Mahendra Jani, Ph.D.


Office:   Science Hall East 3051
Phone:   973-720-2159
Office Hours:   Wednesdays and Fridays 11:00am-12:00pm

Department: Mathematics
Position: Professor of Mathematics
Area Specialization: Enumerative Combinatorics and Algebraic Topology

Research Publications:

  1. “On Generalization of Motzkin Numbers using k-Trees,”  (with M.Zeleke), ARS Combinatoria, 89, 287-297(2008)
  2. “A Bijective Proof of a Tennis Ball Problem,” (with M. Zeleke), Bulletin of Inst. Of Combinat. And its Appli., 41, 89-95 (2004)
  3. “k-Trees and Catalan Identities,” (with M. Zeleke), Congressus Numerantium, 165, 39-49, (2003)
  4. “Enumeration of K-Trees and Applications,” (with M. Zeleke), Annals of Combinatorics, 6, 375-382, (2002)
  5. “Continued Fractions and Catalan Problems,” (with R. G. Rieper), The Electronic J. of Combinatorics, R45, 7(1),1-8,  (2000)
  6. Covering Maps in Top (jointly with H. Hastings), Geometric and Shape Theory, Lecture Notes in Mathematics, Springer-Verlag #1283, 1986.
  7. Equivalences of shape fibrations (jointly with H. Hastings), Glasnik Mathematicki, vol. 20, (40), 1985
  8. Dold Theorems in Shape Theory, Research Announcement, Topology Proceedings, vol. 9, 1984
  9. Cell-like Shape Fibrations which are Fiber Shape Equivalences, Topology Proceedings, vol 7, 1982
  10. Induced Shape Fibrations and Fiber Shape Equivalences (Thesis), The Rocky Mountain J. of Math.  vol. 12, #2, Spring 1982.

Selected Conferences Presentations:

1.   “Ordered Trees and Continued Fractions,” The Mathematics Department Research and Seminar Committee of Addis Ababa University, Addis Ababa, Ethiopia, December 22, 2010.

2.   “Generalizing Motzkin Numbers Using k-Trees,” ALTENCOA III (3rd Annual South American Conference on Algebra, Number Theory and Combinatorics), Universidad Industrial de Santander, Bucaramanga,  Colombia, July 21-25, 2008

3.  “Continued Fractions and Catalan Problems,” Algebra Seminar, Universidad de Antioquia, Medellin, Colombia, July 18, 2008

4.   “The Catalan Numbers and the related problems in Enumerative Combinatorics,”  The Maharaja Sayajirao University of Baroda, Vadodara, India, August 9, 2007

5.   “The Catalan Numbers and problems in Enumerative Combinatorics,”  Late Prof. G.R. Desai  Memorial Lectures, Gujarat University, Ahmedabad, India, July 30, 2007

6.   “Generalized Motzkin Numbers and k-Trees,” 37th Southeastern International Conference on  Combinatorics, Graph Theory and Computing, Florida Atlantic university, Boca Raton, FL., March 2006.

 7.   “Continued Fractions and Catalan Problems,”  Rutgers Experimental Mathematics Seminar, DIMACS (Center for Discrete Mathematics and Theoretical Computer Science), Rutgers University, New Brunswick, New Jersey, March 3, 2005

8.   “k-Trees and Applications,”  International Conference on “Paths, Permutations and Trees,”  Center for Combinatorics, Nankai University, Tianjin, February 27-27, 2004, China.

9.   "Tennis Ball Problem," 34th Southeastern International Conference on Combinatorics, Graph Theory and Computing, Florida Atlantic university, Boca Raton, FL., March 2003.

10.  "Generalized Tennis Ball Problem," Joint AMS (American mathematical Society) and MAA (Mathematical Association of America) Meeting, Baltimore, MD, January 15-18, 2003.

11.  "The Tennis Ball problem," 33rd Southeastern International Conference on Combinatorics, Graph Theory and Computing, Florida Atlantic university, Boca Raton, FL., March 2002.

12.  "Continued Fractions and Catalan Problems", 31st Southeastern International Conference on Combinatorics, Graph Theory and Computing, Florida Atlantic University, Boca Raton, Florida, March 13 - 17, 2000

13.  "Application of K-trees," 9th Quadrennial International Conference on Graph Theory, Combinatorics and Applications, Western Michigan University, Kalamazoo, June 5-9, 2000

14.  Hofstra University, Hempstead, New York, "The Open Problem of Equivalences",  May 1992

15.  Summer Seminar Forum, William Paterson College, "Fractal Exponents by Grids", August 1989,

16.  Inter-University Center of Postgraduate Studies, International Geometric Topology and Shape Theory Conference, Dubrovnik, YUGOSLAVIA, October 1986, "covering Maps in Top ".

 17. The Graduate School of Mathematics, Gujarat University, Gujarat, INDIA, August 1985, "Shape Fibrations".

19. Spring Topology Conference, Florida State University, Tallahassee, Florida, March 1985, "Covering Maps of Towers".

20.  (Participated in) Topology Semester, Stefan Banach International Mathematics Center, Warsaw, POLAND,  May 1984.

21. Spring Topology Conference, Auburn University, Alabama, March 1984, "Equivalences of  Shape Fibrations".

22. Oklahoma Topology Conference of American Mathematical Society, University of  Oklahoma, March 1983, "Fiber Shape Equivalences and Cell-like Shape Fibrations".

