18.100B - Analysis I
Fall 2006

Course Information

	Lecture 1	Lecture 2
Instructor:	Pierre Albin	Enno Lenzmann
Office:	room 4-182	room 2-230
E-mail:	pierre(at)math.mit.edu	lenzmann(at)math.mit.edu
Lectures:	MWF 12-1 PM in 4-163	TR 1-2:30 PM in 4-163

Office Hours:	Pierre Albin	MW 2 - 3 PM in 4-182
	Enno Lenzmann	T 4 - 5 PM ; R 3 - 4 PM in 2-230
	Xiaoguang Ma	TR 1 - 2 PM in 2-229
	Sawyer Tabony	MW 11 AM - 12 PM in 2-094

Optional review sessions:	Tuesday 6-7 PM in 4-163 (4-270 on Oct 24)
Text:	Rudin, Principles of Mathematical Analysis, third edition
Assignments:	Weekly homework will be due each Friday at 3 PM in 2-108. Late homework will not be accepted, but the lowest score will be dropped.
Exams:	There will be two midterms and a final.
Grading percentages:	Problem sets (40%) Two midterms (15% each) Final exam (30%)
Web page:	http://www-math.mit.edu/~pierre/18100/home.html

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Homeworks

Links

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Holidays	Add/Drop Dates	Exam Dates
Student holiday September 25	Add date October 6	First Midterm October 12
Columbus day October 9 - 10	Drop date November 22	Second Midterm November 16
Veteran's Day November 10		Final Exam December 21
Thanksgiving November 23-24		(details below)

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Tentative Syllabus

The following is a rough week-by-week guide to what we will be covering and when. Some topics may be removed due to time constraints, especially toward the end.

• Week 1 (9/6-9/8): Sets and fields, the real numbers
  Read Rudin pgs. 1-17.
• Week 2 (9/11-9/15): Countability, metric spaces
  Read Rudin pgs. 24-35.
• Week 3 (9/18-9/22): Closed sets, compact spaces
  Read Rudin pgs. 34-38.
• Week 4 (9/27-9/29): Compact subsets of Euclidean space
  Read Rudin pgs. 38-40.
• Week 5 (10/2-10/6): Completeness, sequences and series.
  Read Rudin pgs. 42-43, 47-69, 71-75.
• Week 6 (10/11-10/13): Continuity.
  Read Rudin pgs. 83-86.
• Thursday 10/12: Midterm 1 7:30-8:30 PM, room 4-370
• Week 7 (10/16-10/20): Continuity and compactness.
  Read Rudin pgs. 85-93.
• Week 8 (10/23-10/27): Differentiability, Mean value theorem.
  Read Rudin pgs. 103-110.
• Week 9 (10/30-11/3): Taylor series, Riemann-Stieltjes integral.
  Read Rudin pgs. 120-127.
• Week 10 (11/6-11/9): Integrability, fundamental theorem of calculus.
  Read Rudin pgs. 128-136.
• Week 11 (11/13-11/15): Sequences of functions.
  Read Rudin pgs. 143-151.
• Thursday 11/16: Midterm 2 7:30-8:30 PM, room 4-163
• Week 12 (11/20-11/22): Uniform convergenece.
  Read Rudin pgs. 150-154.
• Week 13 (11/27-12/1): Uniform convergence, equicontinuity.
  Read Rudin pgs. 150-161.
• Week 14 (12/4-12/8): Power series, fundamental theorem of algebra.
  Read Rudin pgs.83-86, 180-185.
• Week 15 (12/11-12/13): Final review.
• Thursday 12/21: Final Exam 1:30-4:30 PM, room `Johnson'