MATH 290, Linear Algebra
Fall 2009

August 19, 2009

Bryan Smith

Contents

1  Introduction
    1.1  Goals
2  Attendance
3  Academic Honesty
4  Course Information
    4.1  Textbook
    4.2  Calculator
    4.3  Basic Information
        4.3.1  Logistics
    4.4  Examinations
    4.5  Final Examination
    4.6  Writing Projects
    4.7  Homework
    4.8  Reading Questions
    4.9  Course Information Updates
    4.10  Total Points
5  Math 290 Writing Projects                                Grading Rubric
    5.1  Writing Guidelines

1  Introduction

For an official description of this course, see the MATH 290 Syllabus[4].
The prerequisite for this course is MATH 181 (second semester calculus) but do not expect it to be like calculus - it is an algebra course through and through. However, there are many examples of linear algebra from calculus as well as physics, chemistry, economics, and computer science and, during the semester, we will take a little time away from the algebra to introduce some of these examples.
Linear algebra is the first "proof-based" course offered in Puget Sound's mathematics' curriculum and serves as the gateway course to upper-division mathematics. Since it also meets the university's "Writing in the Major" requirement, there will be at least as much focus on developing mathematical writing skills as on linear algebra itself. More details are provided in the Writing Projects section below.
You should expect to spend at least as much time writing correct proofs of your results as you spend figuring out those proofs. In fact, one of the most important goals of this course is for you to deeply appreciate that you don't really understand a concept unless you can clearly explain it to someone else.

1.1  Goals

By the end of the semester, you should understand linear equations and their solutions, see how vector spaces arise naturally from generalizing solutions of systems of linear equations, and see their utility in a wide range of applications. You should also be able to read a mathematical text for content and deep understanding (see "How to Study"[5] for an excellent description of how to read mathematics and other efficient ways to study), analyze a given problem to determine which linear algebra tools should be used in its solution, use a variety of strategies to determine and prove a solution of the given problem, and follow accepted mathematical style to present an accurate and carefully written formal proof of that solution.
During a normal class day we will work to achieve these goals by discussing new material and addressing questions that arise from reading the text or working on homework problems.

2  Attendance

Daily attendance is both required and expected. You are also expected to participate fully in class by pre-reading the material to be covered, seeking clarification for unclear points, and engaging in mannerly and academically honest discussions of the topics.

3  Academic Honesty

All graded materials are to be your own work. This includes the reading and writing assignments. You are expected to be familiar with the university's policy on Academic Honesty and will be asked to affirm you abide by it on every assignment and exam.

4  Course Information

4.1  Textbook

The textbook is A First Course in Linear Algebra, Waldron Edition (Version 2.00), by Robert A, Beezer, ©2008, and is published by Professor Beezer under the GNU Free Documentation License rather than by a commercial publishing house.
You can purchase a copy from Lulu.com for around $40.00 plus shipping.
Since this is likely to be your first exposure to proof-based mathematics, you should also consider buying one of the many books on "how to do proofs". I recommend "The Nuts and Bolts of Proofs" but I also list a few other good choices in the "References" at the end of this handout.

4.2  Calculator

I require a calculator for this course. It must be able to perform the following matrix operations: row operations, reduced row echelon form, transpose, determinant, and eigenvalues/eigenvectors. I will allow the calculator to be used on examinations but will not allow its use for some problems.
I do not care what calculator you use but I am most familiar with Texas Instrument machines, particularly the TI-86. If you do not have a manual for your calculator, you should be able to find one on the internet - for example at
http://education.ti.com/us/product/tech/86/guide/86guideus.html [6]. Be advised that some students have had trouble getting a TI 83 to do all of the necessary computations.
Here is a link to the department's Calculator Policy [3].

4.3  Basic Information

You can find information pertinent to all of my classes at the link below and, once there, information specific to this class by clicking on the Math 290 link.
http://math.pugetsound.edu/ bryans/ [1]

4.3.1  Logistics

Classes meet for 50 minutes except on examination days when we meet for 80 minutes.
Professor Bryan SmithThompson 390D 879-3562 bryans[at]pugetsound.edu
Math 290A Thompson 283 Mon, Tue, Thu, Fri 11:00 A.M.
Math 290B Thompson 283 Mon, Fri 12:00 P.M.
Tue, Thu 12:30 P.M.
Office HoursMon, Tue, Thu 2:00 - 2:50 P.M
Wednesday 3:00 - 4:30 P.M.
Other Times By Appointment
I am also happy to make appointments for other times.

4.4  Examinations

All examinations are scheduled for Thursday. On test weeks, if there is interest, there will be a review session the night before from 7:00 until 8:15 P.M. Note that the exam period will run for 80 minutes (be sure to know when class starts and ends on an examination day).
There will be four (4) 50-minute, in-class examinations and the lowest score will be dropped. I do not give make-up examinations except for truly exceptional circumstances. You should not expect all examination questions to closely mimic textbook examples or assigned homework problems.
There are copies of old exams on my web site. They might contain typos or even errors. They are offered "as is" for those who wish to use then as a study aid. But they are not part of this semester's course.
Examination One Thursday September 17
Examination Two Thursday October 15
Examination Three Thursday November 12
Examination Four Thursday December 3

4.5  Final Examination

The final examinations are scheduled for
Math 290A Wednesday, December 16 12:00 - 2:00 P.M.
Math 290B Friday, December 18 12:00 - 2:00 P.M.
The final examination will be comprehensive and cannot be rescheduled so do not plan plane flights (or anything else) that will conflict with it. I will allow you to work longer than the two hours scheduled for the final.

