## Department of Mathematics

### RESOURCES

Faculty Office Building
(FOB) E 2
SUNY New Paltz
1 Hawk Drive
New Pa

### News

View the latest School of Science and Engineering news here.

### 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.

### Events

Math & Cookies:  Wednesday Sept. 28, 3:30-4:30 p.m.

Speaker:  Eric Brattain
Title:  Introduction to Neural Networks
Abstract:  We will give an overview of the principles of the neural network approach to supervised learning, including deep learning which has received a significant amount of recent attention for its success in playing Go, creating surreal art, and more.

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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.

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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.

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Location: FOB S14
Time: 11 a.m. — Noon
Date: Wednesday, Sept. 30, 2015

Gibbs Phenomena:
What has happened to Eeyore's Tail?

Dr. Lidia Bloshanskaya

Remember the last time you tried to figure out the details in a small JPEG file you found somewhere on the Web? If the picture is highly compressed, you'll see "halos": hazy and blotchy artifacts around the edges and the sharp color transitions.

We will talk about Fourier series in general, Gibbs phenomena and its consequences in the technology (and in our life). You'll be totally fine with the background in Calculus 2 and might even survive with just Calculus 1. Join us in enjoying some fun math, delicious cookies and lots of pictures (and even movies).

Mathematics Seminar

Location: FOB S14
Time: 11 a.m. — Noon
Date: Wednesday, April 29, 2015

On flexibility of multivariate Tweedie distributions
Johann Cuenin

Université de Franche-Comté, Labortatoire de Mathématiques de Besançon
johann.cuenin@univ-fcomte.fr

Abstract: Univariate Tweedie distributions were introduced by M. C. K. Tweedie in 1984 and
include some well-known distributions such as Gaussian, inverse Gaussian, gamma, α-stable or
Poisson. These laws are very useful in many fields of applications as in ecology, actuarial sciences, quality control or physics. Thus several works were set about the construction of multivariate Tweedie, but all of them propose models only for direct applications.

After the first part dedicated to recall the framework of Tweedie distributions, we introduce
the multivariate Tweedie distributions in the second part. We show that they resume some
characteristics of the Gaussian vector, with both positive and negative correlations. We also specify how to compute these distributions and give some simulation results. In the third part, we establish another type of multivariate Tweedie called multiple stable Tweedie (MST) models. These models are made by a fixed univariate and positive support Tweedie variable and the remaining elements are univariate Tweedie with dispersions parameters equal to the observation of the fixed variable.

Starting from this construction, we give the variance and generalized variance functions of MST models and show that the latter is the product of powered components of the mean vector. Through the establishment of associated modified Lévy measure, we also propose an estimator of generalized variance, which is unbiased and has uniformly minimum variance.