Triet M. Le
Email:
Phone: (203) 432-4011
Office: Dunham Lab. 418
Math 300: Topics in Analysis, Spring 2009
Time: MWF: 11:35-12:25
Office Hours: See Reading week
Location: LOM 205
Textbook: "Fundamental Ideas of Analysis" by Michael
Reed
Another useful Reference: "Analysis, an Introduction" by
Richard Beals.
Both these books are on reserve at the Engineering & Applied
Science Library in Becton Center.
The course will cover most of chapters 1-6 in the textbook. Two theorems
will be of special interests: the Bolzano-Weierstrass Theorem and the Contraction Mapping Theorem.
It is expected that students will be fully familiar with proofs and some applications of these theorems.
Reading and Homework Assignments: The pages listed for each week
contain the topics to be discussed in class that week.
The problems listed in "Homework" are due in class on Friday of the
week they are listed in.
No late homework will be accepted. If an assigned problem has several parts (i.e. a,b,c,d,e) and no
specification is given, you are to solve all parts.
Exams: There will be a midterm and a final exam. The dates will be announced.
Grading: The grading scheme is: 30% for the homework; 30% for the midterm;
40% for the final.
Syllabus: (Tentative)
- Week 1: Jan. 12-16, 2009
- Week 2: Jan. 19-23, 2009
- Week 3: Jan. 26-30, 2009
- Week 4: Feb. 2-6, 2009
- Week 5: Feb. 9-13, 2009
- Structure of Point Sets: 1) open and closed sets; 2) compact
sets;
- Notes:
week5.pdf
- Homework:
hw5.pdf
- Week 6: Feb. 16-20, 2009
- Week 7: Feb. 23-27, 2009
- Week 8: Mar. 2-6, 2009
- Midterm on March 3 from 6:00-7:30
in LOM 214, covering materials up to and including.
week 6.
- Reading: Section 4.1-4.3.
- Notes:
week8.pdf
- Homework:
hw8.pdf. Due Friday
March 27. Typos: In #3, we assume that f is bounded.
- Week 9: Mar. 23-27, 2009
- Reading: Section 4.4-4.6.
- Notes:
week9.pdf
- Homework (due Friday April 3rd):
- Page 133: 2, 3, 9, 13;
- Page 139: 10, 11, 12, 13;
- Week 10: Mar. 30 - April 3, 2009
- Week 11: April 6-10, 2008
- Week 12: April 13-17, 2009
- Week 13: April 20-24, 2009
- Reading: See Reading from Week 12.
- Some practice problems for series (Do not turn in):
- Page 236: 1, 4, 5, 9, 11, 14.
- Reading week:
- Final: Friday, May 08, 2009 at 2pm. Room: WLH 207.