Math Awareness Month — April 2015

I recently came to learn that April is considered to be Math Awareness Month. I’m sure April is also an awareness month for other disciplines and / or causes, but for the purpose of this article it is Math Awareness Month. For more information about the “awareness movement” have a looksy at the AMS’s website.

As I work primarily as a mathematician and (quantitative) software developer, here’s my math story.

Mathematics education (and education generally) was important to both my parents. From second to sixth grade, my parents (and some extended family) would randomly quiz us kids on our basic math facts. Quick what’s seven times eight? We had to know our times tables up to twelve times twelve.

I remember in the summer between fourth and fifth grade, I had forgotten how to multiply. That was the end of that summer. I think all I did was multiply. As torturous as that may sound, I never forgot since then. But it wasn’t just the mechanics that I learned that summer. My dad showed me a thing or two about how he was taught basic math. He also showed me how to compute square roots by hand! Here’s a quick and dirty demo, but I’ll make it a point to write about it more fully some other time.

Let’s say we want to compute \(\sqrt{5}\). Since 2 is the largest integer whose square is less than 5, a first approximation is that \(\sqrt{5} \approx 2\). To obtain the tenths place, we proceed as follows (and this write-up is quick and dirty, which means convoluted):

  1. \(2 \times 2 = 4\)
  2. \(5 – 4 = 1\), and multiply this result by 100 to obtain 100
  3. \(2 + 2 = 4\), and multiply this result by 10 to obtain 40
  4. Find the largest \(x\) such that \((40 + x)\times x \leq 100\)
  5. \(x = 2\)

And we’ve found the tenths place, giving us an approximation \(\sqrt{5} \approx 2.2\)

Next, to find the hundredths place, we proceed similarly from where we left off:

  1. \(42 \times 2 = 84\)
  2. \(100 – 84 = 16\), and multiply this result by 100 to obtain 1600
  3. \(42 + 2 = 44\), and multiply this result by 10 to obtain 440
  4. Find the largest \(x\) such that \((440 + x)\times x \leq 1600\)
  5. \(x = 3\)

And we’ve found the hundredths place, giving us an approximation \(\sqrt{5} \approx 2.23\).

Getting to work that out by hand was sold to me as a cool thing to be able to do — kind of like a superpower. That was my dad’s brilliance — any new skill acquired, however minor or esoteric, was a superpower.

And believe it or not, it came in handy once almost two decades later! And no, I wasn’t stuck on a deserted island requiring that I compute \(\sqrt{5}\). At one university, the entry code to the graduate student lounge was the first four digits of \(\sqrt{3}\). But, my calculator and cell phone were in my backpack locked inside the lounge. Well, I went to an empty classroom and started working out the digits. Huzzah! True story.

Anyway, let’s go back to the summer between fourth and fifth grade. So, I relearned to multiply and picked up a new superpower along the way, which incidentally, required multiplication.

If memory serves correct, around fifth or sixth grade, my mom was studying Calculus for an exam for teacher certification (I’m not sure of these details). But I do distinctly remember seeing that she was working with functions and the notation of functions. Namely, I saw \(f(x)\) everywhere. My mom showed me some of the basics, but what was really neat about this experience wasn’t that I learned something new, it was that I learned that there was something radically different and advanced from what I currently knew. It kept my math curiosity alive. I couldn’t wait to get to learning “that stuff”.

Eventually, I did learn that stuff and a bunch more. In undergrad, I studied Electrical Engineering. The ability to pursue this was made possible in no small part by my earlier math education. An Electrical Engineering program actually does require a lot of mathematics. Unlike what some may believe — that it’s never too late to start, and while in principle / philosophy, I believe this, in practice, good luck — Mathematics isn’t a suggestion or a nice thing to know to pursue Electrical Engineering. Mathematics is an inescapable necessity.

After I finished my undergraduate degree, it was time for the usual rank and file nonsense of getting a job. So job hunting I did. Electrical Engineering wasn’t something that I had ultimately cared for at a professional / career level and I realized that a little too late to change majors (“too late” by the “dollars and cents” metric). What I had really liked was finance. So I looked for jobs in New York.

Lo and behold, to my surprise there was a company looking to hire people with an undergraduate degeree in any of the Engineering disciplines, the hard sciences, or mathematics. They were explicitly not looking for Finance majors! In the interview, I asked why. The response, “We can teach you Finance, we don’t have time to teach you Math.”

