Mathematicians are Needed in Industry

Gregory_Coxson
Greg Coxson

At this point in my career, I have worked at a number of organizations, usually technology companies with military contracts. I am convinced that mathematicians strengthen organizations, and sometimes make revolutionary changes, often in small ways that are not celebrated as often as they should.

My first job was at the Center for Naval Analysis in Alexandria, Virginia. CNA performs long-range studies for the Navy, and is one of the oldest military Operations Research firms. I was working for a crusty old radar engineer, who wanted me to perform Monte Carlo analysis of Russian missile raids. This required thousands of runs of the program. One day, I needed to consult with a mathematician on another floor. I was surprised to find that he knew the simulation I was spending my days with. But what really amazed me was when we started discussing specifics. At that point, he pulled out a big binder containing tables of every possible combination of inputs to the model, and the associated outputs. He had invested the time one week to run all the possibilities and compile them. Having done this, he did not need to run the model for hours a day; instead he had just to pull out the binder and find the right row to pull out the results. It impressed me that this approach was much more efficient.

Later in my career, when I was working for another company, we had a large number of engineers working on a new ballistic missile system for the Navy. The schedules were aggressive, and the work multi-faceted and difficult. On one of the projects, it appeared necessary, despite the tight schedules, to spend a year running cases of flight trajectories. However, there was a PhD mathematician working on this, and he argued that since all the factors were known, mathematics could be used to perform a quick study, and come up with all the possible trajectories. He saved the company a year of effort and countless computer runs.

In these cases, Mathematics is not enough. It is important to get the information into the right hands. A junior engineer or mathematician will not be listened to, at least without concerted effort and the right arguments.

I had the opportunity to learn this first-hand. I was working on a critical program for the Air Force, and one evening before heading home, I was reading the specifications (not always easy reading). Before I went too far with this, I came upon something that stopped me in my tracks. Here, in a system where efficiency was highly emphasized, was an operation being done 80 times in one set, and then in the next set, the inverse of those operations was being done. This seemed to me something that should be fixed. So I went to my boss and pointed this out. However, I was new, and my boss did not know enough mathematics to understand my claim that eaeb = ea+b. No matter how I argued, she was not going to take my word for it. Her approach, ultimately, was to arrange a panel discussion with some scary senior analysts around the table to make me retract my story. But I did not back down. Looking back on it, the issue was a badly implemented discrete Fourier transform. I left the company soon after. It took about a month before I started getting phone calls asking for my notes. They had come around to agree with me.

The point of all this is, that mathematicians are needed outside of academia. Mathematics is used, and sometimes misused, every day in almost every industry. Mathematicians are needed for their training, but also their insights. I believe that mathematicians are able to find efficiencies, and new approaches, that others are blind to. Mathematicians are needed to prevent errors, to analyze complex problems and systems. There is no doubt in my mind that we need more mathematicians in industry.

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Unsolicited Basketball Coaching Advice from a Student Researcher

CharlotteEisenberg
Charlotte Eisenberg

This summer I spent a lot of time with NCAA Division I basketball statistics. As a student researcher at Davidson, I examined at least a hundred statistics tracked across the division, from the height and experience of the players to the team free throw and turnover percentages, each potentially linked to the success of a team. My goal was to find the strongest correlations and use them to predict the outcomes of games. Many of the statistics most strongly correlated with winning games, like offensive and defensive efficiency (points and points against per 100 possessions), felt more descriptive than predictive. I became curious about what sub-statistics contributed to efficiency that could be more easily isolated and coached. What statistics would an analytics minded team focus on to see the greatest increase in their win percentage?

In recent years there have been basketball teams (not many) that have staked out their claims to be the analytics team. For prime examples look to Belmont in Division I or the Houston Rockets in the NBA. Those teams, and others that are vocal about using analytics, are the teams that think they can’t win on skill alone. The first thing an analytics minded team focuses on is taking more three point shots. The theory behind this approach is pretty solid: three point shots have a lower probability of success but a higher payoff, creating more variability in a team’s scoring outcomes. In a simplified example, lets have Belmont scoring between 60 and 70 points per game going up against North Carolina, which scores 77 to 90 points per game. If Belmont gets no better with their shooting percentage but takes a higher proportion of their shots from behind the three point line, they have the potential to see a wider range of scoring outcomes, say between 50 and 80 points instead of between 60 and 70. Belmont’s chances of winning improve because they now have some small chance of a scoring outcome higher than some of the scoring outcomes North Carolina produces. For every one percentage point that underdog teams increase the proportion of their shots devoted to threes, their winning percentages increase by an average of 2.2 percentage points, according to a Peter Keating article in ESPN Magazine last May. They may take some bigger loses, but they make up for it by eking out some unlikely wins. 

 

If I were coaching an underdog basketball team (or a top basketball team), I would definitely push the threes. One pair of three-pointers equals three two-pointers. Simple. Assuming the opponent is shooting twos, my team’s shooting percentage on threes has to be only 66 percent of whatever they’re hitting. An opponent shooting 50 percent for two can be matched by a 33 percent conversion rate on threes. But I don’t think my team’s success will hinge on shooting percentage or distribution. A basketball team wins a game by scoring the most points, which come from shooting baskets, but getting an edge in shooting percentage is tough to possibly unattainable in DI. In the average NCAA Division I basketball contest last year, the shooting percentages for the two teams were separated by just 3.2 percentage points. Assuming the two teams have an equal number of possessions, the “better” team can expect just a couple extra baskets per game, five or six points in a 70 possession game. When I ran logistic regressions on team stats to predict the outcomes of NCAA basketball games I was somewhat surprised to find that the most impactful statistics (largest regression coefficients) were turnovers, steals, and rebounds, not shooting percentage. The team that creates the most opportunities (possessions) for themselves to score usually scores the most. 

 

My (hypothetical) basketball team would need to understand that possessions are key. The average shooting percentage for a Division I team hovers around 50 percent, so each possession is worth at least one point (depending on the number of shots the team takes from three). If a team can raise their shooting percentage from 50 percent to 55 percent (a huge and likely unattainable success to most coaches), the change would translate to an extra three and a half baskets per game. Every percent point gain in shooting will translate to an extra point or two scored per game, the same result as simply pulling off one more steal. I would classify achieving steals as significantly more attainable than improving shooting percentage. There were 77 Division I teams who averaged over seven steals per game last season, with a benefit equivalent to improving their shooting percentages by at least 5 points. Teaching a team to not turn over the ball is hard. Effective ball handling and passing involves years of skill development, talent, and confidence. On the other hand, increased steals (in my opinion) just take a little nerve and boldness.  I would teach my team to be gutsy, stick their hands out there, lunge for the ball. If my team went for a steal on every possession they would create opportunities for themselves and stun their opponents. It could be a new recipe for success.  

An analyst’s dream is to find some underutilized path to success that will allow an underdog team to stun favorites. Teaching a team to emphasize stealing should produce measurable results in scoring efficiency and has the potential to upend the character and mentality of the team. A team that focuses on steals ingrains in its players the value of a possession. Every time a team allows their opponent to dribble down the court, pass and take shots, they are handing over possessions. My team would be relentless on defense, not allowing a single shot or pass or dribble to go uncontested. There is a perception that analytical approaches to sports undermine the value of athleticism by letting teams play smarter instead of harder. My analysis suggests that the smartest thing a team can do is play harder, recognizing the value of every second on the court and not giving any away to an opponent’s possession without a fight. 

The importance and excitement of team science — and how optimization research fits in almost everywhere

XBD201705-00091-010
Juliane Mueller
© 2010 The Regents of the University of California,
through the Lawrence Berkeley National Laboratory

I am currently a research scientist in the Computational Research Division at Lawrence Berkeley National Lab. I got promoted into this position very recently. Before, I was one of the Luis W. Alvarez Fellows in Computing Sciences at Berkeley Lab. 

