General Information:
Meeting Time:  MWF, 9:00  9:50 
Location:  Millington 100

Instructor:  Ryan Vinroot
Office: Jones 130
Office Hours: Wed 12 and Thurs 35 (also by appointment).

Announcements:  All announcements and course information will be on
this webpage. In particular, I will not be using Blackboard.

Textbook:  Linear Algebra, Fourth Edition, by
Stephen H. Friedberg, Arnold J. Insel, and Lawrence E. Spence 
Grade Breakdown:  Midterm  30%, Homework and Quizzes
 30%, Final Exam  35%, Class Participation  5%. The
grading scale will be based on the standard 10point scale, as follows:
A: 93100, A: 9092, B+: 8789, B: 8386, B:
8082, C+: 7779, C: 7376, C: 7072, D+: 6769, D: 6366, D: 6062, F:
059. 
Attendance & Lecture Policy: 
It is expected that you attend all
lectures, with exceptions minimized. It is greatly appreciated when you
are on time. Please do your best to stay awake and attentive during
lecture, please do not email or text during lecture, and keep all cell
phones/hand held devices/laptops put away during lecture. While it is
understandable that you may miss a lecture here and there, or be sleepy in
class once in awhile, repeated absences, late arrivals, naps, or general
nonattentiveness will negatively affect your class participation score.
Any legitimate absence for a test or quiz must be discussed with me (or the
Dean of Students office) *prior* to the test or quiz date.

Calculator Policy: 
Calculators will not be needed or allowed on quizzes or exams. Calculators
could potentially be useful on some homework problems, but there is no
requirement to buy any particular calculator for this purpose. 
Prerequisites:  Linear Algebra (Math 211) and Foundations of
Mathematics (Math 214). Both of these are absolutely crucial for
background. You may find this course extremely difficult if you did not
get at least a B in both of these courses. 

Course Summary:
A more suitable title for this course might be The Theory of Vector Spaces. The main goals of this course are to (1) prove a lot of the results from Math
211 in the context of abstract vector spaces, (2) generalize and expand these results for
abstract vectors spaces, and (3) study the theory of canonical forms and inner
products. In particular, this course will be very prooftheoretic (making Math
214 absolutely crucial), and a
parallel goal will be for you to develop your proofwriting skills in the
context of vector spaces. All of the techniques you learned in Math 211 are
crucial as well, as they serve as basic examples on which the more general
theory we will develop is based.
We will begin the course by reminding ourselves of the abstract definition of a
vector space, and we will immediately broaden our view of vector spaces by
realizing that the scalars need not be the set of real numbers, but can also be
the complex numbers, the rational numbers, or in fact any field (in the
algebraic sense). We will cover Chapters 13 in the first third of the course,
which covers a lot of the familiar topics from Math 211 (such as bases,
dimension, linear transformations, and invertibility). We will prove all of
the claims in the sections we cover, and we will introduce and prove new
concepts and results as well (such as dual bases, in Sec. 2.6). There will be less
concentration on examples in these chapters, because the most important
examples are covered in Math 211. Examples we will discuss will concentrate on
those which go beyond those covered in Math 211.
In the second third of the course, we will review determinants (Section 4.4),
and realize the determinant as the unique (up to scalar) alternating
multilinear form on the space of square matrices (Section 4.5). We will then
review the basic idea of eigenvalues, and introduce a few new concepts
(Sections 5.1, 5.2, and 5.4).
After material from Chapter 5, we will move immediately to the theory of
canonical forms in Chapter 7. The rest of the course will dedicated to the
study of
Jordan and rational canonical forms, and to get as far as possible through the
theory of inner product spaces in Chapter 6.
Dates & Course Announcements:
Midterm and Final Exams:
As agreed, your midterm grade will be determined by your 3 highest quiz scores,
plus your highest HW score. The
final exam is scheduled to be on Fri, May 6, 9 AM12 Noon.
Exam Calendar (Tentative):
Exam 
Date 
Time/Due 
Location

