A while ago I discovered a Podcast called My Favorite Theorem and have eagerly listened to each new episode. The basic format is that a mathematician is invited by the two hosts (Kevin Knudson and Evelyn Lamb) to describe his/her favorite theorem and also to pair the theorem with some non-mathematical thing, usually food or music.

What’s your favorite theorem?  Mine is the Chinese Remainder Theorem.  It’s got an obvious pairing, but that isn’t why I picked it.  My reason is that is appears in several courses I’ve taught and also has connections with my dissertation research way back in the 1970’s.

In an abstract algebra course, the Chinese Remainder Theorem says that if two positive integers, and , are relatively prime, then the ring of integers mod is isomorphic to the direct product the rings of integers mod and .

In number theory, the same fact is framed differently, that the system of congruences and always has a unique solution mod as long as and are relatively prime.

My dissertation research involved approximation and interpolation of functions, and when you generalize the Chinese Remainder Theorem to Euclidean Domains, one immediate implication is that given points on the plane (pick any field) with distinct -values, there is always a unique polynomial of degree or less that passes through the points.

If you have a favorite theorem feel free to post it in the comments!

# UML Participation in the 2019 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 34 UMass Lowell students, did on December 7 to take part in the 2019 William Lowell Putnam Mathematics Competition.

The competition, sponsored by the Mathematical Association of America, took place concurrently throughout the US and Canada. Last year,  4,623 students from 568 institutions participated. There were two 3 hour sessions, each with six problems. As usual, the problems were tough. Here is probably the easiest of them:

Determine all possible values of the expression
A3 +B3 +C3 – 3 A B C,
where A, B, and C are nonnegative integers.

A complete list of problems: 2019 Putnam Problems

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.

# Al Doerr, 1938-2018

Prof. Alan Doerr, Mathematical Sciences

Professor Alan Doerr, one of the longest serving professors at UMass Lowell, passed away on October 14, 2018 at the age of 80. Al retired in 2016, completing a career that spanned the entire history of the UML Mathematical Sciences department.

A Lawrence MA native, Al started his career as a high school mathematics teacher in New York City in 1960. After earning a graduate degree from Hunter College, he was hired as part of the Lowell Technological Institute’s Physics Department. Soon afterward, he was among the physics faculty who became founding members of the Mathematical Sciences Department. He was instrumental in creating both undergraduate and graduate degree programs in the department.

From 1976 to 1987, Al chaired the department as Lowell Tech merged with Lowell State to become the University of Lowell. After completing four terms as chair, he spend another twelve years as associate chair, during which the institution became UMass Lowell. He also was a coordinator in Lowell’s Continuing Education program from 1966 to 2015.

Al’s mathematical interests were primarily in Linear Algebra, Abstract Algebra and Discrete Mathematics. He taught courses in these subjects countless times, but taught virtually every course in the curriculum except statistics (which he admitted to disliking). In 1985, he co-authored Applied Discrete Structures for Computer Science, with his colleague, Ken Levasseur. The book was successful in the 1980’s and has been re-released as an open content text that is currently used at several universities. In 1994, he also coauthored College Algebra and Trigonometry with Leonard Andrusaitis and Ken Levasseur.

The department hopes to establish a scholarship in Al’s name in the near future. As of January 1, 2019, we have raised almost half of what is needed to establish an endowment.   If you’d like to pledge any amount, please contact Ken Levasseur.

# UML Participation in the 2018 William Lowell Putnam Math Competition

2018 William Lowell Putnam Math Competition at UML

Forty-six UMass Lowell students participated in the 2018 William Lowell Putnam Mathematics Competition on Saturday, December 1. The competition, sponsored by the Mathematical Association of America, took place concurrently throughout the US and Canada. Last year, 4,638 students from 575 institutions participated. There were two 3 hour sessions, each with six problems. As usual, the problems were tough. Here is one of them:

Find all ordered pairs (a,b) of positive integers for which 1/a + 1/b = 3/2018.

A complete list of problems:  putnam2018probs

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.

# Rida Mirie, 1953-2018

On February 16, 2018, UMass Lowell Professor Rida Mirie passed away.  Rida joined the faculty of the University of Lowell in 1986. His main area of research was in the modeling of water waves, specializing in the theory of solitary waves.  He also contributed to early work on Buckyballs.

Rida loved teaching.  While at Lowell, he taught Calculus, Differential equations, Numerical Analysis, and several graduate courses. It is estimated that in Differential Equations alone, he taught over 3,000 students. His lectures were sprinkled with anecdotes and jokes that related the theory to his other interests, including people, gardening and John Deere tractors.

Here is a typical student comment on his teaching:

Exceptional mind. It takes some time to learn how he thinks but once you’re there it is hilarious and informative at the same time. He is the only professor who has mastered the art of teaching without the need for a textbook. But you have to do your part – homework and taking a lot of notes. Will definitely take his class again.

Rida was born in Beirut, Lebanon. He graduated from the American University in Beirut and earned a Ph. D in Applied Mathematics from Brown University in 1980.

