The Mathematical Sciences and Work Environment Departments recently completed the design of a five-year program leading to a Bachelor of Science in Mathematics and a Master's in Public Health in Epidemiology. Juniors can apply to the program and double-count up to nine credits toward the two degrees. A bit of planning is recommended since appliants are advised to take a few courses as undergraduates, such as Anatomy and Physiology I & II.

With the outbreak of Ebola in the U.S. last fall, epidemiologists have had their work cut out for them. Whether they investigate the triggers of an infection for a public health agency or collect blood samples at an outpatient care center, epidemiologists examine the causes of diseases to prevent them from transmitting and recurring. These medical scientists might work in hospitals, laboratories or universities, or for pharmaceutical companies or health insurers.

The Bureau of Labor Statistics predicts employment growth of about 13 percent between 2012 and 2022. Job prospects look promising, especially for medical scientists looking to work for state or local governments and general medical or surgical hospitals.

The Sontag Prize in Urban Education recognizes outstanding teaching in Mathematics, English Language Arts (ELA) and other disciplines. Educators chosen for the Sontag Prize will lead classes as part of the LPS Acceleration Academy, a program designed to provide targeted small group support for students.

Any educator from within the city of Lawrence, MA or across the country is eligible to apply for the Sontag Prize. In addition to an honorarium, new Sontag Prize awardees participate in a weekend of professional development at Harvard University February 14th and 15th. The opportunity provides motivated and successful educators like Jarrod the chance to share best practices with their fellow awardees. Most importantly, this award recognizes excellence in teaching and provides students with an extra week of high-quality instruction. This program is generously supported by the Lynch Foundation.

This isn’t the first time Jarrod has been recognized for his teaching, In 2013, Jarrod received a Math Hero Award and grant of $2,500 through Raytheon Corporation’s “Math Moves U” program. He was nominated for this award by current and former students for his instructional creativity and patience, varied use of technology resources, and his ability to share his enthusiasm for mathematics with his students.

Jarrod earned a B.S. in Mathematics from the University of Massachusetts at Lowell and a M.Ed from American International College. In his 12th year as a math teacher, Brown’s teaching experience includes leading classes in Algebra 1, Geometry, Algebra 2 & Trigonometry, Pre-Calculus, and Calculus.

Jarrod has also served as an assistant coach in football and track in addition to being the instructor for the Karate and Martial Arts Club at Central Catholic. Brown and his wife and two children make their home in Dracut, MA.

This spring, we have welcomed **Dr. Hung Phan** to the UML Department of Mathematical Sciences. Dr. Phan is an applied mathematician who was most recently at the University of British Columbia, Okanagan. No doubt he has been right at home in the past few weeks as we've had two major snow storms!

Hung's general research areas are Optimization, Numerical Methods, and Variational Analysis. His Ph. D. was earned at Wayne State University, with a thesis titled *New Variational Principles with Applications in Optimization Theory and Algorithms* (Advisor: Boris Mordukhovich).

Here are three of his recent publications:

**Linear and strong convergence of algorithms involving averaged non expansive operators**,(with H.H. Bauschke, D. Noll)*Journal of Mathematical Analysis and Applications*421 (2015), 1-20**The rate of linear convergence of the Douglas-Rachford algorithm for subspaces**, (with H.H. Bauschke, J.Y. Bello Cruz, T.T.A. Nghia, X. Wang)*Journal of Approximation Theory*185 (2014), 63-79**Restricted normal cones and sparsity optimization with affine constraints**, (with H.H. Bauschke, D.R. Luke, X. Wang),*Foundations of Computational Mathematics*14 (2014), 63-83

His web page is http://faculty.uml.edu/hung_phan/

The problems are all considered "elementary" in that they only require the background of basic undergraduate mathematics courses to understand. They are definitely not "easy." Historically, the median score out of 120 (10 points per problem) higher than single digits, and there have been years when the median was zero! In each session the first two problems tend to be somewhat easier than the other four. Here is the first problem from the morning session, which a Calculus II student should understand.

