Linear Algebra II (15-Math-352)

Department of Mathematical Sciences

This page is a work in progress! All information is subject to change (Last revised 25 March 2011)

Textbook Linear Algebra and its applications (fourth edition) by David C. Lay
Supplementary Text Introduction to Linear Algebra by Donald J Wright

General Syllabus
Chapters 1 thru 7 of Lay's book, although much of this was covered in Linear algebra I. All the material in sections 1.1-1.7 and 2.1-2.4 as well as much of 4.1-4.7 was covered last quarter.

Calculus III (Math 253) and Linear Algebra I (Math 351) are both prerequisites for this course. There are no co-requisites. Here is a review sheet for material covered in Linear Algebra I (well, we never got to items (13,14,15) on page 3).

• 25% --- final exam
• 50% --- three in-class hour exams (each exam counts one third)
• 25% --- five in-class quizzes (each quiz 5%, lowest score dropped)

The main Course Goal is the study of linear vector-valued functions of vectors. We'll begin with a lightening fast review of vector spaces, bases, dimension, coordinates, etc. This is 1.8, 1.9, 2.8, 2.9, 4.1-4.7 in Lay's book. Then we'll briefly touch on the theory of determinants (chapter 3), which in turn we will use to study eigenvalues and eigenvectors (chapter 5). If time permits we will then look at the diagonalization problem, the QR-Algorithm, quadratic forms, and the singular value decomposition (chapter 7).

The Primary Goal of this course is your understanding of the underlying concepts; this is the most important task for you to focus on.

It is crucial that you understand the material covered in Linear Algebra I (Math 351). You must know how to solve systems of linear equations as well as basic matrix arithmetic. You should know and understand basic facts about the null space and column space of a matrix; for example, you should be able to state and use the Rank-Nullity Theorem. There are a number of algorithmic computations that should understand such as: finding the inverse of a matrix, finding coordinates for a vector wrt a given basis, finding a change of coordinates matrix.

If you are seeking help, there are Graduate Student Teaching Assistants on duty at the Mathematics Learning Center located in 614 Old Chemistry. Check their web page for their hours. You can also see me directly after class, during my office hours, or by making an appointment. In addition it is possible to hire a private tutor; the main office has a list available and I will happily help you find someone. Perhaps the best way to get help is to ask your fellow classmates!

It is an excellent idea to go over your notes as soon as possible after class. You may want to get two notebooks for this course: use one to write down class notes and problems that I work in class; do your homework problems in the other notebook. I think you will find it easier to study for exams if your class notes are not cluttered with your homework problems.

The last day to withdraw from this class is Tuesday May 24, 2011. This is an official UC policy and something I cannot change. If you withdraw from this course, I will be required to verify whether or not you minimally participated in the class. Although I will try my best to respond accurately, in the absence of any evidence to the contrary, I will state that you did not minimally participate. Ways for you to provide clear evidence of your presence in the class include taking at least one quiz or taking one exam.

Here I explain my Regrading Policy. Mistakes are made in grading, especially when there is only one person responsible for grading all of your exams and quizzes. Sometimes these mistakes are in the student's favor, and unfortunately sometimes not. By following the procedure outlined below, you can have mistakes in the grading of your tests corrected. Please be aware that just as it is likely that you will receive more points, it is also possible for you to actually lose points -- this generally happens to at least one person each quarter. That is, there are three possible outcomes of a regrade request: your score may remain the same or your score may increase or your score may decrease.

Note that partial credit is awarded only for work that is mostly correct except for one or two minor errors. You will not be given partial credit for attempting to solve a problem by the wrong method. Nor will you receive credit---even for a correct answer---if no supporting work is present.

Here is the Procedure to Follow for a Regrade Request If you believe an error was made in grading your test, then you must appeal the grade in writing within one day of the day the test was returned to the class. A late request for regrading will automatically be denied. To have your test regraded, you must return it along with a clearly written note indicating the mistakes that you believe were made in grading. If your point totals were added incorrectly, simply indicate this on your regrade request. Otherwise, please provide the following information for each problem that you believe was graded incorrectly.

1. The number of the problem to be regraded.
2. The score you think you should receive.
3. An explanation of why you think you deserve more points. This means that you should indicate which parts of your solution were graded incorrectly. You should be able to distinguish which part of your answer is correct and which part is incorrect. For example, you might say something like "I solved the problem correctly but forgot to multiply by 2 at the third step".

Failure to provide any of the above information may result in your test not being regraded.