Linear Algebra: Course Syllabus

Instructor:: Dr. John R. Wicks, email: jwicks@northpark.edu, weekly schedule

Office:: W10B (basement of Carlson Tower, across from Lounge Area)

Office Hours:: See schedule

Phone:: (773) 244-5652 office; (773) 262-7621 home (before 10 pm.)

Class Schedule:: See schedule

Text:: Wicks, Linear Algebra: an Interactive Laboratory Approach
with Mathematica, 1996.

Goals:: Linear Algebra is a wonderful blend of abstract algebra and geometry, which is very well-suited to computations. In this course, we will use the geometrical side to develop our intuition, the theoretical side to provide us with the "big picture" and the computational side to become familiar with new concepts and solve problems. By the end of the semester, you should be able to:

describe the solutions to a system of linear equations,

manipulate and answer questions concerning bases,

compute eigenvectors and associated eigenvalues,

compute determinants and inverses of matrices,

perform Gaussian elimination on a matrix and

use the Gram-Schmitt algorithm to orthonormalize a set of vectors.

You should also know:

how 3) - 6) correspond to decomposition theorems, as well as

the basic theory of subspaces and linear transformations

This course will be quite different from other math classes in that you will learn independently, while using the computer to investigate new concepts. What you take from the course will be directly related to the amount of effort that you put into it. Lectures will be replaced by class discussions, intended to review and preview the material which you will study on your own. You will form study groups of 2 and work your way through the 34 Lessons of the text, completing all Exercises and submitting your responses (either in printed form or by e-mail) for a grade. In general, this course will stress reading and writing mathematics, so you will be expected to learn the language of Linear Algebra and use this to formulate and test your own conjectures, and summarize your conclusions.

Grading:

Grades will be computed as follows:

In class exams (3)	60 %
Final	30 %
Project	10 %

Summary sheets indicating the material to appear on Exam 1, Exam 2, and Exam 3 will be made available.

Grades will be available for each student. Simply enter your email name and password. I will also award 2% extra credit for an detailed and accurate log of how you spent your time in the course.

Homework:

Homework will consist entirely of the Exercises sprinkled through each Lesson. They will include reading, writing, computer experiments, as well as problems. An assignment will consist of a sequence of consecutive Lessons which will be due on the same day, as given in the course schedule. Each assignment should be divided into Lessons, with solutions to each Exercise presented consecutively, clearly labeled and written in clear English prose (where appropriate). You may hand in a single assignment as a group, but you should rotate responsibility for the write-up so that everyone can improve in their communication skills.

Exercises come in three "flavors": standard, drill, and advanced. Everyone should complete all of the standard exercises. You may choose to do as many or as few of the drill exercises as you feel necessary to master the material; you are resposible for gauging whether you have done enough. Advanced exercises are more challenging, and you will not be marked down if you cannot complete them.

Homework may be turned in as Mathematica files or hand-written, or some combination, as appropriate. Mathematica files should be placed in the "drop-box" folder in public:math:Math_3100; written work should be turned in to me personally. Complete solutions will be published in public:math:Math_3100 the morning after the posted due date. Any assignment submitted after the solutions have been posted will be considered late. Each Lesson will be graded on the following scale:

2: Nearly perfect

1: A "good faith" effort

0: Late or lack of a "good faith" effort

for a total of up to 66 possible points.
: Although your homework score is not averaged in the traditional manner into your final grade, it actually is the largest determining factor in your grade. Because you will spend so much time on the homework, we provide a mechanism to directly reward you for your effort. There will be three in-class exams throughout the semester. The original exam average may be modified in two different ways. First, that portion of your homework score above 33 will be added as "bonus points" directly to your exam average, on a percentage basis, up to one full letter grade (i.e., if your homework score is above 33, then exam percentage = exam average + .1*(Homework points-33)/33); otherwise, no bonus points are awarded). In this way, your final grade accurately reflects both your ultimate level of understanding, as well as the quality of effort put into the course.
: Because most of the learning in this course will occur while you are completing the Exercises in each Lesson, your exam scores will very closely reflect the timely effort put into the assignments. To make this connection more apparent, your exam average may be reduced according to the following scale:

48 - 66 pts: exam average is unaffected

38 - 47 pts: exam average = minimum of original average and 90%

18 - 37 pts: exam average = minimum of original average and 80%

Below 18 pts: exam average = minimum of original average and 70%

This means, for example, that it is not possible to earn a B, if you do not complete half of the Lessons on time with what I consider to be a "good faith" effort (i.e., attempting all of the Exercises, clearly following the directions). Note: You will find that this scale is actually quite generous, and only reflects the fact that you will not learn without putting in a consistent, good faith effort; thus, the vast majority of exam averages will be unaffected by this scale.

Project:: Each group will choose a separate application project that will be due by the end of the semester. These will be written up as a term paper and submitted as a group. Suggestions for possible applications topics will be forthcoming, as well as intermediate deadline dates and grading policy. Original ideas are allowable, but all topics must be approved by me beforehand.