12/10/19: Given that we will be having a Final (in Kolthoff Hall 134)
starting at 12:20 tomorrow, Wednesday, December 11, I have to move my
office hours to 11:15-12:05, which could actually be handy for your
last-minute questions.
12/10/19: Given that we will be having a Final (in Kolthoff Hall 134)
starting at 12:20 tomorrow, Wednesday, December 11, I have to move my
office hours to 11:15-12:05, which could actually be handy for your
last-minute questions.
12/9/19: Extra office hours tomorrow, Tuesday, December 10, 1:25-2:15
p.m.
12/8/19: Problem 3 on the Spring 2019 and problems on smooth manifolds
on earlier prelims are definitely not on our syllabus or our Final
coverage.
12/5/19: I have updated the sections of the textbook to read for HW 12
and the remaining classes.
12/5/19: Sasha Pevzner has pointed out a typo in the Fall 2019
Preliminary Written Exam, Problem 4. It should be the obvious
inclusion into
R2. And the problem should not be worded this way,
anyway, because in different courses and textbooks, the surjectivity
of a covering map might be an implicit or explicit requirement. In our
course, the requirement was explicit, so that our answer to the
problem will be: by definition, a covering map must be surjective. I
would reword the problem in the following way: Apart from the lack of
surjectivity, what other condition of a covering projection is
violated by that inclusion map and why?
12/3/19: We have got a room for the Final Exam: Kolthoff Hall
134. This is almost directly across the Mall from Vincent Hall. I
remind you that the exam will start an hour and 5 minutes earlier than
our regular class meeting time. The exam will go from 12:20 to 2:20
pm on December 11. The rules will be the same as described on the
Fall 2019 Preliminary Written Exam. See the link below.
12/3/19: For the 12/9/19 review before the Final, I suggest that look
at the Fall 2019 (and, possibly, Spring 2019) Preliminary Written
Exam(s) (Part A) and ask me which problems you would like to
discuss. See
https://math.umn.edu/requirements/previous-written-exams.
11/26/19: Homework 12, due Friday, December 6, is posted. Have fun!
11/24/19: As per our joint agreement, the Final Exam will
be 12:20-2:20 p.m. on Wednesday, December 11, the last day of
classes. Note that it will start one hour earlier than our regular
class time. The room is to be announced.
11/18/19: Homework 11 is posted. Have fun!
11/13/19: I need to move my Thursday office hours this week up
one hour. My office hours currently stand at: M 3:35-4:25, W
12:20-1:10, Th: 2:30-3:20. However, this week they are: M 3:35-4:25, W
12:20-1:10, Th: 1:30-2:20. You are always welcome to make an
appointment, though.
11/13/19, 1:50 am: Homework 10 is posted. Sorry about the delay. I
have been so busy this week that almost totally forgot about the
homework!
11/10/19: One relation for quaternions is erroneously missing from the
homework Problem 3.9.12: jk = i. BTW, unit quaternions are those of
unit length, if you use the standard Euclidean inner product
on R4= H. You can work with quaternions in a
way similar to that with complex numbers, but remember that
multiplication is not commutative. For example, the inverse of a
nonzero quaternion a+bi is (a-bi)/(a2+b2). It is
useful for the problem to find a similar formula for any nonzero
quaternion.
11/4/19: Homework 9 is posted.
11/4/19: I need to resechedule my Thursday office hours this week to
Friday, 12:20-1:10 p.m., just for this week. Thus, my office hours
currently stand at: M 3:35-4:25, W 12:20-1:10, Th: 2:30-3:20. However,
this week they are: M 3:35-4:25, W 12:20-1:10, F: 12:20-1:10. You are
always welcome to make an appointment, though.
10/30/19, 12:25 a.m.: Homework 8 is posted.
10/29/19, 1 a.m.: I am moving my Tuesday office hours to Thursday,
2:30-3:20 p.m. for the rest of the term. I believe it will better
suite the needs, as nobody has been showing up at my office hours on
Tuesday. Thus, my office hours currently stand at: M 3:35-4:25, W
12:20-1:10, Th: 2:30-3:20. Sorry for the late notice.
10/26/19: In problem 2.11.11 on Homework 7, it is assumed that the
dimensions of K1 and K2 are finite.
10/24/19: The final exam schedule suggests that our final exam should
be held 10:30-12:30, Saturday, December 14. I am thinking of giving
the final on an earlier date. Let me know if this appeals to you.
