Linear Algebra II 15-Math-352 Section 001

Department of Mathematical Sciences

This page is a work in progress! All information is subject to change (Last revised 18 Feb 2012)

Textbook Linear Algebra: A Geometric Approach (2nd edition) by Shrifin and Adams           General Syllabus Chapters 4, 5, & 6.

Calculus III (Math 253) and Linear Algebra I (Math 351) are prerequisites for this course. There are no co-requisites.

• 20% --- final exam (assigned problems due Monday March 12)
• 60% --- three in-class hour exams (each exam counts 20%)
• 20% --- homework assignments

The main Course Goal is the study of linear transformations. We'll start by learning about abstract vector spaces with a quick brief review of the concepts (all from Linear Algebra I) of linear combinations, span, linear independence, bases, dimension, the Rank-Nullity Theorem, etc. Our study of linear transformations will emphasize the notion of projection. We will see that orthonormal bases are especially useful, which leads to the so-called Gram-Schmidt orthonormalization process and the QR-Algorithm. We'll briefly touch on the theory of determinants, which in turn we will use to study eigenvalues and eigenvectors. If time permits we will then look at the diagonalization problem and the all important Spectral Theorem and its many applications.

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

If you are seeking help, there are Graduate Student Teaching Assistants on duty at the Mathematics Learning Center located in French Hall West room 2133. Check their web page for their hours. The Mathematics Learning Center (MLC) is a free, walk-in, mathematics tutoring center for all University of Cincinnati students. The tutoring hours, beginning Monday January 9, are: Monday-Thursday 9am-8pm, Friday 9am-4pm, Saturday Noon-4pm.

Students can get help at the MLC for all basic mathematics courses through Differential Equations including Statistics and Business Mathematics courses. Perhaps the best way to get help is to ask your fellow classmates!

In addition it is possible to hire a private tutor; see the MLC web page.

Finally, here is some friendly advice. I encourage you 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. I will go over as many homework problems as possible. However, mathematics is not a spectator sport; mathematical knowledge is not gained passively; you will not learn by osmosis; you must be an active participant in the learning process. This means that to learn the material you must work the problems yourself and practice constantly every day. You must work lotsa problems, as many as you can. Don't be afraid to work some of the problems over and over again, especially when you're studying for an exam. It is easy to fall behind; try to keep up with the course and seek help immediately if you have problems.
It is a excellent idea to go over your notes as soon as possible after class!

The last day to drop this class (with no entry to your academic record) is Tuesday January 17, 2012. The last day to withdraw from this class is Wednesday February 29, 2012. These are official UC dates and something I have no control over. 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 turning in at least one homework assignment, taking at least one quiz, or taking at least one exam.

Here I explain the Regrading Policy. Mistakes are made in grading, especially when there is only one person responsible for grading all of your work. 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 work 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 term. Thus 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 work, then you must appeal the grade in writing within one day of the day the work was returned to the class. A late request for regrading will automatically be denied. To have your work 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 and the score you think you should receive.
2. 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 work not being regraded.

Please adhere to the following Guidelines when writing your homework assignments. Work that does not meet these requirements will not be graded. You should aim to produce solutions that would be easily understood by a classmate!

• Late assignments will not be accepted. Assignments must be handed in before class on the day they are due.
• Your work must be legible with your solutions/explanations clearly marked.
• Please start each new problem on a new sheet of paper.
• Please start each problem with a statement that clearly indicates precisely what it is that you are about to do. For instance, sometimes you can simply copy the problem from the text book.
• What you actually hand in, your final finished version, should be as polished as you can make it. This probably means that you will have previously written up at least sketchy solutions. Please expect to do a fair amount of rewriting.
• You will be graded on the proper use of mathematical terminology and notation, as well as the validity of your solution. However, please minimize the use of special mathematical notation.
• Please write using complete sentences that form paragraphs and so forth. I find it best to avoid long complicated sentences. All of this is a judgment call -- the judgment of the grader.
• Mistakes must be erased, not scratched out. It is best to use a pencil. Work that has lots of scratched out parts will not be graded.
• Put your name on each page and staple the pages. Please turn in a neat stapled stack of papers. Your work should be done on standard (8.5 by 11) size paper. If paper is torn from a spiral notebook, the edges should be trimmed.