Colorado State University, Pueblo
Math 307 — Introduction to Linear Algebra — Spring 2011

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

Lectures: MTWF 9-9:50am in PM 124      Office Hours: MTWF8-8:50am, T2-3pm, or by appointment

Instructor: Jonathan Poritz     Office: PM 248     E-mail:
Phone: 549-2044 (office — any time); 357-MATH (personal;please use sparingly)

Text: Linear Algebra, A Modern Introduction, Second Edition, by David Poole (the same textbook as was used in Math 207).

Prerequisites: A satisfactory grade (C or higher) in Math 207 (Matrix and Vector Algebra) and Math 224 (Calculus II). The course catalog also says "knowledge of a programming language" is required, but I will be very flexible in this regard — please contact me if you have any concern about this.

Course Content/Objective: Linear algebra is a fundamental tool — almost a way of seeing, of noticing or building a certain abstract structure (that of vector spaces and linear transformations) which then can be manipulated in its own right, nevertheless yielding powerful, concrete consequences wherever it is applied. It is used across all of pure and applied mathematics, but also in physics, chemistry, mathematical economics and sociology, computer science, engineering... the list goes on and on. Our goal in this course is to master a good piece of this theory, in its shimmering, abstract perfection, and also to see how it can be applied in just a few of the myriad possible ways.

The level of abstraction in linear algebra can be a challenge, but it also is part of the power of this subject. In order to take full advantage of this powerful abstraction, we have to start becoming comfortable with reading, understanding, and constructing new proofs. Building these skills relating to proofs will be another significant objective of this course, along with the specific body of knowledge of linear algebra, and we will spend serious time and effort in this area.

Academic integrity: Mathematics is more effectively and easily learned — and more fun — when you work in groups. 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 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 2-3 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 (all of 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 you answers when you have some.

Students with disabilities: The University abides by the Americans with Disabilities Act and Section 504 of the Rehabilitation Act of 1973, which stipulate 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 this assistance, you must be registered with and provide documentation of your disability to the Disability Resource Office, which is located in the Psychology Building, Suite 232.

Homework: The farther one gets into mathematics, the less it is a spectator sport: at the level of this course, the statements and examples we discuss in class or you see in the book will lie there like inanimate, two-dimensional ink or chalk on the page or board until you breathe full, three- (or more!) dimensional life into them with your insight and imagination. There will be plenty of opportunity to exercise these creative talents in class, but you will need to work extensively outside of class to practice and refine them. This will take the form of exercises sets you will work on and hand in essentially every week. One of the things about creativity is that it does not like to be rushed, so it is a very bad idea to expect to be able to slam out your linear algebra homework sets late the night before they are due. I therefore highly recommend that you start working on a HW set as early as possible, so your muse of creativity has time to visit you, no matter what her schedule is that week. If you are feeling uninspired by a problem on a HW set, you might fall back on traditional problem-solving steps like:

Don't forget also to The above strategy, and the attitude behind it, are particularly important: in the roughly twenty years I have been teaching college-level mathematics, I have had only a handful of students who put in the time and energy on their math course (time and energy being, of course, the most basic required student inputs) who were not successful ... and it was always because of skipping some of the above steps. The easiest to skip are usually the understand it yourself and learn from your mistakes steps: e.g., if you have a really helpful tutor who dictates complete solutions to you, and you also do not look over returned HW, quizzes, and tests, then you will get nothing out of (and therefore possibly even fail) this class.

To give you this extensive problem-solving practice, there will be fairly large, weekly homework sets. We will also spend much of our time in class discussing problems. In fact, I am happy to work with you during class time on the homework set due in some future class (or even due that very day).

Some organizational details about homework:

Projects: There will be an opportunity once during the semester for students to work more in depth on a topic (partly) of their own choosing. Details will be forthcoming.

Quizzes: Most Fridays, during weeks in which there is no hour exam, there will be a short (10-15 minute) quiz at the end of class. These will be closed book, but calculators will (usually) be allowed. Quizzes will be graded out of 10; your lowest quiz score will be dropped.

Exams: We will have two in-class hour exams on dates to be determined (and announced at least a week in advance). Our final exam is scheduled for both Thursday, May 5th and Friday, May 6th, both from 8-10:20am in our usual classroom.

Grades: Your total homework points will be scaled to be out of 175. Your project will be graded out of 75 points. Total quiz points (including also the MIs) will be scaled to 100. Each hour exam during the term will be graded out of 100, while the final will be out of 200. This means that the maximum possible course points are then 750. Letter grades will then be calculated in a way no more strict than:

A: 675-750   B: 600-674   C: 525-599   D: 450-524   F: 0-449

(This amounts simply to the old "90-100% is an A, 80-90% a B, etc." business.) Note that by Math Department policy, there will be no +'s or -'s. On quiz or exam days, attendance is required -- if you miss a quiz or 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.

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, no missing quizzes and tests, 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).

The Math Learning Center: located in PM 132, is a fantastic resource for CSUP math students — although, truth to be told, this class is advanced enough that many MLC tutors will not be able to help you with it (some tutors might be able to help, however, and pretty much any faculty member). Use it often! (But during my office hours &mdash or indeed any time you can find me in my office! — come to my office, preferentially, please.) It is free and fun, staffed with friendly and helpful tutors. MLC hours this semester are:

The MLC opens at 8:30
weekdays and closes at:   
5pm 5pm 5pm 5pm 3pm

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 (

Here's a diagrammatic representation of something sometimes called
The Fundamental Theorem of Linear Algebra: