Linear Algebra (Math UN2010)

Instructor: Mike Miller
Time: Tuesday/Thursday 11:40am-12:55pm EST
Email: smm2344@columbia.edu
Webpage: here! Homework will be posted to Courseworks
Office: My dining room table

Office hours: There will be two Zoom office hours per week, times TBA. You will be able to access them in the Zoom Class sessions tab.

Teaching assistants:  TBA

Textbook: Linear Algebra with Applications (5th Edition) by Otto Bretscher. Problems will be assigned out of Bretscher (though I may supplement with my own problems). Math majors may also wish to refer to "Linear Algebra Done Wrong" by Sergei Treil; his textbook is more proof-based. (The title is a reference to a popular proof-based linear algebra textbook; Treil takes a different approach to the material than that author does.)

You can find a copy of essentially every textbook you ever need in PDF form online. Feel free to get in touch to ask if you do not know where to look. 

Topics: Narrowly speaking, linear algebra is the study of linear systems of equations, their properties, and their solutions. Broadly speaking, linear algebra is the study of linear functions, the simplest kind of functions. Linear algebra shows up everywhere because of a simple philosophy: "If you have something complicated, start by understanding the simplest piece (the linearization)". We will see that we can get a lot of control over this "simplest piece". (The second reason it shows up is that, once you know linear algebra, you see that it's so powerful you'd like to use it everywhere you can think to.) 

Some material in the class will not be covered in the textbook. There will be notes posted for this material on Courseworks.

How much you get out of this class will be proportional to how much you put in. Linear algebra is perhaps the single most commonly used math topic past high school algebra, both in and outside math itself. There are more ways to talk about linear algebra than I can count, and certainly more than I can cover in a semester's worth of lectures. To help you explore, I will post completely optional supplemental material guiding your study on some of these different approaches. I plan to have materials both for proof-minded students (math majors, mostly) and for algorithmically motivated students (computer scientists and engineers, mostly), both of which will cover material not usually found in a first linear algebra course.

Prerequisites: Calculus III (UN1201) or equivalent. You should have experience and practice with vectors, dot products, and cross products, as well as determinants of 2x2 and 3x3 matrices.  

Piazza: This term we will be using Piazza for class discussion. The system is designed to get you help fast from me, your TAs, and your classmates. Rather than emailing questions to me or your TAs, you should post your questions on Piazza; we will respond as quickly as we would via email. I try to respond as soon as I see a question. Sometimes your fellow students will be able to help out more quickly than we can, too. 

Homework: There will be a total of approximately 10 homework assignments. Most homework will be assigned on Tuesday and due by the following Tuesday. To submit your homework, you will need to scan it (either with a scanner or with a scanning app on your phone), and upload it on Courseworks; if your homework is not readable, it will not be accepted.

In my experience, homework is not useful as an evaluative tool --- it is important because the only real way to learn and understand math is with practice. To encourage this, homework is graded entirely on completion; the graders will, however, still give weekly comments.

You can work together with other students on the assignments (I encourage it - explaining math helps you understand and remember math), but answers must be written up in your own words, and you must write down who you collaborated with.

Late homework will not be accepted.

Tests: There will be two midterm exams and one final exam. The exams will not be administered in class; they will be available online for the specified time period.
The tests are open-book, and open-note (in the sense that you can refer to your own notes), but nothing else; you may not collaborate with classmates or use any online tools. We are all working hard to make these online semesters work. By offering a take-home exam, I am extending my trust to you. Do not take advantage of that trust. Any and all academic integrity violations will be pursued aggressively.

Each midterm is available for a 12-hour period, but should take no longer than 90 minutes to complete and submit. The final is available for a 24-hour period, but should take no longer than 4 hours to complete and submit. 
The exams must be submitted on time, before the end of the available period. Late exams will not be accepted. Therefore, you should be sure to start submitting at least an hour before the end of the period, and contact me the moment you run into technical issues.

The midterms only cover the material between the tests; the final is cumulative.

(tentative)

Midterm 1: Feb 14 (9AM-9PM EST)
Midterm 2: Mar 21 (9AM-9PM EST)

Final: Apr 22, all day (12AM-11:59PM EST)

There are no make-up exams, and there are no exceptions to this policy. If you foresee an issue with these dates, contact me immediately.

Grading: The final course grade is weighted as:

Homework: 15%
Midterm 1: 25%
Midterm 2: 25%
Final: 35%

Your bottom homework score will automatically be dropped.

Students with disabilities: To receive accomodations for exams (or otherwise), you must register with the Disability Services office and present an accomodation letter.
More information is available here.

Getting help: Math, and college, can be hard; anybody who's done a lot of math will tell you that they've struggled. If you're finding that you're struggling with the course, you should get help immediately.
If you're finding yourself overwhelmed but don't get help, then the tide may very well sweep you away and leave you completely lost!
You can come to my office hours (listed on my main page and this syllabus), or to the help room, where there is always TA - your specific TA's help room hours will be posted as well. And as mentioned above, I recommend working with your friends! Lastly, please do not hesitate to reach out to me. 
There is information here about tutoring services. I will warn that private tutoring, especially in NYC, can be extremely expensive.