12/22/18: Your grades in class have been assigned and can now be seen
in your records. Thank you all for a great semester of learning Linear
Algebra! Well, for me it was not so much learning, but more of a
refining my knowledge... Have a great break and very happy holidays!
12/12/18: Solutions to Sample Final
are now posted.
12/12/18: After classes are over, I am going to keep my office hours
on Thursday, December 13, 11:15-12:15. I will also hold extra office
hours the same day in the late afternoon, 3:30-4:30. I am always
available by email and appointment.
12/11/18: Here is some statistics for Midterm II. For Section
40: the mean is 43.5 and the standard deviation is 8.9. For Section
50: the mean is 45.5 and the standard deviation is 11.5. Great
improvement for all of you!
12/11/18: I have posted Solutions to our
Midterm II.
12/8/18: A sample Final Exam (a
Spring 2017 Final) is posted on the Homework and Sample Tests
page. Note: To correspond with our coverage, Problem 1(c) should ask
about an inner product on ℝ2 and use the formula
w1 z 1 + w2 z 2; Skip
Problems 1(f,g); Replace the word "range" with "image" in Problem 7;
Skip Problems 7(b,c).
12/8/18: Coverage for the Saturday, December 15 (Section 40)
and Monday, December 17 (Section 50) Final (in your regular
classroom) is all we have studied in this class. This will be Sections
1.1-1.6, 1.8-1.9, 2.1-2.6, 3.1-3.5 through p. 171, 4.1-4.2 (through
p. 196), 4.3 (through Example 4.25 on p. 206), 4.4, 5.2, 6.1-6.2
(ignoring batteries and power within Electrical-Mechanical
Correspondence), 7.1-7.2, 8.2 (through p. 417), 8.3, 8.5 (through
p. 438), 8.6 (pp. 447-451) of the textbook. How to get ready for
the test? The best way would be to try to solve as many problems
as you can on your own (opening the textbook when needed, and not
timing yourself) from the sample final
exam, the homeworks, and the textbook. For those problems you
cannot solve, it may be a good idea to discuss them with your friends,
i.e., your study group. Come to my office hours to get hints or other
help. Go over homework problems again without consulting your
solutions and look for problems from exams in similar classes on the
web: search for Linear Algebra tests, exams, midterms,
finals, etc. When you know you can get an idea of how you might
approach most of the problems right away, you may feel more sure that
you will do well on our exam. Good luck!
12/6/18: Sam Payne has pointed out to me that I have not weeded out
all the arithmetic errors from my solution of Problem 4 on Sample
Midterm II. I have corrected it and posted a new version. A few more
points off my exam score!
12/5/18: I have made an error in the original posting of solution to
Problem 4 on Sample Midterm II and now corrected it. See Problem 4
posted separately.
12/5/18: I forgot that I was supposed to give an oral exam on
Thursday, December 6, till noon. In relation to this, I need to move
my Thursday, December 6, office hours from 11:15-12:05 to 12:05-1:15
p.m. I apologize for the late notice.
12/5/18: I have posted solutions to Sample Midterm II on
the Homework
page.
12/5/18: Today at the end of the class, I made a computational error
in finding the third element u3 of the orthonormal
basis in which the matrix A diagonalizes. A correct solution is
posted in the Solutions to Sample Midterm
II.
12/4/18: In addition to my regular office hours, I will be holding
extra office hours on Wednesday, December 5, from 4 to 5 p.m. before
the midterm.
12/3/18: Selected solutions to recommended problems to 8.3, 8.5, and
8.6 are posted.
12/2/18: I have removed page 452 (the text part) from the exam's
coverage.
12/1/18: I have just posted HW 9 solutions and practice problems to
8.3, 8.5. 8.6.
11/26/18: I have updated Homework 9 with a few more hints. Please
reload the Homework 9 page to make sure you see the latest version.
11/26/18: A sample Midterm Exam II is
posted on the Homework page.
11/26/18: Coverage for the Friday, December 7, Midterm Exam
II (in your regular classroom) is basically all we will have
studied since the previous midterm. This will be Sections 4.1-4.2
(through p. 196), 4.3 (through Example 4.25 on p. 206), 4.4, 5.2,
6.1-6.2 (ignoring batteries and power within Electrical-Mechanical
Correspondence), 7.1-7.2, 8.2 (through p. 417), 8.3, 8.5 (through
p. 438), 8.6 (pp. 447-451). How to get ready for the test? The
best way would be to try to solve as many problems as you can on your
own (opening the textbook when needed, and not timing yourself) from
the sample midterm exam, the homeworks,
and the textbook. For those problems you cannot solve, it may be a
good idea to discuss them with your friends, i.e., your study
group. Come to my office hours to get hints or other help. Go over
homework problems again without consulting your solutions and look for
problems from exams in similar classes on the web: search for Linear
Algebra tests, exams, midterms, finals, etc. When you know you
can get an idea of how you might approach most of the problems right
away, you may feel more sure that you will do well on our exam. Good
luck!