Final Exam 
Fri, May 6 
9 AM12 Noon 
Millington 100

Class Announcements:
 All relevant announcements will be listed here. Check back frequently (don't forget
to refresh your browser) for updates.
 Important Dates and Class Holidays:
 Fri, Jan 29: ADD/DROP DEADLINE
 Sat, Mar 5  Sun, Mar 13: NO CLASS (Spring Break)
 Fri, Mar 18: WITHDRAW DEADLINE
 Fri, May 6, 9 AM  12 Noon: FINAL EXAM
 (1/20) My office hours during the first short week of class are as follows:
Wed Jan 20: 12 and 45, Thurs Jan 21: 23, Fri Jan 22: 23.
 (1/20) Between our first and second meetings of class, you need to read
the following sections in the book: Sections 1.1 and 1.2, and Appendices A,
B, and C.
 (1/20) Quiz 1 will be on Monday, Jan 25, at the beginning of class. It
will cover Section 1.2 and Appendix C.
 (1/21) I have to shift (but extend) my office hours today (Thurs, Jan 21).
They will be 2:304.
 (1/25) Quiz 1 is shifted to Wed, Jan 27, due to class being canceled on
Monday. Also, HW1 is now due on Mon, Feb 1.
 (1/25) My office hours today, Mon, Jan 25, will be 2:304.
 (1/27) My office hours for the rest of this week are: Wed, Jan 27 (today),
12, and Thurs, Jan 28, 35.
 (2/1) My regular weekly office hours will be Wed 12 and Thurs 35, and I
will have an extra office hour either on Fridays (if HW is due on Mon) or on
Mondays (if HW is due on Fri).
 (2/8) Quiz 2 will be in two weeks, on Mon, Feb 22.
 (2/10) I have to shift my office hours to 3:304:30 today (Wed), instead of
12. I apologize for any inconvenience. I will have my normal 35 office
hours on this Thurs.
 (2/19) I will have an extra office hour today (Fri, Feb 19), 2:303:30.
Remember that Quiz 2 is on Mon, Feb 22.
 (2/22) I will have an extra office hour today (Mon, Feb 22), 12.
 (2/29) I will have "open door" office hours tomorrow, Tues Mar 1, between
10 and 3. Come by any time during those hours and knock on my door.
 (3/14) I will have walkin office hours tomorrow, Tues Mar 15, between
10:30 and 2:30. Come knock on my door during those times for any questions.
I will have my normally scheduled office hours today as well.
 (3/18) Quiz 3 will be next Friday, Mar 25. Quiz 3 will cover Sections
2.12.4, but with a conentration on Sec. 2.4 (Isomorphisms).
 (3/28) I will have additional office hours this Tues, Mar 29, 12:303:00.
 (4/4) I will have additional office hours today, Mon, Apr 4, 12, and
tomorrow, Tues, Apr 5, 1012.
 (4/4) Quiz 4 will be next Mon, Apr 11. It will cover Sec. 4.2 on
determinants. A nice summary of the results covered is given in Sec. 4.4,
through the bottom of p. 235 (all except for the last line).
 (4/5) Quiz 4 will instead be next Wed, Apr 13. It will cover the same
material as previously planned.
 (4/6) So that you can prepare for your own time management, the following
is the schedule for the final HWs and quizzes for this semester:
Quiz 4: Wed, Apr 13
HW8: Due Mon, Apr 18
Quiz 5: Fri, Apr 22
HW9: Due Mon, Apr 25
 (4/18) The last homework has been posted, and it is due next Mon, Apr 25.
The last quiz will be this Fri, Apr 22.
 (4/20) My office hours today will be shifted, but extended, 23:30. My
office hours on Thurs, Apr 21, will be 1011:30 in addition to the regular 35.
 (4/27) My office hours this week are as follows: Today (Wed, Apr 27) 45,
and tomorrow (Thurs, Apr 28) 1011 and 35.
 (4/28) My office hours during the first week of exams, leading up to our
final exam (Fri, May 6, 9 AM, Millington 100) will be as follows:
Mon, May 2: 12:304
Tues, May 3: 112 and 35
Wed, May 4: 102 and 35
Thur, May 5: 12:304
I give the final exam for my other course on Thurs, May 5, 912, so I will not
be available then.
Homework & Quizzes:
Homework problems and quizzes will be a very important
part of the course, and there will be homework assigned most weeks. Completion of all homework problems is required, and your
grade on a homework assignment will be based on completeness, as well as on the
details of the solutions of the problems graded. Solutions should be written
carefully and neatly, with attention paid to the completeness and clarity of
your proofs and steps. You may work with other students when you are figuring out how to
do homework problems. However, you should be alone when you write up these
solutions. That is, working with other students is only allowed when
discussing the problems, but not when you are writing the solutions themselves. You should not, under any
circumstances, attempt to look up solutions or hints to problems online. I
will consider this plagiarism, an honor offense. You are always welcome to
come to my office hours or to email me if you need any hints or help on
homework problems.
Homework is due at the beginning of
class on the due date of the assignment. Homework turned in by 5 PM on the due
date, but after the start of class, will be allowed once without penalty, and after once will be marked of
10%. Homework turned in after 5 PM the due date will be marked off 20% for each day
late. Any homework turned in late can be turned in on my office door, and
please write down the date and time you turned in the work on your paper. If there are serious reasons for you not getting homework in on time
(severe illness, injury, or family issues, for example),
you should go through the Dean of Students office so that they can let me know.
Please feel free to ask me about this policy if it is not clear.
Homework (and Quiz, see below) scores will each be out of 50 points. Some of
the assigned HW problems will be scored in detail, others for completeness. Your
lowest HW and lowest Quiz scores will be dropped at the end of the semester.
Assignment 
Problems 
Due Date 
1  1.2 #7, 8, 12, 18, 21 1.3 #19, 20

