What I Wish I Had Learned More About in College Mathematics

By Sabrina Schmidt, Data Manager at Time, Inc. and former undergraduate mathematics major at Vassar College

Editor’s note: The editorial board believes that in our discussion of teaching and learning, it is important to include the authentic voices of current and former undergraduate students reflecting on their experiences with mathematics.

When I graduated from Vassar College in 2010 with degrees in math and Italian, I wasn’t sure what was next for me. I applied for math-related jobs at my favorite media companies. Ultimately, Time Inc. offered me a position as a Data Analyst, a job which has been an ideal blend of my mathematical and entertainment interests. I manage store-level distributions for three magazines, Us Weekly, Rolling Stone, and Men’s Journal, all published by Wenner, a primary client. I determine how many copies of every issue go into each store by using formulas based on the store’s available checkout pockets and average sales. At Time Inc., I have been impressed and surprised by the variety of math-related projects. There is a Shopper Insights group that has developed an eye-tracking system that follows the movement of a consumer’s pupils while shopping and helps optimize magazine placement in 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 doing a zone- pricing test for People magazine, where they are removing the cover price and setting different prices for different regions. In this blog post, I use examples from my work experience over the last five years to suggest ways in which undergraduate mathematics majors can be better prepared for math-related positions in companies. I discuss how I wish I had learned more about applications, computer science, statistics, and connections to other STEM fields.

Applications
I wish that I had been introduced earlier and more often to applications, as they would have provided me with a better idea of potential areas of specialization after graduation. For example, in linear algebra we could have learned about the role eigenvectors play in Google’s PageRank algorithm, and in number theory we could have learned about how encryption facilitates e-commerce. My textbooks and courses were mostly filled with theorems, definitions, and proofs, and relatively few examples of applications. With more such examples, I believe that students would think more about the value of a math degree and the growing demand for graduates with a math major. Vassar has recently begun inviting graduates back to talk about their career paths. I wish this program had existed when I was there. I would have also liked to learn more about fields where we are only just starting to discover the prominence of math, such as web development and social networks. Additionally, there are many industries in which math’s long-existing role continues to expand, such as movie animation and national security. Incorporating examples like these into the curriculum shows students that mathematical theories influence new applications, and in turn, new applications drive theoretical research by uncovering additional problems. Perhaps an introductory course focusing on real-world applications (with each unit dedicated to a different field where math is used) could show students more of these connections.

Other STEM fields
The mathematical sciences continue to be the foundation for exciting research and development in the other STEM fields. Yet I’m sure there are other math graduates like me who didn’t take classes on these subjects and were surprised at the extent to which these fields are used in their lines of work. 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 mathematical sciences and to equip students for a wider range of careers, I think a requirement to take a course in at least one other math-related discipline would be an asset to majors. Students would also benefit from improved interdepartmental collaboration, which could include joint courses that count for credit in more than one discipline or classes co-taught by professors from different departments. For example, a class using computer science skills to analyze large data sets could be applied towards either a computer science or math major. Freshmen and sophomores would take comfort in knowing that, regardless of which subject(s) they pursue further, their math departments offer many worthwhile options beyond core math classes. I might have double majored, or at least taken more science and technology-based courses, had an environment more like this existed.

Statistics
I enjoyed the variety of math courses that I took (e.g., linear algebra, modern algebra, multivariable calculus, number theory, probability, and real analysis), yet I wish I had selected my courses with more regard to post-college interests. If I could redo my undergraduate years, I would take more statistics courses. I think a department requirement would help students recognize how important a statistics background is in increasing their mathematical value, and by extension, their employability in data-driven careers. Without taking statistics, students who end up in mathematical jobs would likely have to teach themselves key concepts and tools, such as modeling via simulation or statistical inference, in the workplace. More data than ever is generated, collected, and used for research in today’s world. Because of this, fields from neuroscience to advertising are looking for employees with statistical and computational expertise. The Mathematical Sciences in 2025 says that by 2018, U.S. businesses will need another 140,000-190,000 employees with advanced quantitative skills and deep analytical talent, and who are adept in working with big data. Courses where students work with large data sets and form their own conclusions would be beneficial. I don’t use high-level statistics in my job, but I use many tools that are honed in a statistics class. My work revolves around organizing, analyzing, interpreting, and presenting data. If I had studied some more advanced statistics concepts, I might have been able to find ways to apply them to my job. For example, reading about hierarchical models in The Mathematical Sciences in 2025 made me wonder if my company uses them, especially since it seems like they might be valuable in determining magazines’ sales potential. With the print magazine industry struggling, we analyze data to try to find ways to cut costs without sacrificing revenue. I sift through the numbers to find anomalies, opportunities, and trends, and I use the data to generate ideas for tests and measure results. 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 made deals with new wholesalers. Unsurprisingly, the sales data from that transitional period is one big anomaly.

Computer Science
I also wasn’t aware of the extent to which math is used in computer science, and of how vital computer science is to ongoing developments in countless fields. I didn’t even consider enrolling in a computer science course. Looking back, I wish that I had been required to take courses in that department. Having knowledge in areas that combine math and computer science skills (e.g., math modeling, simulations, programming, and coding) has become more essential for mathematical careers. Although I don’t use advanced computer science concepts in my job, I’ve had to learn certain data analysis and computer systems skills that I wish I had gotten a head start on in college. I was initially surprised to see that Time Inc. has its own systems built by in-house programmers that hold data on each magazine-selling store in the country and suggest a number of copies to put in each store. I have taught myself 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 forming conclusions. I communicate frequently with programmers, testing systems and making suggestions for enhancements. Recently, they were having trouble getting a report to display necessary results, and I gave them a query I had written which helped them finish building the report. I was able to figure out the logic in this instance, but building queries for other reports would be beyond my understanding. There have been numerous situations like this where I’ve felt that having even a basic computer science foundation could have led to faster progress and a stronger group effort.

