## Who did what?

Lindsey Doane is a mathematics major who in Fall, 2014 carried out a research project in MTH 204, Computational Experiments in Mathematics. Her project involved estimating occurrences of Niven Numbers. A Niven number (sometimes known as a Harshad number) is a positive integer exactly divisible by the sum of its (base 10) digits. Examples are 12 and 18. More information at the

No prime number p greater than 10 can be a Niven number because the sum of the digits of p is a number greater than 1 and less than p (and so cannot exactly divide the prime number p).

However, the growth of the Niven numbers is tantalizingly similar to the growth of the prime numbers. The famous prime number theorem says that the number $\pi (n)$ of primes less than or equal to $n$ is asymptotically $n/log(n)$. This means that the ratio of $\pi (n)$ to $n/log(n)$ approaches 1 as $n \to \infty$.

In a paper in 2001 and a later paper in 2003, Jean-Marie De Koninck, Nicolas Doyon, and later Imre Katai, establish there is a constant $C$ such that the number of Niven numbers less than or equal to n is asymptotically $C\times n/log(n)$.

Lindsey investigated how to better approximate the constant $C$, and also investigated the ratio of the number of Niven numbers up to n, to the number of prime numbers up to n (since they both grow in much the same way, yet are quite different sets of numbers).

## Who’s doing what?

Sidafa Conde, a graduate student in the Engineering & Applied Sciences Ph.D. program, specializing in Scientific Computing,  is working on numerical solutions of non-linear partial differential equations.

Sidafa said about his experience at U Mass Dartmouth: “I’d say that UMass Dartmouth is truly amazing. Balanced. One-of-a-kind. And actually very affordable. My experience at UMass Dartmouth has been phenomenal.That whole “world class. within reach” is definitely true. The professors care. They’re here not just to teach but to actually show us. It’s awesome. When you walk through the department, they always call you in to have a conversation, even if it’s not about classes. They ask you about your plans for the future. They always encourage you to try new opportunities.”

## FACULTY

Bo Dong, an Assistant Professor in the Department of Mathematics, works on finding accurate numerical solutions to certain non-linear differential equations. The differential equations she studies are closely related to the so-called Korteweg-de Vries equation (so called, because the original equation was discovered by Joseph Valentin Boussinesq in 1877  and re-discovered 18 years later by Diederik Korteweg and Gustav de Vries) which provides a mathematical model of waves on shallow water surfaces. A nice historical background to the KdV  equation can de found here. Differential equations similar to the KdV equation have many applications in fluid mechanics, nonlinear optics, acoustics, and plasma physics. For example, the KdV equation has been used in the modeling of shallow water waves and the study of Tsunami waves. The study of equations of KdV type has had an enormous impact on the development of modern nonlinear mathematical science: vast areas of mathematics (ordinary differential equations, algebraic geometry, Lie group theory, differential geometry, asymptotics) and theoretical physics (quantum field theory, string and conformal field theory, quantum gravity, classical general relativity) opened up as a consequence of the basic research into the KdV type equations.

Boris Grigoryevich Galerkin, 1871 – 1945

Bo uses a method for numerically approximating solutions to KdV type equations known as the discontinuous Galerkin method. (not to be confused with discontinued gherkins!).  This method is named, in part, after Boris Galerkin, a Russian mathematician and engineer, who introduced numerical methods, now known by his name, for solving differential equations. The discontinuous Galerkin (DG) method was introduced in 1973 by W.H. Reed & T.R Hill, in the context of modeling neutron transport. A critical feature of the use of DG methods is that KdV type equations may develop discontinuous solutions and at those discontinuities quite complex behavior can occur, making numerical approximation a delicate issue. A very nice account of DG methods is available in:  The Development of discontinuous Galerkin methods

## ALUMNUS

Jorge Fernandez is a recent UMass Dartmouth mathematics graduate. Jorge started his studies as a College Now student, and as a Junior and Senior worked on a number of research projects. One of these projects, of his own choice, involved modeling the ingress of hurricanes from water to land. After graduation Jorge applied for an internship at the Hartford, a Fortune 500 insurance company in Hartford, CT. His research work on hurricanes stood him in good stead, and he got the internship that was updated to employment as a data analyst at the end of summer. Jorge commented that he made a fundamental change in his outlook to studies when he started doing research, focusing on learning rather than on grades.

## Math Jokes

Professor Naiomi Cameron telling math jokes at an Open Math Night,  November 22, 2008.

## What was up with Pythagoras?

Welcome to all mathematics majors, and especially to our 22 Freshman majors. This is the first Department of Mathematics Newsletter for Fall 2014.

