chapters 0-3 from the textbook. Some of the material will be covered in a more extended way than it is done in Folland's book. From time to time, I may write notes, which will be posted on the web site.
In the Spring semester, I will cover chapter 3 and parts of chapters 4,5,6, and 8. Time permitting, I may also cover elements of the distribution theory.
Problem sets:
1. Due on August 29: Problem set 1
2. Due on September 10: Problem set 2
3. Due on September 19: Problem set 3
4. Due on October 3: Problem set 4
5. Due on October 17: Problem set 5
6. Due on October 26: Problem set 6
7. Due on November 9: Problems 13, 14, 15, 16, p. 52, and
19, 25, 26, 27, 28, p.p. 59--60.
8. Due on November 21: Problems 32, 33, 34, 36, 37, 38, 41, 43, 44,
p.p. 63--64.
9. Due on December 3: Problems 46, 47, 49, 50, p.p. 68--69;
55, 56, 58, 60, 61, p. 77
10. Due on January 30: Problems 4, 5, 7, p. 88; 8, 9, 11, 12, p. 92;
20, 21 p. 94
11. Due on February 11: Problem set 11
12. Due on February 20: Problems 30, 31, 32, 33,35, 37, 39, 40, 42,
p.p. 107--109
13. Due on February 29: Problem set 13
14. Due on March 14: Problems 3, 4, 5, 6, 9, 10, 11, 13, 14, 15, p.p. 186--187;
17, 18, 19, 20, 25, p.p. 159--160
15. Due on April 9: Problem set 15
16. Due on April 16: Problem set 16
17. Due on April 23: Problem set 17
18. Due on May 5: Problems 7, 8, 9, page 246; 13, 14, 15, 17, 18, p.p.
254--255
FINAL EXAM PROBLEMS
Class notes:
1. Banach--Tarski Theorem
2. Solutions of selected problems from assignments 8 and 9