Much of 21st century research will have a foundation in math, and there will be surprising connections to other fields, as well as jobs that haven’t even been conceived yet. Building on core math concepts through the incorporation of more real-world applications and further linking these concepts to statistics, computer science, and other STEM disciplines will help broaden the perspective of potential math majors, and better prepare them for the rest of college and their subsequent careers. This will not only create more well-rounded students, but will also strengthen math’s relationship with the other disciplines in the real world.

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8 Responses to What I Wish I Had Learned More About in College Mathematics

  1. Avatar Caballieri says:

    It seems you chose the wrong major. Applied mathematics covers exactly what you thing you should have learned. Next time go for a major in applied mathematics 😉

  2. Avatar Kevin O'Bryant says:

    At my school, we would love to offer more classes in big data and statistics, but we have difficulty hiring in these fields as the salary we can offer is just not competitive. Ironically, the more useful a subfield is the less able we are to afford anyone who can teach it.

    We don’t offer very many cross-department courses for a variety of reasons. The two departments need to cooperate on the syllabus and scheduling, for example. This doubles the number of people involved, which squares the number of conflicts and amount of inanity.

    I’m not defending the status quo, just trying to explain it.

  3. Avatar Toby Driscoll says:

    I agree with Caballieri that an applied math major would have been a perfect fit. But students coming in for math often don’t know much about it, and smaller schools in particular may not offer it.

    I completely recognize the problems that Kevin O. brings up. Not all (or most) cross-listed or required courses can be co-taught. But if we want to serve all of our students, not just those we think are headed to graduate school, we need to invest some time and effort to retrain ourselves a bit and reconsider the foundations we offer.

    For example: does it make sense in 2015 to teach every calculus student the root test for power series convergence, yet allow students to get through four years without learning a real programming language or basic statistics and physics?

  4. Avatar Mandy says:

    I love this article. It expresses my collegiate frustrations and post-graduate realizations. When I was an undergrad, I was told there were numerous career opportunities for a mathematics graduate. But, when forced to list possible career options, I got actuary and teacher. I would love to see freshmen or sophomores take a Careers in Mathematics class. Give students possibilities including computer sciences and STEM fields, but also include architecture, aviation, and animation.

  5. Avatar Mike says:

    The AMS’s Mathematical Moments show over 100 individual applications of mathematics www.ams.org/mathmoments .

  6. Avatar Murray Pendergrass says:

    Im glad you decided to write this article and share your experience, hopefully the right people come across this, but personally I think some of it is questionable. Why would your pure math text books have been filled with anything other than theorems and proofs?

    Most schools departments have some form of mission statement for each individual degree as to what the focus of the degree is and typically a degree in math is the in depth study of mathematical theory. Not application.

    As already mentioned in comments it sounds like an applied math degree would have better suited you seeing as an applied math degree focuses on all of the areas you mentioned (computer science , statistics, communication etc.). It seems like your college degree was intended to serve as an economic earning power booster and working in industry was the route of intention from the start for you (which is fine) but this is just more testament that applied math was the right route since it appears you were strictly interested in learning *how to apply math*.

    Math, pure math, is the study of math. It does not need application nor reason its is simply the study of pure math and patterns. It often gives birth to applied math but some people need and want to study the pure math so that new mathematics can be created and then lent to the applied. There is need and demand for both. For example, mathematical logic is an extremely fundamental area of pure mathematics but under the umbrella of mathematical logic we get out proof theory and theoretical computer science. Thats right pure mathematics gives us theoretical computer science!

    What I take away most from this article is that perhaps there should be more emphasis on students looking into and researching their degrees, it is important to be informed and make the right decision and know what your options are. But fortunately there are a lot of applied mathematicians and statisticians out there compiling data for us so we can do so. SIAM, AMS and Bureau of Labor Stats are good places to start and your colleges program and degree descriptions are too.

    One last tid bit, when the amazing mathematician Alexander Grothendiek learned that his mathematics institute in France was receiving funding from the French Ministry of Defense he became concerned about the misuse of mathematics and left, expecting others to follow but none did. I wonder how he would have felt about working on a project to apply his math skills to track eye movements of consumers in stores to pin point optimal magazine placement to boost sales. That was the most startling part of the article for me.

    May mathematicians and applied mathematicians continue to work together in peace.

    • Avatar Ben Braun says:

      The eye-tracking study generated a fair amount of attention on social media — I think many people aren’t aware how widespread such studies are. For example, in the August 2015 Notices of the American Mathematical Society, there is an article titled “Investigating and Improving Undergraduate Proof Comprehension,” http://www.ams.org/notices/201507/rnoti-p742.pdf , that uses eye-tracking techniques to study how undergraduates read mathematical proofs. As the authors state in that article, “Eye-tracking is used widely in research on reading, and the empirically established close link between fixation location and attention location means that it provides a useful window into the processes involved in reading a text.” I’m betting that many mathematicians would find this article interesting and enlightening precisely because of the insights made possible through this technology. I’m not defending any particular use of eye-tracking techniques (obviously these can be applied in both positive and negative ways), rather pointing out that the techniques themselves are common in studies of human behavior.

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