Math 3410 Course Outline

Subsection 1.1 Welcome to the University of Lethbridge

Oki, and welcome to the University of Lethbridge. Our University’s Blackfoot name is Iniskim, meaning Sacred Buffalo Stone. The University of Lethbridge acknowledges and deeply appreciates the Siksikaitsitapii peoples’ connection to their traditional territory. We, as people living and benefiting from Blackfoot Confederacy traditional territory, honour the traditions of people who have cared for this land since time immemorial. We recognize the diverse population of Aboriginal peoples who attend the University of Lethbridge and the contributions these Aboriginal peoples have made in shaping and strengthening the University community in the past, present, and in the future.

Unless you took a pass on the last semester, this is not your first crack at learning online. Making connections as we learn remotely will be a challenge, but somehow we'll do our best to make this happen. One of the ways we'll try to encourage community is by having regular group work, where you'll be able to interact with other students in the class. Another is by having an active discussion platform. This year we're trying out a new system, called Campuswire.

As usual, everything you need to know for the course will flow through our Moodle learning management system. Make sure you check in regularly to keep on top of what's happening in the course. (Possibly the hardest part of learning online is keeping track of deadlines.)

Don't hesitate to reach out if you have questions. I'll do my best to answer all of your course-related questions as quickly as possible. (See Section 3 for details on how to get in touch.) If you have questions that are not related to the course, you can ask those too, and I'll try to answer, or to direct you to someone who can. Some resources can be found on the University's Health and Safety website.

Subsection 1.2 Course staff and contact information

Math 3410 is running for Spring 2021 with a single section of 40-50 students. My name is Sean Fitzpatrick. I can be reached via email at sean.fitzpatrick@uleth.ca.

Office hours: I'll do my best to arrive a few minutes early for class. If you do too, that's a great time to get in some questions (or attempt to influence the content of that day's lesson). Check Moodle for the most up to date information on office hours. I will also use Moodle's Scheduler booking system to let you book individual appointments.

Subsection 1.3 Course description

Math 3410 is the continuation of the study of linear algebra you began with Math 1410. Some topics will be familiar, like vectors, matrices, and systems of equations. But Math 3410 has a much greater focus on theory and proof.

At many universities, linear algebra is offered as a first course with rigorous proof. (Many places do not have an equivalent of Math 2000.) One reason for this is that most proofs in linear algebra are straightforward (relatively speaking). Many theorems in linear algebra follow the classic “if … then” format of a conditional statement. The corresponding proofs tend to follow a familiar script:

1. Assume the hypothesis.

2. Translate the hypothesis using the definition of some term in the hypothesis.

3. Rearrange some terms (i.e. do some algebra).

4. Recognize that you've met the definition of some term in the conclusion.

5. Translate to the conclusion using that definition.

We won't focus entirely on theory and proof, however. Linear Algebra has many interesting applications, and we'll try to fit in a few. We'll also include computational content. In particular, we'll spend some time learning how to use the computer to do some of our calculations for us.

Subsection 1.4 And what about the whole online thing?

Ah, right! More details on that throughout the outline. But to get us started: what changes?

• More emphasis on:

  • Conceptual understanding

  • Discussion

  • Context (the whole “what is this good for?” routine)

  • Being generally swell human beings

• Less emphasis on:

  • Memorization (because how am I gonna stop you from looking stuff up, anyway?)

  • Routine computational proficiency (let's be honest: the computer can do this better than us most of the time)

  • Tests and exams (so I can spend more time teaching and less time as the Math Police)

The course is set up with synchronous meetings (via Zoom) that follow the original timetable. I do not have the same volume of asynchronous content for Math 3410 that I do for Calculus. As a result, this will be more of a synchronous courses than my calculus offerings, making it more important that you attend class.

It's also understandable if you can't. Bad internet. Bosses who don't understand that online classes still have, well, classes. Maybe you have to share your computer with your little brother. Maybe travel restrictions mean that when class meets, it's 2 am where you are.

I'll do my best to also support asynchronous learning when needed. Lots can be done on your own time, even if you do make it to class. You have free access to an online textbook (two of them, in fact), and while I don't have pre-recorded videos, I will record most of what I present in class.

In Subsection 2.4 you're going to see that there are lots of pieces to your grade. And yes, most of them have deadlines. But don't worry! Most of those pieces are small: designed to be done in class, or to take up no more than an hour or so of your time. Learning any kind of math is a marathon, not a sprint. So I'm giving you a little bit to do every day. Keep at it, and you'll do well. (Also, many deadlines are flexible, so don't hesitate to ask if you need more time.)