Math 22, Spring 2003

Course Information

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Course Description:

(from catalog) This course presents the fundamental concepts and applications of linear algebra with emphasis on Euclidean space. Significant goals of the course are that the student develop the ability to perform meaningful computations and to write accurate proofs. Topics include bases, subspaces, dimension, determinants, characteristic polynomials, eigenvalues, eigenvectors, and especially matrix representations of linear transformations and change of basis. Applications may be drawn from areas such as optimization, statistics, biology, physics, and signal processing.

Textbook:

Linear Algebra and Its Applications, second edition update, by David C. Lay. Note that we are NOT using the third edition, which was published earlier this year. All references to the text (section numbers, homework exercises, etc.) will correspond to the second edition update. We will cover most of Chapters 1 through 6.

Class Location and Times:

Bradley 105 MWF 10:00-11:05 a.m., Th 12-12:50 p.m. (x-hour)
We will be using the x-hour on a regular basis.

Office Hours:

M 3:45-5:15 p.m., Th 1:30-3 p.m., or by appointment
I encourage you to visit during office hours if you have any questions, need help with homework problems, or would just like to talk about the material.
My office is in the basement of Bradley. To get there, go down the stairs to the left of the main entrance to Bradley, take the second left (first left is a dead end to the elevator), then turn left just before the exit doors. Go up the steps and my office is the third one on the right, 1-N.

Class Participation:

It is important that you come to class prepared and ready to participate. Each class will begin with a few questions which will require you to be able to state definitions, summarize concepts, and state or apply theorems which have been presented to date. The style will be informal. There are several different reasons for this exercise: (1) to encourage you to keep up with class material, as reviewing your notes from the previous class and having a good understanding of the main ideas will be essential; (2) to tell me what concepts are not being understood and need more explanation; and (3) to serve as a "warm-up" and context for the new material that subsequently will be presented. You are STRONGLY encouraged to ask questions during class.

X-hours:

As mentioned above, we will be using the scheduled x-hours. In most cases, these periods will be used for workshops focusing either on proof-writing or on applications of linear algebra. Carefully developed proof-writing skills are useful not only in future mathematics courses, but also in crafting clear arguments in various fields. I hope to be able to tailor the applications to the interests of the class.

Homework Policy:

Homework will be assigned daily and collected weekly. The daily assignments will be posted on the Homework Assignments page of the website. In addition to doing the assigned exercises, you should read the section(s) to be covered in the next class and reread the section(s) to which the exercises pertain. Every Friday, you will turn in assignments from the previous Friday, Monday, and Wednesday. Although homework is only collected weekly, it is important that you keep up with the assignments on a daily basis.

Homework should be legible and submitted on 8.5 x 11 inch paper. If your assignment consists of more than one sheet, please staple the sheets together (paper clips and clever corner-folding do not always keep the papers attached). If using paper torn from a spiral notebook, please cut off the messy edge. Homework is to be submitted BEFORE class begins on Friday - late homework will not be accepted. However, your lowest homework grade will be dropped. This includes missing one homework for any reason (e.g. illness, death in family, ungraded homework due to illegibility, etc.).

Exams:

There will be two midterm exams and a final. The first midterm exam is scheduled for Wednesday, April 16, during class. The second midterm is scheduled for Thursday, May 8, during x-hour. The final, which will be cumulative, is scheduled for Friday, May 30, at 8 a.m. You must plan to take all of the exams during the scheduled times.
If you believe there are problems with the grading of an exam, you must submit the exam to me for review by three days after it is returned. Please attach a note explaining your concerns to the front of the exam. I will review the exam IN FULL, adding (or subtracting) points as appropriate, and return it to you at the next class.

Grading:

Your final grade for the class will be determined as follows:
Homework: 20%
Midterm 1: 25%
Midterm 2: 25%
Final Exam: 30%

Honor Principle:

Dartmouth students are expected to adhere to the honor principle. In this course, that means that while you are free (and encouraged!) to discuss homework with your classmates and with me, your written submission must be your own. Please list all those with whom you discussed the work at the top of your paper. All exams will be closed book and closed notes unless explicitly stated otherwise. No calculators or computers are to be used during exams, and there is obviously no collaboration during exams.

Special Needs:

Any student with a documented disability for whom special accommodations would be helpful is requested to discuss this with me before the end of the second week of class (April 4).

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