Mathematics in College?
Mathematics is the underlying
structure of knowledge and logic. It is a framework for describing
and predicting observable phenomena in the universe. It gives its
users a varied arsenal of techniques for understanding and solving
otherwise difficult problems—problems that may not even seem
mathematical at first glance.
When students ask me “When will we ever need
math in real life?”, I have a hard time answering the question. This
is not because I lack an answer, but because it is difficult to know
where to start. Mathematics is all around us—in nature, in our daily
lives, and particularly in modern technology:
Have you ever played a video game with 3-D
graphics? Those graphics are made possible by using 3x3 matrices to
move (rotate) 3-D points through space.
Have you ever depended on a weather
report to plan your day or weekend? Weather models are dynamic
systems that use differential equations that are not unlike the ones
you solve in calculus class.
Have you ever boarded an airplane?
The airline boards passengers using an order that mathematicians
found to be the most efficient. They used a certain kind of geometry
(called Lorentzian geometry) to discover this method.
Cell phones? They use error
correcting codes (based on algebra) to allow you to have
conversations in areas where you have spotty cell phone coverage.
MP3s? They are small enough to fit
on your iPod because mathematicians used a development from
trigonometry (Fourier series) to compress them in way that makes the
file sizes manageable, while still keeping the track of a high
enough quality to listen to.
Try to think of the most random
thing you learned in math class over your school career, and we
could find an example of how it is used in the real world. Do you
remember Cramer’s Rule from Algebra II? Maybe, maybe not. If you
just Googled it, you saw that it’s a way of using determinants of
matrices to solve systems of equations. Sounds pretty random and
useless, right? Random perhaps, useless no:
My brother designs software for a
living. One day, his boss was trying to make an iPad app, and he
wanted to add a feature that allowed customers sign documents with
their finger directly on their iPad. Unfortunately, his original
program caused the signatures to look really jagged. This was
because the iPad was sampling points where the customer’s finger was
over time, then connected the dots. In order to smooth them out, he
needed to find the intersection points between the jagged segments.
My brother asked me about this problem, and I immediately realized
the easiest way to find these intersection points was with Cramer’s
Rule! It was perfectly tailored to a computer program. They used my
suggestions in their app, and now the customers can sign documents
with their fingers. The customers probably don’t realize it, but
they are benefiting from mathematics (particularly Cramer’s rule)
every time they pick up their iPad.
You may not want to be a
mathematician for a living, but I would encourage all of you to
consider the possibility of pursuing a
major or minor alongside your main course of study. By a
“quantitative major,” I mean something like mathematics, statistics,
applied mathematics or computer science. Majors like these teach you
new skills, allow you to think and solve problems in ways you never
could before, and could even unlock new career possibilities.
Innovations in biology, physics, economics, sociology, linguistics,
and even art have been made by people who approach these disciplines
from a mathematical perspective.
I know that my career as a math
teacher may bias my opinion on this matter, but please understand
that I am not saying that everybody in the world should be a math
major. If your true passion is theater, you should study theater. If
your passion is history, you should study history. If nothing in the
world brings you joy like art, then you should study art. I am
merely suggesting that you consider a minor or double major in a
quantitative field as well. You might be surprised to find out how
much it will augment your achievements in your main area of study.
At the very least, you will be looked on by future employers as a
well-rounded individual who can think in many different ways. I was
a double math and English major and I wouldn’t give up either of
those experiences for anything—they helped make me the person I am
I truly believe that our country
and our planet needs more young people like you to innovate, express
your creativity, and tackle the world’s problems. I also believe
that one of the tools that helps make this possible is mathematics.
University: Why Should I Major In Math?
Wall Street Journal Lists the Top 3 Jobs in America as (1)
Mathematician (2) Actuary and (3) Statistician
News Article About How Big Companies Are
Recruiting Math Majors
the Same Way that Professional Sports Teams Scout for College
TED Talk from Conrad Wolfram (the brother of
the founder of Mathematica) about how being able to apply
mathematics to the real world will be the main skill you need to
succeed in the 21st century: (Youtube)