UML Participation in the 2017 Putnam Math Competition

Twenty-six UMass Lowell students competed in the 2017 William Lowell Putnam Mathematics Competition on Saturday, December 2. The competition, sponsored by the Mathematical Association of America, took place concurrently throughout the US and Canada. Last year, 4,164 students from 568 colleges and universities participated. There were two 3 hour sessions, each with six problems. As usual, the problems were tough. Here is one of them:

The 30 edges of a regular icosahedron are distinguished by labeling them 1, 2, …, 30.  How many different ways are there to paint each edge red, white, or blue such that each of the 20 triangular faces of the icosahedron has two edges of the same color and a third edge of a different color?

In case you’ve forgotten, an icosahedron looks like this:

A complete list of problems:  Putnam2017.

Professor Kenneth Levasseur served as supervised competition at UML.   Thanks to the Honors College for providing refreshments for the students on the day of the event.

Results will be announced in late March.

2016 William Lowell Putnam Mathematics Competition


Twenty-one UMass Lowell students competed in the 2016 William Lowell Putnam Mathematics Competition on Saturday, December 3. The competition took place concurrently throughout the US and Canada. Last year 4275 students students from 554 colleges and universities competed participated. 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 problem was one of the easiest:

Suppose that S is a finite set of points in the plane such that the area of triangle ABC is at most 1 whenever A, B, and  are in S. Show that there exists a triangle of area 4 that (together with its interior) covers the set S.


Thanks to the Honors College for providing refreshments for the students on the day of the event.

Results are normally announced in late March.

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.


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.

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.

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Curriculum Guides in Mathematics: JMM2014 update

I attended a panel discussion on curriculum guides at the 2014 Joint Mathematics Meetings last week. Here are a few comments on them.

  • The CUPM Curriculum Guide is produced by the MAACommittee on the Undergraduate Program in Mathematicsto 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 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:
    1. 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.
    2. 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.
    3. 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.
  • TheAmerican Statistical Association (ASA) will be releasingThe 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.
UTeach UMass Lowell helps us at the middle and high school levels. Functions and Modeling (92.210), which is required for mathematics certification, revisits many high school topics from an advanced point of view. Research Method (UTL.302), which is required of all UTeach students, is a data analysis course that matches both MET2 and SET recommendations. Finally, the inquiry-based approach that many UTeach courses emphasize is consistent with that of all three curriculum guides.
There will be more for us to do to address these recommendations, but I think we are on the right track!

Mathematical Weaving

In recent years, Prof. Shelley Rasmussen has be doing research into the mathematics of weaving. She has gotten several students involved in her work. Most recently, math majors Olivia Demers and Mary Mersereau had been working with Shelley. They recently shared their enthusiasm for the subject with some children in a local summer camp. For more information on the mathematics of weaving:


Embedded Sage Cells


sagecell.makeSagecell({“inputLocation”: “.sage”});
$(function () {
// Make the div with id ‘mycell’ a Sage cell
sagecell.makeSagecell({inputLocation: ‘#mycell’,
template: sagecell.templates.minimal,
evalButtonText: ‘Activate’});
// Make *any* div with class ‘compute’ a Sage cell
sagecell.makeSagecell({inputLocation: ‘div.compute’,
evalButtonText: ‘Evaluate’});


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: To learn how to embed Sage into your web page:


Embedded Sage Cell

# You can put virtually any Sage code in this section, or simply edit the existing
# code any way you choose.
def f(x):
return x * sin(pi*x)