Tom Roby's Math 2210Q Home Page (Spring 2014)|
Applied Linear Algebra
Questions or Comments?
COORDINATES: Classes meet Tuesdays and Thursdays
11:00-12:15 in MSB 215 The registrar calls this Section 003, #2644.
PREREQUISITES: MATH 1132, 1152, OR 2142.
TEXT: David C. Lay:
Linear Algebra and Its Applications, 4th Ed., available in
the bookstore. Let me know if you have any trouble getting it.
WEB RESOURCES: The homepage for this course is
http://www.math.uconn.edu/~troby/Math2210S14/. The author also has
a useful site with review sheets and downloadable data
SOFTWARE: In most areas of mathematics it is
frequently helpful to use computer software not only for computations,
but also to explore examples, search for patterns, or test
conjectures. For linear algebra there are several extensive
and sophisticated commercial software packages, including MATLAB,
Maple, and Mathematica. Matlab is particularly good at linear
algebra for applications. All of these can be expensive, depending on
your site license.
An excellent alternative to the above is the free
open-source computer algebra
system Sage. There are many
commands for linear algebra, and a textbook (linked below) has been
written that makes significant use of Sage examples. Sage also
provides a full-fledged programming environment via the
programming language, but you don't need to be a programmer to use
it. I highly recommend trying it out online, and installing a copy
on your computer.
GRADING: Your grade will be based on two midterm exams, a final
exam, homework, and quizzes.
The breakdown of points is:
| Midterms || Final || Quizzes || Homework
|20% each ||30% ||20% ||10% |
EXAMS: The exam dates are already scheduled,
so please mark your calendars now (midterms in class on 27 February and 15
April at usual time; final [tentatively] on 6 May 2014, 10:30-12:30). All
exams (like math itself at this level) are cumulative. No makeups will
be given; instead if you have an approved reason for missing an exam,
the final will count for the appropriately higher percentage.
QUIZZES: Quizzes will be given each Thursday (except
midterm exam days), covering (a) sections from the previous week (at
the level of HW exercises) and (b) the reading assigned for the
current week (at the level of True/False exercises). Your lowest two
quiz scores will be dropped.
HOMEWORK: Homework will be assigned most
weeks, and is DUE at class the following TUESDAY. Since I may discuss
the homework problems in class the day they are due, late assignments
will be accepted only under the most extreme circumstances. Please
let me know as soon as possible if you find yourself with a situation that
might qualify. The lowest written homework score will be dropped in
any event. I've color coded the schedule by week to help clarify what the HW
is for a given week.
You may find some homework problems to be
challenging, leading you to spend lots of time working on them and
sometimes get frustrated. This is natural. I encourage you to work
with other people in person or electronically. It's OK to get
significant help from any resource, but in the end, please write your
own solution in your own words. Copying someone else's work
without credit is plagiarism and will be dealt with according
policy. It also is a poor learning strategy.
ACADEMIC INTEGRITY: Please make sure you
are familiar with and abide by
Student Code governing Academic Integrity in Undergraduate Education
and Research. For quizzes and exams you may not discuss the
material with anyone other than the instructor or offical proctor, and
no calculators, phones, slide rules or other devices designed to aid
communication or computation may be used unless otherwise specifically
indicated on the exam.
CONTENT: Linear Algebra is a beautiful and
important subject, rich in applications within mathematics and to many
other disciplines. For many of you this is the first course to begin bridging
the gap between concrete computations and abstract reasoning.
Understanding the notions of vector spaces, linear (in)dependence,
dimension, and linear transformations will help you make sense of
matrix manipulations at a deeper level, clarifying the underlying
ACCESSIBILITY & DISABILITY ISSUES: Please
contact me and UConn's Center for
Students with Disabilities as soon as possible if you have any
accessibility issues, have a (documented) disability and wish to
discuss academic accommodations, or if you would need assistance in
the event of an emergency.
LEARNING: The only way to learn
mathematics is by doing it! Complete each assignment to the best of
your ability, and get help when you are confused. Come to class
prepared with questions. Don't hesitate to seek help from other
students. Sometimes the point of view of someone who has just figured
something out can be the most helpful.
We will often spend classtime doing things in
groups, presenting mathematics to one another, or having interactive
discussions. There will not be time to "cover" all material in a
lecture format so you will need to read and learn some topics on your
own from the book (or otherwise).