Prove that every nonzero coefficient of the Taylor series of \[(1-x+x^{2})e^{x}\] about \(x=0\) is a rational number whose numerator (in lowest terms) is either 1 or a prime number.

If you work on this, remember that the the competition prohibits books or any electronic devices!

The participants from UMass Lowell this year included 12 "rookies" who had not previously competed in the Putnam. All were part of the Honors Problem Solving course taught by Ken Levasseur this semester. They were Kenneth Allen, Marissa Ard, Anna Baturin, Stephanie Bellerose, James Carbone, Damir Ismagilov, Alex Kane, George Katsaros, Chanson Lim, Erinn McLaughlin, Grant Moyer, and John Romano.

Returning for their second year in the completion were Jonathan Edwin and Alvin Kow. Graduate student Chuck Bradley was ineligible for the competition, but participated in practices and lent moral support to the participants.

Scoring the competition is a long process carried out by Putnam staff at the University of Santa Clara. Scores normally are announced in April.

Next year's competition will be on Saturday December 5, 2015.

Jong Soo earned his Ph. D. at Rice University with a thesis titled *Aspects of Functional Data Inference and Its Applications* (Advisor: Dennis Cox).

This has come just at the right time for Prof. Tibor Beke, who is teaching a section of Explorations in Math to students in the Humanities, Fine Arts and Social Sciences who have accepted the challenge to explore some mathematics as a somewhat higher level than is normally offered to students on our South Campus.

We all know the formula \[ 1+ 2 +3+ \dots + n = \frac{n(n+1)}{2} \]

that can be justified in a number of ways --- by induction, but adding the left-hand sum to itself in the reverse order, or by decomposing an \(n\) by \(n+1\) rectangle into two congruent pieces, each of which contains \(1+2+3+\dots+n\) unit squares. But what about \(1^2 + 2^2 + 3^3 + \dots + n^2 \)? A nice way to visualize such a sum is as the number of cubes in a skewed "Mayan pyramid." Here is are six Mayan pyramids printed by Rida that are a visual representation of \(1^2 + 2^2 + 3^2 + 4^2 \).

Three such pyramids can be combined to form a cuboid with a set of steps next to one of the faces. The steps in two such formations can, if you orient the pieces correctly, be fit together.

When this is done, you get a single cuboid. In this case, it's a \(4 \times 5 \times 9\) cuboid, demonstrating that \(6(1^2 + 2^2 + 3^2 + 4^2) = 4 \times 5 \times 9 \). The 5 in this equality is one more the 4 and 9 is one more than \(2 \times 4 \).

This configuration works for the sum of the first \(n\) squares for all positive values of \(n\), which demonstrates a general identity, after dividing by 6: \[ \sum _{k=1}^{n } {k^2} = \frac{n(n+1)(2n+1)}{6} \]

The nice thing about having a tactile representation of this fact is that students can actually put the pieces together and see how it is really not dependent on the number of squares. "Proofs with no words" such as this one have traditionally been accepted as valid proofs. They are limited to our three dimensions, but the printing of complex objects opens up possibilities that we haven't had until now.

Early in January of this year we were authorized to do faculty searches for two tenure-track positions, a statistician and an applied mathematician. Although it was a late start, we are happy to announce that both searches were successful.

Dr. Jong Soo Lee, a statistician who was most recently at the University of Delaware, has joined us this fall. His general research areas are functional data analysis, nonparametric statistics and the application of statistics. His Ph. D. was earned at Rice University with a thesis titled Aspects of Functional Data Inference and Its Applications (Advisor: Dennis Cox).

Dr. Hung Phan, an applied mathematician who was most recently at the University of British Columbia, Okanagan, will join us in the spring. His general research areas are Optimization, Numerical Methods, and Variational Analysis. His Ph. D. was earned at Wayne State University, with a thesis titled New Variational Principles with Applications in Optimization Theory and Algorithms (Advisor: Boris Mordukhovich).

This infusion of new personnel comes just in time to offset losses due to retirement. Charlie Byrne retired after being with us since 1986. He served as department chair for a term, and graduate coordinator for many years. His expertise in areas such as optimization and image processing is hard to replace.

Congratulations to Charlie on his recently published book, An Introduction to Optimization.

