MA 504 Homework assignment - Fall 2010

#1 - Due Sept. 3: Read sections 1.1-1.21, 1.23; Chapter 1: Pb. # 1, 4, 5, 6, 7 (a) (b).

#2 - Due Sept. 10: Read sections 1.35-1.38 (Appendix optional), 2.1-2.14; Chapter 1: Pb. #15, 16, 18; Chapter 2: Pb. #4.

#3 - Due Sept. 17: Read sections 2.15-2.40; Chapter 2: Pb. #7,8,9,10,15,16,22,29. Show that, for a subset E of a metric space X, E coincides with the intersection of all closed sets containing E.

#4 - Due Sept. 24: Read sections 2.41, 2.42, 2.45-2.47, 3.1-3.7; Chapter 2: Pb. #19; Chapter 3: Pb. #1,2. Prove that if a sequence {p_n} converges to a point p, then every subsequence of {p_n} also converges to p. Please note: Pb # 20 and 23 in Chapter 3 are not due with this homework assignment (as incorrectly announced in class).

#5 - Due Oct.1: Read sections  3.8-3.23;  Chapter 3: Pb. #20,23,5,21.

#6 - Due Oct. 8: Read sections  3.24-3.28, 3.30; Chapter 3: Pb. #5, 21 (if you did not turn them in on 10/1). Prove Thm. 3.25, part (b), using Thm. 3.24.

#7 - Due Oct. 15: Read sections 3.31-3.49; Chapter 3: Pb. #6 (a), (b), (c), 7, 9 (a)-(d).

#8 - Due Oct. 22: Read sections 3.50-3.51, 4.1-4.12. Chapter 3: Pb. #8,11,13. Prove Theorem 4.4 using: 1) The definition of limit; 2) Theorems 4.2 and 3.3. Chapter 4: Pb. #1, 3.

#9 - Due Oct. 29: Read sections 4.13-4.30, 5.1-5.4. Show that the function f(x)=x² is not uniformly continuous on R. Chapter 4: Pb. #6, 8, 20, 21 (use continuity!), 14, 16, 23.

#10  - Due Nov. 5: Read sections 5.5-5.15. Chapter 5: #1,2,6,7,14.

#11  - Due Nov. 12: Read sections 5.16-5.19, 6.1-6.7. Chapter 5: #26,27, Chapter 6: #1,2.

#12  - Due Nov. 19: Read sections 6.8-6.18. Chapter 6: #4,5,10,11; Prove Thm. 6.12, (b)-(e).

#13  - Due Dec. 3: Read sections 6.19-6.25, 7.1-7.9, 7.11-7.24. Chapter 6: #15; Chapter 7: #1,2,5,7,9.

#14  - Due Dec. 10: Read sections 7.25-7.26, 9.1-9.5, 9.10-9.13, 9.15-9.19, 9.22-9.25. Chapter 7: #16,18,20; Chapter 9: #2,6,11,13.