How to Survive MAT202 - Linear Algebra

This guide is written for one of my good friends who is about to take this class.

Is MAT 202 for you?

MAT 202 – Linear Algebra with Applications is the lowest level linear algebra course that most STEM students will be required to take in the first or second years of undergraduate study at Princeton. You likely will not have a choice in the matter, but there are alternatives. For example, the EGR sequence is a full substitute for MAT 202 but you will likely have to be taking the equivalent PHY course as well, which many people may not be. From what I’ve heard, the EGR sequence is less rigorous than MAT 202, so that may be more your cup of tea.

Check here whether MAT 202 is necessary for you as well as consulting with your various advisors and (probably more helpfully) other fellow concentrators.

What Semester Should You Take It

As many students have used their AP Calculus BC credit or have just completed MAT 103 and 104 (Calculus 1 and 2), most students follow the “natural” progression of taking MAT 201 (Multivariable Calculus) in the fall and MAT 202 in the spring semester. From what I’ve heard, taking MAT 202 in the fall instead may be easier, but the difference between the semesters is most likely marginal and the advice will apply either way.

The Course Structure

The course is structured with two components: lectures and precepts. Lectures are where a majority of the information is disseminated and are not interactive while the precepts are with a smaller group (10-15 people) and are taught by a post doctoral student or assistant professor. I’d say there is much more learning in the precepts because the preceptors attempt to synthesize the material into problem solving methods as well as entertain questions and encourage participation.

I cannot really attest to the value of the lectures because I did not watch them. I usually attempted the assignments while in precept and wrote down any questions that I had while doing so. When precept was over, or at a convenient time during precept, you can ask your professor your question without having to worry about an office hours queue. All my professors were happy to talk after precept as well.

The assignments are split between problem sets (book problems) and exam preps (problems created by the instructors). There are more problem sets but they are worth less. The majority of your core understanding of the material will come from completing these assignments, so even if you plan on using one of your drops (dropping an assignment), take a cursory glance at the material of those chapters.

Learning the Material

1. Start with the assignments. Attempting to do the material will force you to learn what you need to learn and only that. I find reading the textbook passages daunting and unintuitive as many of the examples given are written in the abstract. Instead, go to the book assignment and just begin to attempt problems. In the textbook problems, which part of the reading the problem comes from is listed, so read only the relevant portions, and you will begin to understand the material as well as work on the assignment. This is more straightforward and an efficient use of your time. I did not use the lectures, but I’m sure that there are worked-through problems in the lectures, or at the very least, YouTube.
2. Do not check as you go. The trick to completing the work quickly is to immediately move on if you encounter difficulty on a problem. Since you are learning the material as you do problems, you might understand how to do a previous problem by attempting a later problem. Do not spend too long on any one problem. When you check your work in the back of the book, or with a friend or professor, then you can fill in the gaps in your knowledge.
3. As you do the assignment, write down the steps for each type of problem in your notes. See below.
4. Complete the entirety of the week’s assignments before the week begins. I started the semester doing that, and it was a relief knowing that I had no work for the class the entire week. Make sure you complete the problem sets before the exam preps since completing the problem sets is how you are learning the material anyways.

Preparing for Exams

1. Take a cursory glance through your notes. This is purely to refresh your mind on what the assessment is on.
2. Begin taking the practice tests with the oldest exam material you can find. Take the exams untimed and referencing your notes. If you don’t figure out how to do a problem or even part of a problem, look at the solutions and continue to work. This does not mean have the solutions next to you when completing the exam, but when you are stuck, look at that particular problem, and then continue.
3. When you get to recent test material, then attempt to take the exams without your notes but still utilizing the solutions when necessary.
4. Complete every single practice exam.
5. Go back to the book and complete every single True and False question. Some of the answers are in the back of the book; email your preceptor for the rest.
6. Immediately before the exams, go through your step-by-step instructions for completing the problems of the assessed chapters.

How I Organized My Notes

I use these Tops Steno Notebooks that are small and easily flippable. They are not durable by any means but they get the job done. Each page is divided in the middle. For each chapter, I write the title up top. If you work like I described above, then you will only do select parts of the readings. Any part of the readings that is boxed (i.e. a formula or definition) and you encounter, write down: the title on the left side, the actual formula on the right side. While you are solving problems, write down each step you take (in the abstract) as well. Writing down how you do complete each problem forces you to understand what you are doing and allows you to replicate those steps when you complete a similar problem later. When you have finished your assignments, you will never have to consult the textbook again because you have the important definitions (none of the abstract nonsense) and the steps to solve every problem you can think of.

Additional Tips

1. Linear algebra computations are usually the easiest part. There is almost always a way that you can check your work, whether that is multiplying the inverse of the matrix with the original matrix or at least confirming the dimensions of the input and output of a matrix operation.
2. Most of the algebraic operations that you are familiar with (especially multiplying and dividing) have linear algebra equivalents, but make sure you understand that the order that you complete matrix operations matters immensely.
3. Get a solid visual / geometric grasp of what each matrix operation does. 3Blue1Brown can help you with that. I would continually watch each of these videos until you have built that sense.
4. This course is manageable, as long as you stay on top of it. Find people that can help you, whether that is preceptors, McGraw tutors, students who previously took the course, or friends.
5. Know which assignments you can drop.
6. Start to prepare for your exams at least two days before hand.
7. Make sure you submit regrade requests, even if you don’t think that you can get points back, you probably can.
8. Don’t compare grades with your peers; it will always make someone feel bad.