My Math Courses

Here is a list of all the math courses I've taken in university and the most important thing I learned from each of them!

First Year, 2015-2016

Analysis I (MAT157)

Wow, there is so much more math to learn than I could have ever imagined.

Algebra I (MAT240)

Good definitions can make hard things much easier.

Algebra II (MAT247)

You can't always make a matrix look perfect, but you can always make it look pretty nice.

Second Year, 2016-2017

Analysis II (MAT257)

Not only do all the theorems from calculus generalize to manifolds, but they can be stated so nicely!

Advanced Ordinary Differential Equations (MAT267)

Sometimes I do have to memorize a few things, even in math.

Groups, Rings, and Fields (MAT347)

Simply-defined things can end up being incredibly complicated.

Introduction to Topology (MAT327)

The difference between square brackets and circular brackets matters more than I could have ever predicted.

Third Year, 2017-2018

Complex Analysis I (MAT354)

Every so often, you can solve a problem by passing into an ethereal realm and bringing something back with you to show for it.

Introduction to Real Analysis (MAT357)

Even if a function isn't very nice, sometimes things will be alright because it's close enough to one that is.

Computability and Logic (CSC438)

Peano arithmetic might not be consistent, but I can learn to live with this fact.

Graduate Algebra I (MAT1100)

Back in linear algebra, I wish I were more thankful for the fact that we were working over a field.

Graduate Algebra II (MAT1101)

Mere exposure to a topic can go a long way toward building understanding.

Graduate Topology I (MAT1300)

Everything can be further generalized - even the definitions.

Graduate Topology II (MAT1301)

Just reversing some arrows can make things different in a way I wouldn't have expected.

Seminar in Number Theory (MAT477)

Math papers are often hard to read, but also often aren't impossible.

Reading Course in Number Theory & Modular Forms (MAT395)

The connection between geometry and number theory can be fascinating.

Reading Course in Algebraic Geometry (MAT496)

Category theory isn't so scary, and often it's a big help.