Math 4377/6308
Advanced Linear
Algebra I
Fall 2013
Endofterm announcements:
 Office hours for December 2 and 4 are
cancelled, as I will be out of town at a
conference. Lectures will continue as
normal, with guest lecturers. HW 11 should
still be turned in during lecture on Wednesday,
December 4.
 The final exam is Friday, December 13, from
58pm, in the usual classroom (F 154). It
will be similar in structure to the two tests
and is cumulative  all topics covered in
lecture this semester are fair game.
 The week of the final exam, there will be a
review session on Tuesday, December 10 from
23pm in PGH 646. This will be an informal
review session  I will not prepare a
presentation, but will be available to answer
questions and review details of homework
assignments, tests, etc.
 Office hours the week of the final exam will
be 10am12pm Thursday, Dec 12 and 23pm Friday,
Dec 13. If you have questions and cannot
come during these times or to the review
session, email me and I will either answer your
questions via email or will set up an alternate
time to meet.
Instructor: Vaughn Climenhaga
 Office: 651A PGH
 Office hours: Mondays and Wednesdays,
23pm or by appointment
 Email: climenha [at] math.uh.edu
Course description:
 Lectures: Mondays and Wednesdays,
45:30pm, room F 154
 Textbook: Linear Algebra and its
Applications, second edition, by Peter D.
Lax. (Wiley, 2007)
 Course
syllabus
 The course will cover Chapters 17 of the
textbook. Topics include vector spaces and
linear maps from the abstract point of view;
determinant, trace, and spectral theory
(eigenvalues, eigenvectors) of linear maps; and
the structure of Euclidean space. Some
topics appear similar to those in Math 2331, but
in this course we will take a more abstract
approach and discuss the topics in more
generality and rigour. In particular,
note that this is a proof based course.
In addition to the
office hours listed above, you are encouraged to
make use of the tutoring resources available to
you at CASA.
You may occasionally find it helpful to have access
to other resources
that give a more expanded and detailed presentation
of various topics than is available in Lax’s book or
in the lecture notes. To this end I suggest the
following list of external references, which are
freely available online.
 “A First
Course in Linear Algebra”, by Robert A.
Beezer, University of Puget Sound. Long and
comprehensive (1027 pages). Starts from the very
beginning: vectors and matrices as arrays of
numbers, systems of equations, row reduction.
Organisation of book is a little nonstandard:
chapters and sections are given abbreviations
instead of numbers.
 “Linear
Algebra”, by David Cherney, Tom Denton,
and Andrew
Waldron, UC Davis. 308 pages. Covers similar
material to Beezer's book.
 “Linear
Algebra”, by Jim Hefferon, Saint Michael’s
College. 465
pages. Again, starts from the very
beginning.
 “Linear
Algebra as an Introduction to Abstract
Mathematics”, by
Isaiah Lankham, Bruno Nachtergaele, and Anne
Schilling, UC Davis. 247 pages. More
focused on abstraction than the previous three
references, and hence somewhat more in line with
the present course.
 “Linear
Algebra Done Wrong”, by Sergei Treil,
Brown University. 276 pages. Starts from
the beginning but also takes a more abstract
view.
The books listed above can all be obtained freely
via the links provided. Another potentially
useful resource is the series of video
lectures by Gilbert Strang from MIT’s Open
CourseWare project.


Test 1 materials
 Review sheet
 An old
test for practice
 Solutions
to the practice test
 Test 1 with
solutions
Test 2 materials
 Review sheet
 An old test
for practice
 Solutions
to the practice test
 Test 2 with
solutions
(Caution: the old test does not include questions on
eigenvalues, eigenvectors, or determinants, all of which
are included in the material for this test.)
Final exam materials
 Review
sheet
 An old exam
for practice (I do not have written solutions for this exam)
Homework
HW 1 (due Wed Aug 28)
 Solutions
HW 2 (due Wed Sep 4)
 Solutions
HW 3 (due Wed Sep 11)
 Solutions
HW 4 (due Wed Sep 18)
 Solutions
HW 5 (due Wed Sep 25)
 Solutions
HW 6 (due Wed Oct 9)
 Solutions
HW 7 (due Wed Oct 16)
 Solutions
HW 8 (due Wed Oct 23)
 Solutions
HW 9 (due Wed Nov 13)
 Solutions
HW 10 (due Wed Nov 20)
 Solutions
HW 11 (due Wed Dec 4)
 Solutions
