WHAT I WISH I HAD LEARNED IN THE FIRST TWO YEARS OF COLLEGE MATHEMATICS
CBMS FORUM – Reston, VA - October 5-7, 2014
Sabrina Schmidt, Vassar College 2010
Sabrinaschmidt8@gmail.com
In May 2010, I graduated from Vassar College with a degree in Math and Italian. While many of my friends had jobs,
grad school, or internships lined up, I was not sure what my next move would be. I decided not to apply to graduate school
because there was no particular area of math that I knew I wanted to study further. I had a growing feeling that I wanted to
use my math skills in the entertainment or music industry but wasn’t sure where to start. I decided to apply to math-related
jobs in some of my favorite entertainment and music companies. Ultimately, Time Inc., the magazine publisher, offered me a
position as a Data Analyst. I accepted the job offer since it seemed to be an ideal blend of my math and entertainment
interests. At my job, one of my main responsibilities is managing store-level distributions for three magazines, Us Weekly,
Rolling Stone, and Men’s Journal, all published by Wenner, a primary client of ours. I determine how many copies should go
into each store for each issue by using formulas based on store-level average sales and the amount of available checkout
pockets in the store. In the past four years working for Time Inc., I have been astounded by just how vital math is to the
magazine industry. I was really impressed and surprised to learn about the math-related projects that different divisions are
involved in. There is a Shopper Insights group that has developed an eye-tracking system which follows the movement of a
consumer’s pupils while shopping. They use this data to optimize magazine placement in the stores. The Research divisions
work on projects that include using subscriber data to help expand the reach of our brands, and analyzing historical data to
create new pricing strategies. They are about to do a zone pricing test for People magazine, where they will remove the cover
price and set different prices for different regions. It turns out math is a surprisingly key component in this field that most
people wouldn’t think to associate it with. But should this be surprising? Math knowledge and research is essential in countless
areas, and I think college students in particular could benefit from learning more about these links. In the past few weeks, I
have reflected on my college math experience (particularly the first two years) and will share some thoughts about what I wish
I learned, and how I feel the math department could have prepared me even more for my post-Vassar career. I consulted with
some of my fellow Vassar math majors, whose input is reflected throughout this talk, and I also enjoyed reading the book The
Mathematical Sciences in 2025, which validated many of my thoughts and gave me more insight.
Now that I see firsthand the impact of math in the magazine publishing world, I wish I had learned more about math’s
crucial and expanding contributions in today’s business landscape. Introducing math students early on to various applications
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(making sure to include fields where the students are not as aware of math’s role), will trigger them to think about the value of
a math degree and the growing demand for math graduates. The textbooks for the courses I took were mostly filled with
theorems, definitions, proofs, etc. and barely any examples of applications. I feel that I didn’t think or learn enough about
connections to real-world uses during college. Separating core and applied math is not practical anymore – most every concept
covered in class has proven to have importance beyond the math science discipline. To give students a better idea of postgraduation options and potential areas of specialization, professors could discuss the relevance of topics covered in class to
today’s math landscape (such as the role eigenvectors play in Google’s PageRank algorithm or how encryption uses number
theory to facilitate Internet commerce). I hear Vassar has recently begun inviting graduates back to talk about their career
paths -- a program I wish had been available to me when I was there. I would have liked to learn more about emerging and
evolving fields where we are only just starting to discover math’s prominence, like web development and Social Networks and
other areas which may be too new to even be in our textbooks. And there are many industries in which math’s long-existing
role continues to expand, such as aviation, movie animation, and national security. Incorporating examples like these into the
established curriculum shows students that existing math theory influences new applications, and in turn, new applications
drive new theoretical research by highlighting more problems. There could even be one introductory-level course that focuses
specifically on real-world applications of math science, where each unit is dedicated to a different field where math is used. A
course like this could be taught by a few different professors.
If students were more aware of which areas of math are prominently used in the applications that most interest them,
I believe they would be more apt to take some introductory courses in statistics and computer science in their first two years
of college. Regardless of career direction, the other STEM fields (Science, Technology, and Engineering) are arguably more
important for math students to learn now than ever before. The math sciences continue to be the foundation for exciting
research and development in technology, computer science, and statistics. Yet I’m sure there are other math graduates like me
who didn’t take classes on any of these subjects, and were surprised at the extent to which these fields are used in their lines
of work. Not only I, but also some fellow Vassar math majors I talked with, wish the math department put more emphasis on
these areas of study and worked alongside these other departments to make us more aware of the strong connections. Much
of the work in rapidly evolving areas such as compressed sensing or drug design is being done by people with a foundation in
multiple STEM disciplines. To keep up with the broadening of the math sciences, I wish math departments would require
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majors to take courses in at least one other math-related discipline in addition to the core math classes. This would better
equip them for a wider range of careers. I can certainly attest to this with my Data Manager position at Time Inc. Although I
don’t use high-level statistics or computer science concepts in my job, through the years I’ve had to learn certain data analysis
and computer systems skills that I wish I had gotten a head start on in college. Upon entering my job, I was surprised to see
that the company had its own systems built by in-house programmers. For instance, we have a system that houses data on
each magazine-selling store in the country and another system that uses formulas to suggest an optimal number of copies to
put in the stores based on certain data parameters. I communicate frequently with programmers, making suggestions for
system enhancement and performing user QA testing. Greater computer science knowledge on my end could have led to
faster progress and a stronger group effort.