SCHEDULE: I will update the following schedule
over the course of the semester. Generally we will cover three sections
per week, which means splitting a section between two
lectures. Lecture notes are linked section by section: I
recommend you review them before or after lecture, allowing you to
spend lecture time focussing on the material rather than copying
things down. If you have a religious observance that conflicts with
your participation in the course, please meet with me within the first
two weeks of the term to discuss any appropriate accommodations.
I've color coded
the schedule by week to help clarify what the HW is for a given week.
2210Q LECTURE AND ASSIGNMENT SCHEDULE |
|| 1/21 T
|| Intro to Linear Alg & Systems of Eqns.
|| 1, 2, 3, 10, 12, 13, 15, 16, 21, 24, 25, 31, 32
|| 1/23 R
|| Row Reduction & Echelon Forms
|| 2, 10, 13, 14, 19, 21, 24, 29, 31
|| 1/23 R
|| Vector Equations
|| 3, 6, 7, 9, 12, 14, 15, 21, 22, 23, 25 due 1/30
|| 1/28 T
|| Matrix Equations
|| 1, 4, 7, 9, 11, 13, 17, 19, 22, 23, 25, 31
|| 1/30 R
|| Solution Sets of Linear Systems
|| 2, 6, 11, 15, 18, 19, 22, 23, 27, 30 HW
|| 2/4 T
|| Linear Independence
1, 2, 5, 7, 9, 15, 16, 20, 21, 32, 35
|| 2/6 T
|| Linear Transformations
2, 4, 8, 9, 13, 15, 17, 21, 26, 31
|| 2/6 R
|| Matrix of Linear Transformation
1, 2, 5, 13, 15, 20, 23, 26, 32, 34
|| 2/11 T
|| Matrix Operations and Inverses
2, 5, 7, 10, 15, 20, 22, 27, 28
|| 2/13 R
|| Inverse of a Matrix
3, 6, 7, 9, 11, 13, 15, 23, 24, 29, 32, 37
|| 2/18 T
|| Characterizations of Invertible Matrices
1, 3, 5, 8, 11, 13, 15, 17, 26, 28, 35, 40(challenge!)
|| 2/18 T
|| Partitioned matrices
1, 4, 9, 10, 11, 13, 16, 19
| Ch. 1
|| 2/18 T
|| Supplementary Exercises
6, 7, 10 ,18, 22, 23
|| 2/20 R
|| Matrix Factorizations
2, 5, 7, 21, 23b, 24
|| 2/25 T
|| Intro to Determinants
4, 8, 11, 13, 20, 21, 31, 32, 37, 39
|| 2/25 T
|| Properties of Determinants
2, 3, 8, 10, 16, 17, 20, 26, 27, 32, 34, 40
|| 2/25 T
|| Catchup & Review Day
|| Do Practice Midterm by today!
THURSDAY 27 FEBRUARY: FIRST MIDTERM EXAM (through §2.4) |
|| 3/4 T
|| Cramer's Rule & Volumes
4, 5, 6, 13, 16, 22, 23, 26, 29, 30; HW
|| 3/4 T
|| Vector Space & Subspaces
1, 3, 8, 12, 13, 15, 17, 22, 23, 31, 32
|| 3/6 R
|| Null Spaces, Column Spaces & Lin. Transf.
3, 6, 11, 14, 17, 19, 21, 24, 25, 32, 33, 34, 36
|| 3/11 T
|| Bases and Lin Ind. Sets
3, 4, 8, 10, 14, 15, 21, 23, 24, 29, 30, 31;
|| 3/13 R
|| Coordinate Systems
2, 3, 5, 7, 10, 11, 13, 15, 17, 21, 23, 32
Midterm #1 rewrites due.
17-21 MARCH SPRING BREAK NO CLASSES |
|| 3/25 T
|| Dimension of a VS
1, 4, 8, 11, 14, 21, 23, 26, 28, 29
|| 3/25 T
2, 5, 7, 10, 13, 19, 24, 27, 28;
|| 3/27 R
|| Change of Basis
1, 3, 5, 7, 9, 11, 13, 15
|| 4/1 T
|| Eigenvectors & Eigenvalues
2, 6, 7, 11, 13, 15, 19, 21, 23, 24, 25, 27, 31
|| 4/1 T
|| Characteristic Equation
2, 5, 9, 12, 15, 19, 20, 21
|| 4/3 R
1, 4, 5, 9, 11, 15, 17, 21, 24, 26
|| 4/7 T
|| Eigenvectors & Linear Transformations
1, 3, 6, 7, 10 ,15, 16, 23, 25
|| 4/7 T
|| Inner Product & Orthogonality
3, 5, 10, 16, 18, 19, 23, 25, 27, 29
|| 4/10 R
|| Catchup & Review Day
|| Do Practice Midterm 2 by today
TUESDAY 15 APRIL SECOND MIDTERM EXAM (through §5.2) |
|| 4/17 R
|| Orthogonal Sets
3, 6, 8, 9, 11, 14, 20, 21, 23, 26, 27, 28, 29 HW
5.4 and 6.1 due.