### New Mathematics Gallery, Science Museum , London

Zaha Hadid Architects design for the new maths gallery that will open at the Science Museum in London in 2016:

### Meanwhile, back in New York city …

The Museum of Math  in NYC, opened in 2012, is going strong. The Museum is located at 11 East 26th Street in Manhattan and is open from 10:00 AM to 5:00 PM, seven days a week, 364 days a year (MoMath is closed on Thanksgiving Day).

### BA-BS/MAT 4+1 program

Each year several of our Mathematics majors intend to teach mathematics at the Middle or High School level. The Department of Mathematics is currently in discussions with the STEM Education Department to give intending Middle and High School mathematics teachers the option of taking Education courses in their Junior and Senior years. For students admitted into this program, this arrangement will have the effect of allowing them to complete a Master’s degree in Education, and gain their teaching license, just one year after graduation. Stay tuned.

### Data science: how is it different to statistics ?

“The end product of an analysis is not a model: it is rhetoric. An analysis is meaningless unless it convinces someone to take action. In business, this typically means convincing senior management who have little statistical expertise. In science, it typically means convincing reviewers.” Hadley Wickham

Professor Gary Davis

When Gary Davis’s wife wanted to start an online subscription knitting business, the UMass Dartmouth professor did what any statistician would do — he began seeking out available data to analyze. After a few days of online searching, Davis found just what he needed — a site that surveys knitters. “I didn’t go looking for big databases, I went out looking for surveys and it turns out there’s a group that does surveys on people who knit,” Davis, a mathematics professor, said. “In the United States, there are 54 million people who identify themselves as knitting.”

After reviewing the data, Davis, advised his wife to specialize in sock knitting, a style he learned attracts one-third of all U.S. knitters. “If your website is based around socks, you know you’re going to get a higher hit rate because it’s a much more specific, well-defined area,” said Davis. “So using the available data to cut down and focus your demographic can lead to higher returns.”

Leveraging large quantities of data to optimize business strategies, better understand customers, and grow profits is a tactic regularly used by large companies, but all too often small businesses shy away from big data analysis in their decision-making. But Davis and his UMass Dartmouth colleague and data scientist Donghui Yan say today’s data world includes new options for small business to collect and crunch information and that even small steps can lead to profit gains. Yan and Davis are behind a university move to create a degree program in data science, training undergraduate and graduate students, and serving as a local resource for small business. Yan was recruited to UMass Dartmouth this year to help build the program, having worked in big data analysis for Walmart Labs in San Bruno, Calif.

“Almost every major corporation has either a department or some employees dedicated to modeling or data science because they want to leverage this data and use the information to help their business,” he said. “Data is money… It’s very valuable.” Walmart, Yan said, knows this lesson well, translating its big data analysis into \$10 billion in online revenue last year alone. A statistician with a Ph.D. in the field, Yan’s role at Walmart was to help create an online recommendation system for the retail giant to suggest additional products that other customers have purchased together. Walmart also uses data to optimize placement of its products in stores, he said, tracking one arrangement versus another and then implementing the better model. “Walmart is very famous for its logistics,” said Yan. “They use this kind of information for the so-called buy together products…to ship those together and save costs.”

So how do small businesses follow in Walmart’s footsteps without becoming overwhelmed with data? One possibility, Yan said, is simply to observe the bigger companies who do this well, like Walmart and Amazon. Pay attention to how they group and sell products and begin formulating simple tests of your own, he said. “Basically, small businesses don’t need to own data or find data, they can take advantage of the bigger data that exists,” he said. Valuable information can also be sourced online, including restaurant review sites, surveys, and databases. Other sources, like tapping into Google’s big data research through Google Adwords, are worthwhile paid services, Yan said.

One Dartmouth small business owner believes her decision to collect and analyze data has led to the continued growth of her seven-employee salon. Nine years ago, Lisa Leite, of Salon en Vogue in Dartmouth, installed a system that allows her to track salon customers and purchases. The data she gets helps her keep adequate inventory of fast-moving products, decide when a slower-moving product needs a marketing boost, and create incentives for her staff to sell products. “We can keep track of what goes out, how much, and with whom and how much we’re using in a month,” said Leite. “It helps me look at everything and have a goal for the next year.” She has never regretted the investment, she said. “It just really organizes your business. I would never go back.”

For small businesses, starting with the right questions can be crucial to success, so getting expert assistance in the design stages of a data project can facilitate the process. Big data analysis is a cyclical process, Yan said, progressing from collecting information, to simple analysis and then communication of results in a way that makes sense to stakeholders. More data is generally collected through the three-step process at which point, you start again, he said.

Davis is hoping the university’s new data science degree, which only needs Board of Higher Education approval, can also provide a local resource and help make New Bedford a “data-rich city.” “We’re hoping our students will be able to work in internships with people in small business around the area. We’re really looking for a lot of connections with the local businesses and local community,” he said.