I received my Ph.D in Computer Science at University of Minnesota in 1984 under the advising of Prof. J.B. Rosen. Prior to this I received an M.S. degree in Operations Research and an M.S. degree in Mathematics, also from U. of M. As undergraduate, I majored in mathematics and physics at University of Wisconsin.
I joined Rutgers University after I received my Ph.D in 1984. My main research interests have ranged in optimization: linear programming, convex programming, interior-point methods, non-convex optimization, discrete and combinatorial optimization. My research interests in computational geometry, machine learning and game theory are mainly on the type of problems that have a flavor of optimization.
In the nineties I accidentally became interested in polynomial root-finding and years later my research led to introducing the term polynomiography, standing algorithmic visualization in solving polynomial equations. In 2005, through Rutgers University, I received a U.S. patent for a corresponding software technology. Since its introduction around 2000, polynomiography and sample images have featured in national and international media (see www.polynomiography.com).
Polynomiography has also connected me with the fine arts and I have even been complemented to be considered an artist. However, my goal is to develop and spread it widely as a powerful medium for creativity, discovery, and playful learning. It is a medium that finds numerous applications in education, math, science, art and design. On the one hand, polynomials are the most fundamental objects, present in every branch of math and sciences. On the other hand, polynomials are the kind of mathematical abstractions that are taught early on in education. Ideally, polynomiography can enter K-12 education and more and there is good evidence in support of this. Nevertheless, there are challenges along the way but I have never given up and in collaborations with educators, there are attempts to introduce the demo software and a corresponding lesson to interested high school teachers.
● Introduction to Discrete Structures I, CS 205.
● Discrete Structures II, CS 206.
● Numerical Problems and Computer Programming, CS 221.
● Numerical Analysis, CS 323.
● Design and Analysis of Computer Algorithms, CS 344.
● Numerical Analysis CS 510.
● Design and Analysis of Data Structure and Algorithms I CS 513.
● Linear Programming CS 521.
● Network and Combinatorial Optimization Algorithms CS 522.
● Nonlinear Programming Algorithms CS 524.
● Interior Methods for Linear and Quadratic Programming, Graduate Seminar CS 672 .
● Polynomials and Polynomiography in Computer Science & Math, Graduate Seminar CS 672,.
● Introduction to Polynomiography: the Art and Science in Polynomial Visualization, CS 442
● Visualization via Polynomiography and Application in CS, Math and Art, CS Topics 442,
● Polynomiography: Art from Science & Science from Art, University College Honors Course.
● Creating Art and Discovering Science Through Visualization in Polynomiography, SAS Honors.
● Byrne First Year Seminar: Mathematics of Art.
● Governor's Summer School of Engineering and Technology: Polynomiography.