|| 4/22 T
|| Orthogonal Projections
1, 6, 7, 9, 11, 13, 17, 21, 23, 24
|| 4/22 T
|| Gram-Schmidt Process
1, 3, 7, 9, 11, 17, 19
|| 4/24 R
|| Least-Squares Problems
3, 5, 7, 9, 11, 17, 19, 21
|| 4/24 R
|| Diagonalization of
1, 3, 5, 8, 10, 13, 17, 19, 25, 29
|| 4/29 T
|| Quadratic Forms
1, 5, 8, 11, 13, 19, 21, 27
|| 4/29 T
|| Constrained Optimization
1, 3, 5, 7, 11
|| 5/1 R
|| Singular Value Decomposition
1, 3, 9, 11, 17
|| 5/1 R
|| Catchup & Review Day
MONDAY 5 MAY 8:00PM–10:00PM FINAL REVIEW IN MSB 215 (Do Practice Final by today)|
TUESDAY 6 MAY 10:30–12:30 FINAL EXAM IN MSB 215 |
Use this form to send me anonymous feedback or to answer the question:
How can I improve your learning in
this class? I will respond to any constructive suggestions
or comments in the space below the form.
Feedback & Responses
- [23 Jan] From today's notes, I'm having trouble understanding why columns 1,2,
and 4 are the pivot columns.
I tried to address this in class. The pivot columns are just the
columns in which the pivots appear; perhaps the real question is identifying
- [26 Jan] Can you go over problem 12 from the 1.1 homework on Tuesday?
I think we did this. You should always feel free to ask about HW
problems at the start of class on Tuesday, and feel free to copy solutions I write
into your HW. I probably won't post more questions like this, but will try to
note them and go over them as requested.
- [29 Jan] I feel that, in the future, solutions to the practice quizzes should
be posted. How do we know that we are prepared for the quiz if we can't check
Thanks for asking. I posted (and emailed for safety) solutions
to the practice quiz. There's only one, since I wanted everyone to have a sense
of the format before the first one. The best way to prepare for the quiz is to
spend more time with HW questions, particularly some of the true/false in each
section. The text provides answers to most odd-numbered problems, so you can try
some of those to check.
- [2 Feb] I do not understand almost any of the 1.5 homework. Is it still due on
Tuesday even though we did not complete the section in class?
Sorry you're having trouble with 1.5. We did finish the notes
for that section on thursday, though. Please do the best you can on the HW and
come to class tuesday with lots of questions! Perhaps this would be a good time
to visit the Q Center?
- [2 Feb] Will solutions to quizzes be posted?
Not usually, but we'll go over them in class after they are
handed back. That allows me to address common issues and make connections that go
beyond just the solutions. As always, if I don't address your specific concern,
feel free to ask!
- [5 Feb] Practice quiz 2?
Sorry, there was only a practice quiz #1, and that was over and
above what I've done in previous semesters. There will also be
practice midterms and finals. Best way to study for the quizzes is to go over
homework problems (assigned and unassigned), particularly the True/False in each
- [8 Feb] Is there any way to get the solutions for the even numbered problems
because it will be great to be able to check them without asking you to go over
them in class which might waste class time if I ask to go over all the even
Hmm. Some problems you can check yourself if they involve getting
an answer you plug back in to check, but for others that won't work. It doesn't
take long to go over just the answers without the solutions if there are some
where you lack confidence in your answer. Buddying up with another student and
comparing answers is also a good strategy. Unfortunately, in real life there is
no solutions manual, so it's a good skill to learn to self-assess how likely you
think it is you solved a problem correctly.
Pedagogically I don't mind at all going over HW problems.
It gives me a chance to address common confusions, and provides a forum for
questions to come out. I don't think it's wasted time.
- [9 Feb] In class could we stress what terms mean more? I understand how to do
things mathematically, but sometimes in the homework I don't quite know what
they're asking because of the lingo.
There's certainly a lot of terminology to wrap one's head around,
especially in the beginning. I do try to give some of the intuition behind the
various definitions as we discuss them. I'll look for opportunities to do more.
