Math 240-01 Linear Algebra Spring 2004
Daily Syllabus Peter Greim's home page MACS home page Registrar's page Citadel home page
Class Mo, We, Fr 11:00-11:50 TH 317
P. Greim, Thompson 329,
Tel. 9535035, Email: peter.greim@citadel.edu
http://macs.citadel.edu/~greimp
Office hours are posted at my door and at my class schedule web page. You can read it as long as you are using a Citadel terminal. The class schedule will give you an idea which times might be available if you need to make an appointment.
Text:
Introduction to Linear Algebra, 3rd ed.
Wellesley-Cambridge Press (ISBN 0-9614088-9-8)
Covered material: Chapters 1-6 and parts of 8 (details in the Daily Syllabus )
Course purpose:
The course Linear Algebra is a combination of procedures for solving systems of linear equations and a study of the underlying mathematical structure.
For most of you it is the second course (after Discrete Mathematics) in which you are expected to reason mathematically, so that you yourself can prove or disprove a conjecture.
This is the part of the course where you will need to spend some time contemplating new notions or theorems rather than just doing problems.
Then there is of course also the algorithmic aspect, involving very tedious computations, and here computers (or even some calculators – see below) can make your life much easier.
Specific course goals:
You should
- learn to identify a
system of linear equations and, in the case of two or three variables,
interpret it geometrically
- understand the Gauss
(or Gauss-Jordan) elimination method and become able to solve a small system
with simple rational coefficients by hand
- learn to use a
computer algebra system as a tool for the solution of a (possibly large) system
and become aware of the effects of rounding errors
- understand the role of
matrices and matrix multiplication in the description of linear systems and in
the Gauss (or Gauss-Jordan) process
- know the notion of
invertibility and its relevance for linear systems, be able to determine
whether a matrix is invertible, and find the inverse
- understand the notions
of a (finite-dimensional) vector space, linear span, linear independence, dimension
and their relation with linear systems
- know a definition of
the determinant of a square matrix, a geometric interpretation in the case of 2
by 2 or 3 by 3 matrices, and understand the relation between determinant and
invertibility
- understand the notions
of eigenvalue and eigenvector of a square matrix and the role of the
characteristic polynomial
- know how to compute
the eigenspace to a given eigenvalue.
Calculators and computer software
For some homework assignments you will need to and for many you will want to use a computer algebra system or equivalent (for example, TI89 or 92). Several software packages are available on campus: MathCad 11 in Thompson Hall 220 and in LeTellier Hall, DERIVE and MatLab on the Novell network, Scientific Notebook (student edition) in Thompson 220 and Grimsley Hall.
Grades
are based on the final, 4 tests, and quizzes and homework assignments (including some projects requiring the use of a computer algebra system of your choice). Each test counts 100 points; homework and quizzes count 200 points together, for a total of 600. The final exam counts 200 points. You'll receive 0.5, resp. 1.25 percentage points extra credit for each correctly solved problem of the week or problem of the month. (See Prof. Trautman's webpage http://155.225.48.46/potw/potw.htm and look out for weekly, resp. monthly, announcements on the classroom bulletin boards.) I will follow the usual 10% per grade scheme and not grade "on a curve". However, if after grading a test the statistics show a particularly bad performance of the whole class at one problem, I may adjust that problem's weight within the whole test.
Missing a test unexcused will result in a score of zero. I will not allow you to miss a test because of a lack of preparation. If your absence is excused, I may choose to drop it and prorate the other test and homework scores, or give you a makeup test.
You can check your standing in the course here. You'll need to know your code number to identify your record. It will be on your first exam.
Since its total weight is only 25%, you can ignore the homework and still make a "C" in the course, right?
Wrong. You don't even have a remote chance to pass the course without doing the homework. Not only will it enable you to test your understanding of the material you saw in class - you will understand Linear Algebra through trying, failing, and eventually succeeding in solving the problems.
When you work problems, first try to do them by yourself. After that, whether you succeed or not, you may discuss them with others. You will learn from talking about mathematics. However, do not copy homework from others. I want you to understand a problem solution (either through own research or discussion) and then formulate it in your own words. Discussing a problem solution with a classmate, understanding it, and then formulating it in your own words is allowed. Copying a solution from others is not.
Occasionally I may let you do or redo part of a test as take-home. In that case you are completely on your own - almost. I am the only person with whom you may discuss a test problem before turning it in.
Homework
assignments are given in class and/or posted on the web after class. The Homework
assignment page at
http://macs.citadel.edu/~greimp/240calendar.htm also contains the test
dates, and it tells you how much time we will spend on each chapter. The
bold-faced homework problems are due 11 a.m. on the day in the Due date column,
regardless of whether you are attending class or not.
I suggest you work the homework
problems on the day when we cover the corresponding section in class. I'll
reserve some time for your questions during the following class period. That
should enable you to submit the homework and take the occasional quiz at the
beginning of the next class period.
is available: you may work with other students, see me after class, during office hours, or make an appointment (or just drop by my office, taking a chance that I may be busy). I’m on campus Monday nights and, by appointment only, Thursday nights.
One last advice: when you are getting behind (or can't even get started right) - let me know right away. I'll go out of my way to help you if you try. Your grade will be based on your success - not on your effort. However, your effort will determine how much I help.