Interdisciplinary Honors Seminars

Polynomials and Polynomiography

Polynomials and Polynomiography


Index# 10964

Professor Bahman Kalantari

W 2:50-5:50

HC S126 College Ave Campus

Will NOT Count Towards SAS – Computer Science MAJOR
Will NOT Count Towards SAS – Computer Science MINOR

This seminar will study polynomials and polynomiography. Polynomials are the most fundamental entities in all of STEM. Polynomiography unravels a new but beautiful facet of these mathematical abstractions through their algorithmic visualization in the search for their roots. Could this lead us to the roots of art and design? Through polynomiography you learn about many mathematical and algorithmic concepts, not all about polynomials. You learn about classic and modern concepts, such as solving a polynomial equation, complex numbers, fractals, dynamical systems, Newton's method, techniques for solving polynomials equations, geometric concepts, and modern applications of polynomials.

However, the goals in this seminar are interdisciplinary. You will also learn to create art and design by turning the polynomial root-_nding problem upside down. That is, through the ease of polynomiography software you will be able to experiment with polynomials and root-_nding algorithms as the basis for creating intricate designs and patterns, or animations. Not only polynomiography and individual student's creativity could result in art and design analogous to the most sophisticated human creations, but artwork of a degree of complexity and sophistication not possible without the use of its algorithms and software. Polynomiographer does virtual painting using the computer screen as the canvas.

About Professor Kalantari

Bahman Kalantari is a professor of computer science at Rutgers University. He received his Ph.D in Computer Science from the University of Minnesota, as well as Masters degrees in Mathematics and in Operations Research. His main research areas are theory and algorithms in optimization, computational geometry and polynomial root-_nding. He has introduced the term polynomiography for algorithmic visualization of polynomial equations and holds a U.S. patent for its technology. Polynomiography has been featured in several national and international media. He has delivered over 100 presentation on the subject in _fteen countries to middle and high school students and teachers, university students and professors, and the general public. He is also interested in algorithmic mathematical art. He is the author of the book Polynomial Root-Finding and Polynomiography. His article, “The Fundamental Theorem of

Algebra for Artists” was selected for inclusion in Princeton University Press book, The Best Writing On Mathematics 2014. He maintains the website