Perhaps you could also make sure to ask about any specific HW lingo that you find
- [10 Feb] Since you collect homework on Tuesdays, would it be possible to upload
the answers to the problems (like the ones you were using to go over homework
problems) or hand them out in class so we have something to study off of for the
quiz on Thursday? It would also save class time if we could see the answers
after handing in the homework with the steps to see our mistakes without having
to use class time.
Thanks for the suggestion. I now think a good solution to giving
yourself something to study from is to just scan or snap a picture of your HW for
reference before you hand it in. For various reasons, I think that handing out
canned solutions raises more issues than it solves. Most even problems have an odd
counterpart which you can try to solve and check against the answer. (See also my
reply above to the feedback from 8 Feb.)
- [10 Feb] 30 problems for a homework seems a bit excessive, by the end it is
feeling like busy work
Sorry you feel that way. By all means feel free not to do
problems which you're sure you know how to do, and could do on a quiz. I certainly
would not want to waste anyone's time with exercises only for their fingers, not their
brains. In my experience most students need to do a fair number of problems to
master the various techniques. My basic assumption is that on average students
spend about six hours per week doing HW and studying for a class that meets three
"hours" per week. If you are finding you need significantly more than that,
please see me, and I'll do my best to help!
- [10 Feb] Practice Midterm(s) + Final links do not work.
Thanks for noticing! They become active as the practice tests
become available. I just (on 11 Feb) posted the first practice midterm below, and
the link in the schedule above should also work now.
- [15 Feb] Is the link for the take home quiz posted?
Nope, it only went out by email. If you didn't get it, please
email me directly! It means there's a glitch somewhere in the email system, which
should get resolved asap.
- [18 Feb] Are the chapter 1 supplementary problems mandatory for the homework?
Will we get penalized for not doing them?
The main benefit to doing them, as with all HW, is that you'll
improve your understanding of the material. This may translate later on to higher
scores on quizzes or exams. Supplementary problems have the advantage of helping
you integrate your knowledge from different sections. But as far as an explicit
penalty goes, it would be at most 1–2 points out of five on that week's HW,
which is negligble in the scheme of things.
- [5 Mar] What was the mean score on the test?
Mean and median were both mid-sixties. I'll bring the exact
values to class tomorrow. With the rewrites, if you all take them seriously, I
expect it to be much higher, probably in the 80s.
- [10 Mar] We did not take any notes on 3.3. I took some myself from the book
but I don't feel there are a sufficient amount of examples to do the homework. I
am fairly confused on almost every problem.
I hope this means that you generally like the notes provided for
most sections as an outline of lecture! Still, it's good to learn how to seek
other resources when the ones you used so far are insufficient. These include:
Of course, I can try to eventually create notes for this section or try some other
way to make this material more accessible—that's easier for me if I understand what
students are confused about. But the broader point of becoming more independent in
your learning is a life skill that will serve you well at UConn and beyond.
- Googling the topic and seeing what you find in the way of wikipedia entries,
notes made by others, or videos that show things step by step;
- Discussing things with a classmate or student who may already have had the
- seeking help at the Q Center;
- emailing the instructor specific questions;
- asking on Facebook or other social media;
- asking in class during the time dedicated to this;
- [15 Mar] Did enough people hand in Quiz 5 for everyone to get full credit for it?
- [21 Mar] Very useful.
- [23 Mar] Do we have homework due this Tuesday?
Yes, for §4.3-4 as indicated on the syllabus.
- [15 Apr] Which homework is due Thursday?
All the homework from last week, which would ordinarily have been
due on Tuesday, specifically §5.4 and 6.1.
- [16 Apr] I love the simple layout of the notes with minimal words. They don't
give too much which is overwhelming or too little that I can't make the
connections from step to step. Keep it simple.
Thanks! The Goldilocks Principle in action.
- [17 Apr] Would we have a quiz the Thursday after the midterm?
No. The midterm is enough testing for one week.
- [Date] This is a test.
This is only a test.
NEWS, NOTES, AND HANDOUTS
[16 Feb] I sent an email on 13 Feb to the entire class with (a) the take-home quiz #3
and (b) a link to a video lecture for §2.2. Please email me if you didn't get
it! Notice also that the first practice midterm is now posted.
[23 Feb] Practice Midterm 1 Solutions are now posted. Homework for sections 3.1 and
3.2 postponed until the Tuesday after the exam. We'll go over those sections (which
are computational and straightforward) briefly
this Tuesday, 2/25 before starting the review (revised schedule above).
[5 Mar] Rewrites for Midterm #1 are due Thursday 13 March in class. Please follow
the guidelines in the handout below. This is a great opportunity to learn
the material you missed and improve your grade.
Back to my home page.