My education (MSc and PhD) was in applied mathematics. Early on during my Master’s education, I got interested in optimization and I enjoyed learning about different mathematical algorithms that were developed for solving application problems to optimality. The applicability and in particular the usefulness of mathematical algorithms for improving life and solving real life problems intrigued me. After my PhD, I went to Cornell University as a postdoc where I was introduced to optimization applications related to climate model development and the environment. Through my advisor, I learned about the different National Labs and their named postdoctoral fellowships which basically allow a recipient to develop their own research agenda. I applied for and accepted the Alvarez Fellowship at Berkeley Lab. In contrast to other National Labs, Berkeley Lab did not have an optimization research group. Some might consider this as a disadvantage because there is no senior person to give me guidance and feedback on my work. However, the non-existence of an optimization group also poses an opportunity. It means that there are many domain scientists who may have difficult unsolved optimization problems that they may not know how to tackle.  This means a lot of collaboration possibilities, and eventually, with some momentum and a lot of effort, even the possibility to establish an optimization group at Berkeley Lab. 

In contrast to the more academic setting that I had so far been exposed to during my education, Berkeley Lab offered a completely new setting of interdisciplinary work and opportunities to collaborate with domain scientists from all science areas. I reached out to many scientists to discuss about their work and to see if they run into optimization problems that they do not know how to address efficiently. Sure enough, I found many takers. Collaborating with domain scientists and the breadth of application problems I get to work on are the most interesting part of my work. I constantly get to learn about new science areas, I learn new terminology, and I encounter new classes of unsolved optimization problems. Throughout the three years I have spent at Berkeley Lab so far, I have worked together with scientists in climate research, combustion, cosmology, spectroscopy, light source lattice design, and plasma accelerator design. 

I mostly collaborate with scientists who develop simulation models to study physical phenomena. Although the scientists understand the physics extremely well and are able to model the physics with high accuracy, most simulation models have parameters that must be adjusted. This is often done based on the scientists’ knowledge and experience, which is a valid approach for some science areas. But in other areas, an efficient approach for adjusting the simulation model parameters is needed and sophisticated optimization algorithms (and thus my work) enter the game. The challenge lies often first in learning enough about the domain scientists’ work to understand the goals of the research. The next challenge is in formulating a sound optimization problem, and then finally developing new solution methods. The most rewarding part of my work is the excitement of the domain scientists as they are able to use a new tool to solve their problems more efficiently (I make my codes publicly available), as they see completely unexpected solutions that they would have otherwise never expected (which often uncovers characteristics of the problem that were not expected), and as their simulations now make better predictions and allow scientific results to be found more efficiently. 

The reason why I decided to stay at Berkeley Lab beyond my postdoc are the exciting and relevant problems I can collaborate on with other scientists. I constantly learn new things and most importantly, other scientists are completely open to explore new ideas, and they welcome the opportunities to learn about new methods. I have not met a single scientist who wouldn’t agree on a meeting to talk about collaboration possibilities. Obviously, being willing to reach out to and collaborate with other domain scientists is a necessity at any National Lab. Research is not done all by yourself, at least not if your goal is to do more than just publishing. You have to be willing to sometimes go out of your way (meaning your comfort zone of research topics) to explore new ideas. You have to be willing to invest a bit of your time in running some initial optimization trials to see if there is actually any hope at all for the domain scientist’s problem. But this also means that you can use these preliminary results as a starting point for a grant application. 

The soft funding situation (all of your salary comes from projects with finite duration) may make some people anxious at times. Somewhere in the back of your head, there will always be this question of whether or not you will have money next year. That’s a thought one has to be willing to live with, but then again, in today’s world, nothing is certain and I don’t feel too stressed about this (yet). But as mentioned, you need to be willing to approach other scientists, especially if you are a bit junior and not that well known around the lab. I started doing this early on during my postdoc already. Even if not every discussion leads to a project, at least people will know what you are working on and they will come back to you in the future if they encounter a problem they know you can help with. For this, I find it extremely important to be able to talk about my work in layman’s terms since not everyone has a thorough mathematics education. 

