How to do well in linear algebra! As mentioned in the introduction video, this course is a theory course. And even though a significant part of the course will require you to do calculations by hand, to do well in this course you will need to achieve at least a moderate level of understanding of the concepts, definitions, theorems, and proofs. Simply memorizing the algorithms and formulas will have no long term benefits. In the real world, when applying linear algebra in any area, calculations are typically done by a computer. It's up to you to use the theory of linear algebra to set up the problem, input it into the computer, and interpret the results. So why do we make you do calculations by hand if they can be done by a computer? To help you understand the theory! In particular, whenever you are solving computational problems, you should spend some time thinking about how the method of solution and the answer compares to the theory of linear algebra.

In this course we will see that computations and proofs often go hand in hand. We will see that sometimes we can use the solution to a computational problem to help us figure out a proof, and that we can use a proof to teach us how to solve a computational problem. On that note, in this course examples and exercises will typically have two, three, or four variables and integer coefficients, but in the real world, problems could easily have thousands or hundreds of thousands of variables and irrational coefficients. Keep that in mind when studying the concepts of this course.

I will now give you several tips about how to do well in linear algebra:

Tip number 1: Read the material in the course notes before it is taught in the lectures. University lectures are typically fast-paced and contain alot of information. If you understand some of the material before the lecture, you will find that you will get even more out of the lectures.

Tip number 2: Take the time required to not only memorize the definitions, theorems, algorithms, and formulas, but to try to understand them. Gaining a level of understanding will really help when solving computational and theoretical problems as well as making future concepts easier to understand.

Number 3: Practice! Math is learned by doing! Make sure that you are practicing both computational and theoretical problems enough so you can solve the questions on the test quickly and correctly.

Tip number 4: Spend the time required to understand the proofs presented in the lectures and in the course notes. Understanding these proofs will really help you when making your own proofs on assignments and tests.

Tip number 5: Seek help from your course instructor and your fellow classmates. It is very important if you don't understand something to seek help to help you understand it. But also remember that you have to write tests without aid, so make sure that you can understand problems on your own before the tests

And finally tip number six: Study! I know that's rather obvious but most students do not do enough of this in linear algebra especially early on. Getting a good understanding of the material at the beginning of the course will really help you in uderstanding the more complicated material that comes later. I hope you find these tips very helpful. Study hard and good luck!