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Bill Karr, Mathematics, Undergraduate

Math major deepens knowledge through physics research

Bill Karr | Mathematics, Undergraduate | Department of Mathematical Sciences I am young eager mathematician on my way to graduate school to learn as much mathematics as possible.

I would like to specialize in mathematical physics. I would like to eventually become a professor at a university teaching mathematics and engaging undergraduate students in research.

What have been your most valuable learning experiences during your time at IUPUI?

The first is my undergraduate research experience with Dr. Yogesh Joglekar in the physics department at IUPUI. Yogesh has been an invaluable mentor to me for a couple years now and has been crucial to my academic growth. He has an incredible ability to engage with undergraduates and give them things to "chew on," mentally speaking. This allows his students to learn how to critically think by themselves, without being spoon fed instructions from the professor.

My experiences with Yogesh have led to two published papers in well-known scholarly physics journals, as well as invaluable research skills that are going to carry me through graduate school.

The second important experience has been the graduate courses I have taken through the Department of Mathematical Sciences at IUPUI. These courses have introduced me to the extreme intellectual stimulation and curiosity that mathematics invokes in those who study them. All of the Mathematics professors at IUPUI have instilled in me an immense work ethic and appreciation for the subject. These include Michal Misiurewicz, Ron Ji, and Vitaly Tarasov.

Who have been your mentors here at IUPUI in addition to Dr. Joglekar?

All of my mathematics professors have had a profound impact on my future and my attitude towards mathematics. In addition to those mentioned above, these professors include: Jeff Watt, Carl Cowen, Patrick Morton, Michael Penna, Rodrigo Perez, and Slawomir Klimek.

A few physics professors have also had a similar impact: Yogesh Joglekar, John Ross, Andrew Gavrin, Horia Petrache, Andrew Rader, and Marcos Betancourt.

Without the support of these faculty members, I could not have accomplished what I have while at IUPUI. Now because of these people, I have been accepted to a few graduate schools with support. They have all helped me achieve this goal.

Please describe your experience with undergraduate research and its impact on you:

My research was in approximation techniques in quantum mechanics and is now in random matrix theory. These projects were performed under Dr. Yogesh Joglekar, a theoretical condensed matter physicist at IUPUI and were and are funded by the IUPUI Center for Research & Learning under the UROP grant and a UROP Summer Fellowship. In quantum mechanics, we produced a way of numerically solving Schrodinger's equation for localized radially symmetric potentials in momentum space. Our article that summarized our results was published in the American Journal of Physics in April 2010.

We are currently performing research in random matrix theory, which tangentially relates to the earlier research project. We have been investigating statistical properties of the spectra of a class of random matrices that are non-symmetric, but still have real spectra. I have presented both of these research projects at several undergraduate research conferences, most notably the Young Mathematicians Conference at Ohio State in 2009 and 2010.

Please describe your extracurricular activities and their impact on you:

I have participated in IUPUI's Math Club since 2007 and am currently president of Math Club. This has given me the opportunity to have professors engage with undergraduate students outside of the classroom by giving presentations on fun talks about mathematics.

I have also been part of IUPUI's competitive math problem solving team under Rodrigo Perez. We have participated in several math competitions, including the prestigious Putnam exam.

These experiences have introduced me to the exciting fun side of mathematics that happens outside of research and the classroom.

What's your advice for incoming freshman?

Engage yourself in academia! Talk to professors! Take courses in things that you are interested in. Ask lots of questions! Major in something that interests you, no matter what it is.

Also, use the excellent facilities that IUPUI provides to its students, particularly the Mathematics Assistance Center and other similar tutoring centers. IUPUI has a fantastic community of young mentors and tutors on campus that bring our campus to life.

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