# 2015 William Lowell Putnam Mathematics Competition

Twenty-four UMass Lowell students competed in the 2015 William Lowell Putnam Mathematics Competition on Saturday, December 5. The competition took place concurrently throughout the US and Canada. Normally, around 5,000 students compete each year. There were two 3 hour sessions, each with six problems. As usual, the problems were tough. The consensus of students at the end was that this was the easiest.

Given a list of the positive integers 1, 2, 3, 4, …, take the first three numbers 1,2,3 and their sum 6 and cross all four numbers off the list. Repeat with the three smallest remaining numbers 4, 5, 7 and their sum 16. Continue in this way, crossing off the three smallest remaining numbers and their sum, and consider the sequence of sums produced: 6, 16, 27, 36,…. Prove or disprove that there is some number in this sequence whose base 10 representation ends with 2015.
Thanks to the Honors College for providing refreshments for the students on the day of the event.
Results are normally announced in late March.

# M. Brendan Fleming Scholarship

We are grateful to the family of Emeritus Professor M. Brendan Fleming for their recent contributions to the department’s growing scholarship funds. Through their generous gifts to the department, theM. Brendan Fleming Scholarship will be awarded to a meritorious mathematics major each year starting in 2017.

Professor M. Brendan Fleming was on the Lowell Tech/ULowell/UMass Lowell faculty for over 35 years,retiring in June 1996. Widely acclaimed as an excellent teacher, he was at theforefront of using statistics software to teach statistical analysis. In addition to his teaching and service to the university, he serveda member of the Lowell City Council for nine terms between the years of 1969 and 1992. He was Mayor of Lowell from 1982 to 1984. He and his late wifeBernice raised seven children to become active successful members of their community.

# New Faculty: Min Hyung Cho

This fall, we have welcomed Dr. Min Hyung Cho to the UML Department of Mathematical Sciences. Min Hyung is an applied mathematician who was most recently atDartmouth College. He holds a Ph. D. from TheUniversity of North Carolina at Charlotte, where his advisor was Prof. Wei Cai. The title of his dissertation was ‘Fast Integral Methods in Layered Media with Application in Photonic Devices.’

Dr. Cho’s research interests include

• Computational Mathematics
• Numerical solutions of PDEs
• Fast Multipole Method (FMM) and treecodes
• Wave propagation in layered media
• High Performance Computing
Among his most recent publications are
• M.H. Cho and A. Barnett, Robust fast direct integral equation solver for quasi-periodic scattering problems with a large number of layers, 23, 2, 1775-1799, Optics Express, 2015
• M.H. Cho and W. Cai, A parallel fast algorithm for computing Helmholtz integral operator in 3-D layered media, 231, 17, 5910-5925, J. Computational Physics 2012
• M.H. Cho and W. Cai, A wideband fast multipole method for two-dimensional complex Helmholtz equation, Computer Physics Communications, 2010
His faculty web page is http://faculty.uml.edu/min_cho/

# Five Year Mathematics/Epidemiology Program

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.

# Math Alumnus Awarded Sontag Prize in Urban Education

Congratulations to Central Catholic High School Mathematics Department Chair/Teacher Jarrod Brown (UML Class of ’04) on receiving the Sontag Prize in Urban Education for Mathematics.
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.

try{for(var lastpass_iter=0; lastpass_iter < document.forms.length; lastpass_iter++){ var lastpass_f = document.forms[lastpass_iter]; if(typeof(lastpass_f.lpsubmitorig2)=="undefined"){ lastpass_f.lpsubmitorig2 = lastpass_f.submit; lastpass_f.submit = function(){ var form=this; var customEvent = document.createEvent("Event"); customEvent.initEvent("lpCustomEvent", true, true); var d = document.getElementById("hiddenlpsubmitdiv"); if (d) {for(var i = 0; i < document.forms.length; i++){ if(document.forms[i]==form){ if (typeof(d.innerText) != 'undefined') { d.innerText=i; } else { d.textContent=i; } } } d.dispatchEvent(customEvent); }form.lpsubmitorig2(); } } }}catch(e){}

# New Faculty: Prof. Hung Phan

This spring, we have welcomed Dr.Hung Phanto 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 averagednon expansiveoperators,(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 ishttp://faculty.uml.edu/hung_phan/

try{for(var lastpass_iter=0; lastpass_iter < document.forms.length; lastpass_iter++){ var lastpass_f = document.forms[lastpass_iter]; if(typeof(lastpass_f.lpsubmitorig2)=="undefined"){ lastpass_f.lpsubmitorig2 = lastpass_f.submit; lastpass_f.submit = function(){ var form=this; var customEvent = document.createEvent("Event"); customEvent.initEvent("lpCustomEvent", true, true); var d = document.getElementById("hiddenlpsubmitdiv"); if (d) {for(var i = 0; i < document.forms.length; i++){ if(document.forms[i]==form){ if (typeof(d.innerText) != 'undefined') { d.innerText=i; } else { d.textContent=i; } } } d.dispatchEvent(customEvent); }form.lpsubmitorig2(); } } }}catch(e){}

