MTH 309LR T: Introductory Linear Algebra

Fall 2023

Instructor: Alexandru Chirvasitu

Lectures: Office: 216 Mathematics Building
Office hours: TR 08:00 - 09:20 and 11:00 - 12:30
Email: achirvas AT buffalo.edu

TA: Christian Cuevas

Recitations: Office: 139 Mathematics Building
Office hours: W 2:00 - 4:00 PM
Email: ccuevas AT buffalo.edu

There is a sample Math 309 syllabus here. Ideally, that'll be a pretty good indication of the material and pace of the class.

Note that the syllabus specifies a computer-based component to the course; this might entail some computer-assisted assignments or exercises (more on this below).

Text

As mentioned the sample syllabus linked above (both available free of charge under various CC licenses):

Reading

I'll probably ask you to read some of the sections in the text(s) before most lectures, so we're in sync. I'll post the reading assignments here, numbered as sections of the textbook. The date is that of the lecture, so please do the reading before that.

Due date Assignment Remarks
1 Th Sep 07

[S]: 1.1 - 1.5

The dash '-' means everything in between; so it's five (5) sections in total.

2 Th Sep 14

[S]: 1.6, 1.7, 1.11

[S]: 2.1 - 2.4

3 Th Sep 21

[S]: 4.1-4.3

[S]: 5.1-5.4

The portion in Chapter 4 is intended more as brushing up on matrix algebra. You will have seen this sort of thing in high school. The main reading material consists of the four sections in Chapter 5.

Th Sep 28

[S]: 4.4-4.6

[S]: 5.5

4 Th Oct 05

[S]: 2.5, 2.6

[S]: 6.1-6.4

5 Th Oct 12

[S]: 6.5

[S]: 7.1-7.4

6 Th Oct 19

[S]: 7.5, 7.6

[S]: 8.1, 8.2, 8.4

7 Th Oct 26

[S]: 8.5, 8.6, 8.9-8.11

Notice the dash between 9.9 and 8.11; so this includes 8.10.

8 Th Nov 02

[S]: 9.1-9.3

Th Nov 09

[S]: 9.4

9 Th Nov 16

[S]: 10.1-10.4

No classes the whole week of Nov 20

10 Th Nov 30

[S]: 11.1-11.3

Th Dec 07

[S]: 11.4, 11.6, 11.7

Supplementary material

On occasion, I'll post extra notes, comments, etc. in this space.

Homework

The homework will mostly consist of problem lists from our textbook, posted either here or on UBLearns.

No late homework for any reason, but we are dropping the three lowest scores.

Due date Assignment Remarks
0 Th Aug 31

Get acquainted with SymPy and Jupyter notebook for the purpose of doing linear algebra computations.

That link is to a tutorial / walkthrough once you have the software; see this for a quick setup guide.

1 Th Sep 07

  • [S] 1.4: 1.4.11, 1.4.12, 1.4.16 (d)
    1.4.19*, 1.4.26, 1.4.27 (e)

  • [S] 1.5: 1.5.1, 1.5.4, 1.5.6*, 1.5.7

The star indicates my suggestion that you also work out that problem in a Jupyter notebook, for practice with that technology. You do not need to turn in that computer-assisted work in any way; it's just a good opportunity for you to practice.

To help you along, I have worked out problem 1.4.18 as a model (it's a close cousin of assigned problem 1.4.19).

You can either stare at the html page produced from the Jupyter notebook I worked out or, even better, download the notebook for yourselves and modify it on your own machine (if your browser tries to open it directly, right-click the link and select 'Save Link As' or some analogous option).

2 Th Sep 14

  • [S] 1.6: 1.6.3

  • [S] 1.7: 1.7.1, 1.7.2

  • [S] 1.11: 1.11.1*, 1.11.2*

  • [S] 2.1: 2.1.3

  • [S] 2.2: 2.2.2

  • [S] 2.3: 2.3.3

  • [S] 2.4: 2.4.2, 2.4.3*

As before, the stars indicate I'm suggesting you take the opportunity to play with Python while trying to solve those problems. For guidance, here is a problem similar in spirit to 2.4.3 in your assignment; you can also download the notebook source to modify and/or run in your own Jupyter instance.

3 Th Sep 21

  • [S] 5.1: 5.1.1*, 5.1.4, 5.1.5

  • [S] 5.2: 5.2.2, 5.2.4, 5.2.7*

  • [S] 5.3: 5.3.1, 5.3.3

  • [S] 5.4: 5.4.1*, 5.4.2, 5.4.8

As previously, stars mean try to also employ Python to work through these. HTML and source for a Jupyter notebook working out an analogue of problem 5.4.1.

Th Sep 28

exam 1, so no homework due. I am suggesting the following problems for practice:

  • [S] 4.4: 4.4.5, 4.4.7

  • [S] 4.5: 4.5.5, 4.5.8, 4.5.18*, 4.5.20*

  • [S] 4.6: 4.6.2 (a) (b), 4.6.3 (a) (d), 4.6.4 (c) (d)

  • [S] 5.5: 5.5.1*, 5.5.2*

No homework due this week.