23. United States of Naval Academy, Spring Topology Conference, Annapolis, Maryland, March   1982, "Cell-like shape fibrations which are fiber shape equivalences"

24. Inter-University Center of Post-graduate Studies, Shape theory and Geometric Topology Conference, Dubrovnik, Yugoslavia, January 1981, "Fiber shape equivalences"

25. Hofstra University, Hempstead, New York, May 1980, "Fiber  shape equivalences and shape fibrations"

26. Brooklyn College of the City University of New York, February 1979, "Fiber shape equivalences"

27. Oklahoma Topology Conference, University of Oklahoma, March  1978, "Induced shape fibrations and fiber shape equivalences"

Other Publications:

Text-Book:  “An Introduction to Mathematics,” Simon & Schuster Custom Pub. (1998), and Pearson Custom Publishing (2002).

Workshop Manuals for Teachers I, II, III (product of the joint product with Prof. R. Kaplan), “Upgrading the Mathematical and Pedagogical Knowledge of Upper Elementary Certified Teachers to meet the challenges of a new curriculum,” William Paterson University Pub., Wayne, NJ, 1995

Biographies of Mathematicians:  Biographies of the following mathematicians were published in “Suganitam,” a mathematics magazine in Gujarati, published by the Graduate School of Mathematics, Gujarat University, Ahmedabad, India.

-          Gauss I & II, Suganitam, vol.3, and vol. 5, 1986

-          Newton, Suganitam, vol.1, 1969

-          Archimedes, Suganitam, vol. 2, 1968

-          Abel, Suganitam, vol. 2, 1967

-          Galois, Suganitam, vol. 1, 1966

-          Srinivas Ramanujan, Suganitam, vol. 2, 1965


1.         DHE Grant, Auguest 1991 - June 1993  (jointly with Dr. R. Kaplan) from  the New Jersey Department of Higher Education, Grant No. 7040, Grant Amount: $60,705

Title of the grant: "Upgrading the mathematics competence of upper grade elementary-certified teachers to meet the challenge of implementing a new curriculum"

2.         DHE Grant, Auguest 1993 - June 1995,  (jointly with Dr. R. Kaplan) from the New Jersey Department of Higher Education, Grant No. 9019, Grant Amount: $74,702

Title of the grant: "Upgrading the mathematics competence of upper grade elementary-         certified teachers: An extension and continuation project"

Titles of Capstone Projects (advised to math majors):

-          “Counting on Chebyshev Polynomials,” (Jose L. Orozco, Fall 2011)

-          “Tropical Mathematics” (Mihriban Gulistan, Spring 2010)

-          “Diagonalizability over the Complex Numbers” (Jaclyn Dellosa, Spring 2010)

-          “Pascal Matrices,” (Yelena Borysenko, Spring 2009)

-          “The Broken Spaghetti Noodle,” (Krystle Reilly, Spring 2009)

-          “In Search of Birthday of Elliptic Functions,” (Mily Ahmed, Spring 2009)

-          “Classification of Finite Abelian Groups,” (Eric N. Aponte, Fall 2007)

-          “Applying Burnside’s Lemma to a One-dimensional Escher Problem” (Maira Cedeno, Fall 2006)

-          “Breaking Secret Codes” (Jennife Winer, Fall 2006)

-          “Math and Sound of Music” (Laura Weinstein, Fall 2006)

-           “What is the best seat in a movie theater?” (Megan Surpless, Spring 2006)

-          “Unique Solutions of Sudoku” (Jeff DiStefano, Spring 2006)

-          “Polytopes and Pick’s Theorem (Gunjan Mehta, Fall 2005);

-          “Subgroups of Permutation Groups and Permutahedron” (Nancy Jimenez, Fall 2005)

-          “Polytopes and Enhart Polynomials” (Alaina Benarquista, Fall 2005)

-          “Age of the Earth”  (Richard LoBoi, Spring 2005)

-          “Three Optimization Problems” (Robert Fisch, Spring 2005)

-           “The Calculus of Rainbow”  (Batoul Baterdouk, Fall 2004)

-           “The Actions of Groups and Symmetries”( Fall 2002) 

-          “The Catalan Numbers”(Spring 2002)


- B.S.   (Second Class), Mafat Gagal Arts and Science College of the Gujarat University, INDIA, May 1963

-M.S.   (First Class Honours), The Graduate School of Mathematics, Gujarat University, INDIA, May 1965

-Ph.D.  (Mathematics; Algebraic Topology, Adviser:  Prof. Eldon Dyer), The Graduate School and University Center of New York, U.S.A., June 1978


-          The William Paterson College of New Jersey, 1980-present, Professor

-          Brooklyn College of the CUNY (City University of New York), 1978-1980, Instructor

-          Hunter College of the CUNY, 1977-1978, Adjunct Lecturer

-          John Jay College of Criminal Justice of the CUNY, 1975-1976, Adjunct Lecturer

-          Herbert H. Lehman College of the CUNY, 1973-1975, Adjunct Lecturer - Graduate Fellow A

-          Balabhai Damodardas College of the Gujarat University, INDIA,1965-1971, Assistant Professor

Former Chair:

-          Acting Chair of Mathematics Department, WPUNJ (Spring 1991)

Chair of Mathematics Department, WPUNJ  (1998-2004)