For Friday, January 15, read pages 1-11 (including the
exercises).
For Friday, January 15, do exercises 4, 5, 7.
For Monday, January 18, do exercises 10, 11, 12.
Outstanding from earlier: (Re: problem 5 in Section 1) how
can you prove that you need at least 3 polygons to form an
annulus, if no cell can be sewn to itself, or sewn to any other
cell along more than one edge?
Read Section 2 -- pages 11-21 (including the exercises).
For Wednesday, January 20, do exercises 1 and 3 and any one
of 4, 5, or 6.
For Friday, January 22, do any three of problems 7-12.
Read Section 3.
For Monday, January 25, do problems 2 and 4, as well as 3
or 6 (on page 24).
For Wednesday, January 27, do any two of 7, 8, 9, 11, and
either 12 or 15 (on page 26).
For Friday, January 29, finish up the stuff from Section 3,
and read Section 5. (When you have a chance, read Section 4; we
are skipping it for now, though.)
For Friday, January 29, do 3 parts of problem 2 on page 36.
For Monday, February 1, do the stuff from Section 5. Also,
try to write up a careful solution of the first part of
problem 2 on page 24.
For Friday, February 5, read Section 6 and do problems 2,
5, 6, 7 (pp. 39 and 43)
For Monday, February 8, read Section 7 and do a few parts
of problem 1, as well as 2, 3, and 5 (pp. 46-48).
For Wednesday, February 10, read Section 8 and do a few
parts of problems 1 and 2 (pp. 53-54).
For Friday, February 12, read Section 9 and do a few parts
of problems 1 and 2, and do problem 3 (pp. 56-57); also do a
few parts of problem 5, and do problem 6 (p. 58).
For Monday, February 15, do problems 7, 8, 9, 11
(pp. 59-60). Also, read Section 10 and look at a few of the
problems, if you have time.
For Wednesday, February 17, read Section 10, do a few parts
of problem 2, do problem 3, and look at either 5 or 6
(pp. 66-67). Oh, and if you haven't done it already, do
problem 11 on page 60, in the cases of 3 and 4 sectors.
For Friday, February 19, skim Sections 11 and 12 (making
sure to read the theorem on page 68). Read Section 13 and do
problems 1-5 on page 83.
For Monday, February 22, continue with the problems from
Section 13. (We've done #2, so look at the others.) Also,
for problem 3, try to figure out why the curve mentioned is
space-filling.
For Wednesday, February 24, continue with problems 3-5 on
page 83, focusing particularly on problem 5. Also, read
Section 14 and do problems 1, 2, 4 on page 87.
For Friday, February 26, do problems 2 and 4 on page 87.
Read Section 15 and do problems 2, 3, 5, 9(especially part
(i)), and 11.
For Monday, March 1, do problems 3, 4, 5, 6, parts of 9,
and 11 (pages 89-90).
For Wednesday, March 3, continue with parts of 9,
and 11 (pages 89-90). Read Section 16, and work on problems
2-10 (pp. 93-96).
For Friday, March 5, continue with problems 2-10
(pp. 93-96).
Over Spring break, if you have the time and inclination,
skim Section 19. We will be getting to this stuff a week or
so after break.
For Monday, March 15, continue with problems 5-10
(pp. 93-96).
For Wednesday, March 17, continue with problems 8-10
(p.96). Read Section 17.
For Friday, March 19: read sections 17 and 18. I'll be
lecturing on these sections (the proof of the Jordan curve
theorem) on Friday and probably Monday.
Due on Friday, March 19:
Turn in your portfolio of homework problems for the semester
so far (actually, up to and including Section 15).
I am looking for an indication that you have tried
the assigned problems, and that either you solved them
yourself or you learned (and recorded) something from the
class discussion of the problem. Or both.
The perfect portfolio would be organized and
would have complete, well-written solutions to all of the
problems so far; it could be published as part of a
solution manual for the book.
The good porfolio would be organized and have
well-written, almost complete solutions to almost all of
the problems.
Skipping a few levels in quality, the barely
acceptable portfolio would have something for most
of the problems; the something would be relevant, but
perhaps scrawled on the backs of envelopes or those paper
placemats from Chinese restaurants.
The almost acceptable portfolio would have
something relevant for about half of the assigned
problems.
For Friday, March 26: read section 19 and do problems 3-8
on pages 109 and 113.
For Monday, March 29: continue with problems 6-8 on page
113; also do problem 10 and parts of 9, 11, 12 on page 115.
For Wednesday, April 7: Read section 20, and do problems 1,
3, 4, and parts of 5 and 8 (pp. 120-122).
For Friday, April 9: Read Section 21, and do problems 1, 5,
and 8. If you need help understanding the proof of the main
theorem, try parts of problems 2, 3, 4 (pp. 124, 128).
For Monday, April 12: Do problem 8, p. 128. Also, read
Section 23, and do problem 5 and parts of 1 and 6 (pp. 136 and
140). Try to get started on problems 10, 12, and 13
(pp. 142-143).
For Wednesday, April 14: Continue with 6, 10, 12, and 13
(pp. 140-143).
For Friday, April 16: Read Section 24. Do problem 1, 5,
and 6, and parts of 2 (pp. 146-147). Do all of 8, 9, 10 (p. 150).
For Monday, April 19: Continue with 5, 6, and 8-10. Also
start on 11-13 (p. 152).
For Wednesday, April 21: Continue with problems 10-13.
Also, read section 25, and start on problems 3 and 5 (p. 158).
For Friday, April 23: Continue with problems 11-13,
especially 12 (p. 152), and do problems 3 and 5 (p. 158).
Next week, I will be giving an overview of what we've done
and what would come next: further directions in topology.
There will be no homework, except for working on the
portfolios.
Due on Wednesday, April 28: Turn in your
homework portfolio for Sections 16-25.
Questions or comments? E-mail me at palmieri.2@nd.edu.