MCS-221 Linear Algebra

Catalog description: An introduction to the theory and applications of linear algebra. Topics include vector spaces, matrices, linear transformations, determinants, eigenvalues and eigenvectors, and inner product spaces.
Prerequisite: MCS-121 or MCS-131. MCS-220 is recommended prior to or concurrently with MCS-221.

Syllabus

Dates	Sections	Topics	Tests
Sept. 5-24	1.1-1.5	Vector spaces and systems of linear equations	Tuesday, Sept. 24
Sept. 26-Oct.10	2.1-2.3	Linear independence and dimension	Thursday, Oct. 10
Oct. 11-31	3.1-3.5	Linear transformations	Thursday, Oct. 31
Nov. 1-18	4.1-4.2, 4.4-4.5	Orthogonality and applications	Monday, Nov. 18
Nov.19-25	5.1-5.3	Determinants
Nov. 26, Dec. 2-11	6.1-6.3, 6.5	Eigenvalues, eigenvectors, and diagonalization
Dec. 12-13	Chs. 1-6	Review
Dec. 16	Chapters 5-6 plus Chs. 1-4	Final examination 8:00-10:00 a.m.	Monday, Dec. 16

The topic dates are subject to change. The test dates are firm.

Instructor: John Holte

Office: Olin 307
Telephone: x7465
Office hours: M 11:30-12:20; T 2:30-3:20; R 2:30-3:20; F 11:30-12:20; & when my door is open
E-mail: holte@gac.edu
My homepage: http://www.gac.edu/~holte
Course homepage: http://www.gac.edu/~holte/courses/mcs221/fall02/

Class meetings

1:30-2:20 Monday, Tuesday, Thursday, and Friday in Olin 320
Regular attendance is expected.
If you have a disability that requires an accommodation, please see me as soon as possible.

Textbook

Linear Algebra: Ideas and Applications
by Richard C. Penney
Wiley, New York, 1998

This is the computer algebra system used in this course.

Problem assignments

Click on the Assignments link on the home page or go to http://www.gac.edu/~holte/courses/mcs221/fall02/problems.html   for assignment updates.

Homework and collaborative learning

I encourage you to work with other students in learning the material, both in class and on homework, provided that you do so in such a way that everyone in your group learns the material. You should write your solutions neatly and show clearly how you get your answers, at least in nontrivial problems. Your write-ups should be done independently, in your own words; solutions should not be copied from someone else's paper. You must give credit to those who helped you, including fellow students, and if you get part of your solution from any text (including ours) or internet source, you must cite it so that it can be traced.

Homework rules

• Acknowledge your sources (people and texts).
• In nontrivial problems, show how you get your answers.
• Turn in neat, well-written solutions, not messy first drafts. Trim "fringes." Staple.
• Do not copy collaborative solutions; write up solutions in your own words.
• Turn in homework on time. Each class day late reduces the possible points by 25%.
• Do extra credit problems entirely on your own.

Academic honesty

Page 31 of the Gustavus Adolphus College Academic Bulletin states in part: "The faculty of Gustavus Adolphus College expects all students to adhere to the highest standards of academic honesty... In all academic exercises, examinations, papers, and reports, students shall submit their own work. Footnotes or some other acceptable form of citation must accompany any use of another's words or ideas."

Make-up policy

Make-up exams will not be given except for medical or family emergency reasons. Students who will be absent from an exam for a school-sponsored event should arrange with me in advance to have an exam sent along with the coach. Late homework will be penalized as stated under Homework rules.

Your work will be weighted as follows:
• 2/3     Tests
  • You will have four unit tests and one final examination. The best four will be counted at 1/6 each.
• 1/3     Problem solutions
  • Regular homework problems
  • Proof portfolio
  • Maple exercises
  • Solutions presented in class

Participation and performance factors may modify your grade.

You are expected to contribute to a classroom atmosphere that encourages learning and is marked by respect for your fellow learners. This involves, in part, faithful attendance, preparation, and participation, including attendance in the classes before and after each break. I value students who are more interested in points of mathematics than in points of grading.

What is linear algebra?

Linear algebra is a branch of mathematics that is remarkable for its marvelous beauty and incredible utility. It provides a compact, expressive language for the description of models arising in a wide variety of fields of study, including biology, chemistry, computer science, data transmission, ecology, economics, engineering, image processing, medicine, physics, psychology, sociology, and statistics, as well as other areas of mathematics. Its study typically is a requirement for students of engineering, science, and mathematics.

The fundamental theme of linear algebra is the solution of systems of linear equations, like

2 x + 3 y = 4 and 5 x - 6 y = 7. The equations are called "linear" because geometrically they describe lines (or planes or higher-dimensional counterparts). The central equations of linear algebra, in matrix notation, are the linear system A x = b and the eigenvalue problem A x = m x. At any given time, a significant fraction of the planet's computer resources is involved in solving such problems.

The fundamental concept of linear algebra is the vector space. This notion embraces lines, planes, and Euclidean 3-dimensional space. But vector spaces include much, much more. The student who masters this abstraction will obtain a key to understanding a huge variety of problems. Another key concept is that of a linear transformation between vector spaces. This abstract concept has concrete representations in the form of rectangular arrays of numbers called matrices.

The text and the instructor of MCS-221 will both emphasize understanding the fundamental ideas of linear algebra. Students will be encouraged to gain their understanding the GAC way: geometrically, algebraically, and computationally. Through a variety of applications, students will gain an appreciation of the widespread usefulness of linear algebra. In addition, students will be encouraged to see the beauty of the subject as they gain experience in mathematical abstraction and logical deduction.