Mathematics 309

Spring, 2011

Instructor: Edward N. Wilson

Cupples I, Room 18

E-mail: enwilson@math.wustl.edu

Office Tel: 935-6729 (O.K. to leave messages, better to use e-mail)

Office Hours: MWF 12-1, MWF 2-3 and by appointment

Class Meeting Times and Place: MWF 11-12, Brown 100

Textbook: Linear Algebra and its Applications, 3^rd Edition (2006), by David C. Lay, published by Pearson/Addison-Wesley.

Overview: During the course of the semester, we will try to cover most of the material in the textbook but will not proceed in the same order as in the textbook and will use some different notations. The book covers a lot of ground, discusses some excellent applications, and contains a host of fairly good homework problems, but is written in a rambling, repetitive style and is a bit murky on some topics. We will try to be a little clearer on the main results in the subject and the proofs of these results.

We will begin as the textbook does with the historical origins of linear algebra (also known as matrix algebra), introducing matrix notations for systems of linear equations and the very efficient manipulations of matrices used to obtain solutions of linear equations. We then move to the closely related topic of linear transformations and apply our results for matrices to obtain geometric results for linear transformations. Before obtaining the nicest results for matrices and linear transformations, we have to pause to discuss determinants and their properties. This is a topic where we’ll discuss the properties but not take the time to do all of the tedious algebraic calculations needed for proofs. Once we’ve established the basic theory and computational techniques for matrices and linear transformations, we’ll turn attention to some special types of transformations, covering as much of the material in the latter part of the textbook as time permits.

Likely most of the students in 309 will already have been told by their major advisors and other professors in their major departments that linear algebra is fundamental for just about everything in theoretical and applied mathematics. It would take at least four or five semesters to adequately cover even the basic applications and requisite theory of linear algebra in such disparate areas as mathematical economics/finance, statistics, computer science, signal processing and imaging, quantum mechanics and statistical mechanics, chemical systems, harmonic analysis, differential geometry and relativity, genetics and other parts of the biological sciences, …. Devoting most of the semester to a small sampler of isolated applications would produce only a confusing mish-mash since each applied mathematics area has its own vocabulary, notations, techniques, theorems, and interpretations; in addition, up-to-date models in each area are usually complicated and specific to that area. We’ll refrain from giving any such sampler, instead will concentrate on the common denominator theory and calculation techniques for basic lincear algebra and will leave interested students to obtain an over-simplified glimpse of some applications from the textbook.

Homework: There will be weekly homework assignments to be written up and handed in except for the weeks in which there is an in-class exam. Each week, the instructor will select certain problems on the assignment to be graded by the course graders. The reason for this is that the large size of the class would make it very difficult to have all problems graded. As a “standing” assignment not to be handed in,

always look at the True/False questions appearing in the textbook’s homework sections.

These will be a very good way to check whether or not you’ve understood the material in the section.

Examinations: There will be two in-class exams during the semester plus a final exam.

The date of the final exam is determined by the College of Arts and Sciences and is inflexible. Possible dates will be suggested one to two weeks in advance for the in-class exams and, as necessary, we’ll have a show of hands to determine the least objectionable date. Nearly all of the exam questions will be short answer questions, always including some True/False questions similar if not identical to those in the textbook. Make-up exams won’t be contemplated in the absence of written documentation from the Health Service or the Dean’s Office. Students should be aware that make-up exams tend to be more difficult than original exams since it’s impossible to write two exams of identical difficulty and an instructor never wants to penalize those who take the original exams by having make-ups be easier.

Academic Integrity: When there is evidence strongly suggesting that cheating took place on an exam, the evidence will be forwarded to the Arts and Sciences Integrity

Committtee. If, after a hearing with the instructor and affected student(s), a majority of the Committee members are convinced that cheating did occur, the Committee will assess a penalty and inform the instructor and sudent(s) of its decision. For exam cheating, the most common penalties are either a failing grade on the exam or a failing grade in the course. In brief, please don’t cheat since cheating cases, however they turn out, are very painful for all concerned.

Grading Scale: Each of the two in-class exams will account for 25% of the course grade average, homework will account for 20%, and the final exam will account for the remaining 30%. Letter grades for exams and course averages will be determined as follows:

A 90-100%

B 80-89%

C 65-79%

F below 65%

In no case will final grades be lower than indicated by this scaling. However, the instructor reserves the right to switch to a more lenient scaling if he decides that it is warranted.

For homework assignments and notes, you may enter HERE .