An increase in the number of students trained in multiple quantitative disciplines would probably lead to more exciting
collaborations among the different fields, whether it be in the classroom, the workplace, or in research labs. Students would
also benefit from improved interdepartmental collaboration on the college’s part, which could involve joint courses that count
for credit in more than one discipline. For example, a class using computer science skills to analyze large data sets could be
applied towards either a computer science or math major. Professors from different departments could even co-teach courses
like this. The departments might even encourage students with multiple math-related interests to consider double majoring in
math and another quantitative discipline. Students would let the department know where their interests lie and the faculty
would then advise them on the courses best tailored to those topics. A list of suggested courses provided by the departments
for different combinations of dual majors would be an invaluable tool for students to have in the early years of college.
Freshman and sophomores would take comfort in knowing that, regardless of which subject(s) they decide to pursue further,
there are many worthwhile mathematical options beyond just core math classes that the department has made available to
them. Keeping these interconnected departments closer in proximity to each other would make it easier and more likely for
students to take classes in multiple disciplines, and would facilitate collaboration among students with related interests. If an
environment more like this had existed, I probably would have taken more science and technology-based courses, and fewer
theory-based courses, and I would have at least considered a double major.
I enjoyed the variety of math courses that I took (some of which include linear and advanced linear algebra, modern
and advanced modern algebra, multivariable calculus, number theory, probability, and real analysis). Not only I, but also a
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number of my Vassar classmates who I consulted with, wish we had selected our courses with more regard to post-college
interests. I learned a minimal amount of statistics in the probability course I took, but the department offered a good amount
of statistics classes, which I know now that I would have really benefited from in the long run. I think math departments should
require math majors and even those going for a correlate or minor to take at least one statistics-based course in their first two
years. This would help them to recognize early on how important a statistics background is in increasing their mathematical
value, and by extension, their employability in data-driven careers. And taking one course would likely lead to them taking
additional statistics courses, especially after they realize the wide range of careers these topics and skills are useful for. I also
realize now that I would have learned about more applications had I taken statistics since it lends itself more to real-world
examples. Without taking statistics courses, students who end up in mathematical jobs would most likely have to teach
themselves some of the concepts and tools, like modeling via simulation or statistical inference, in the workplace. I don’t use
any high-level statistics concepts in my job, but I definitely use many tools that are honed in a statistics class. My job requires a
quantitatively astute person who works accurately and efficiently to make meaningful conclusions from large data sets. As I
mentioned before, I was impressed and surprised by the amount of research that goes on within my company, much of which
I’m sure requires a statistical background. Although college statistics courses involve more complex concepts than I currently
use at work, I am still organizing, analyzing, interpreting, and presenting data, all of which is at the core of statistics. And
perhaps if I had learned about some more high-level statistics concepts, I might be able to find ways to apply them to my job. I
wish I had learned about hierarchical modeling, for example, which has become more vital in math in recent years with our
increased computational power. Reading about this topic in The Mathematical Sciences in 2025 made me think of my
company and made me wonder if any of our research departments are using hierarchical models. I feel they could be valuable
for sales predictions or for figuring out each magazine’s “potential” to sell, with a minimal margin of error. My Vassar
classmate who works at a hedge fund and I were talking about heuristic techniques and how learning more about advanced
heuristics methods would have proven advantageous in our fields of work. I find many anomalies in the store-level magazine
data, anything from sales that look inflated to incorrect chain or wholesaler information. I have to estimate how much of the
data is off-base, and then I make a decision on whether I need to dig into these anomalies further or whether I can proceed
with my analysis. Sometimes you work out a lengthy, rigorous, seemingly logical solution, but when you apply some common
sense it’s clear that you’ve wasted your time. Heuristic techniques may have slightly larger margins of error but maximize
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return on effort. We don’t always need the most perfect solution. Heuristic techniques are also frequently used with pattern
recognition and data mining, other areas we would have been interested to learn more about.
