Policies for Linear Algebra
Math 221
Fall 2001
last modified 8/23/01
Instructor: Janice Sklensky
Office Phone: (508)286-3973
Office: Science Center 109
Office Hours: See my schedule
E-mail: jsklensk@acunix.wheatonma.edu
Below, I discuss
Course Materials:
Linear Algebra and Its
Applications, by David Lay.
Optional: The Study Guide for Linear Algbebra and Its
Applications, ISBN 0-201-64847-4. There are (or will be) two copies
of this on reserve in the library. Take a look at it, and if you
decide you'd like to order it, the book store will order it for you
for you, I believe.
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
At first glance, this may seem simple or even boring,
and you can't imagine how we're going to spend an entire semester on
this topic.
You may not be surprised to find that it turns out that people run into systems of
equations like these (sometimes with many more equations and variables) all
the time. What you may indeed be surprised at is how interesting the
prospect of solving systems of equations is! For one thing, these seemingly mundane
algebraic questions have very deep geometric
interpretations. We will be able to play 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.
Course Organization and Expectations:
As you probably already know, math is best learned by doing, not by
watching. Therefore, the class will be structured to combine some time
spent on
lectures to introduce material or to emphasize particular topics with
much time 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.
As you probably began to learn in Calculus, being able to do problems
similar to those in the book is not really what math is all about,
although it is certainly necessary. Really learning mathematics
involves being able to solve problems that are different from anything
you've ever seen and communicating the results. Solving new problems requires
starting a problem
even if you don't know how to finish it, being able to think of
and try several different approaches, and being able to easily
translate from English to ``math'' and back again. Communicating
mathematics of course goes in both directions -- not only to you have
to be able to read and write clear and concise mathematics, but you
have to be able to understand it when it's communicated to you.
To help you gain in your abilities to dive into mathematics and to
communicated mathematics, the course will emphasize problem-solving,
and reading, speaking, and writing mathematics.
Thus in addition to the usual homework problems, quizzes, and exams, you will also be
reading the textbook (and answering questions on the reading), working
in groups, and doing two projects which will consist of larger, more
open-ended problems.
Reading:
As mentioned above, one of the goals of this class is that you become
comfortable reading mathematical material.
Before each class meeting, you will read the material that
we will be discussing that day.
To
give you credit for your efforts,
I will post questions on the web
that cover each day's reading. You will send the responses to those
questions by 8am of the day they are due.
See the guidelines for submitting reading assignments .
You can get to the appropriate chapter's web page from the course's
web page.
These reading assignments are required, and will be graded out of 2
points each: 2 points if you respond in
full (whether correctly or not) and
1 point for a partial response. Late responses will not be
accepted. I expect to drop each person's lowest three score at the end of the semester.
People who do not miss any reading assignments will receive
a small amount of extra credit.
Problem Sets:
Weekly problem sets will
alternate between being done individually and in groups.
Problem sets will be due most Wednesdays at the beginning of class. You should begin each new problem set on Wednesday afternoon and work on it throughout the week, as these problem sets represent a week's worth of learning.
Your assignments will be posted on the web, and can be
found through links toward the bottom of the course web page.
Consult the Guidelines for Homework Presentation
for information on
how your problem sets should look.
| Late problem sets will not be accepted! | |
Projects:
To give you an opportunity to solve problems that are more
realistic--problems which do not necessarily have one ``right'' answer,
which can be approached in a variety of ways, and which
take several days of pondering to solve --you will work on two group projects this term.
The due dates are (tentatively) listed on the syllabus.
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.
Every member of the group is responsible both for understanding the
mathematics of the project and for the clarity and quality of the
explanation in the report. You may not divide the mathematics in any
significant way, but you may divide the
writing of the report in whatever way is agreeable to the group. Everyone should
completely understand the whole of the paper and each member should proofread the entire paper
for consistency and typos.
Late projects are only accepted in extreme circumstances, and
usually with penalties.
Quizzes and Exams:
The takehome exams will have some problems that are similar, but not identical, to
homework exercises. However, most of the exam problems will ask you to combine your
knowledge of several different topics from the course. You can ask me as many questions
as you want about the exams, but you may not discuss the exams in any
way with anybody except me.
The quizzes will be short and on very specific topics. They will be mostly
computational, but you may also need to state definitions or theorems precisely.
I will tell you the exact topics that each quiz will cover.
See the Tentative Syllabus for the dates of the exams and quizzes.
The final will also be a take-home exam, and will be due at 2pm on
December 14th.
Evaluation:
I expect to use the weights below, although I reserve the right to
change my mind if the semester does not go as expected.
| Reading Assignments | 5% |
| Problem Sets | 20% |
| Projects | 16% |
| Quizzes | 9% |
| Two Takehome Exams | 30% |
| Final Exam | 20% |
If you question the fairness of any grade, bring it to me within a week of receiving it.
Honor Code:
I expect you to abide by the Honor Code. Below are some guidelines on what
constitutes violations of the honor code in this class.
Reading assignments: You may discuss the questions with your
classmates, but you must enter the responses yourself, in your own
words.
Homework and Projects: You may work with anybody you want.
You may use any references that
help you figure out how to do the problem on your own; you may not
use any references (people, old homework or projects, books, the web, for
instance) which tell you how to solve it or lead you to the solution.
You must understand how to do every
problem, and you must cite references if you've received assistance
from any source. When doing group projects or
group problem sets, you may not divide the mathematics into different parts--you
must do them all together, and you must make sure every member of your
group understands every part.
Exams: All of the exams are take-home exams. The only person
you may discuss the exam with is me. You may use
calculators, Maple, and your text. You may not look in other texts
for solutions, or look at any exams from previous Linear Algebra
classes.
Janice Sklensky
Wheaton College
Department of Mathematics and Computer Science
Science Center, Room 109
Norton, Massachusetts 02766-0930
TEL (508) 286-3973
FAX (508) 285-8278
jsklensk@acunix.wheatonma.edu
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