Colorado State University, Pueblo
Math 207 — Matrix and Vector Algebra with Applications
Fall 2011

Here is a shortcut to the course schedule/homework page.

Class meets: MWF (22 Aug to 24 Oct!) in PM 103, 2-2:50pm
Instructor: Jonathan Poritz     Office: PM 248 E-mail:
  Phone: 549-2044 (office — any time); 357-MATH (personal; please use sparingly)
  Office Hours: M-F 9-9:50am or by appointment (or walk-in!)

Text: Linear Algebra, A Modern Introduction (2nd ed.), by David Poole. [Note: please make sure you get the second edition, the third is indeed available, but we are not using it.] We will cover much of Chapters 1, 2, and 3, and parts of 4. The book is fairly good — please actually read the text sections assigned on the HW/schedule web page!

Prerequisite: MATH 124 or equivalent. Corequisite: Majors and minors should take this course concurrently with MATH 224 or MATH 325.

Content/objectives: The catalog description of course content is:

Systems of equations, matrix representation of systems, solution of systems, inverses, determinants, and Cramer's Rule. Vectors, scalar and cross-products, applications to two- and three-dimensional geometry.

Certainly, some of the catalog topics will receive fairly light emphasis (such as Cramer's rule), while other, unmentioned topics (such as eigenvalues and eigenvectors) will take a lot of our time.
Over-all, a more poetic description of our goal would be that it is to introduce students to the geometric and algebraic ideas behind, and techniques for working with, matrices and vectors. Where possible and relevant, we will also discuss applications of these ideas and techniques in other fields, including physics, engineering, computer science and other parts of mathematics.
Note that this course covers material which is both a tremendously useful, practical tool in many disciplines ... and it is also the first step on the road where mathematics becomes more formal and abstract. This is not a bad thing! It means we get to work on building careful and complete mathematical statements and even proofs, in the context of a beautiful collection of ideas which are fundamental in a host of applications

Academic integrity: Mathematics is more effectively and easily learned — and more fun — when you work with others. However, all work you turn in must be your own, and any form of cheating is grounds for an immediate F in the course for all involved parties.

Attendance and work ratio: Regular attendance in class is a key to success. I will assume students will be present although I will not take attendance after the first few classes and will try to keep my HW/schedule web page up to date will all important notices in case you do miss a class. Outside of class, you should expect to spend at least 2 hours per day on this course, mostly on homework. This is not an exaggeration (or a joke), and you should make sure you have the time and energy — but I guarantee that if you put in the time and generally approach the class with some seriousness you will get quite a bit out of it (certainly including the grade you need).

Classroom participation: There will be organized opportunities for students to be active class participants, such as when working in groups and presenting problem solutions, as well as less formal opportunities — when students ask questions (which will be worth extra-credit points!). And even if you do not speak out loud, you must participate in class in the sense of engaging with the material, of working through the abstract statements we are covering and the applications they are yielding. As each thing comes up in class (and probably goes onto the board), you should be actively thinking:

Please feel free to ask any of these questions as they occur to you, or to offer your answers when you have some.

Students with disabilities: This University abides by the Americans with Disabilities Act and Section 504 of the Rehabilitation Act of 1973, which stipulates that no student shall be denied the benefits of education "solely by reason of a handicap." If you have a documented disability that may impact your work in this class for which you may require accommodations, please see the Disability Resource Coordinator as soon as possible to arrange accommodations. In order to receive accomodations, you must be registered with and provide documentation of your disability to: the Disability Resource Office, which is located in the Library and Academic Resource Center, Suite 169.

Homework: will generally be due weekly. You will probably enjoy it more, and learn more from it, if you work with your friends, so I encourage you to do so. However, you must each turn in your own write-up of the solutions.

A large part of mathematics is a learned skill of which you will need to acquire active mastery, by practice and independent struggle, so I expect you will spend at least two hours of effort on this course outside of class for each hour actually in class. Most of this time will be spent on your homework, which will be essentially impossible to do at the last minute. So please start your homework early and talk to me, in class and my office hours (or any other time you can find me), for help as you are working on it.

There may also be quizzes and/or classroom worksheets which can be turned in and which will count as part of your homework grades.