I read in the book The Mathematical Sciences in 2025 that by 2018, U.S. businesses will need another 140,000-190,000
employees who have advanced quantitative skills and deep analytical talent, and who are adept in working with big data. I feel
the types of courses that best suit these characteristics are statistics and computer science. More data than ever is generated,
collected, and used for research in today’s world, thanks to more complex technological systems. This complexity is helping to
push math science research forward. And because of this, all different kinds of fields, from neuroscience to national defense to
advertising, are looking for employees with statistical and computational expertise who are at home working with messy data
and who don’t always have to rely on existing models. As the global math landscape becomes more data-centric, so should the
math curricula and requirements for college students. Requiring math majors to take a course that gets students started on
working with large data sets and forming their own conclusions would be beneficial. Even though I don’t use super-complex
data concepts in my work, I feel that taking courses like these would have sharpened many of the data analysis skills necessary
for my job. My company collects an abundant amount of data, starting at the store-level. Location, demographic information,
and average weekly magazine sales are just a few of the data points we keep track of for each store. We collect information on
the number of copies received and sold for each issue of most US magazines on a store by store basis. A new piece of data we
have started collecting in the last few years is day of delivery, which is the day of the week each store receives the weekly
magazines. Having this data has helped us increase pre-weekend delivery percentage for certain chains. We also compare day
of delivery to day-of-first sale – ideally, the copies get merchandised properly and the first copy of the title sells within a day or
two of the initial delivery. I sift through data to find anomalies, opportunities, and trends. I use data to come up with ideas for
tests, to read tests, and to determine optimal next steps. With the print magazine industry struggling, we analyze data to try to
find ways to cut costs without sacrificing sales revenue. I also have to make the best of messy data. For instance, our second
largest wholesaler recently went out of business, so the twenty thousand stores serviced by that wholesaler were suddenly
without magazines until the chains were able to make deals with new wholesalers. We had all kinds of disordered data files
coming at us from different chains and wholesalers, and we had to track the status of each store. It took a few months for all of
the stores to get back to their normal magazine routine, so the sales data from that transitional period is one big anomaly.
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Many of my fellow Vassar math students and I wish we had learned more about computation and simulation in
college. Often times, data is of a scale that can only be analyzed through statistical and math techniques, such as
dimensionality reduction, uncertainty quantification, and analyzing separate subsets before aggregating the results. I would
have enjoyed learning about these methods. With the growth of computing power, there is more reliance on simulation via
math models in many different disciplines, and more math scientists are getting experience in these areas. It would be
advantageous for students to learn about current applications of computation and simulation, like how simulations help us
decide which medical treatments might work or how in movies and computer games, certain action scenes and characters are
the product of math models and simulations. Introducing these concepts in early years of college shows math students right
out of the gate how powerful and relevant these topics are to the math sciences and to our society.
I wish it had been a requirement for math majors to take at least one computer science course in the first two years. I
didn’t even consider enrolling in courses in the other STEM departments or the economics department that may have really
broadened my math knowledge. Many of my fellow students and I weren’t aware of the extent to which math is used in
computer science, and of how vital computer science is to ongoing developments in so many fields. Computer science helps
bridge the gap between theory and practical application. It seems optimal now for computer scientists to have a math
background, and for math scientists to have a computer science background before entering the workforce. Experience in
areas that combine math science and computer science skills (like math modeling, simulations, programming, and coding) is
now even more essential for a mathematical career. I wish that the math department took this more into consideration. And
again, there could even be some interdisciplinary classes that could count as credit in either department. I now see that more
background in programming and coding would have been an asset for me in my job. Having knowledge of these subjects in
today’s world is extremely powerful, and it is beneficial to start learning these skills as early as possible. I was even just reading
on the flight here about an iPad app called Hopscotch that aims to teach the fundamentals of programming to young kids. In
the app, you drag and drop colorful blocks of code to build routines. Facebook, Google, and any other web or mobile-based
company are built on a foundation of coding and algorithms. And almost every company, from internet start-ups to mom-andpop brick-and-mortar retail stores, has some sort of web presence. At Time Inc., I work in Microsoft Access and SQL building
some queries and scripts that analyze large amounts of data. I have taught myself some rudimentary coding to better
understand the logic, structure, and language, but I would have loved to have had a jumpstart in college on querying data and
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forming conclusions from these queries. We have a data portal that has many important reports that anyone in our company
can run, and my group makes suggestions to the programming team for new reports as well as enhancements to existing ones.
I recently had a unique situation where I had to collaborate more with the programmers than usual. They were having trouble
getting the report to display the necessary results. Meanwhile, I had created my own personal query that got me the data I
needed so that I didn’t have to wait for them to create the report. Eventually, I had to give the programmers my query so they
could copy the logic in order to build this company-wide report. This particular report happened to be one that I was able to
figure out the exact logic for, but building the queries for many other reports would be beyond my understanding. If I had
more of a background in programming, I could potentially collaborate with that team more often.
I feel that building on core math concepts through the incorporation of more real-world applications and
interdisciplinary links in the first two years of college will help to broaden the perspective of potential math majors, and will
better prepare them for the rest of college and their future careers. Setting this precedent will not only create more wellrounded students, but will also strengthen math science’s relationship with the other disciplines in the real world. Much of 21st
century research will be built on a math science foundation, and there will be new surprising connections to other fields as well
as jobs that haven’t even been conceived yet. Ongoing progress, recent breakthroughs, and theorems mathematicians are still
working to prove are some of the things that will propel math sciences to the next level, and would all be worthwhile to
incorporate into existing curriculum. With these adjustments in the department and these updates to the curriculum, I feel
that future generations will be even more ready for what lies ahead.
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