Mon, Feb 1 
2  1.3 #13, 15, 23, 31(a,b) 1.4 #10, 13, 1.5 #9

Mon, Feb 8 
3  1.3 #12, 1.6 #16, 22, 29(a), 31, 32 1.7 #4

Mon, Feb 15 
4  2.1 #13, 14, 15, 28 2.2 #4 (also prove T is linear), 8, 13

Fri, Feb 26 
5a  2.3 #3, 12(a), 13, 2.4 #16 
Fri, Mar 4 
5b  2.3 #12(b,c), 2.4 #9, 2.5 #5, 10 
Fri, Mar 18 
6  2.4 #19, 2.6 #6, 7, 13(a,b), 17 3.1 #2, 3.2 #14 
Wed, Mar 30 
7  3.2 #4, 7, 8 4.1 #3, 9, 4.2 #20, 25 
Wed, Apr 6 
8  4.2 #4, 29 4.3 #12, 15, 17, 20, 21 
Mon, Apr 18 
9  4.5 #16, 17 6.8 #2, 5(a,b), 6 
Mon, Apr 25 
Final Review Material  1.2 #13, 17, 1.3 #14, 30, 1.4 #12,
14 1.5 #3(af), 11, 14, 1.6 #6, 12, 23 1.7  Understand Theorems
1.12, 1.13 2.1 #4, 6, 20, 33, 2.2 #5, 10 2.3 #4, 11, 2.4 #3,
15, 18 2.4 #3, 15, 18, 2.5 #6(a,b), 11 2.6 #3, 15, 3.1 #3,
3.2 #5, 17 4.1 #6, 4.2 #3, 10, 26, 4.3 #11, 13, 24 4.5
 Understand definitions from notes and the book, and Theorem 4.12 6.8
#4(ad), 5(c), also understand notes from class 
Not Due 
Quizzes:
There will be several (between 4 and 6) quizzes during the semester, and each will count the
same weight as a homework score. Quizzes will be announced the week before
they are given, along with what material they will cover. Quizzes will
typically be given at the beginning of class. There will be no makeup
quizzes, unless your absence is discussed with me prior to the quiz, or there
is a serious issue which is reported through the Dean of Students. The quiz solutions will be posted below
throughout the semester, following each quiz:
Quiz 1 solutions.
Quiz 2 solutions.
Quiz 3 solutions.
Quiz 4 solutions.
Quiz 5 solutions.
