Professor: Jeff Johannes
Section 1 MWF
1:30-2:20p Sturges 105
Office Hours: Monday 2:30 - 3:30p, Tuesday 8:00 - 9:00p,
Wednesday 12:00N - 1:20p, Thursday 4:00 - 5:00p, Friday 12:30 - 1:20p, and
by appointment or visit.
Email Address: Johannes@Geneseo.edu
Linear Algebra Done Right, third edition, by
Sheldon Axler (errata
Extract from Linear Algebra
Through Geometry by Banchoff & Wermer
In Linear Algebra I you learned about matrices and
systems of equations, invertibility, determinants, linear transformations,
bases, and eigenvalues (and much more). How will our Linear
Algebra II be different? There are many options for direction.
Our text avoids determinants. I don't believe as strongly as the
author that this is "right", but I do agree that it is convenient. We
will begin revisiting arbitrary vector spaces and spend most of our time
thinking about linear transformations, with a rather minimal and occasional
role played by the matrices which were so central to Linear Algebra I.
Probably more so that any other course, we will be
constantly navigating different backgrounds. Linear Algebra I,
especially taught at different institutions can be quite varied.
Because of this, each student's experience will be different. I can
promise there will be topics we discuss (mostly early) that everyone will
have seen before. I can promise there will be topics that are familiar
to some and not to others (mostly in the middle). And, unless someone
has learned a significant amount of theory of linear algebra on their own,
I'm pretty confident there will be topics that are new to all. I have
taken data from my colleagues who have taught Linear Algebra I here to know
what was seen here, but please tell me if something is unfamiliar to
Upon successful completion of Math 333 - Linear Algebra
II, a student will be able to:
finite and infinite dimensional vector spaces and subspaces over a field
and their properties, including the basis structure of vector spaces,
the definition and properties of linear transformations and matrices of
linear transformations and change of basis, including kernel, range and
with the characteristic polynomial, eigenvectors, eigenvalues and
eigenspaces, as well as the geometric and the algebraic multiplicities
of an eigenvalue and apply the basic diagonalization result,
inner products and determine orthogonality on vector spaces, including
Gram-Schmidt orthogonalization, and
self-adjoint transformations and apply the spectral theorem and
orthogonal decomposition of inner product spaces, the Jordan canonical
form to solving systems of ordinary differential equations.
Half of your grade will come from problem sets.
Another tenth will come from each of two midterm exams. Your
mandatory in-class problem presentation will contribute three percent, and
your final project will contribute seven percent. The final fifth will
come from the final exam.
will be six problem sets due on indicated dates. The problems will
be mostly proofs. I
strongly recommend consulting with me as you work on these problem sets.
I also recommend working together on them, however I want to
carefully emphasise that each must write up their own well-written
solutions. A good rule for this is it is encouraged to speak to each
other about the problem, but you should not read each other's solutions.
A violation of this policy will result in a zero for the entire
assignment and reporting to the Dean of Students for a violation of
academic integrity. Each question will be counted in the following
0 missing or plagiarised question
1 question copied
2 partial question
3 completed question (with some solution)
3.5 completed question with only "fixable errors" -
minor missteps or minor writing errors
4 completed question correctly and well-written
entire homework set will then be graded on a 90-80-70-60% (decile)
scale. Late items will not be accepted.
Solutions and Plagiarism
There are plenty of places that one can find all kinds of
solutions to problems in this class. Reading them and not referencing
them in your work is plagiarism, and will be reported as an academic
integrity violation. Reading them and referencing them is not quite
plagiarism, but does undermine the intent of the problems. Therefore,
if you reference solutions you will receive 0 points, but you will *not* be
reported for an academic integrity. Simply - please do not read any
solutions for problems in this class.
When discussing the new material for each section, each
day will begin with an opportunity for student presentation. Potential
problems will be offered in class and maintained here.
student must present at
least one problem
during the semester. Presentations will be scored out of 7 points.
be graded roughly as follows:
very good - at most minor errors
some problems, but the main idea of the solution is clear
some correct things
will determine priority for presenting problems. Each student who
has not yet presented will have priority over students who have presented.
A second (or more) problem may be presented in order to replace a
prior presentation. Students may also earn one extra point
for the corresponding problem set by presenting at the 7 point level.
I will have a priority list at all times for presentations. Students
may present more than once per problem set, but representations have lowest
priority. Students may earn no more than one point per problem set in
Students will earn one extra point on the first problem
set by visiting office hours during the first two weeks of classes, i.e. no
later than 10 September.
Your final project will constitute writing up a 1200-2000
word detailed explanation of a linear algebra topic beyond Linear Algebra I
material selected by you and approved by me. Projects may be completed
individually or in pairs. Project proposals must be submitted before
fall break. There will not be duplicate topics - first proposals will
be given priority. Selecting
the topic by the deadline will be worth 10%,
the draft will be worth 40%, and the final paper will be worth 50%.
The exams will consist of a few problems at a level
between the presentation problems and the problem set problems.
Occasionally you will be given anonymous feedback
forms. Please use them to share any thoughts or concerns for how the
course is running. Remember, the sooner you tell me your concerns, the
more I can do about them. I have also created a web-site
accepts anonymous comments. If we have not yet discussed this in
class, please encourage me to create a class code. This site may also
be accessed via our course page on a link
feedback. Of course, you are always welcome to approach me
outside of class to discuss these issues as well.
While working on homework with one another is encouraged,
all write-ups of solutions must be
your own. You are expected to be able to explain any solution you
give me if asked. The Student Academic Dishonesty Policy and Procedures will
be followed should incidents of academic dishonesty occur.
SUNY Geneseo will make reasonable accommodations for
persons with documented physical, emotional or learning disabilities.
Students should consult with the Director in the Office of Disability
Services (105D Erwin) and their individual faculty regarding any needed
accommodations as early as possible in the semester.
It is my policy to give students who miss class because
of observance of religious holidays the opportunity to make up missed
work. You are responsible for notifying me by September 10 of plans to
observe a holiday.
Schedule (loose and subject to variations)
August 26 Introduction
September 4 1C
October 2 PS3 due
Review for exam
7 Exam 1 (Chapters 1-3)
Exam return, 4
Deadline for selecting project topics
23 PS4-5 due
November 1 PS6 due
Review for Exam
Exam 2 (Chapters 4-6)
Exam return, 7B
11 7C Project draft due
(more material in §7.4.2
18 PS7 due
Review, Final Project due
Review, PS8+ due
Wednesday, December 11 8:00-11:00a Final Exam (half 7-8, 2.8, half
1-6) (maybe 8:30-11a? 8-10:30a? 8:30-11:30a?)