The Average Math Undergraduate
Imagine you are still in your freshman or sophomore year. Your alarm rang at 7 in the morning, you hit that snooze button, dreading for that 8:30 linear algebra lecture.
Your professor starts to give an introduction to eigenvectors while attempting to make connections to previously learned formulas, theorems and corollaries.
Your head is filled with 40% of “What the f***?”, 30% of getting distracted by your phones or other Chrome tabs, 20% of “I wonder what‘s good for lunch” and 10% of “Ah, I get it now! No wait — ”
You started the lecture with a fresh mind and finished with “What‘s the point of learning this?”
Eventually the process repeats until you fall into the “I’m just studying for the grades” pit as finals draw near. We drag ourselves through the course and dump away the knowledge at the end of the semester, getting ready for that trip we have been planning for summer/winter break. This happens to so many undergraduates up until their final semester that the process of going through that math degree barely gives them any meaning.
Yes your math degree is a very general degree. But because it is a general degree it opens up to so many career opportunities. A biostatistician may not see the complete use of linear algebra apart from possibly dealing with matrices but its application extends to the use of Principal Component Analysis (PCA) to image processing for data scientists.
The Basics of College Math
I’d like to think that every math major will most likely offer the three foundations of mathematics: statistics, calculus and linear algebra. I would like to share the importance of the three foundations in this section.
Calculus — The Mathematics of Change and Optimization: To the untrained eye, this topic is all about solving differential and integral equations with the additional concepts of certain theorems such as the Rolle’s Theorem or the L’Hôpital’s Rule. However, the application of calculus extends to finding the optimal solution and predicting the future.
“Given a revenue function of selling this product, what is the required number of products to sell to maximize business profits?”, asked the business analyst.
“How can I use the Gradient Descent algorithm to optimize my regression model?”, asked the data scientist.
“What is the optimal temperature for the healthy growth of my crops?”, asked the agriculturist.
Statistics — The Mathematics of Probability and Intelligence: This is the most widely used discipline of math in any field that requires insights and predictions. It will be a whole new article for me to list down its applications but this article does the job well.
Linear algebra — The Mathematics of Transformation: This math topic is for the technical professionals. Even till today, I barely use the concepts of linear algebra for my work except when experimenting with image processing and reducing the dimensions of my data using PCA. The application of linear algebra is not exclusive to data crunchers, but I would imagine it to be exceptionally useful for engineers as well.
Data analysts and scientists dealing with transformation and operation of matrices will find this topic particularly important to them.
It is quite a challenge to visualize the use of linear algebra, but let’s skim through the surface of image recognition as an example without going into technical details.
A traditional binary computer is only capable of processing inputs of 0s and 1s. How would you teach a computer to learn that the above image is a tiger? Understanding how to transform pixels of a picture into 0s and 1s and feeding it into the computer is one application of linear algebra.
Choosing your Modules
Assuming a 4-year full-time degree, the first 2 years of a math undergraduate are often the most abstract but rather manageable. These 2 years are also the most important in building the basic mathematical foundation for the upcoming specialized courses in your senior years. There are 4 types of students that I encounter in my undergraduate life when picking their modules for their upcoming semesters:
The Gradekeeper — These are the students who do their research on which course is the easiest to get that A. Reasons range from “I need to pull up my GPA because I want to get that second uppers” to “I don’t want my GPA to drop or else it will limit my job hunt opportunities”. But sometimes they get the last laugh when they receive offers from large corporations with many benefits. So that’s something I guess.
The “Oh Shit I’m Late” — These are the classic. They missed the start of their module registration period by as little as a couple of minutes and the vacancy got immediately snapped up (Yes, module registration in my university is on a first-come-first-serve basis). They do their best to stay on their PC till the last minute, hoping that the vacancy opens up. Some would suck it up and pick whatever is vacant and move along, whereas some would go the distance and write a “heartfelt” message to the course coordinator to open up a slot for them.
