Math 310: Linear Algebra
Fall 2011
8 MWF, Dennis 220

Mic Jackson, D208, 765-983-1620, micj@earlham.edu
Office Hours: 10-12 W; 2:30-4 W; 9-9:50 TR

Introduction and Overview

Linear algebra is a number of things, including:

• an area of mathematical study that is accessible to students who have completed at least one semester of calculus,
• an introduction to some of the most important and commonly used applications of mathematics, and
• an introduction to mathematics as the formal study of abstract structures.

Linear algebra covers material used by biologists, computer scientists, physicists and economists, and is a required course for many economics and MBA programs. For budding mathematicians, it is a prerequisite to the study of abstract algebra and has close ties with differential equations and multivariate calculus.

As such, an institution's introductory linear algebra course is often a battle ground between competing interests. A course that focuses on matrix manipulations and applications of linear systems is often judged by mathematics students as too shallow and dry. A course that focuses on abstract theory is too disconnected from what interests the typical computer science, physics or economics student. We will try for a good balance.

First, we will focus on the systems of linear equations, like you studied in high school algebra - their translations into matrices, and the use of matrix operations to find solutions to those systems. We'll extend our understanding of systems of linear equations to some important applications of linear systems and to two fundamental and pervasive mathematical concepts, linear transformations and vector spaces. Finally, we'll consider important ways of describing, understanding and using linear transformations. Along the way, you will develop expertise with SAGE, a computer algebra system that has useful linear algebra capabilities.

Prerequisites and Options

We expect that students complete Calculus A and Calculus B before beginning this course. However, that is more a statement of necessary mathematical sophistication than a claim that this course builds directly on calculus. The study of linear algebra can include work with derivatives and integrals, and with systems of differential equations. However, we will do little calculus in this course. If you have not completed the prerequisite courses, but feel you have the ability and commitment to succeed in linear algebra, come talk to me about the appropriateness of this course for you.

Resources

• Textbook - Linear Algebra, Third Edition, David C. Lay
• Maple computer algebra system (all campus computer labs)
• TI-89 and TI-92 calculators (Science Library)
• SAGE computer algebra system

A few other resources that might be helpful include:

• The mathematics collection in the basement of Wildman Science Library contains numerous linear algebra textbooks. I encourage you to find a favorite alternative textbook. It is often helpful to read more than one explanation of a difficult concept or to find more examples of certain computations.
• Linear algebra textbooks in the collection in the Mathematics Lounge. You are free to use any of those volumes. We ask that you keep them in the lounge where they are available to other students.
• The author has provided some useful material at his course website Lay Linear Algebra.
• There are some nice Mathematica demonstrations of various concepts and computations.
• If you find another good link, let me know, and I'll update this list.

Procedures

Class will begin promptly at 0800 with a moment of silence. Weekly assignments should be on my desk Monday before class starts. I expect you to attend each day and to hand in your assignments on time. Late work will not be accepted without my previous approval.

Since an 8 o'clock class is rough for many of you, it is fine if you bring something to class to help you stay awake and alert: coffee, tea, bagels, fruit. Please arrange your schedule to get to sleep no later than midnight; sleep deprivation is a scourge to be avoided. I'd be glad to work with you individually on techniques to help you stay healthy and alert.

At the beginning of each class, you will have time to ask questions about current and previous assignments. I expect you to read any assigned material prior to coming to class each day; my lectures and our class work will relate to the reading, but will not be a rehash of the material. I strongly encourage you to interrupt the process at any time with a cogent comment or a request for clarification. If you ask no questions, I will have to assume that you understand the material (which often is a very poor assumption). Most days, I will take the majority of class time to lecture on new material, discussing important notions and working example problems.

You should plan to study 2 to 4 hours between each class meeting. Make use of my office hours. Find a few classmates who will be reliable study partners, and help one another. The Mathematics Lounge (Dennis 210) is a nice place to have regular group or individual study sessions. Things get particularly tight around midterms and finals. Plan to work ahead and avoid the rush!

Evaluation

I will collect assigned homework each Monday and have it graded and returned to you by Friday. Each assignment has the weight of 1 unit.

There will be two tests (one-hour in class, with some take-home work due the following class) and a comprehensive final examination. The tests have a weight of 4 units and the final exam has a weight of 8 units.

That means that homework, tests and examination will combine for a total of approximately 30 units. Your course grade will be a weighted average of the letter grades (A=4, B=3, C=2, D=1, F=0) from all evaluations.

A Note On Honesty

Earlham has an honor code comparable in spirit and in application to the one I learned to value during my undergraduate experience. I continue to struggle with the challenge of living a life of integrity, finding regular motivation to not "do the right thing". I have observed over the years that most people experience similar difficulties learning to live under an academic honor code or other commitment to community values.

I hope you will read and consider Earlham's statement on academic integrity. If you take this seriously, as one should, it is a bit scary. The cost of a breach of academic integrity can be significant. At the heart of Earlham's honor code is the notion of trust. I've learned that any healthy adult relationship must be founded on trust. I hope you'll come to understand that sooner rather than later. Please see my comments on integrity.