He is survived by his daughter, Aysha Rida Mirie. We’ll miss Rida, particularly for his generosity and humor.

A daughter’s last words:

“ You can be as mad as a mad dog at the way things went. You could swear, curse the fates, but when it comes to the end, you have to let go” – Benjamin Button

I will truly miss my father’s full out belly laugh and his ability to never complain about life. He would often say “take it like a man” when things didn’t go as planned. My father was a true fighter for what he believed – in life, love and education. He challenged everyone: myself, his students and even his friends. He absolutely loved his land- tending to his fruit bearing trees, rose bushes, grape vines and often had numerous projects in the works.

I will find comfort remembering him relaxing on top of the grape pergola he built all by himself. (His last project)

He was a very proud man. To honor the remarkable man that he was,  as you drive by his pergola “beep” your horn and find comfort as you picture a huge smile on his face.

If you would like to share memories of Rida, use the comments box below.

# 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.

# New Faculty: Erica Yankowskas

Ms. Erica Yankowskas  is a Visiting Professor in the Department of Mathematical Sciences.  She teaches traditional and applied/business calculus courses, both on-campus and on-line.

Professor Yankowskas holds a Master of Science in Applied and Computational Mathematics from the University of Massachusetts Lowell and a Bachelor of Arts in Mathematics from Assumption College.

# New Faculty: Sedi Bartz

This fall we are welcoming Dr. Sedi Bartz to the Department of Mathematical Sciences. Dr. Bartz’ research focuses on topics of nonlinear analysis and variational analysis. He develops refinements of abstract convex analysis, and in turn, transforms his refinements into a unifying language for phenomena in variational analysis which used to be considered quite apart. Dr. Bartz is also a specialist in classical convex analysis and monotone operator theory, theories which are among the most popular tools of modern optimization.

Dr. Bartz holds a Ph.D. from The Technion-Israel Institute of Technology. He arrives to UML after a 3 year term as a Post-Doctoral Fellow at the University of British Columbia, Kelowna, Canada.

# New Faculty: Nilabja Guha

This fall, we are happy to welcome Dr. Nilabja Guha to the Department of Mathematical Sciences. Dr. Guha is a statistician who was at Texas A&M University in a postdoctoral position prior to joining UML. He received his doctoral degree in statistics from the University of Maryland Baltimore County where his adviser was Dr Anindya Roy.

Dr Guha’s research interest include Bayesian Modeling, Inverse problems, Uncertainty Quantification, High-dimensional Problems and Graphical Modeling.

Some of his recent publications are

• Guha, Nilabja, Anindya Roy, Yaakov Malinovsky, and Gauri Datta., 2016. An optimal shrinkage factor in prediction of ordered random effects. Statistica Sinica 26: 1709-1728.
• Guha, N. and Tan, X., 2017. Multilevel approximate Bayesian approaches for flows in highly heterogeneous porous media and their applications. Journal of Computational and Applied Mathematics, 317, pp.700-717.
• Yang, K., Guha, N., Efendiev, Y. and Mallick, B.K., 2017. Bayesian and variational Bayesian approaches for flows in heterogeneous random media. Journal of Computational Physics, 345, pp.275-293.

# The River Hawk Prime

At first glance the 1680 digit number

111111111111111111111111111111111111111111 111111111111111111111111111111111111111111 111111999999911111111111111111111111111111 111111111111111999999999999999999999991111 111111111111111111111111111111119999999999 999999999999999999111111111111111111111111 111111111199999999995555555599999999991111 111111111111111111111111199999999999999555 555555559999999911111111111111111111111999 999999555555555555555555555559999999111111 111111111111199999955555555555555999995555 555555599999911111111111111199999955555555 555555555555599999555555559999911111111111 111999999999999995555555555555555599999555 555999991111111111199999999999999555555555 555555555555997995555599991111111111999999 999999995555555555555555555555597799555559 991111111119999999999999555555599955555555 599795591199999559991111111199991111999995 555999995555555555591179999111995559999111 111991111119999955999999955555555555991197 799999555599999111111111111199999999999995 555555555555599991119799559995999911111111 111199999999999955555555555555591191199991 919999999911111111111999999999999955999999 555555559191119111999999999911111111111999 999999999999999999995555712499999999999999 999911111111119999999199999999999999999955 555555555559999999999911111111119999911199 999999999999999999955555555999991119999111 111111199999111199991111111111999999999999 999999111119999111111111199911111999111111 111111111999999999999111111119991111111111 199111111911111111111111111111111111111111 111199911111111111991111111111111111111111 111111111111111111111199111111111111911111 111111111111111111111111111111111111111111 111111111111111111111111111111111111111111 111111111111111111111111111111111111111111 111111111111111111111111111111111111111111

would not appear to be remarkable, other than in the preponderance of 1’s and 9’s that comprise its digits. However, there are two interesting observations about this number. First, it is prime. The only integers that divide evenly into it are 1 and itself. Second, if the digits are arranged in a rectangular fashion, 60 digits to a row, we see why it has been dubbed the “River Hawk Prime.”