The Explorer — They probably fall within the majority of the students who find a compelling course description a major factor that influences their choice, because hey, learning a new sport could be fun and rewarding right?
The Enlightened — These are the legends. They have already mapped out their career goals and picked courses that are the most suitable for them. And this is where I step in and provide some help about which math courses are required for which career.
The Statistician (Data Analyst, Biostatistician, Business Analyst, Data Scientist, Geostatistician,…)
These are the people who provide intelligence in any business in the form of insights and prediction. Understanding the importance of quality data to make robust analysis is the job of a statistician on a day-to-day basis. Obviously picking courses that are heavy in statistics and computing is recommended for this role.
Suggested courses: Statistics, Data Analysis with Computing, Business Operations and Process Optimization, Regression Analysis, Data Mining/Machine Learning, Time Series Analysis, Database Management, Computational Economics, Survival Analysis,…
Suggested technical skills: R, Python, SQL, SAS, SPSS, Excel, Tableau
The Financial Wizard (Quants, Actuaries, Economists, Financial Analyst, Pricing Analyst,…)
It is no surprise that employers would favour business undergrads who specialize in finance to fill their roles. The generality of math courses takes away the perception of students about how it is applicable to business and finance. No pure math courses are going to teach you about ROE, CAPM, PE Ratio and other financial ratios. Math undergrads who are interested in pursuing this field will need to take finance electives to compete with business undergrads for the same position. Of course, certain prestigious positions such as actuaries would require further specialized studies.
Fun fact: Billionaire mathematician Jim Simons was a pure mathematician turned cryptographer and eventually owning a multi-billion hedge fund who is also “infamous for passing over MBAs and finance PhDs in favor of physicists, mathematicians, even astronomers”
Suggested math courses: Statistics, Data Analysis with Computing, Business Operations and Process Optimization, Regression Analysis, Computational Economics,…
Suggested technical skills: R, Python, Excel, VBA
The Academic (Teacher, Mathematician,…)
Math undergrads who are not very sure of their career prospects tend to fall into teaching or further their studies in Masters or Phd. Don’t get me wrong, I think teaching is a noble job but the difference between a good teacher and a bad teacher affects the upbringing of their students.
Good math teachers are not only capable of delivering mathematical concepts into bite-sized digestible information, but also an inspirational model to the students and a guiding light to their aspirations.
Do note that being a qualified teacher means you have to undergo further studies in teaching in your respective schools for proper certification.
And then there is the pure mathematician. This profession is not a popular option in my country Singapore. No one I knew so far has applied for the job to be a pure mathematician. Incidentally these are also the math professors in your school. So yes the limited number of universities offering math degrees in Singapore makes it an unpopular choice. However, I’d like to think this is a highly respected profession in other regions such as America, Europe and China.
If pure mathematics is within your interest, consider checking out Numberphile Youtube channel. I watch their videos often during my undergraduate days to get a casual perspective of pure mathematics.
Suggested courses: Master the basics, then choose a specialization topic that appears the most interesting to you. These include:
- Differential Geometry
Suggested technical skills: Python, Matlab, C++, R, Excel
Finding a career related to math degree can be a massive challenge for most math undergraduates who find it difficult to establish a link between what they learned and its application in real life. Theorems and formulas are typically learned and forgotten. However, there are still reasons why we are still sought after in any industry.
Math fresh graduates are typically strong in logical-thinking, analytics, problem-solving and finding original solutions to an underlying problem. Apart from those, we are exposed to various programming languages that opens up many IT role opportunities for us. These are highly sought-after skills by many organizations. Combine those with the industry of your interest and you are very likely to land a career of your choice.
So before you think,
“What’s the whole point of proving this theorem?”
“Why do I need to know how to solve this problem? What is its significance?”
Know that you are subconsciously upgrading yourself to be a well-rounded critical thinker that will eventually open doors for you in the future.