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Bahman Kalantari

(848) 445-7297
Hill 444
Office Hours: 


Research Area: 
Mathematical Programming
Computational Geometry
Numerical Analysis
Machine Learning
Polynomial Root-Finding


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

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.


Awards & Distinctions: 
  •  The article, ``The Fundamental Theorem of Algebra for Artists,''  selected for publication in ``The Best Writing on Mathematics, 2014,'' edited by Mircea Pitici, Princeton University Press.
  •   One of Three invited keynote speakers at MAA-NJ meeting, November 14, 2015,  ``Polynomial Root-Finding and Polynomiography''.
  •   U.S. PATENT No. 6,894,705 for POLYNOMIOGRAPHY, May 17, 2005.
  • Author:   Polynomial Root-Finding and Polynomiography,  World Scientific, 2008.
  •  Guest Editor: Transactions on Computational Science XX, Special Issue on Voronoi Diagrams and Their Applications,  LNCS (Lecture Notes in Computer Science), Springer, 2013.
  •  FOCUS, newspaper for Rutgers University faculty and staff, November 2, 2001.
  •  DCIS EXPLORER, Newsletter of the DCIS, Rutgers, Volume 1, Issue 1, ``Polynomiography: New Visions in Mathematics and Art,''  3-7, Fall 2001. B. Kalantari. (invited)
  •  ``Art of Science/Science of Art," Pamphlet of Academy of Medicine of New Jersey- Annual Awards Dinner, 16-17, 2001.
  •  The Star-Ledger newspaper article,  ``Paint by numbers,'' by Kevin Coughlin, Oct 12, 2002.
  •  Rutgers Magazine, ``Paint by number,'' Scrapbook, by Renee Olson, page 48, Fall, 2002.
  •  Math Forum Electronic Newsletter, Volume 7, No. 19, Summer 2002.
  •  Science News online - Math Trek article, ``The Colors of an Equation's Roots,'' by Ivars Peterson, April 19, 2003.
  •  Princeton Packet (Time off section),``Algorithms and Hues,'' December 5, 2003.
  •  DISCOVER Magazine, July 2003.
  • The Randolph Reporter, March 2003.
  • New Jersey SAVVY LIVING magazine, ``Beauty by the Number,'' by Lee Lusardi Connor, Spring issue 2003.
  • SCIENZA ESPERIENZA, Online Italian journal, ``Il matematico pittore,'' 05 giugno 2003, article by Silvia Annaratone.
  • The Blake School: Da Vinci and Friends Newsletter, July 2003.
  • The Times of Trenton, ''Computer art offers diverse, intricate design,'' by Janet Purcell (Good Times magazine section), January 9, 2004.
  • Newsletter of ASCI (art and science collaboration Inc), 2004.
  • Computer Graphics Quarterly, ``About the Cover - The Frustration and Joy of Computer Graphics," by Hans Westman, Computer Graphics Cover Editor, page 4, 38, August 2004.
  • ``Art and Science," Letter of the Month (Letter to the Editor)  Artists & Illustrators magazine, page 5, September 2004 issue.
  • FOCUS, newspaper for Rutgers University faculty and staff, ``Mathematical Artistry," By Joseph Blumberg, Volume 59, Number 13, 2005.
  • Engineering & Computer Science Faculty Quarterly, Concordia University, Montreal, ``You Don’t Have to be a Mathematician to be a Polynomiographer," by Dalia Radwan, Volume 8, Number 2, Spring 2005.
  • ``Polynomiography,"  in Mathematics & Arts - Arts & Mathematics, a catalogue for the art-math expo at Henri Poincare Institute, pages 36-38, Paris 2005.
  • Polynomiografia,   in  Tiede, a science magazine of Finland, 2007.
  • Arte con los  numeros,   Muy Interesante, science magazine of Spain, April 2007.
  • Montgomery News,  ``MHS Students Turn Math into Art with Polynomiography,'' by Lea Florentine,  July-August Issue, 2011.
  • The Princeton Packet, ``The art of science", by Pat Ellard, June 24, 2011.
  • Polynomiography image appears in,  ``Math in 100 Key Breakthroughs,’’ by Elwes, Richard with full acknowledgment, 2013.
  • The Newsletter of The Consortium of  Mathematics and Its Applications,  by Jon Choate, Number 105, Fall/Winter 2013.
  • Polynomiography in  Donga-Science   (in Korean) Popular mathematics magazine, January 2016.
  • Polynomiography artwork on the cover of ``President's Report of the Decade: 1990-2000,'' report by President Lawrence, former Rutgers' President.
  • Polynomiography artwork on the cover of Rutgers Graduate Catalog, for years 2001-2003.
  • Polynomiography artwork on the cover of Rutgers Department of Computer Science Progress Report 2001-2003.
  • Polynomiography artwork ``Summer,'' Electronic Art and Animation Catalog, page 87,SIGGRAPH 2003.
  • Polynomiography artwork on the cover of Proceedings of international art-math conferences ISAMA-BRIDGES, July 2003.
  • Polynomiography artwork as the month of June image for the electronic bulletin of ASCI, the Art & Science Collaborations, Inc, 2003.
  • Polynomiography artwork on the cover of Computer Graphics Quarterly, 38, August 2004.
  • Polynomiography artwork in the Pamphlet of ``Voronoi Diagram -Evolutionary Space," page 16,  from the First International Exhibition of Voronoi Art, Seoul, Korea 2005.
  •  Polynomiography artworks in a Brazilian  Math Book, 'Etico Sistema de Ensino), 2005.
  • Polynomiography artwork on the cover of ``Fearless Symmetry: Exposing the Hidden Pattern of Numbers," by Ash and Gross,  Princeton University Press, 2006.
  • Polynomiography artwork on the cover of Princeton University Press Mathematics Catalog, 2006.
  • Polynomiography artwork on the cover of Tiede, a science magazine of Finland, 2007.
  • Polynomiography artwork in Accromath, ``Les mathématiques du coeur,''2007.
  • Polynomiography artwork in  Physics World, ``Reflecting symmetry,'' 2007.
  • Polynomiography artwork on the cover of World  Scientific Publishing book ``Polynomial Root-Finding and Polynomiography," by Bahman Kalantari, 2008.
  • Polynomiography artwork in Algebra 2, a publication of PEARSON publishing company, 2009.
  • Polynomiography artwork in ``The Mathematics That Every Secondary School Teacher Needs to Know,''  Taylor and Francis,  Alice Artzt and Alan Sultan, 2010.
  • Polynomiography art on the cover the book, Introduction to Computational Cultural Psychology,  Yair Neuman, 2014.


Personal News: 

Classes Taught: 


 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.


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