Mathematical Science

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The Department of Mathematical Sciences at the University of Alabama in Huntsville is dedicated to education, scholarship and service in the mathematical sciences. We offer programs of study leading to bachelors and masters degrees in mathematics and to the doctor of philosophy degree in applied mathematics.

Mathematics ... is indispensable as an intellectual technique. In many subjects, to think at all is to think like a mathematician.--Robert M. Hutchins, The Learning Society

Mathematical Sciences (MA) Catalog Materials

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UNIVERSITY OF ALABAMA IN HUNTSVILLE MATHEMATICAL SCIENCES COLLOQUIUM

Friday, September 13, 2013 3:00 p.m. Shelby Center Room 218

Ms. Christina Branson, Archarithms Inc., and Mr. Toanl Nguyen, Department of Mathematical Sciences

"An Introduction to Machine Learning Using Principal Component Analysis"

Humans are natural classifiers. From a young age, we learn without effort how to tell the difference between objects: cats versus dogs, 0s versus 1s. However, instructing a computer to classify similar objects can be challenging. A familiar example is the use of CAPTCHAs on the internet. An acronym for "Completely Automated Public Turing test to tell Computers and Humans Apart", these tests take advantage of a human's ability to easily read and reproduce a string of letters and/or numbers and a computer's struggle to do so.

Machine Learning is a subject of mathematics and computer science which aims to help computers "learn" how to classify objects. We will be exploring an elementary learning technique called Principal Component Analysis (PCA), a dimensionality reduction algorithm which transforms a set of vectors to a more representative basis. We will discuss the proof of the PCA Theorem and how it relates to machine learning, which will include a variety of topics from Linear Algebra including Schur's Theorem, basis transformation and orthogonal projections. Some applications of Principal Component Analysis will be presented including our work in classifying hand-written digits.

Refreshmgents will be served at 2:30 p.m. in SC 201 suite landing.

Dr. Karen A. Ames Memorial Lectures on Applied Mathematics

Friday, September 27, 2013 3:00 p.m. Shelby Center 109

Dr. Robert Devaney, Professor of Mathematics, Department of Mathematics & Statistics, Boston University

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"The Fractal Geometry of the Mandelbrot Set"

In this lecture we describe several folk theorems concerning the Mandelbrot set. While this set is extremely complicated from a geometric point of view, we will show that, as long as you know how to add and how to count, you can understand this geometry completely. We will encounter many famous mathematical objects in the Mandelbrot set, like the Farey tree and the Fibonacci sequence. And we will find many soon-to-be-famous objects as well, like the "Devaney" sequence. There might even be a joke or two in the talk.

Dr. Robert Devaney received his Ph.D. from the University of California at Berkeley in 1973 under the direction of Stephen Smale. His main area of research is dynamical systems, primarily complex analytic dynamics, but also including more general ideas about chaotic dynamical systems. Lately, he has become intrigued with the incredibly rich topological aspects of dynamics, including indecomposable continua, Sierpinski curves, and Cantor bouquets.

Dr. Devaney has over 100 research papers in the field of dynamical systems as well as a dozen pedagogical papers in this field. He is the (co)-author or editor for 14 books including An Introduction to Chaotic Dynamical Systems, Chaos, Fractals, and Dynamics: Computer Experiments in Modern Mathematics, and the series of 4 books called A Tool Kit of Dynamics Activities. Dr. Devaney has also delivered over 1500 invited lectures in all 50 states in the US and in over 30 countries worldwide.

Dr. Devaney has been accorded many honors and awards including the NSF Director's Award for Distinguished Teaching Scholars and the Carnegie/CASE Massachusetts Professor of the Year. He was inducted into the Massachusetts Mathematics Educators Hall of Fame in 2009, and was named a Fellow of the American Mathematical Society in 2012. He is the current President of the Mathematical Association of America.

Refreshments will be served at 2:30 p.m.

UAH Math Club News

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We would like to thank the 2012-2013 Math Club Officers (Courtney Wood, Colm, Kane, Andrea Winchester, and Tim Entz) for their fund raising efforts this past school year. The Math Club raised enough money last year to support a child this year for the Secret Meals For Hungry Children Program sponsored by the Alabama Credit Union. We would also like to thank the 2013-2014 Math Club Officers (Christina Dent, Patrick Klan, Wiliam Dent, and Matthew Blendermann) for presenting the check to Ms. Toni Jones, Branch Supervisor for the South Huntsville Branch of the Alabama Credit Union. The Math Club is looking forward to an exciting 2013-2014 academic year and again will be diligent with their fund raising efforts for group this year.

The Secret Meals feeds well over 1,100 disadvantaged schoolchildren. 100% of each donation goes entirely to the purchase of Secret Meals food packs, so every dollar of support makes a difference. A donation of $120 would feed one child weekly for an entire school year.

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Shelby Center for Science and Technology, Rm 258A

301 Sparkman Drive

Huntsville, AL 35899

256-824-6470

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