HTML and source for a Jupyter notebook working through a version of problem 4.5.20.

No solutions will be available here for the midterm. Instead, if you want to check your answers, please run the problems yourselves through SymPy; this will be a good incentive to use that tool.

4 Th Oct 05

  • [S] 2.5: 2.5.8, 2.5.9

  • [S] 2.6: 2.6.7, 2.6.10

  • [S] 6.2: 6.2.3*, 6.2.6

  • [S] 6.3: 6.3.6

  • [S] 6.4: 6.4.7, 6.4.10*, 6.4.12*

Stars have the same meaning as before (problem good for Python practice). HTML and source for a Jupyter notebook working out problem 6.2.4, which in turn is a version of your assigned problem 6.2.3.

5 Th Oct 12

  • [S] 7.1: 7.1.1, 7.1.2*

  • [S] 7.2: 7.2.2*, 7.2.3, 7.2.5*, 7.2.7

  • [S] 7.3: 7.3.1

  • [S] 7.4: 7.4.1

You presumably know what the stars mean by now. HTML and source for a Jupyter notebook working out problem 7.2.6 (very similar to homework problem 7.2.5).

6 Th Oct 19

  • [S] 7.5: 7.5.13

  • [S] 7.6: 7.6.5, 7.6.7

  • [S] 8.1: 8.1.5*, 8.1.6

  • [S] 8.2: 8.2.4, 8.2.6, 8.2.7

  • [S] 8.4: 8.4.2*, 8.4.6*

HTML and source for a Jupyter notebook finding eigenvalues and eigenspace bases for a matrix (so relevant, say, to homework problem 8.1.5).

7 Th Oct 26

  • [S] 8.5: 8.5.3*, 8.5.5*

  • [S] 8.6: 8.6.2

  • [S] 8.9: 8.9.1*, 8.9.2

  • [S] 8.10: 8.10.2, 8.10.3

  • [S] 8.11: 8.11.1, 8.11.2

HTML and source for a Jupyter notebook relevant, say, to problem 8.9.1 (working out algebraic / geometric multiplicities, diagonalizing, etc.).

8 Th Nov 02

  • [S] 9.1: 9.1.1, 9.1.2, 9.1.9

  • [S] 9.2: 9.2.2*, 9.2.4, 9.2.6* (b), 9.2.7*

  • [S] 9.3: 9.3.12, 9.3.16, 9.3.19

HTML and source for a Jupyter notebook working through Problem 9.2.6 (a) (very similar to your 9.2.6 (b)).

Th Nov 09

exam 2, so no homework due. I am suggesting the following problems for practice:

  • [S] 9.4: 9.4.1, 9.4.4*, 9.4.5, 9.4.7, 9.4.8*

No homework due this week.

HTML and source for a Jupyter notebook working through Problem 9.4.3 (very similar to your 9.4.4).

No solutions will be available here for the midterm. Instead, if you want to check your answers, please run the problems yourselves through SymPy; this will be a good incentive to use that tool.

9 Th Nov 16

  • [S] 10.1: 10.1.1, 10.1.2

  • [S] 10.2: 10.2.2

  • [S] 10.3: 10.3.1*

  • [S] 10.4: 10.4.2*, 10.4.3, 10.4.4, 10.4.6*

HTML and source for a Jupyter notebook working through the textbook's problem 10.4.1 (similar to 10.4.2 on the homework).

10 Th Nov 30

  • [S] 11.1: 11.1.3

  • [S] 11.2: 11.2.2, 11.2.4* (a) (c) (d)

  • [S] 11.3: 11.3.3*, 11.3.5*

HTML and source for a Jupyter notebook working through problem 11.3.2 (similar to 11.3.3).

Th Dec 07

exam 3, so no homework due. I am suggesting the following problems for practice:

  • [S] 11.4: 11.4.2*, 11.4.3, 11.4.4*

  • [S] 11.6: 11.6.1, 11.6.2, 11.6.3*

  • [S] 11.7: 11.7.1*

No homework due this week.

HTML and source for a Jupyter notebook that works out a problem similar to 11.7.1.

No solutions will be available here for the midterm. Instead, if you want to check your answers, please run the problems yourselves through SymPy; this will be a good incentive to use that tool.

On computer use

As mentioned above, this class has a "computer component", but it is by no means central: this is still a math course. For that reason, I cannot focus on the relevant computer tools directly during lectures, but I nevertheless urge you to take seriously the task of learning those tools, mentioned in the homework table above:

To illustrate the power these wield, let me illustrate a point (this will make more sense after we've learned some of the incipient material). Suppose I ask you to solve a system of linear equations (something we'll do often). You'l learn how to do this on your own, but you can have a computer do it for you: see how I got SymPy to do this for me here.

In fact, as an exercise, you might try your hand at replicating that notebook by yourself (after you've installed Jupyter Notebook and all of the rest).

Exams

We're having three of these scheduled during regular class time; the dates are as follows.

Please note that UB academic-integrity policy very much applies to this class, and the integrity of the exams is taken very seriously.

Grading

Some links

If you have any questions, don't hesitate to email me.

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