This survey treats two connected questions in analytic number theory: given a set of natural numbers, one may seek numbers with large prime factors in the set. Alternatively, one searches for smooth numbers in the set. Many examples have been studied: the set of values of a polynomial, the set of integers in a short interval, the set of shifted primes p+a and so on. These are discussed at some length, with references to the literature.
Professor Michael Dorff of the Department of Mathematics will be announced as the recipient of the Lawrence K. Egbert Teaching and Learning Faculty Fellowship award at next year’s Annual University Conference.
The teaching and learning fellowship award, which has only existed for a few years, was created to recognize faculty members that have made a significant impact in the area of mentored learning.
Professor Dorff, who has been teaching at BYU for 12 years, was nominated and eventually selected as the recipient because of his extensive involvement in mentoring undergraduate students and helping other professors explore similar mentoring opportunities.
As part of Professor Dorff’s efforts to improve undergraduate research, he received a $1.26 million NSF grant in 2006 to create and direct the BYU sponsored “Center for Undergraduate Research in Mathematics,” (CURM). NSF has since renewed funding of the program with another $1.28 million grant to continue the successful project.
Dorff explains the purpose of this organization. “It is used to take the BYU model for mentoring and share it with professors and students at other institutions. CURM trains and offers financial support to these professors and students.”
Professor Dorff is very excited to continue working with students on a regular basis. Sometimes at a university, especially one the size of BYU, it’s difficult to maintain a close student-professor relationship. However, “when you are a mentor,” says Dorff, “you really get to know the students. You get to give help and guidance. You can offer career advice, spiritual advice and even sometimes you can help them with dating. You get to see them grow, and that’s really neat.”
The fellowship award will “provide some flexibility to do more things,” says Professor Dorff. “It’s nice to have funds to support undergraduate research and I’m very grateful to BYU.”
—Brian Shaw, College of Physical and Mathematical Sciences
—Photo credit to Mathematical Association of America
It’s the most wonderful time of the year.
Forget the mistletoe and holly berries. Bring on the calculators, pencils, and scratch paper.
Mathematics students found all of these at this year’s Intermountain Math Competition, an annual test that determines whether BYU, University of Utah, Boise State University, Idaho State University, or University of Nevada Reno has the best math students. In this math competition among 36 students, the top six scores were all from BYU.
“My hand is tired because you have to write really fast,” said Sam Dittmer, a junior from Indianapolis, who got a perfect score of 70/70. The two students who tied for second (also from BYU) received 60/70, still a score to be reckoned with at the Intermountain Math Competition.
BYU uses the competition to prepare for the more difficult Putnam Exam that happens every year on the first Saturday of December. The Putnam brings 4,000 students from 600 universities face to face in one enormous battle of brains.
“The Intermountain Math Competition is not as hard as the Putnam, where the median score is zero, but it’s a good stepping stone to prepare for the event,” said Dr. Pace Nielsen, who compiles the questions from various universities for the Intermountain Math Competition.
The scores of the Intermountain Math Competition help professors decide which three students will represent BYU at the Putnam Exam. And this year, they are very excited about the current team of “mathletes.”
“We’ve got a really good group right now. We’re all excited to see how the team does on the Putnam test this December,” Dr. Gary Lawlor said. “We think they can score in the top 10 this year.”
Dr. Lawlor received 30th place on the Putnam his senior year at BYU in 1983. He went on to get his PhD in mathematics at Stanford. Now he passes on his Putnam wisdom by teaching Math 391R, a class dedicated to preparing students for the challenging exam, with Dr. Tiancheng Ouyang.
“To prepare for the Putnam competition, we help them with five different subjects including algebra, calculus, number series, combinatorics, and probability,” Dr. Ouyang said.
For many Putnam veterans, solving equations and winning competitions is something they’ve loved since their youth.
“The biggest thing that honed my skills in mathematics was just the desire to do well in these competitions,” Dr. Lawlor said. “As a byproduct of that, I did well in my classes. And because I did well on the Putnam test, that opened doors for me to go to graduate school.”
Those who participate in the Putnam Exam get instant recognition by many of the top graduate programs in the nation, as well as the National Science Foundation. This can help winning students receive scholarships and be accepted to their preferred grad school.
Perhaps this December, a little Christmas magic will rub off on this year’s competing Putnam “mathletes,” and they’ll finally crack that elusive top 10 ranking.
—Curtis Penfold, College of Physical and Mathematical Sciences