MA 504 Homework assignment - Fall 2010
#1 - Due Aug. 27 Read sections 1.1-1.20; Chapter 1: Pb.
# 1, 4, 5.
#2 - Due Sept. 3 Read sections 1.21-23, 1.35-1.38, Appendix optional,
2.1-2.19 ; Chapter 1: Pb. 6, 15, 16, 17, 18; Chapter
2: Pb. 4, 8, 9 (a)-(c).
#3 - Due Sept. 10 Read sections 2.20-2.36; Chapter 2: Pb. 7, 9 (d)-(f), 10, 15, 16. Show
that, for a subset E of a metric space X, Ē (the closure of E) coincides
with the intersection of all closed sets containing E.
#4 - Due Sept. 17 Read sections 2.37-2.42, 2.45-2.47, 3.1-3.11; Chapter
2: Pb. 19, 22, 29; Chapter 3: Pb. 1, 2 ,3. Show that a sequence {pn} is converging to
a point p if, and only if, every subsequence of {pn} converges to p.
Show that a sequence {pn} is Cauchy if, and only if, diam(EN)
→0 as N →∞ (here, EN={pN,
pN+1, ...}).
#5 - Due Sept. 24 Read sections 3.12-3.28, 3-30-3.32. Chapter 3: Pb. 5, 20, 21, 23.
#6 - Due Oct. 1 Read sections 3.33-3.48. Chapter 3: Pb. 6 (a)-(c), 7.
#7 - Due Oct. 8 Read sections 3.49-3.51, 4.1-4.8. Chapter 3: Pb. 8, 9, 11, 13. Prove Theorem 4.4 using: 1) The
definition of limit; 2) Theorems 4.2 and 3.3.
#8 - Due Oct. 15 Read sections 4.9-4.20. Show that the function f(x)=x2 is not uniformly continuous on R. Chapter 4:
Pb. 1, 3, 6, 8.
#9 - Due Oct. 22 Read sections 4.21-4.31, 5.1-5.12. Ch. 4: Pb. 20, 21 (use continuity!), 14, 16, 23; Ch.5: 1, 2.
#10 - Due Oct. 29 Read sections 5.13-5.16, 5.19, 6.1-6.9. Ch. 5: 5, 6, 9, 14, 26, 27.
#11 - Due Nov. 5 Read sections 6.10-6.20. Ch. 6: 1, 2.
#12 - Due Nov. 12 Read sections 6.21-6.22, 7.1-7.9, 7.11-7.13. Ch. 6: 4, 5, 10, 11; Ch. 7: 2, 5.
#13 - Due Nov. 19 Read sections 7.14-7.17, 7.19, 7.21-7.26, 9.22, 9.1. Ch. 7: 7, 9, 1, 16, 18, 20.
#14 - Due Dec. 3 Read sections 9.2, 9.4, 9.6, 9.7, 9.10-9.17. Ch. 9: 6, 11, 13.
Final Exam Info: Tuesday, Dec. 16, 8-10 am, BRNG 1268. Books and notes allowed.