Some organizational details about homework:

Exams: We will have two midterm exams: the first, covering Chapter 1 and §§2.1-2.2, in class partly on Wednesday, September 14th and the rest on Friday, September 16, 2011; the second exam, covering the rest of Chapter 2 and Chapter 3, in class on Friday, October 7, 2011. The final will include some material from both of these parts of the course, but will have a special emphasis on later material from Chapter 4, which will not have been tested yet. It will be given in two parts, on Wednesday, October 26, 2011, and Friday, October 28, 2011, in class.
[On exam days, attendance is required -- if you miss an exam, you will get a zero as score; you will be able to replace that zero only if you are regularly attending class and have informed me, in advance, of your valid reason for missing that day.]

Grades: I will drop your lowest homework score. After that, the various parts of the course will be weighted as follows:
                                        Class Participation: 5%
HW Exercises: 17%
Main Ideas: 10%
2 Midterms: 17% (each)
Final Exam: 34%
Course grades will then be computed in a manner not more strict than the traditional "90-100% is a A, 80-90% a B, etc." method. [Note that the math department does not give "+"s or "-"s.]

No fractionated grading/extra credit: Let me repeat that: by Math Department policy, there will be no +'s or -'s. It therefore is particularly useful to have accumulated a bit of extra credit by the end of the class, so that if you are near a grade cut-off, you will receive the higher letter grade. You can earn extra credit in the following ways:

  1. After tests (and other written work?), there will be opportunities to hand in revised solutions to problems where you lost points. New (correct!) solutions solutions will be worth extra credit points up to the number of points you missed on the original problem.
  2. Using recycled paper for your written assignments, which will yield Green Points that are converted into extra credit at the end of the term.
Also with no fractionated grading, it is particularly important not to loose points needlessly. Therefore, make sure you get lots of credit on your Main Ideas and (conquering your shyness if necessary!) for class participation, that you don't simply neglect to hand in some assignment, etc.

Nota bene: Most rules on due dates, admissibility of make-up work, etc., will be interpreted with great flexibility for students who are otherwise in good standing (i.e., regular classroom attendance, homework (nearly) all turned in on time, etc.) when they experience temporary emergency situations. Please speak to me -- the earlier the better -- in person should this be necessary for you.

Contact outside class: Over the years I have been teaching, I have noticed that the students who come to see me outside class are very often the ones who do well in my classes. Now correlation is not causation, but why not put yourself in the right statistical group and drop in sometime? I am always in my office, PM 248, during official office hours. If you want to talk to me privately and/or cannot make those times, please mention it to me in class or by e-mail, and we can find another time. Please feel free to contact me for help also by e-mail at, to which I will try to respond quite quickly (usually within the day, often much more quickly); be aware, however, that it is hard to do complex mathematics by e-mail, so if the issue you raise in an e-mail is too hard for me to answer in that form, it may well be better if we meet before the next class, or even talk on the telephone (in which case, include in your e-mail a number where I can reach you).

Only 10 weeks! This is a 2 credit course given with class meetings MWF — therefore it will meet only for the first ten weeks of the term. Hence all important dates (drop/add, finals, etc.) are somewhat compressed: see the course schedule for details.

Calculators: A calculator, such as the TI-84 (or higher), which can do matrix operations, is recommended. Students will be expected, however, to learn to do all computations on their own.

A request about e-mail: E-mail is a great way to keep in touch with me, but since I tell all my students that, I get a lot of e-mail. So to help me stay organized, please put your full name and the course name or number in the subject line of all messages to me. Also, if you are writing me for help on a particular problem, please do not assume I have my book, it is often not available to me when I am answering e-mail; therefore, you should give me enough information about the problem so that I can actually help you solve it (i.e., "How do you do problem number n on page p" is often not a question I will be able to answer).

Jonathan Poritz (




Trinity: I know why you're here, Neo. I know what you've been doing... why you hardly sleep, why you live alone, and why night after night, you sit by your computer. [...] It's the question that drives us, Neo. It's the question that brought you here. You know the question, just as I did.
Neo: What is the Matrix?
Trinity: The answer is out there, Neo, and it's looking for you, and it will find you if you want it to.


Morpheus: Unfortunately, no one can be told what the Matrix is. You have to see it for yourself.
  from The Matrix, (1999), written and directed by Andy and Larry Wachowski, Warner Bros.

  from Toothpaste for Dinner, webcomic by "Drew",