Catholic University Declassified School Survival Guide: Mathematics

Image Courtesy of physicsforums.com

By Garrett Farrell

When I was a senior in high school I, like every other senior in high school, stared at the Common App for hours, puzzled at the labyrinthine assortment of questions and essays. At that time, I was unsure of what I wanted to major in; I was considering politics, chemistry, and computer science; until I stepped foot in my AP Calculus class that fall, majoring in Mathematics had never even entered my mind. Sure, my mom was a math teacher and I had breezed through all the classes in high school, but I had no idea what studying math actually entailed. So, for all those like that young, 17-year-old who deeply misunderstood what he signed up for, here is everything I needed to know before becoming a Math major.

1. Numbers? Pshhh, forget that!

Contrary to popular belief, numbers play a very small part in higher level mathematics. Aside from calculus classes, I’ve only ever had one class that focused on arithmetic, and even then calculations were only involved in a minor way, and didn’t go beyond what one would learn in a high school precalculus class. 

In high school, a simple TI-84 calculator got me through every math class I had to take; in fact it was so useful that it was the first thing I put in my backpack when it came time to leave for college. When my first day of Math classes began at CUA, I quickly realized that the device which had gotten me through two AP math courses and an AP chemistry class was now next to useless. My professor for Math 122 (Calculus and Analytic Geometry II) laid out the definitions we needed to know on the blackboard for the Intermediate Value Theorem, which I was already somewhat familiar with thanks to my high school Math classes, and then he went into examples. The examples were when everything became very… abstract. After the first example, there were no constant coefficients in the examples; there was only the phrase, “Let a, b, c, d, and e be real numbers. Show that

This is maybe the best piece of advice I can give to anyone considering a math degree: invest in a good 3’x4’ whiteboard and a twelve pack of dry erase expo markers (or a chalkboard if that’s more your speed). This will save you so many trips to Leahy Hall and your chiropractor, as you won’t need to schlep your Calculus, Computer Science, and Physics books halfway across campus.

A whiteboard is pretty much a necessity for any math class; you will have to write out long equations for homework, you will need visual assistance for certain problems, and it will help you think better. Trying to work out homework problems can get a little… messy from time to time if you’re just working from a notebook, and a good whiteboard will also help you save pages, which brings me to my next piece of advice.

3. Always get the big notebooks

Full honesty, I knew about this one before coming to CUA. In Calc BC senior year of high school, I managed to plow through four 150 page notebooks before the AP test. If you think it gets lighter from there, you’re sadly mistaken. Good notes are often essential to reviewing and understanding the material you’re given in class, and they’re worth their weight in gold when studying for midterms and finals. 

I’ve seen different math majors do different things, from taking pictures of the board and focusing on listening to the lecture material to simply bringing a few pieces of loose leaf to class, but in my opinion there is no better way to take notes for a math class than a five subject notebook and a good pen(yes, yes I know: a pen? In math? What heresy? But notes taken in pen are just easier to read, which makes them infinitely more useful.) 

4. Math is always complementary

Understanding higher level Math always boils down to one basic principle: how well do you understand the math classes you’ve taken before? It may sound borderline impossible, but you really can’t forget a concept if you want to do well. I’m sure we all had an algebra teacher in high school who always said “Well math is cumulative” when asked if the exam would be cumulative. I used to hate that teacher for giving us an answer like that, and I still do, but now I see where they were coming from, because more than once I’ve been struggling with a homework problem, only to find the exact formula I needed in another textbook.

5. Don’t sleep on LC Philosophy Classes

This one might be a bit out there, but bear with me. One of the most important classes that Math majors at CUA have to take is Math 248, the Fundamentals of Advanced Mathematics. This class is heavily aimed at teaching students about various proof methods, which form the basis of every math class we take from that point on. Proofs require a large capacity for logical reasoning, and people who haven’t been exposed to propositional logic tend to struggle with that part of the class. 

For me, a major part of LC Philosophy (shout out Dr. Druart) was our unit on Logic. While I suspect that not everyone had the same exact experiences in their LCs, I am sure that most students are asked to read some of Aristotle’s Categories for their classes. These readings, and even Aristotle’s style of writing, are enormously helpful when it comes to understanding the logical structure of proof based mathematics.

6. Be Prepared for classes different from any math classes you’ve taken before

This great piece of advice comes from Junior math major Michael Dotzler. “ I wish I knew more about the kinds of classes that I would be taking, cause proof based classes are not my thing.” 

This is definitely something that every incoming math major needs to hear. Yes, there will be classes based on calculations and traditional mathematics, but when you come into junior year, a vast majority of your classes will be proof-based, and more centered on deriving important information rather than simply applying it. Yes, tests still do make sure you can apply what you learned, but oftentimes tests ask you to use the material to derive other facts. Like proving that if a matrix is diagonalizable and only has eigenvalues of -1 and 1, then its inverse matrix is also diagonalizable. This problem does not ask you to apply principles to a given real world example, but it does make sure you know properties of a diagonalizable matrix and how the matrix’s eigenvalues factor into it.

This article does not encompass everything I wished I knew before I became a math major, but it does encompass everything I needed to know. Half the fun of my first year at CUA was figuring out everything else, and that fun is the reason why I’m still a math major, and why I love it more and more with every class I take.