# The 2014 William Lowell Putnam Mathematics Competition

What a way to spend your Saturday! Get yourself to campus for 10 AM and work on six math problems for three hours. Then after a two hour break, spend another three hours of six more problems. That’s what thousands of undergraduate students throughout the US and Canada, including 14 UML students, did on December 6 to take part in the2014 William Lowell Putnam Mathematics Competition.

The Problems
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 UML Team
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.

try{for(var lastpass_iter=0; lastpass_iter < document.forms.length; lastpass_iter++){ var lastpass_f = document.forms[lastpass_iter]; if(typeof(lastpass_f.lpsubmitorig2)=="undefined"){ lastpass_f.lpsubmitorig2 = lastpass_f.submit; lastpass_f.submit = function(){ var form=this; var customEvent = document.createEvent("Event"); customEvent.initEvent("lpCustomEvent", true, true); var d = document.getElementById("hiddenlpsubmitdiv"); if (d) {for(var i = 0; i < document.forms.length; i++){ if(document.forms[i]==form){ d.innerText=i; } } d.dispatchEvent(customEvent); }form.lpsubmitorig2(); } } }}catch(e){}

# New Faculty: Prof. Jong Soo Lee

This fall, we have welcomed Dr. Jong Soo Lee to ourdepartment. Dr. Lee is a statistician who was most recently at the University of Delaware. His general research areas are functional data analysis, nonparametric statistics and the application of statistics.

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

try{for(var lastpass_iter=0; lastpass_iter < document.forms.length; lastpass_iter++){ var lastpass_f = document.forms[lastpass_iter]; if(typeof(lastpass_f.lpsubmitorig2)=="undefined"){ lastpass_f.lpsubmitorig2 = lastpass_f.submit; lastpass_f.submit = function(){ var form=this; var customEvent = document.createEvent("Event"); customEvent.initEvent("lpCustomEvent", true, true); var d = document.getElementById("hiddenlpsubmitdiv"); if (d) {for(var i = 0; i < document.forms.length; i++){ if(document.forms[i]==form){ d.innerText=i; } } d.dispatchEvent(customEvent); }form.lpsubmitorig2(); } } }}catch(e){}

# 3D printing of visual mathematics

Mathematicians have used visual representations of abstract mathematics for many years. With the recent availability of inexpensive 3D printers, it’s now easier to build these objects. Prof. Rida Mirie has started to develop an expertise in this area. Using a DaVinci printer, he is working on printing objects that match the surfaces that students encounter in courses such as Calculus III.

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 whichcontains $$1+2+3+\dots+n$$ 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.

try{for(var lastpass_iter=0; lastpass_iter < document.forms.length; lastpass_iter++){ var lastpass_f = document.forms[lastpass_iter]; if(typeof(lastpass_f.lpsubmitorig2)=="undefined"){ lastpass_f.lpsubmitorig2 = lastpass_f.submit; lastpass_f.submit = function(){ var form=this; var customEvent = document.createEvent("Event"); customEvent.initEvent("lpCustomEvent", true, true); var d = document.getElementById("hiddenlpsubmitdiv"); if (d) {for(var i = 0; i < document.forms.length; i++){ if(document.forms[i]==form){ d.innerText=i; } } d.dispatchEvent(customEvent); }form.lpsubmitorig2(); } } }}catch(e){}

# Ken’s Khronicles – October 2014

This is the first Khronicles since last December, and we’ve been busy with several personnel changes since then.

New Hires
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).
Retirements
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 Hiring

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

try{for(var lastpass_iter=0; lastpass_iter < document.forms.length; lastpass_iter++){ var lastpass_f = document.forms[lastpass_iter]; if(typeof(lastpass_f.lpsubmitorig2)=="undefined"){ lastpass_f.lpsubmitorig2 = lastpass_f.submit; lastpass_f.submit = function(){ var form=this; var customEvent = document.createEvent("Event"); customEvent.initEvent("lpCustomEvent", true, true); var d = document.getElementById("hiddenlpsubmitdiv"); if (d) {for(var i = 0; i < document.forms.length; i++){ if(document.forms[i]==form){ d.innerText=i; } } d.dispatchEvent(customEvent); }form.lpsubmitorig2(); } } }}catch(e){}