MATH 413, HONORS INTRODUCTION TO ANALYSIS (SPRING 2006)
TR 8:40 -- 9:55, 224 Malott
Greg Lawler
TA: Nikolai Dimitrov
Office Hours: Greg Lawler (567 Malott): T 10:00 -- 11:00, Th 2:00 --
3:00
Nikolai Dimitrov (218 Malott) MW 1:15 -- 2:15
Text: Strichartz, The Way of Analysis. We will cover most of
Chaps. 1--7 and a few other topics.
Math 413 provides a rigorous introduction to analysis. Emphasis
will be placed upon understanding and performing mathematical proofs.
Homework
There will be weekly homeworks due on Thursday covering the previous
week's material. Assignments will
be posted here. Late homeworks will not be accepted but you may turn in
assignments early.
Students may discuss homework problems and work together in finding
solutions, but the write-up of solutions must be done individually.
Week 1
Week 2: Reading: 2.1, 2.2; p. 37: 1,3,4,5,6,7,8; pp 48-49: 2,7,9
Week 3 (revised)
Week 4: Reading: 3.1.2, 3.2; pp. 84-85: 1,3,7,9; pp. 98-99: 1,2,5,8,13,14
Week 5: Reading 3.3, 4.1;
p. 98, 6; pp. 106-107, 4,6,8,9; p. 126, 2,3,7,8,11
Week 6: Reading 4.2:
EP6-1 , pp. 126--127: 12,14,15;
pp. 138--139: 4,8,9,10,11,17
Week 7
Weeks 8-9: Reading 5.3, 5.4.1, 5.4.2, 5.4.4, 6.1.1, 6.1.2;
EP8-1, EP8-2 ; pp. 176-177: 2,3,7,10; pp. 192-193: 2, 3, 23 (a),(b),(c);
217--219: 1,2,4,10, 14(a)
Week 10: Reading 6.1.4, 6.2, 6.3; pp. 217--218: 3,6,9,11; pp. 232:
9(a), 10;
EP10-1, EP10-2, EP10-3 .
Week 11: Reading 7.1, 7.2; p.250: 3,4,7; pp. 262-263: 1, 6, 8, 9, 11, 12,
14
Week 12: Reading: 7.3, 7.4.1; p. 275: 7,8,9,12,13; pp. 294--295: 2,3,4,8,10,11
Week 13: Reading: 7.6, 8.1; pp. 314--315: 1,3,4,6,9;
pp. 335: 1,2,4,14
EP13-1, EP13-2
Week 14: Reading 8.2: Exercises (do not need to be handed
in), pp. 349-350: 4,8,9,11,12
Exams and Grading
There will be an in-class prelim on Thursday, March 16 and
a final examination. According to the University schedule, the
final exam will be on
Tuesday, May 16 at 7:00 pm in 205
Malott. There will also be frequent
quizzes (10-15 minutes) on Tuesdays covering the material from the
the previous week.
Grading will be based on: 40% homework and quizzes, 25% prelim, 35% final.