William Lowell Putnam
Mathematical Competition

Dr. Vadim Ponomarenko writes, “the William Lowell Putnam exam is the premiere mathematics competition for undergraduates in the United States and Canada.  The seventy-third competition was held on December 1, 2012.  A total of 4277 students from 578 colleges and universities took part; the top three teams this year were from Harvard, MIT, and UCLA, respectively.

“SDSU was well-represented in this competition; we had four students successfully complete a difficult exam in which typically half of all participants score 0 points.  Congratulations to Henok Tadesse, Ismael Perez, Amadeo Candido, and Angel Prado.  Henok’s performance is particularly noteworthy — he scored 30 points, which tied him for 319.5th place (top 8%) of all participants, who themselves are the best undergraduate mathematics majors in the US and Canada.  Congratulations to these fine students on their accomplishments.”

Dr. Imre Tuba, IVC Campus adds, “With full recognition of the four San Diego campus students’ effort and Vadim’s work on the Putnam, and duly impressed with Henok Tadesse’s 30 points, I should add that SDSU was represented by another two students on the Putnam exam. Congrats are due to Horacio Lopez and Eddie Palomares of the SDSU Imperial Valley campus for competing. Their scores didn’t match Henok’s, but participation counts for something.”

“Bose-Einstein condensation is a state of matter of boson particles at ultra cold temperatures. The Gross-Pitaevskii (GP) equation, a variant of the nonlinear Schroedinger equation that includes the external trapping, can effectively describe the mean field dynamical properties of Bose-Einstein condensates (BECs). Experimental progress has been made to create BECs with particles with a strong dipolar moment such as in chromium. The dipole-dipole interaction adds a nonlocal term to the GP equation in the form of a convolution.

On the other hand, previous work has focused on vortex nucleation in non-dipolar condensates by dragging impurities at supercritical speeds in the condensate. In the case of the one-dimensional GP equation with no external potential nor dipolar effects, a critical velocity can be found analytically above which dark (grey) solitons are emitted from the moving impurity. However, the case pertaining the supercritical velocity for vortex nucleation in dipolar condensates has not been considered so far. In this talk, we present analytical and numerical results for the nucleation of dark solitons in one-dimensional condensates with dipolar terms. Numerical results will also be presented for two-dimensional dipolar condensates.

Interestingly, since the dipole-dipole interaction is anisotropic in two dimensions, the critical speed is found to depend on the orientation of the trajectory of the moving impurity with respect to the dipolar axis.”

Who Chooses Not to Persist in Calculus and Why?

Professor Chris Rasmussen was selected to present one of only six MAA Invited Addresses at this past winter’s Joint Mathematics Meetings, the largest gathering of mathematicians in the U.S. with over 6700 attendees.  The address presented Dr. Rasmussen’s findings as part of a major NSF-funded initiative on student success in calculus, on which he serves as a co-PI.

The transition from high school to college mathematics is one of the most critical junctures in the preparation of individuals to meet the mathematical demands of the 21st century in science, technology, engineering, and mathematics (STEM). Even while more students are taking more advanced mathematics in high school than ever before—including over half a million each year who study calculus while in high school—the percentage of all college students in 4-year undergraduate programs who are enrolled in mathematics at the level of calculus or above has decreased steadily over the past decades. Moreover, a substantial percentage of students who enroll in Calculus I intending to take more Calculus, consequently, may end up deciding not to continue in Calculus. This represents a huge loss to the nation in terms of the need for more students to pursue a major in one of the STEM disciplines. In this presentation, I examine the characteristics of STEM-intending students who begin their post-secondary studies with Calculus I and either persist or switch out of the Calculus sequence.  Hence, either remain or leave the STEM pipeline. The data used for this analysis comes from a unique, in depth, national survey aimed at identifying characteristics of successful programs in college Calculus.

