Assignments, Math 5520, Winter 2001

Schedule and assignments
Topology, Math 5520, Winter 2001
There are two kinds of assignments here.

First, there are the daily discussion questions which you should answer by email before the assigned class, or hand in on paper at the start of class.
Second, there are weekly homework assignments which will be collected at the start of each week. There is a brief summary of the homework assignments at the end.

Both will play an important role in your learning and in your grade.

Week 1:

Mon, Jan 8: no assignment, naturally.

Wed, Jan 10: Discussion questions due at the start of class:

The two exercises in the Introduction to the course.
The two exercises in Logic Practice.

Fri, Jan 12: Answer the questions following Theorems 1.5.4 and 1.5.13. That is, indicate briefly what goes wrong when you try to prove the reverse inclusions in 1.5.4.(a), 1.5.13.(a) and 1.5.13.(b)

Homework, due Wednesday, Jan 17 rather than Monday, Jan 15, because Monday is Martin Luther King Day and there will be no class.:

Sect. 1.2 # 1,4,5,9,10.
Sect. 1.3 # 4,5,10.
Sect. 1.4 # 1a, 2a, 3a, 7,8,9,11.
Sect 1.5 # 1c, 2b, 4, 5.

Week 2:

Mon, Jan 15: Martin Luther King Day. No class.

Wed, Jan 17: Homework due Mon, Jan. 22: Section 2.1 # 2,3,4,5,7,9.
Discussed proofs, logic, set constructions.

Fri, Jan 19: Discussion questions: may be handed in Monday instead.
Started section 2.1: open sets in the real line.

Week 3:

Mon, Jan 22: Discussion questions: the 4 possible topologies handed out last Wed. You may turn these in Wed if you wish.
Homework due Mon Jan 29: Section 2.2 # 1,3,11. Section 2.3 # 1,3,4,11,13.
Started 2.2: topological spaces.

Wed, Jan 24:
Discussed open sets in different topologies. (Sect 2.2) Discussion Q for Fri: example of sets which are neither open nor closed in R with the usual topology, the half-open topology, and the Cofinite topology.

Fri, Jan 26:
More on open sets and constructions. Start closed sets (Sect 2.3). Homework for 2.3 not due until Wed, Jan 31.

Week 4:

Mon, Jan 29: Discussed closed sets (sect 2.3). Discussion questions for Wed:
classify as open/closed/neither the sets
(a,b), (a,b], [a,b), {3}, Z, R-Z, Q, R-Q
in the usual, half-open, C and cofinite topologies.

Wed, Jan 31:
Discuss closed sets and closure, as well as role of variables in logical statements and definitions, and in proofs. Homework for Mon Feb 5: Sect. 2.4 # 3,6,14,15,16,17.

Fri, Feb 2: Start section 2.4, limit points, interior, exterior, boundary>

Week 5:

Mon, Feb 5: Continue 2.4.

Wed, Feb 7: Discuss bases, section 2.5.
HW for Mon Feb 12, Section 2.5 # 2,9,10, and Review exercises for chapter 2, # 2, 5-9,19.

Fri, Feb 9: Discuss relative topologies, section 3.1.
HW for Wed Feb 14 Section 3.1 # 1,2,13,14.

Homework summary

Due date Problems

Wed, Jan 17 Sect. 1.2 # 1,4,5,9,10.
Sect. 1.3 # 4,5,10.
Sect. 1.4 # 1a, 2a, 3a, 7,8,9,11.
Sect 1.5 # 1c, 2b, 4, 5.

Mon, Jan. 22 Section 2.1 # 2,3,4,5,7,9.

Mon Jan 29 Section 2.2 # 1,3,11

Wed Jan 31 Section 2.3 # 1,3,4,6,7,8,11,13.

Mon Feb 5 Section 2.4 # 3,6,14,15,16,17.

Mon Feb 12 Section 2.5 # 2,9,10.
Chapter 2 Review Exercises # 2, 5,6,7,8,9,19.

Wed Feb 14 Section 3.1 # 1,2,13,14

Due date	Problems

Wed, Jan 17	Sect. 1.2 # 1,4,5,9,10. Sect. 1.3 # 4,5,10. Sect. 1.4 # 1a, 2a, 3a, 7,8,9,11. Sect 1.5 # 1c, 2b, 4, 5.
Mon, Jan. 22	Section 2.1 # 2,3,4,5,7,9.
Mon Jan 29	Section 2.2 # 1,3,11
Wed Jan 31	Section 2.3 # 1,3,4,6,7,8,11,13.
Mon Feb 5	Section 2.4 # 3,6,14,15,16,17.
Mon Feb 12	Section 2.5 # 2,9,10. Chapter 2 Review Exercises # 2, 5,6,7,8,9,19.
Wed Feb 14	Section 3.1 # 1,2,13,14