Linear algebra is a very different kind of math than what many students are used to, especially those coming from small schools without the IB program or AP classes who have only done a bit of calculus. Some say it is harder than MAT137, but others have a much easier time in MAT223. You will soon learn what works for you in a course like this, but until then here are some tips that helped me get through.
1. Pay attention to theorems
Most students are accustomed to studying for math by doing one thing: practice problems. However, MAT223 requires a different approach. The theorems in this course are essential knowledge to answer questions and do proofs. Many of the test questions require an understanding of theorems and are not just computation.
2. Learn the basics
Although this one may seem obvious, it is a necessary point. At the start of the course you will learn row-reduction of matrices, and almost everything you will learn beyond that uses this skill. In order to answer many more complex questions, you will first be obligated to row-reduce. The term tests are only 50 minutes, so struggling to do this elementary step will cost you.
3. Definitions, definitions, definitions!
Similar to theorems, you will learn many definitions in this course. REMEMBER THEM! It’s easy to learn a definition at the start of the semester and completely forget what it means by the end, when it’s necessary again. Words like span, basis, linear dependence, etc. will come up frequently and without a proper understanding of them, you will have a hard time with the more complex material.
4. Go to tutorials and do assignments
A common mistake students make is to skip tutorials and put off assignments. However, these are easy marks that are almost guaranteed to boost up your grade. The assignments on Tophat supplement the course lectures and introduce new topics that you may glaze over in lecture, so pay attention! The tutorials have quizzes that are easy as long as you stay caught-up with the lectures. Make the best out of these easy marks!
5. Use the resources available to you and practice
This is a more general tip for any math course here at the University of Toronto. U of T can be daunting at times, but many classes offer a lot of great resources. Go to math aid centers, and ask your TA’s for help. Piazza is a great way to get help without leaving the comfort of your dorm. Also, the textbook for this course is very helpful, the examples and explanations will help you understand lecture and tend to be more thorough. There are suggested questions to do from the textbook online for every section, do these often to make sure you are up to speed!
All in all, most students must work hard in this class to succeed. Find what study methods work best for you and run with them. Don’t be afraid to get help, and remember that if you’re struggling, other students are too.