Welcome to Linear Algebra for Math Majors! This is a rigorous, proof-based linear algebra class. The difference between this class and Linear Algebra for Non-Majors is that we will cover many topics in greater depth, and from a more abstract perspective. There will be a correspondingly smaller emphasis on computation in this class, and greater expectations for proof-writing and abstraction.
This course has high expectations. You should plan to spend 9 hours per week on this class, not including lecture. It will also be necessary to supply independent motivation as not all of the work you need to do for this class will be collected, or even assigned. It is also essential to recognize early when you are struggling with a concept and discuss it with me.
Above all, you must engage actively with the material as we learn it. If you are studying actively, you will have questions. Use this principle to measure whether you are actively engaged.
The first thing to do when joining this course is to make sure these expectations align with your goals.
I encourage you to consult outside sources, use the internet, and collaborate with your peers. However, there are important rules to ensure that you use these opportunities in an academically honest way.
To avoid plagiarism, you should always cite all resources you consult, whether they are textbooks, tutors, websites, classmates, or any other form of assistance. Using others' words verbatim, without attribution, is absolutely forbidden, but so is using others' words with small modifications. The ideal way to use a source is to study it, understand it, put it away, use your own words to express your newfound understanding, and then cite the source as an inspiration for your work.
Do you have a question or comment about the course? The answer might be in the course policies, on this page. If your question isn't answered in the course policies, please send me an email. Or, if you prefer, you may send me a comment anonymously.
Instructor: Jonathan Wise
Office: Math 204
Office hours: calendar
Phone: 303 492 3018
My office is Room 204 in the Math Department. My office hours sometimes change, so I maintain a calendar showing the times I will be available. I am often in my office outside of those hours, and I'll be happy to answer questions if you drop by outside of office hours, provided I am not busy with something else. I am also happy to make an appointment if my office hours are not convenient for you.
We will use several texts in this class. Most of them are available online, except for the following one, which is out of print:
Hans Samelson. An introduction to linear algebra.
We will use the following text more in the first third to half of the course than we will towards the end. It is available for free via the University of Colorado's subscription to SpringerLink.
Paul R. Halmos. Finite-dimensional vector spaces
The next two texts are both available for free online. We may or may not make explicit use of them in class, but you could find them useful regardless:
Jim Hefferon. Linear algebra, 3e.
Sergei Treil. Linear Algebra done Wrong.
Here are a few other textbooks I have used in the past, but that I don't plan to rely on explicitly in this course. You may find them useful if you are looking for another perspective.
Stephen H. Friedberg, Arnold J. Insel, and Lawrence E. Spence. Linear algebra, 4e.
Sheldon Axler. Linear Algebra done Right, 3e.
Your grade will be the average of your scores on approximately 4 in-class quizzes, approximately 4 problem sets, and the final exam. Quizzes and problem sets will count equally, and the final exam will count as the equivalent of 2 quizzes.
The scoring on these assessments will be based on the goals listed above. Notably, your score will not be a simple sum of point values from each problem, but will instead be my overall assessment of the degree to which you have achieved the course's goals on the relevant topics.
At the end of the semester, I would like for your final grade to reflect your mastery of the course material. Exams and problem sets do not always measure this optimally, so you will be allowed to revise your scores by the following process: 1) decide which score you wish to revise; 2) identify the topics that were assessed (for example, from the course outline) and put these in a list to be handed in with your revision (you may want to clear your list with me before going on to the next step); 3) find or devise a list of problems that you can use to demonstrate your mastery of those topics (again, you may want to discuss these with me); 4) solve those problems and submit your solutions to me. I will assign a replacement grade based on your submission.
As a practical matter, I insist that your revisions be submitted within two weeks of the due date of the original assignment. This is meant to prevent an influx of revisions at the end of the semester, when I will not have time to look at all of them.
The revision policy will also be used to address missed assignments and exams. No grades will be dropped, apart from those replaced by revisions.
The following is an abbreviated list of topics covered in this course (the definitive list is in the assignments below) and may be a good guide for topics that will be addressed on the exam.
A reference discussing most of the important aspects of LaTeX you will use.
A very quick introduction to LaTeX.
If you need to know the command for some symbol, try using Detexify.
The Mathematics Academic Resource Center (MARC) is staffed with learning assistants and undergraduate and graduate students that can help you with concepts in this class. This is an excellent resource, and I encourage you to use it, but remember to use this resource responsibly!
Do ask for help from MARC with the daily, uncollected homework assignments in this class.
Do Ask for clarification of ideas from the textbook and from discussion in class.
Do not ask for help from MARC with specific problems on the the larger, collected (graded) assignments.
Do not under any circumstances submit a solution that was given to you by MARC as your own work.
The Office of Academic Affairs officially recommends a number of statements for course syllabi, all of which are fully supported in this class.
If you need special acommodation of any kind in this class, or are uncomfortable in the class for any reason, please contact me and I will do my best to remedy the situation. You may contact me in person or send me a comment anonymously using the form below.