Information for Math 215—Linear Algebra Section 2 Fall 1995

Instructor: Doug Ulmer
Office: Math 716
Phone: 621-6861
Office Hours: Mondays and Wednesdays 2-3 in my office,

Wednesdays 1-2 in Math Annex, or by appointment

Class: 11-12 MWF, Math 101

The subject: It is not unreasonable to say that there are only really two big ideas in mathematics, namely calculus and linear algebra. Certainly these two subjects are at the base of almost all mathematical analyses and models. Moreover, linear algebra has many applications, for example in economic models, computer graphics, probability and statistics, and dynamical systems.

Fundamentally, the subject is just a systematic method for solving systems of linear equations. We want to know whether a system has any solutions, and if so, how many are there and how can we find them. There will of course be some complications and abstractions, but it is good to always keep in mind this basic point.

The course: We will first learn the basic method of solving systems of equations, its formulation in terms of matrix algebra. We will then discuss some more abstract concepts which naturally arise in this direction, such as vector spaces, linear independence and bases, eigenvectors and eigenvalues. We will also consider a number of applications. I expect that you will:

• learn the ideas actively, i.e., well enough to be able to apply them in new and nonstandard situations.

• express yourselves clearly and elegantly, both in speaking and writing.

• have some fun. (The last point is optional, but encouraged!) To acheive these goals, I sometimes use unusual methods: I will continually be trying to get you to think in class, instead of just copying from the blackboard. We will spend a lot of time discussing ideas and problems, and I may occasionally ask you questions to be answered on the spot.

The book: We will use “Linear Algebra and Its Applications” by David C. Lay. This book has many nice applications of linear algebra to other fields, and we will cover a few of them.

Technology: I’m all for it. We will sometimes use computers during class and many homework problems will require using the “Linalg” package. There is an open access computer lab in Math 226/228, open M-Th 8-7 and F 8-5. You can copy and use any of the programs loaded on those machines (including Linalg) for free. These programs run on all standard PCs, including those available at many of the dorms.

Working together: Please do. You are free to organize yourselves into groups and discuss homework, study for tests, etc. Just make sure that any work you turn in is your own, i.e., that you have written things down in your own words. Copying and other forms of cheating will be dealt with harshly: at the very least both the copier and the provider will get no credit whatsoever for the assignment in question.

Help!: If you need help, you can: i) come to office hours; ii) see me after class; iii) go to the Tutoring room (in the Math Annex on 6th street) from 11-2, M-F; iv) talk to other students in this section or others. Requirements: The basic requirements are to participate in class discussions, to turn in homework assignments, and to take 3 hour exams and a final exam. Attendance: Experience shows that very few students can succeed in this course without

coming to class every day. There are more students than spaces in class, so out of fairness I will “administratively drop” anyone who misses the first two classes or any three classes in a row.

Homework: This is the single most important factor for success in this course. There will a homework assignment for each day of class and I’ll collect them once a week or so. Keeping up with these assignments is essential; besides helping you achieve understanding of the ideas, homework will be a big chunk of your grade. Homework, homework, homework!

Exams: There will be 3 one-hour in class exams, tentatively scheduled for October 11, November 8, and December 6. The final exam will (definitely) be on December 20 from 11 to 1 pm, in this room.

Grades: Basically, if you work hard you will get a good grade. Unfortunately, this brief statement isn’t good enough for official purposes, so here is my system: Grades will be given on a point system, based on homework and tests. The proportions are

Homework 200 points 1/3 of grade
The 3 1-Hour exams 200 points  1/3 of grade
Final exam  200 points  1/3 of grade

The lowest hour exam score will be dropped before computing the hour exam points. Final grades are based on a straight percentage scale: 90-100% is an A, 80-90% is a B, 70-80% is a C, and 60-70% is a D.

Late homework and missed exams: Late homework is unfair to everybody so try to avoid it. To turn in something late, you should have an excellent reason and a definite date when you will have it done. Even then I might not accept it. Don’t even think about missing an exam.

I’s and W’s: If you drop the course between September 20 and November 1 and you are passing the class at the time you drop (which means you have earned at least 60% of the credit assigned up to then) you will receive a W; if not, you will get an E. The grade “I” will be given only in very special circumstances, and in no case after the last day of classes. See me for details.