4.6  Writing Projects

In order to meet the Writing in the Major requirement, I will assign two written proofs for each chapter. You are to find a proof for each and then write up your proof. These papers will be graded pass/fail for both mathematical content and written presentation. They are due in class on every Thursday. You may resubmit each problem repeatedly provided: 1) you make a serious effort on each retry and 2) it has not been more than two weeks since you last submitted the problem. Problems that are not submitted within the two week deadline receive an automatic fail. All work on these proofs is to be your own with two exceptions: you are allowed to discuss problems with me and you may use any ideas that you witness during a classroom exchange.
Note specifically that
  1. You may not discuss any aspect of these problems with anyone except me.
  2. You may not use any written resources other than your textbooks for this semester.
See the grading rubric on the last page of this document for further details pertaining to written mathematics.

4.7  Homework

It is wise to work most, if not all, of the homework problems in the textbook. Although they will not be collected, they will form the basis for much of our in-class discussions.

4.8  Reading Questions

It is very important that you read the material at least twice. Once before and once after it is discussed in class. It is also important that you read correctly. Mathematics requires that you read slowly and with a pencil and paper at hand. (See "How to Study"[5] on the course webpage for more details.)
There are reading questions at the end of each section of the book. You are to read these before we cover that material (see the tentative schedule and email your answers to me by 7:00 AM the morning we discuss that section in class. Note that these will not be accepted late.
When submitting your answers to the questions use the following structure.
  1. Sent to me at bryans(at)pugetsound.edu
  2. The "Subject" line must contain "290" followed by the section acronym. For example, the first reading assignment should have "290 WILA" in it's subject line.
  3. Have your full name as the first line of your response.
  4. Do not type the questions into your email - just answers.
  5. Give very brief answers. Do not include computations for numerical questions but do give brief reasons.
  6. Send only pure text. Do not send attachments, WORD files, or graphics. Do not send your answer in HTML if you can avoid it.
  7. Mathematical notation is cumbersome in text-only email but don't worry too much about it. I should be able to decipher most reasonable attempts.

4.9  Course Information Updates

If you wish, I will periodically post a grade report of your current standing in the class on my university web page. You should keep track of your grades on the various assignments and check them against these reports. If there are any discrepancies they should be dealt with immediately.
To have your information posted you need to print your name, the class (MATH 290), and a code on a sheet of paper. Then sign the paper and physically hand it to me. The code is to be a sequence of up to 23 symbols I can type on a keyboard.

4.10  Total Points

 
Writing Projects25%
Reading Questions10%
Examinations 45%
Final Examination 20%

References

[1]
Bryan Smith's Homepage
http://math.pugetsound.edu/~bryans/
[2]
Math 290 Course Webpage
http://math.pugetsound.edu/~bryans/Current/Fall_2009/290Index_Fall2009.html
[3]
Department Calculator Policy
http://www.math.pugetsound.edu/info/calcpolicy.pdf
[4]
Department Syllabus for MATH 290
http://www.math.pugetsound.edu/~matthews/Syllabi/MA290Syllabus.pdf
[5]
William Rapaport's "How to Study"
http://www.cse.buffalo.edu/~rapaport/howtostudy.html
[6]
TI-86 Manual
http://education.ti.com/us/product/tech/86/guide/86guideus.html
[7]
"Proofs and Fundamentals: A First Course in Abstract Mathematics", Bloch
http://www.amazon.com/exec/obidos/ASIN/0817641114/
[8]
"The Nuts and Bolts of Proofs", Antonella Cupillari
http://www.amazon.com/exec/obidos/tg/detail/-/0120885093/
[9]
"Thinking Mathematically", Mason/Burton/Stacey
http://www.amazon.com/exec/obidos/ASIN/0201102382/

5  Math 290 Writing Projects                                Grading Rubric

Code Logic and Mathematics
Accept Arguments are correct, complete and without inappropriate material.
L Logic or Mathematics are incorrect
T Terminology is incorrect
W Writing does not adhere to the guidelines.
 

5.1  Writing Guidelines

It is best to think of these projects as officially assigned papers in which you completely explain and justify your analyses of the problems. There is to be no collaboration at all when you work these problems and write them up. Your sole outside resources are direct discussions with me or discussions that occur during class.
In addition I expect your papers to be
  1. Fully documented - specifically:
    1. Any idea obtained during in-class brainstorm sessions or in discussions with me is cited in-line.
    2. All textbook results (theorems, propositions, and lemmas) are cited in-line and include the acromym of the result.
    3. Any use of technology is cited in-line.
  2. Carefully handwritten in ink or written with a word processor. (I can show you how to use Scientific Notebook in the labs or you can use Mathematica or Microsoft Word. Please check with me before using any other program.)
  3. Written using complete, accurately punctuated sentences.
  4. Presented in active voice, the first person plural and with a clear, easy-to-follow expository style.
  5. Targeted at an audience consisting of students not in this class but with an equivalent mathematical background - say those currently in another section of this course.


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On 24 Aug 2009, 10:23.