And so, I worked in commercial real estate finance for a few years. I ultimately left because there was a financial instrument that no one in the company knew how to price. And so, they had to hire a consultant to work on this one project. The consultant’s background? PhD in Mathematics with a focus in Financial Mathematics. Once again, just like that moment with my mom and Precalculus, I realized that all that math I had learned in Electrical Engineering, was just the tip of the iceberg. So, I promptly resigned and applied for graduate school in Mathematics with a focus in Financial Mathematics. And this pursuit was made possible because of an already reasonably strong background in Mathematics.

I got into graduate school and studied more Mathematics. Measure Theory, Complex Analysis, Monte Carlo Methods, Numerical PDEs, Stochastic Processes, etc. Then I was accepted into a PhD program and worked in Probability Theory, (randomized quasi-) Monte Carlo Methods, and Financial Mathematics. I published a few papers, solved a few problems, and was awarded a PhD in Mathematics.

Then it was back to the job search. I struck out with landing an academic position — there was a confluence of factors, Wall Street was imploding and the PhDs in industry losing their jobs were applying for teaching positions in addition to the regular load of applicants. Even small colleges that would normally see 50 applications for one position, saw 1000 applications. It was also fairly difficult for a new PhD to get a job in New York because of the general flood of talent on the open market.

So I set out to advertising myself as a mathematician for hire. I worked on small projects and I worked with a lot of out-of-work adults looking to go back to school for an MBA, or a degree in Finance, or those who just wanted to learn a new skill so that they could be competitive and marketable. Amazingly, I also landed a few consulting roles through this as those folks found employment (or started their business) and remembered the working relationship that we had.

Business was great! As luck would have it, my PhD advisor forwarded to me an opening he saw in the gaming and gambling industry. The company was looking for someone to join their math team and eventually take ownership of the Math Department. I applied for the position and got the job. I stayed with the company for a few years first as a senior researcher and then serving as the Math Director. That was a fun and rewarding job since as the Director, I didn’t just have math responsibilities, I also had business responsibilities — ensuring that clients’ needs were met, implementing quality control procedures, understanding the regulatory and compliance burdens of the industry, setting global corporate math policy and work flow procedures, ensuring that project costs and timelines weren’t being exceeded, etc. I initially had many hats. I helped out with some of the tough math questions, wrote a bulk of the testing software, did some project management, and did a lot of the general organizational leadership that was needed. Eventually, I had hired to capacity for a lot of the mechanical and day-to-day work, so I could focus on long-term decisions and further operational organization. All in all it was a great job and I had helped to create a successful global math operation — projects were within their budgets and timelines, work could move easily from one office to another (there were several offices around the globe) resulting in increased operational efficiency, there was a unified global policy on how math work should be done with consistent statistical quality control measures put into place, etc. Eventually, there was nothing left for me to do other than to watch the math machine hum along. And since there was nothing left to do and it was made explicitly clear that the company wanted me in the Director role only, it was time to leave. If there’s no growth, then there’s boredom, and life under normal circumstances, ought not be boring.

I took a few months off and then got back to working. But this time it was back to the consulting work. I landed some early work in the collateralized securities space as well as some of the older business of helping working professionals looking to develop their skill set. Some smaller projects have also come in — things like inventory management and promotional game analysis and development. There are some projects in pipeline in the edtech space as well as in the music technology space, but there’s still a lot of groundwork that has to be done before I’ll be engaged on those. I also continue to work in the gaming and gambling industry analyzing casino games for regulatory compliance. Part of my heart will always remain in education and so I teach part-time as adjunct faculty at a local community college.

Mathematics has enabled me to go from Electrical Engineering, to finance, to professional development and mentorship, to gaming and gambling, to art, and to piano (I’ve been taking lessons for a bit now and let me tell you, learning music theory is a whole lot easier when you know some math), to name a few.

That’s been my math journey so far. One of my goals is to work with primary and secondary schools. I’d like to be able to help with curriculum design, math enrichment, math and coding integration, reinvigorating those who have lost their math desire, providing math professional development to teachers (not necessarily in terms of “this is how you teach math”, but “hey, so you’re teaching Algebra, let’s work to develop the experiences that your students crave within the curriculum mandates”). Just get in touch and be part of this journey!

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One thought on “Math Awareness Month — April 2015

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