“An arithmetic congruence monoid (ACM) is an arithmetic progression defined by integers a and b such that both a and b are positive satisfying the following conditions: a is less than or equal to b and a squared is congruent to a modulo b.  This algebraic structure is a non-unique factorization domain, which means elements may have more than one distinct factorization.  Elasticity of an element, say g,  is defined as the longest length factorization of g divided by the shortest length factorization of g.  Our specific research was regarding full elasticity, which is satisfied by the following condition: an ACM is fully elastic if for every rational number h, where h is greater than or equal to one and less than or equal to the elasticity of the monoid defined by a and b, then there exists an element h’ such that the elasticity of h’  is equal to h.

Our approach was to construct sub-monoids where we could fully characterize elements and then show full elasticity using only that subset of elements.  This process relied on taking specific prime numbers p and q and then generating a product PQ, where the number of copies of p and the number of copies of q in the element PQ varied.  These elements, PQ are the elements that allowed us to construct the particular rational numbers required to satisfy the full elasticity requirement.

The summer REU program hosted by SDSU and led by Dr. Vadim Ponomarenko provides students with the opportunity to investigate different areas of mathematics and feel the excitement of conducting mathematical research.”

Cody’s poster may be seen in greater detail at: http://www-rohan.sdsu.edu/~allen1/research.html

“We consider, experimentally and theoretically, a mechanical system consisting of a sliding car on an inclined plane that bounces on an oscillating piston. The main aim of our study is to reproduce the different types of orbits displayed by nonlinear dynamical systems. In particular, we are looking to identify the parameters and initial conditions for which periodic and chaotic (irregular) behavior are exhibited. The data in our experimental model is collected by using infrared lights that are monitored by a Nintendo Wii remote which is linked to a laptop computer via Bluetooth.

By varying the piston’s frequency and amplitude, it is possible to produce, for relatively small amplitudes, periodic orbits. As the amplitude of the piston is increased (for a fixed piston frequency) we observe bifurcations where the original, stable, periodic orbit is destabilized and replaced by a higher order periodic orbit. For larger amplitudes, periodic orbits are destabilized and replaced by chaotic trajectories.  After carefully measuring all experimental parameters, we are able to successfully produce periodic orbits (up to period 3), sticking solutions (the car does not bounce, but gets stuck to the piston), and seemingly chaotic (irregular/unpredictable) behavior that are in very good agreement with the model for the same parameter values.”

Twelve SDSU students researching areas from medicine to engineering received scholarships totaling $90,000. Lucie Sharpsten, a Computational Statistics student, appears in the center to the right of President Hirshman.

by Hallie Jacobs with additions by Rich Levine

Lucie Sharpsten, Computational Statistics PhD student, received a scholarship from the Achievement Rewards for College Scientists foundation (ARCS).  This will be her second year serving as an ARCS scholar, one of twelve ARCS scholars on campus.  Lucie’s research involves developing data mining tools for studying glaucomatous progression. In particular, she has developed decision (classification) tree methods for handling clustered  (fellow eyes from a subject) and longitudinal (sequential office visits) patient observations.  Lucie is working with dissertation adviser Professor Juanjuan Fan.

2013 awards and ceremony

The San Diego chapter for Achievement Rewards for Colleges Scientists foundation donated $90,000 for student scholarships at an Oct. 26 ceremony.

Students will receive scholarships ranging from $5,000 to $15,000.

The unique ceremony brought donors and scholarship recipients together, providing students an opportunity to share the focus of their research and academic interests at SDSU.

Leaders of the foundation, including Robin Luby, chapter president, Diane Chalmers, chapter vice president of university relations and Barbara Hartung, SDSU liasion, joined SDSU President Elliot Hirshman to honor the students.

About Achievement Rewards for Colleges Scientists

Since the San Diego chapter began in 1985, 966 awards totaling $7,187,000 have been allocated to students attending San Diego universities. For academic year 2011-2012, the San Diego Chapter awarded $405,000 to 56 foundation scholars.

The foundation’s San Diego Chapter, one of 17 chapters across the country, has provided continued support of San Diego State University students studying to complete degrees in science and engineering since 1988.

