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-119 or MCS-121. MCS-220 is recommended prior to or concurrently with MCS-221.

Instructor: John Holte

Office: Olin 307
Office hours: 10:30 MF, 3:30 TR, and when my office door is open.
My schedule
Telephone: x7465
E-mail: holte@gustavus.edu
Homepage: http://www.gustavus.edu/~holte/
Course web site: http://www.gac.edu/~holte/courses/mcs221/fall08/

Class meetings

2:30-3:20 Monday, Tuesday, Thursday, and Friday in Olin 318
Regular attendance, both physical and mental, is expected.

Textbooks

Matrices and Linear Algebra 2/e by Hans Schneider & George Barker, Dover, 1989.
Introduction to Linear Algebra by Marvin Marcus & Henryk Minc, Dover, 1988.

Syllabus

Dates	Schneider & Barker	Marcus &Minc	Topics	Tests
Sept. 2-25	1, 2	p. 2	Fields, matrices, and systems of linear equations	R 9/25
Sep 27-Oct 17	3, 5	1	Vector spaces and linear transformations	F 10/17
Oct 22-Nov 14	5, 7.1-7.3	1.3	Linear transformations, inner products, and orthogonality Fundamental Theorem of Linear Algebra	F 11/14
Nov 17-Dec 9	4, 6	3	Determinants, eigenvalues, and eigenvectors	Final exam
Dec 11-12	1-7	1-3	Review	T 12/16 10:30-12:30

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

Problem assignments

http://www.gac.edu/~holte/courses/mcs221/spring08/problems.html

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%.
• Use graph paper or quadrille (crosshatch) paper when you are asked to plot vectors, lines, etc.
• Do extra credit problems entirely on your own.

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 contributes and 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.

Extra help

• Please feel free to see me during office hours and at other times when my door is open.
• Disability services
  The College Catalog states: "Section 507 of the Rehabilitation Act of 1973 and the Americans with Disabilities Act (1990) work together to ensure 'reasonable accommodation' and non-discrimination for students with disabilities in higher education. A student who has a physical, psychiatric/emotional, medical, learning, or attentional disability that may have an effect of the student's ability to complete assigned course work should contact the Disability Services Coordinator in the Advising Center, who will review the concerns and decide with the student what accommodations are necessary." The Disability Services Coordinator Laurie Bickett (x6286) can provide further information.

Academic honesty

• 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." The complete statement may be found at: http://www.gac.edu/oncampus/academics/general_catalog/current/acainfo.cfm .
• The following code will be written in full and signed on every examination:
  "On my honor, I pledge that I have not given, received, or tolerated others' use of unauthorized aid in completing this work."
• "By enrolling classes at Gustavus, you have taken up membership in a worldwide community of scholars, and like any community, Academia has ethical standards to which you are expected to adhere. You are expected to learn and follow the principles of honesty and integrity that apply in academic life. Among those standards are that you faithfully represent your own work, acknowledge any borrowing from the work of others, avoid falsifying data or sources, be respectful of other scholars' efforts and not interfere with their access to resources (e.g., by misappropriating or damaging library materials), do a fair share of the work in group efforts, give others the benefit of your informed opinions and observations in discussion, and be respectful of others' values, knowledge, and feelings while developing your own.... Regrettably, serious and deliberate violations of ethics may incur serious penalties.... If you are in doubt about whether your work conforms to ethical standards, please inquire--you are, after all, a learner." --John Rezmerski, Advising and Registration Manual 1995-96, pp. 60-61.
• A first violation of the academic honesty policy will result in a zero grade on the paper in question and a report to the office of the Dean of the Faculty. A second case will result in a failing grade for the course.

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.

Grading

Your work will be weighted as follows:
• 2/3     Tests
  • Three one-hour unit tests
  • One two-hour final exam, which will be partly a unit exam and partly comprehensive and which will be counted as two one-hour tests
  • Then the best four of your five scores will be counted equally.
• 1/3     Problem solutions
  • Regular homework problems
  • Proof portfolio
  • Problem 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.

MCS 221 students will be encouraged to understand the fundamental ideas of linear algebra the GAC way: geometrically, algebraically, and computationally. They will apply their understanding both to "problems to solve" and to "problems to prove." 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.