My advice for anyone who is looking for a successful career at Berkeley Lab is that you have to be able to work independently as much as collaboratively. You have to be able to come up with novel ideas to solve problems. At the same time, the concept of team science as introduced by E.O. Lawrence in the 1930s remains an integral part of the Lab’s efforts today, and the success of collaborating teams with mixed skills and diverse backgrounds has proven to be the best way to tackle the most complex science problems. Therefore, it is important that you stay curious, that you are open to new ideas, that you are willing to step out of your research comfort zone to learn new things and explore new science areas. The lab setting gives you the opportunity to grow. Take the chance! You don’t have to know all the details of everyone’s research, but keep on learning, keep asking questions in meetings — people are more than happy to explain their research to you. If you are still in college, attend some introductory lectures on topics that are outside your area — engineering, economics, programming. I found that the classes I took on intercultural communication were extremely valuable. National labs attract researchers from all over the world and you will end up in a very diverse setting. Having some kind of an idea how to navigate this setting effectively is extremely helpful. Lastly, be open to talk to people, volunteer to help at outreach and other lab events. It takes some effort, especially if you are more on the shy side, but it pays off, I promise!

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My BIG Math Experience: A Java Web Development Boot Camp

Joyce-YangJoyce C. Yang

This summer, Codework Academy at Montgomery College had its first Java Web Development boot camp.  The program was in Gaithersburg, MD and taught students how to write and deploy web applications in eight weeks.  I participated in the boot camp, which was full-time, 9 am to 5 pm every day.  Starting from object-oriented programming fundamentals, I learned how to think like a programmer. The main things I gained from the camp were the programming skills and the professional network.

bootcamp

One of the model-view-controller (MVC) projects that our team worked on: a boot camp finder that that enabled users to search for boot camps from a database, apply to a camp as a student, and accept applicants as an administrator. Top: a preliminary version of the code for the boot camp model.  Bottom: the final version on the live site

Programming Skills

Until the boot camp, I did not have experience in Java or C.  While looking for employment opportunities, I examined software engineering job listings and they generally required those languages.  Since I had had experience in Python, R, Matlab, and Visual Basic, I was familiar with programming fundamentals.   The Java boot camp was a good way to learn new programming concepts that were relevant and apply them immediately.

Some of the skills I learned

  • Using relational database management systems—we used MySQL and PostgreSQL
  • Using the concept of encapsulation for data hiding
  • Making “Input–Processing- Output” (IPO) diagrams
  • Developing the model, view, and controller of an application
  • Using an application framework (Spring) to streamline the development process
  • Deploying applications to a cloud service (Heroku)

 

Building networks

I learned a lot outside the classroom by talking to others, and I expanded my professional network.  One graduate student had switched majors from chemical engineering to computer science, and they helped me decide to learn more about careers in web development.  Another student was considering applying to a four-year college, and in my capacity as a college graduate, I offered some advice.  The Montgomery College web development boot camp was supported by a grant.  As a result, it was completely free, and people who were underemployed and unemployed could attend! Students were constantly talking about new ways of solving problems, and the environment was collaborative.

The boot camp was quite challenging, and students needed to meet strict requirements.  The program’s aim was to make assignments as close to “real life” as possible.  Each day at camp consisted of testing code, determining new issues to fix, and fixing them.  One of the main differences between web development and math is that web development does not usually have well-posed problems.  There can be times when the problem is not clear.  I was prepared for the boot camp, but I wish that, before I started, I had learned a bit more object-oriented programming.   Overall, I gained software skills and a great professional network from this Java web development boot camp.

 

About the author: Joyce C. Yang graduated from Harvey Mudd College in December 2016 with a Bachelor’s degree in Mathematics. An experienced K-12 teacher, she has also worked on research problems in graph theory, statistics, and abstract algebra.  Currently living in the DC area, she is looking for employment opportunities. Joyce can be reached at jcyang@hmc.edu

Summer Internship with an Impact

by George Baldini and Kendall Thomas

The end of the school year marks a break from exams, homework, and classes. It’s also a desirable time to dive into experiences outside the classroom, notably in research or an internship. Academic research allows students to explore untrodden intellectual territory and potentially create new knowledge. Business internships allow undergraduates an opportunity to apply their academic learning to business, try their hand in industry, and potentially make connections for future employment. Research or business internship? Many data analytics companies hire rising seniors with a possible job offer coming at summer’s end. We are rising juniors. Internships are possible but difficult to find. What did we decide for our summer? Both!

