Clare Written by Clare (she/her), student

There are quite a few differences between studying math in high school and university.

For instance, in high school, you probably have math homework, but most of your math learning is done in class. In university, the amount of time in the classroom is less, but you spend much more time on assignments outside of class, which are just as important for learning as the lecture.

Studying in the math lounge

Studying in the math student lounge.

Taking it to the next level

Studying math in university allows for a much more in-depth understanding of mathematics than high school. You will have the opportunity to learn about math fields that you might not even know exist!

I am majoring in Combinatorics and Optimization, a field that I had never heard of before university. I even get excited to take math courses that were not offered in high school, classes like scheduling, cryptography, and game theory.

The importance of proofs

However, I would say the biggest difference between studying math in high school and university is the focus on proofs in university. High school math--in most case--is largely computational: learning to solve problems that require calculation. This is very important, but math in university (especially in the upper years) focuses on proofs.

Paul Simon has a song called “Proof” in which he sings

Sane people go crazy on you
Say No man that was not
The deal we made
I got to, I got to go

But you don’t have to be scared of proofs!

If you don’t know, a proof is essentially a mathematical argument showing concretely that a statement is true or false. If this makes you worry, keep in mind that most students going into first year will also not have any experience with proofs, and there are courses designed to help you learn how to do them.

At Waterloo, we have MATH 135, a course all first-year math students take that teaches you how to write a proof, starting from the very basics. Even if you’ve never heard the word “proof” before first year, you will learn in due time.

So, those are the main differences between studying math in high school and university. Enjoy your future math studies!


I find it easier to remember/understand proofs if I write them by hand.

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