Major in Mathematics!
A mathematics degree from New Paltz accommodates both applied and theoretical interests, and provides exceptional preparation for future careers in law, medicine, education, insurance, and business.
Our small class sizes enable students to work closely with faculty and receive the personal attention that only a liberal arts education can offer. Recent research projects have included angular determinations in pentagons; software development for algebraic evolution; and modeling the success of protest groups, to name a few.
With major tracks in mathematics, adolescence education in mathematics, and elementary education in mathematics, our graduates go on to attend Ph.D. programs, work as financial analysts on Wall Street, secure positions at high-level companies like Microsoft, and teach mathematics in both public schools and the country's most prestigious universities.
This summer, math majors Simon Li and Finley Hartley were part of the XXXV Workshop on Geometric Methods in Physics and Summer School (http://wgmp.uwb.edu.pl/wgmp35/). The conference and follow-up summer school were held in Bialowieza, Poland, one of the major meeting venues for researchers in Mathematical Physics and Differential Geometry. Simon Li has been working with Dr. Ekaterina Shemyakova for two semesters on a research project and has been presenting his results at various conference poster sessions among PhD students and postdocs from all over the world. Finley Hartley has just begun working on a related project and enjoyed being a participant this year.
The trip was sponsored by the National Science Foundation.
Math Seminar: Wednesday Oct. 12, 3:30-4:30 p.m.
Speaker: Natalie Cartwright
Title: Electromagnetic Pulse Propagation and Asymptotic Expansions: The basics, applications, and the yet unknown
Abstract: Asymptotic expansions of integrals have been used to provide insight into electromagnetic pulse propagation since the early 1900’s. Theoretical advances in asymptotic techniques through the 20th century have enabled more studies, and led to some surprising results. Of considerable interest is the so-called Brillouin precursor whose peak amplitude experiences algebraic, rather than exponential, decay with propagation distance. It has been speculated that this slowly-decaying precursor may be used for improved detection and imaging. Here, we will discuss its use in a synthetic aperture radar application.
Asymptotic techniques have been so valuable in illuminating propagation phenomena of one-dimensional pulses, one would hope similar investigations could be performed for three-dimensional beams. Unfortunately, this has not been the case. We will formulate the beam propagation problem and discuss what is needed in order to make progress in this area.
Math & Cookies:
Wednesday Nov. 2, 3:30-4:30 p.m.
Speaker: Hyunchul Park
Title: Absolutely convergent sequence, a measure of finite variation, and Hardy space
Abstract: In Mat252 (Calculus 2) students are first exposed to a notion of absolutely convergence of real numbers, which describes a strong convergence of series compared to a weak notion of convergence of series, conditional convergence. Conditional convergent series can be rearranged to converge to any numbers including $\pm\infty$ while the absolutely convergent series converges to the same limit under any rearrangement and can be written as difference of two convergent nonnegative series. In mathematics, there are other cases that are similar to the notion of absolute convergence of series of numbers. We will introduce measure, which is a generalization of length or area and introduce a notion of measure of finite variation. Measures of finite variation can be decomposed into positive and negative parts (Hahn-Jordan decomposition). We also discuss Harmonic functions and Hardy space. For Harmonic function which is in the Hardy space, it can be written as a difference of two nonnegative harmonic functions.