In addition, we've lost the services of Alan Kaplan, who retired after forty years of service. His many contributions to the department will be missed.

More good news is that we've been authorized to do two more searches for tenure-track faculty. We've decided to search for another statistician and a mathematician. The research area for the mathematician is a bit less focused that in our earlier search. To see details of our postings, go to the UML Jobs site.

There is plenty of other news to report, but I intend to make these postings more frequent. So I'll close here.

Naturally, the plot labeled MRKT BSKT is our spending at Market Basket. The SHAW graph is actually a combination of our spending at Shaw's and Hannaford's. I think I stopped at Shaw's around February and bought a few items, but other than that, spending there started at the same time as the boycott.

Instead of making this a one-time exercise, I decided to develop a function that would create other graphs like this one. My main summer project has been to rebuild the stairs at my son's house in Chelmsford, adding a small deck. Out of convenience, my main spending on the project, which started in mid-July, has been at three locations. They are my local NH Home Depot (no sales tax!), where I've bought most of the smaller items I could fit into my Subaru, the Lowell Lowe's, which is five minute from the project and where I've bought several last minute items I didn't expect to need, and finally, Friend Lumber from whom I've had lumber delivered. Here is the spending plot at those locations for 2014, with another ~$100 spending to go at this point:

One more example, here is my coffee spending - this is flawed in that it is only the debit card spending, so a lot of my purchases at Einstein's during the year are not included. A&E is my local coffee roaster, and I definitely spend more there that anywhere else, even if I took into account cash sales. Also, I use the Starbucks app on my phone, which is why larger, less frequent purchases are recorded there.

If you'd like to try this with your spending, you can download a copy of the Mathematica Package that creates these graphs. The package assumes you have a Bank of America debit card. You would download activity from your account and use the file path to that .csv file on your computer to specify the data file. With a bit of Mathematica expertise, it shouldn't be hard to adapt the package to other banking systems.

Erinn McLaughlin, together with Michelle Scribner-MacLean (Graduate College of Education) and William Morton (Lowell National Historical Park), described how she and her classmates teamed with the National Park to create science and math projects for high school students. The work was part of the required UTeach course, Project Based Instruction.

At a poster session that included dozens of student submissions, John Romano won the *best student poster for a research project* for the work he did as an intern with M2D2 and Lowell High School. Erinn also displayed a poster on the mathematics of water wheels.

- The
**CUPM Curriculum Guide**is produced by the MAA Committee on the Undergraduate Program in Mathematics to guide mathematics departments in designing curricula for their undergraduate students. The 2004 version was the last to come out. The new version will be out in 2015. We were told that a draft will appear at maa.org/cupm in the near future. - In 2012, the Conference Board of the Mathematical Sciences issued the latest recommendations for teacher preparation in mathematics:
**The Mathematical Education of Teachers II (MET2)**. A few highlights of the new recommendations:

- Elementary teachers should take four mathematics courses on elementary school mathematics. This doesn't mean that the mathematics they are taught are elementary. The objective is to give teachers a deeper understanding of the mathematics that is taught in elementary grades. For example, while an elementary school teacher may teach division, coursework might include continued fractions or a study of the periodic nature of decimal fractions.
- Recommendations for middle school teachers include at least 24 credits of mathematics, including at least 15 credits designed specifically for future middle grades teachers that address essential ideas in the middle school curriculum.
- It is still recommended that prospective High school teachers complete coursework equivalent to that of a mathematics major. One change is that at least nine credits involve advanced study of secondary mathematics.
- The American Statistical Association (ASA) will be releasing
**The Statistical Education of Teachers (SET)**in 2014. It is expected to put a greater emphasis on data analysis.

I think that a few developments at UMass Lowell have put us in a good position with respect to these recommendations. A few years ago, the College of Education and Mathematical Sciences Department collaborated with other UMass campuses on the development of mathematics courses for prospective elementary school teachers. This gives us a good start toward being in line with recommendations at that level.

There will be more for us to do to address these recommendations, but I think we are on the right track!

