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.