10/24/19: Problem 2.11.10 on Homework 7 was there by mistake, as a
leftover from the file which contained Homework 6. I have removed
2.11.10 from HW 7.
10/22/19, 2 a.m.: Homework 7 is posted.
10/16/19: Homework 6 is posted. Sorry for the delay. I have made the
homework not too long, accordingly.
10/9/19: Tomas has pointed a typo in one of the homework problems. In
Exercise 2.11.4(a), just ignore the "and a single 2-cell" line.
10/7/19: Homework 5 is posted.
10/2/19: In Problem 2.2.23(ii) on Homework 4, the space X should be
assumed Hausdorff and the existence of a partition of unity
subordinate to the covering should also be assumed. This is the
drawback of using a very recent textbook: there are inevitably more
errors in them, as compared to those which passed the time check. I
have reported this error, which was pointed to me by Tomas, to the
author.
10/1/19: Homework 4 is posted. Sorry for the delay, but it is a little
shorter this time around.
10/1/19: I will be holding office hours today from 12:05 to 1:25
p.m. These Tuesday office hours will replace my Thursday office hours
this week and for the rest of the semester. Sorry about a short
notice.
9/27/19: Note that the second definition of an extreme point of a
convex set in the textbook, the one given in parentheses after the
definition of a face, Definition 2.1.12, has to be corrected to
"implies x = y or x = z." Use these definitions for arbitrary convex
sets. For polytopes, it is equivalent to the half-space definition I
gave in class on Wednesday.
9/23/19: Homework 3 is posted.
9/23/19: I have to reschedule my today's office hours, which are
normally 3:35-4:25, to 12:20-1:10 p.m. If you wanted to see me tonight
and cannot see me within the rescheduled time, please make an
appointment.
9/22/19: In problem 1.5.19 (iii) on Homework 2, the weird notation,
dotted I, means the boundary {0,1} of the interval.
9/16/19: Homework 2 is posted on the class web page!
9/16/19: Suggestion on doing homework: I believe working in study
groups and consulting the hints is beneficial to learning things
neither is cheating. But give the problem a thought before
discussing it with friends or consulting the hints section.
9/16/19: If you have questions related to grading, make an
appointment with our grader Wenjie Lu at lu000005 at umn.edu, office: 522
Vincent Hall,.
9/13/19, 9:28 p.m.: Note that I have changed my original correction,
which was not quite correct, below.
9/13/19: The hint in the textbook to HW Problem 1.9.19 has a couple
of typos and needs to be corrected to be understandable. Here is the
correction. You define A(n) := the set of points on A1
with the x-coordinate: 0 < x ≤ 1/n. Then to show that S is not
path connected, for any continuous path ω in S, show that the
image ω(I) lies in S\A(n) for some n. Note that this set
S\A(n) has two obvious connected components: A2 and
A1\A(n). The hint to part (b) and the proof of the claims
that ω(I) is contained in S\A(n) for Part (a) and C\A(n) for
Part (b) do not seem to have typos.
9/11/19: I need to move my Thursday, 09/12/2019, office hours this
week to Friday, 09/13/2019, 11:15-12:05. If you wanted to see me at
my office hours on Thursday, but cannot see me on Friday, make an
appointment to see me some other time.
9/9/19: Since I am going a little slower in class than I was
planning to, I am putting off the due date for Homework 1 to next
Monday.
9/4/19: Homework 1 is posted on the class web page!
9/4/19: I have done some research regarding the two editions of the
textbook. The Library pretends to have online versions of the 1st and
2nd editions, but both links lead to the 2nd one. The 2nd edition
corrects a few errors and makes minor changes in exercises. To access
a full copy of the online edition, you should use the buttons
"Download" or "Read online" in the upper right corner of the Taylor &
Francis web page, if you follow the link from the UofM Library. If you
prefer to download chapters one by one, use the "download" buttons for
individual chapters.
Updated corrections are available online at
http://www.math.iitb.ac.in/~ars/algtoperr.pdf.
I will be giving homework using the 2nd edition.
9/4/19: I recommend the following way to study for this class. Attend
each class, take notes, participate in class actively. After each
class review your notes and study the corresponding part of the
text. You can find out which part of the text at the Class Outlines
page. Then do the assigned homework problems pertinent to that
material. I also encourage you to work in study groups on the
homework, as you probably did in the first term.
1
9/4/19: If you need to register for this course, please, send a
message to Stephanie Lawson at ugrad@math.umn.edu and ask for a permission number. If
permission is granted, go to OneStop and register.
Last modified: (2020-01-17 01:31:54 CST)