11/23/18: I have updated Homework 9 with a few hints and notes, such
as that the answer for the equilibrium configuration in Exercise
6.1.16(c) in the Students' Solutions Manual is incorrect. Please
reload the Homework 9 page to make sure you see the latest version.
11/18/18:
Homework 9, due Friday, November 30, has been posted. Have a great
Thanksgiving, but do not forget Linear Algebra!
11/15/18: I have updated Homework 8 with a few hints and notes. Please
reload that page to make sure you see the latest version dated
2018-11-15, 12:51:31 CST.
11/15/18: There is another error in the Students' Solution Manual,
found by Cassandra Chanthamontry: the answer to Exercise 7.2.1(c-ii)
in the Students' Solution Manual is incorrect. Also, in Exercise
6.1.8(b) in the textbook, "Answer Exercise 6.1.8..." should be
replaced with "Answer Part (a)..."
11/13/18: There is an error in the Students' Solution Manual,
discovered by Jacob Boerjan. There is a weird shift in the solution
numbering in 7.2.6. Solution (a) answers the unlabeled problem to draw
the given parallelogram. Solution (c) answers Question (b), Solution
(g) answers Question (f).
11/13/18: I have moved Problem 6.1.6 from the Assigned part of
Homework 8 to the Challenge part and replaced it with Problem
6.1.3. Make sure to reload the page to see the change.
11/13/18: Selected solutions to Homeworks 6 and 7 are now posted in
the Homework page.
11/12/18: I have added hints to Problem 7.2.1(c,f) on Homework
8. Reload the Homework 8 page, if you do not see the hints.
11/9/18:
Homework 8, due Friday, November 16, has been posted. I am heading
back to Minnesota and looking forward to seeing you all on
Monday. Have a great weekend!
11/3/18: Since I will be out of the country, I will not be holding any
office hours during the week of November 5-9, unfortunately. But feel
free to send me a message with questions, and I will respond from
China.
11/2/18:
Homework 7, due Friday, November 9, has been posted. Bring it to
class on Friday as usual: Prof. Westerland, who will be substituting
for me, will pick it up.
10/31/18: During the week of November 5-9, I will be out of town at a
conference in China and asked two professors to substitute for me in
each of my sections. I will not be able to hold office hours that
week, but I will be available by e-mail for questions. There will
still be homework due Friday, November 9, as usual.
10/29/18: I have changed the reading part of Homework 6 slightly.
10/26/18:
Homework 6, due Friday, November 2, has been posted. Reminder:
Late homework is penalized. If you turn in your homework after the
beginning of class, penalty will be assessed after the second
occurrence.
10/23/18: I have posted Solutions to our
Midterm I.
10/22/18: Here is some statistics for Midterm 1. For Section
40: the mean was 30.4 and the standard deviation was 10.6. For Section
50: the mean was 37.1 and the standard deviation was 12.8.
10/19/18: Congratulations on getting through the first exam! We will
discuss solutions of it on Monday. No homework will be due next week.
10/17/18: Selected solutions to HW 5 are posted now.
10/17/18: Our Undergraduate Office (VinH 115) used to offer a list
of private tutors, but has abolished it starting this Fall. One
Math TA has replaced it with a list on the
web: https://umnprivatemathtutorslist.com/list. It
may come handy, if you need a tutor.
10/17/18: You may be sure that a problem on checking positive
definiteness of a symmetric matrix and completing the square (as in
the last in-class example, see also Section 3.5 before p. 171) will be
on the upcoming Midterm 1.
10/17/18: I have been posting solutions to selected homework and
sample midterm problems on
the
Homework page. Selected solutions to HW 5 are still coming.
10/15/18: I have added a hint to Problem 3.3.48(i) on the set of
recommended practice problems for Sections 3.3-3.5 and moved it to the
challenge problem section.
10/10/18: I have posted suggested practice problems from Sections
3.3-3.5 on
the
Homework page. This problem set will NOT be collected or
graded. It is just a way for you to practice on problem solving on the
material of the last sections of Chapter 3 as part of your preparation
for Midterm Exam I.
10/8/18, 2 a.m.: A sample Midterm Exam
I is posted on the Homework page.