This summer, we worked at Davidson College with Dr. Tim Chartier in an internship with Athlete Intelligence. Athlete Intelligence is sports technology and data analytics company headquartered in Kirkland, Washington. The company makes wearable devices for athletes, like mouthguards (seen below) and helmet sensors, that track head impacts as well as biometric data. These devices provide instantaneous data for each impact during a session, alerting coaches and training staff if an impact magnitude exceeds a preset threshold or a player surpasses a certain number of hits in a small period of time. Their unique user platform empowers coaches and athletic trainers to access useful insights from this data to help reduce the risk of injury and improve performance.

Baldini_Thomas_1Our group served as a data analytics research branch of the company. As Jesse Harper, CEO of the company stated, “This is a mission to Mars. We’ll know what we find when we find it.”

If you don’t know where you’re going, where do you begin? With analytics, a first step is data. The company supplied impact data from high school and college football teams for one or more seasons. For each impact, Athlete Intelligence devices record the corresponding player, position, head location, magnitude, and time.

Armed with data, we turned to research goals. First, find “coachable moments,” actionable insights which aid coaches. For example, one team’s impacts increased towards the end of the game, possibly from fatigue’s effect on technique. If a coach verified fatigue’s influence, the team could emphasize conditioning and remind players to keep their heads up when tackling late in games.

Our second goal, connecting to the first goal, enrich the data. We wanted to add data that leads to additional insights. Since Athlete Intelligence will partner with Davidson Women’s Soccer team this fall, we asked our soccer coaches what data they currently track and would like to track in the future. In the end, we augmented the data with hours of sleep for each player, weather, elevation, location, and type of event (game or practice).

While the new data came from our soccer coaches’ interests, we added these new data points to our current impact data, which occurred in football. Insight followed. For example, one team’s centers and defensive ends were hit significantly harder in games than in practices; and, a little unnerving, quarterbacks and special teams got hit harder in practice than in games as seen in the graph below. An immediate question followed: why? Presented with such information, coaches could revisit game tape and practice plans to identify these situations and make any necessary adjustments.

Baldini_Thomas_2

To conclude our summer, we visited the company’s office in Kirkland. We presented our research and discussed how it could enrich the company’s user platform. Our research met their business goals and would help the company.

Our summer was fascinating and productive. Our internship introduced us to a new company, exposed us to cutting edge research, and included a trip to the Seattle area. Even better, our work wouldn’t end with the summer. While in Kirkland, our Athlete Intelligence colleagues presented us with more interesting projects. We enter the fall ready to get back to work through our continued collaboration and make more impacts with our analytics research.

Baldini_Thomas_3

 

 

 

ICME Data Science Workshop

ICME will hold one-day summer workshops on Fundamentals of Data Science from August 14-18th at Stanford.  You can sign up for one workshop, or several, with topics ranging from Machine Learning to Natural Language Processing to Programming in R. Visit our Summer Workshops website for more information and to register.  

Feel free to spread the word! We hope to see you there.

Judy and the ICME team

Judy Logan

Institute for Computational and Mathematical Engineering (ICME)

Stanford University

Women in Data Science (WiDS) Conference

New Career Brochure from the Society for Industrial and Applied Mathematics (SIAM)

The 2017 edition of SIAM’s careers brochure, Careers in Applied Mathematics: Options for STEM Majors , is now available and is a great resource for anyone wondering what they can do with math.

Available in both print and PDF format, this full-color, 32-page publication contains personal stories and advice—as well as salary and job skills information—from 27 women and men working in a variety of capacities at companies ranging from industry giants to small start-ups, research labs, and non-profits.

View, download, and order print copies of the brochure here.

This brochure is a long standing and important resource for the SIAM community—present and future—and SIAM is proud to make it available to the broad public. If you would like to give feedback on the SIAM careers brochure, please send your thoughts to leblanc@siam.org.