The nonprofit, all-women, volunteer organization is dedicated to helping the best and brightest U.S. graduate and undergraduate science, engineering and medical students. The organization was formed nationally in 1958 in response to Sputnik and the lack of U.S. supremacy in the technology race.

All of the members contribute funds toward these scholarships which are awarded locally to local universities.

In addition to member donations, contributions come from corporations, foundations and other individuals.

Students in the SDSU Society of Statisticians and Actuaries:
(Top left to right) Nicolette Molina, Alex Wissman, Michael Izbotsky, Nadine Ayouty, Mayra Nunez, Sylvie Lekhac
(Bottom left to right) Ivan Remigar, Zack Vasil, Breanna Jo McArdle, Kieran Sprunk, Jenna Grantham, Geliza Gervacio

Student Life & Leadership at SDSU has recognized the Society of Statisticians and Actuaries as an official organization at the University.  The effort to form the Society was lead by Statistics undergraduate students Jenna Grantham and Breanna Jo McArdle at the beginning of the Fall 2012 semester.  The mission of the Society is to allow students interested in statistics to interact, create study groups, and learn about careers in the industry.

Professor Barbara Bailey will serve as the faculty advisor, Jenna as President, Breanna as Vice President, and fellow Statistics student Kieran Sprunk as Treasurer.  As the name suggests, the Society is open to all statistics students, right now focusing on undergraduates though with a planned extension to graduate students.

In addition to several organizational meetings, the Society kicked off its inception with a panel discussion November 26 on Careers in Statistics with Professors Kristin Duncan and Rich Levine.  The Spring 2013 semester will begin with a visit from San Diego actuaries and continue in proposed sessions with statisticians/biostatisticians in local area industries.  The Society is also considering formal study groups and review courses as students prepare for the actuarial (SOA) exams.

As Breanna and Jenna shared, “Overall we plan on aiding our members in deciding what exactly they would like to do with their degrees in the future all while creating friendships for future networking!”

If you are interested in joining, contact the Society at Stats.actuaries@yahoo.com.

Wednesday, November 7, 2012
12:00PM GMCS 405

“How to Solve (Almost) Any Maximum Likelihood Problem Using Markov Chain Monte Carlo (MCMC)”

Abstract:

MCMC sampling has allowed for simulation from complex, massively multivariate distributions even when that distribution is only specified up to an unknown normalizing constant. This talk presents the theory behind maximum likelihood parameter estimation using simulation (MCMC-MLE), and little known but vitally important implementation issues and heuristics focusing on exponential families of distributions. In particular, a useful approximation to the normalizing constant in the exponential family likelihood is presented which increases the stability and accuracy of the MCMC-MLE algorithm. We also show how MCMC standard errors can be used as a measure of when to trust this approximation. Finally, simple examples are used to illustrate how this algorithm can be used to perform inference on a new class of models for social networks dubbed Exponential-Family Random Network Models (ERNM).

http://fellstat.com/files/ifellows.pdf ]]> http://www.math.sdsu.edu/statsemfellows/feed/ 0 http://www.math.sdsu.edu/lecpos/ http://www.math.sdsu.edu/lecpos/#comments Wed, 24 Oct 2012 21:56:33 +0000 Staff http://www.math.sdsu.edu/?p=2893 The Department of Mathematics and Statistics at San Diego State University is accepting applications for its pool of Lecturers. The Lecturers will teach one or more introductory mathematics, statistics, and/or mathematics education courses. Minimum qualifications include a Masters degree in mathematics, statistics or related fields. Salary is commensurate with credentials and experience, and according to University policy. Please fax or mail your letter of application including a statement of which courses you are qualified to teach, a vita, and two letters of recommendation, to:

Brenda Wills
Lecturer Application
Department of Mathematics and Statistics
San Diego State University
5500 Campanile Drive
San Diego, CA 92182-7720
Fax:     619-594-6746
SDSU is a Title IX, equal opportunity employer and does not discriminate against individuals on the basis of race, religion, national origin, sexual orientation, gender, marital status, age, disability or veteran status, including veterans of the Vietnam era.