]]>I hadn’t expected to be writing this column up until last May, but here I am serving as chair of Mathematical Sciences again after a 14 year break. I had been chair for nine years, roughly coinciding with the Clinton administration. There are several news items to report, but first I’d like to reflect on what’s changed in 14 years.

- The last time I was chair we were housed in Olsen, now we’re in Olney. With new buildings starting to pop up on campus, several departments, including us, could be moving again in the coming years.
- Since my first “retirement” as chair, we’ve seen the retirements of Professors Yin, Makovoz, Weinberg, Spiegel, Mueller, Winslow, Berkovits, Ruskai, and Samarov. We currently have seven tenured faculty and seven Instructors who have joined us since then.
- When I left the chair’s position in the 20th century, we offered a two semester version of Calculus I, Calculus IA and Calculus IB. After trying “Preparation for Calculus” for a few years, we now we have a new two semester version of Calculus I. Same name, but different catalog numbers. Everything is cyclic.
- Scholarships: Toward the end of my first run as chair, Russ and Mary Bedell’s generosity had just brought us our first endowed scholarship. As you can see below, we’ve been fortunate to have two more endowed scholarships started since then and hope to be able to announce more in the future.
- Finally, Tangents didn’t exist in 1999 - the first issue was in 2002. So now I will move to the present.

One of the main reasons why I agreed to take on the chair’s position is that Kiwi has agreed to help me out as associate chair. In addition, I’m getting lots of help from other members of the faculty and, of course, Cori Lee, our Administrative Assistant. I thank all of them for helping make my return reasonably smooth.

It’s helped that I’ve been able to divest some of the things I was doing. Steve Pennell has started his “chair’s retirement” by taking over as coordinator of the Industrial Math PSM program. Also, I had been editing Tangents since 2002 and I’m glad to announce that Jim Propp has agreed to take over as editor.

Tibor Beke has returned to us after a year on sabbatical traveling through Europe and the States in 2012-13 and Ravi Montenegro has left us for a 2013-14 sabbatical to collaborate with researchers in Japan and New Zealand.

Math majors Olivia Demers and Mary Mersereau had been working with Shelley Rasmussen in doing research on the mathematics of weaving. They recently shared their enthusiasm for the subject with some children in a local summer camp.

In the past year, Industrial Mathematics PSM Students Isaac Duodu (Putnam Investments) and Lauren Edwards (Genscape) completed internships that gave them valuable experience to further their careers. Undergraduates Gifty Bado and Tyler Gilzinger spent their summers as Co-Op students at Putnam Investments. After completing a co-op position at Mercury Computer, recent B. S. graduate Owen Welch accepted a full-time position at Mercury. Krithika Manohar, who graduated last May, is in her first semester of the Applied Math doctoral program at the University of Washington.

Last May, we held our annual Awards Ceremony and Alumni Reception where we presented the following awards:

- Outstanding Graduate Student: Nour Almansour
- Shapiro Scholarship: Chris Leger
- Bedell Scholarship: Tyler Gilzinger
- Zamanakos Scholarships: David Campbell, Mary Mersereau and Kevin Southwick
- Hall Prize: Kevin Cerritelli.

The 2014 awards ceremony will be held at the UML Inn and Conference Center on April 25 from 5:30 to 7:30. Alumni are always welcome to attend. It’s a great setting.

]]>Here is a visualization of the Fall 2013 Math Schedule showing the times at which each course is offered.

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One of the neat things about Sage, the open-source computer algebra system is that you can easily embed it into any web page. Here is an example of some code that can be evaluated to plot a function and it's derivative. For more information about Sage: http://sagemath.org. To learn how to embed Sage into your web page: http://aleph.sagemath.org/static/about.html.

- The book is now listed as part of the American Math Institute's Open Textbook Initiative.
- It has its first outside adoptions: classes at the University of the Puget Sound, Grinnell College, Casper College and Luzurne Community College are all using the book in the spring of 2013.

Resources, such as this dynamic demonstration of cyclic subgroups of the group of integers mod n are continuing to be developed. Move the sliders to see the different subgroups with varying moduli:

Applied Discrete Structures by Alan Doerr & Kenneth Levasseur is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License.]]>