10/7/18: Coverage for the Friday, October 19, Midterm Exam
I (in your regular classroom) is basically all we will have studied
before it. This will be Sections 1.1-1.6, 1.8-1.9, 2.1-2.6, 3.1-3.5
through p. 171. How to get ready for the test? The best way
would be to try to solve as many problems as you can on your own
(opening the textbook when needed, and not timing yourself) from
the sample midterm exam, which will be
posted soon, the homeworks, and the textbook. For those problems you
cannot solve, it may be a good idea to discuss them with your friends,
i.e., your study group. Come to my office hours to get hints or other
help. Go over homework problems again without consulting your
solutions and look for problems from exams in similar classes on the
web: search for Linear Algebra tests, exams, midterms,
finals, etc. When you know you can get an idea of how you might
approach most of the problems right away, you may feel more sure that
you will do well on our exam. Good luck!
9/26/18: Solutions to past homeworks are now available on the
Homework page.
9/26/18: Please address our grader Peihang Wu only in relation to
questions on how your homework has been graded. Questions not related
to grading should be addressed to me rather than him, though.
9/24/18: Homework 3 problem 2.1.7 (a) is asking whether the given
functions are elements of the vector
space F(ℝ2,
ℝ2), i.e., functions from ℝ2
to ℝ2.
9/21/18: I have just removed a couple of problems from Homework 3, as
compared to my original posting of it about an hour ago. The correct
homework assignment is supposed to end at Exercise 2.3.4 (b,d,f).
9/21/18:
Homework 3, due Friday, September 28, has been posted. Reminder:
Late homework is penalized. If you turn in your homework after the
beginning of class, penalty will be assessed after the second
occurrence.
9/21/18: I am changing my 2:30-3:20 office hours for all Wednesdays
from now on to 11:15-12:05 on Thursdays. An experiment with a similar
change this week has been popular with most students.
9/17/18: If you have a question to the grader, you may send a message
to him at wu000294@umn.edu. If you need to see him, make an
appointment. His name is Peihang Wu. Questions not related to grading
should be addressed to me rather than him, though.
9/17/18: I need to cancel my 2:30-3:20 office hours this Wednesday,
September 19. I will hold office hours on Thursday, September 20,
11:15-12:05, instead.
9/14/18:
Homework 2, due Friday, September 21, has been posted. Reminder:
Late homework is penalized. If you turn in your homework after the
beginning of class, penalty will be assessed after the second
occurrence.
9/14/18: Faced with the first homework, you might have been
contemplating the idea to participate in a study
group. Various rooms
throughout the Twin Cities campuses are available for small groups
of students to work together or individual study. You may
also reserve a space in the
libraries for group study. And check
out How
to Form a Successful Study Group.
9/13/18: The Undergraduate Mathematics Research Seminar is back
this semester. The goal is to help undergraduates communicate
mathematics and get more people interested in seeing what math
research could be about. If you would like to speak in the seminar
and/or be added to its email list, you can contact the seminar
organizer Harini (chand409@umn.edu). The seminar will be on Tuesdays
at 12:20PM in Vincent 364. Details can also be found on
the seminar
website.
9/12/18: It seems like little, if any, free tutoring service is
regularly scheduled for Math 4242 by the School of
Mathematics and SMART
Learning Commons at Walter, Wilson, and Magrath
Libraries. However, you may find a one-on-one SMART tutor at
https://www.lib.umn.edu/smart/tutor-schedules. There is also a
similar
Multicultural Center for Academic Excellence, which offers free
tutoring, a study place, jam sessions before exams, and more. They
definitely have free tutors who could help with Math 4242 on the
schedule.
9/11/18: I would like to emphasize that, according to the principle
"You must show all work," a full answer to a True/False exercise is
not merely a T or F, but must include a detailed explanation of
the reason, e.g., a proof, or a counterexample, or a reference to a
result in the text, etc.
9/11/18: Clarification for Section 1.4 and Exercise 1.4.14:
an elementary permutation matrix is a matrix obtained from the
identity matrix by a single row interchange.
9/6/18: Now a dedicated and
renewed Library
Course Page offers links to the text and Students' Solution
Manual, as well as additional study resources, such as encyclopedias
and other reference materials, alternative textbooks, and study
guides. Note: copying solutions from the solution manual can
place you in violation of scholastic honesty. Many solutions only
provide the final answer anyway, while for full credit you must also
supply an explanation of how you this is found. A more serious problem
is that passive reading of solutions will not get you ready for the
exams. You should try hard to do problems on your own.
9/5/18: I have posted the
first
Homework, due Friday, September 14. It will be collected and
(partially) graded. Making sure to do homework on your own, possibly
collaborating with others in a study group, will be the best way to
get ready for the exams. Your friend is your TA. :-)
9/5/18: 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. Some students find it helpful to read the
material before it is covered in class, some prefer to do the reading
after class.
Last modified: (2018-12-22 14:57:05 CST)