 Overview
At the very basic level, Linear Algebra is concerned with solving
systems of linear equations like
2x + 3y + 2z = 10
x - 6y + 2z = 2
The beauty of Linear Algebra is that these seemingly mundane
algebraic questions have very deep geometric interpretations. We will
be able to play off the algebraic and geometric views against each
other to gain insights and build intuition about both. Fundamental to
developing this intuition is an understanding of the relationship
between matrices and linear transformations, which are
special types of maps from n-space to m-space.
The interconnections among systems of linear equations, matrices,
and linear transformations provide a framework for applications to
vastly different areas. Some of the applications we will look at
this semester include applications to population dynamics, computer
graphics, and the long-term behavior of dynamical systems. This is
going to be a really fun semester.
Reading the Text and Working with Other Students
Two of the goals of this course are that you learn to read a math text
and that you learn to communicate mathematics with other students.
Mathematics is a very personal discipline that is best learned by doing
rather than by observing.
Therefore, the class will be structured with some lectures to emphasize particular
topics, but much of the time will be spent on in-class work. The
class meetings are not intended to be a complete encapsulation of the
course material -- There will be material in the text for which you are
responsible that we will not cover in class.
Many of the assignments this term will be group assignments where
you will work in groups of two or three (of your choosing). Each
assignment will receive a grade, and the group will
determine how the points are allocated to each member.
For example, if a group of
three receives an 85 on an assignment, then the group will have
3 x 85=255 points to distribute among them.
I will be available to mediate this process, if necessary.
You will have a reading assignment for nearly every class meeting, and
it is extremely important that you complete the reading before the
next class meeting! See the section below on Reading Assignments and
the Guidelines for Submitting Reading Assignments
for more information.
Evaluation
Your final grade will be determined by
| Two Exams | 30%
| | Comprehensive Final Exam | 20%
| | Two Group Projects | 25%
| | Homework | 20%
| | Reading Assignments | 5%
|
Exams
On each of the two exams, there will be a short inclass part and a
more substantial takehome part.
See the Tentative Syllabus for the dates of the
exams.
The final will be entirely takehome and is due Thursday, December 17.
Group Projects
There will be two group projects assigned during the semester. You will
always have at least a week to complete the assignment
(see the syllabus for the due dates).
One of the main goals of the projects is that you learn to communicate
mathematics precisely, both verbally with your group and in
writing. The reports should be written in complete sentences explaining
the results and major ideas involved.
You may divide the writing of the report in whatever way is
agreeable to the group, but everyone should completely understand
the whole of the paper. Further, each member should proofread the
entire paper for consistency and typos.
Homework
Homework will be collected every Tuesday. I will carefully
grade three or so ``spotlight'' problems from each homework assignment, and
very quickly scan the rest of the assignment. I will tell you which
are the spotlight
problems, and these should be
especially well-written and placed at the beginning of your
assignment. Each spotlight problem will be receive a score between 0 and 4, and
I will also assign a total score of 0--4 for the non-spotlight problems.
The homework assignments will alternate between Individual
assignments and Group assignments. For the Group assignments,
each group will turn in one paper. On each assignment, one student will
be designated as the
primary author who writes-up the solutions. The role of primary
author must rotate among the members of the group.
For the Individual assignments, I encourage you to work with other
students, but each person must turn in a separate paper.
Here are a few guidelines for the presentation of your homework.
If you do not follow these, I reserve the right to return your homework ungraded!
- Place the spotlight problems at the beginning of your
assignment.
- Your writing must be clear and legible.
- Your homework should be well-written,
using complete sentences to justify your results where necessary.
A list of answers without explanation is not acceptable.
- Here is a good rule of thumb to follow when writing up your
Write your solutions so that you could hand them to another student in
the class and she could understand your
explanation.
- If you write in pen, there should be no scratch-outs.
- Do not turn in paper torn from a spiral notebook with ragged
edges.
- Clearly label each problem.
The homework is due in my office by 4:30 on Tuesday. Be aware
that
Late homework is not accepted!! No exceptions!!
Reading Assignments
I will put a copy of each reading assignment on the course homepage.
Each assignment will indicate which parts of the section are especially
important and which can be skipped. Each assignment will also have
three (or so) questions that you should be able to answer after you have
read the section.
See the Guidelines for Submitting Reading Assignments
for more information.
Class Attendance
Although class attendance is not a specified percentage of your grade,
I will keep a class roll to help me determine borderline grades at the
end of the semester. If you do miss class, you are responsible
for the material that was covered.
Getting Help
Please come see me during my office hours! If you have a conflict
and cannot make my office hours, please call or email me and we can set up
an appointment for another time.
If you want to know check on your grade at any time during the
semester, please ask me and I can give you a rough idea of your
current standing.
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