(updated: (August, 2012))

Books and Monographs

Graphs, Models, and Finite Mathematics (with W. Meyer), Prentice-Hall, Englewood Cliffs, l974.

For All Practical Purposes (with co-authors), 8th ed., W.H. Freeman, New York, 2009. (Also earlier editions, which vary considerably from the later ones in content. Part of the philosophy of this book is that themes and modeling approaches to mathematics are more important than the specific mathematical techniques that are taught, so the book has changed more from one edition to another than many other books.)

Graphs With Uniform Vertex and Face Structure (American Mathematical Society, 1970)

The Mathematical Theory of Elections (with G. Froelich) (COMAP, undated, c. 1986)

Codes Galore (with G. Froelich) (COMAP, 1991)

Loads of Codes (with G. Froelich) (COMAP, 1993)

Graph Models (COMAP, 1996)

Discrete Geometry and Convexity (co-editor), Annal 440, New York Academy of Sciences, 1985.

Combinatorial Mathematics (co-editor), Annal 555, New York Academy of Sciences, 1989.

Mathematical Vistas (co-editor), Annal 607, New York Academy of Sciences, 1990.

Geometry's Future, COMAP, (1st ed., 1991), (2nd ed.), 1992.


For All Practical Purposes (Content developer (with others) (Annenberg Project: Corporation for Public Broadcasting).)

Geometry: New Tools for New Technologies (COMAP)

Breaking the Code (COMAP)

Square One (Children's Television Workshop, Consultant)

National Technological University (Mathematical Sciences and Their Applications Throughout the Curriculum)


Applications of Vertex Coloring Problems for Graphs (Module) UMAP Module 442, COMAP, 1980.

Mathematics' Image Problem (unpublished) 1989.

Bin Packing: A Mathematical Application, Mathematics Teacher 84 (1991) 29-31.

Geometry Yesterday, Today, and Tomorrow; Geometry in Utopia, in Geometry's Future (2nd. ed.) J. Malkevitch (ed.), COMAP, Lexington, Ma. 1992.

The role of geometry in a principles of mathematics course, in A New Start for College Mathematics, ed. W. Meyer, COMAP, Lexington, 1992, p. 65-74.

Tomorrow's Geometry, in Heeding the Call to Change, ed. Lynn Steen, MAA, Washington, 1992, p. 45-80.

Discrete Mathematics and Public Perceptions of Mathematics, in "Discrete Mathematics in the Schools," (eds.), J. Rosenstein, D. Franzblau, and F. Roberts, DIMACS Series, Vol. 36, American Mathematical Society, Providence, 1997.

You can find a pdf version of this article here.

Finding room in the curriculum for recent geometry, in Perspectives on the Teaching of Geometry for the 21st Century, (eds.) C. Mammana and V. Villani, Kluwer, Dordrecht, 1998, p. 18-25.

Geometry and Reality, in Perspectives on the Teaching of Geometry for the 21st Century, (eds.) C. Mammana and V. Villani, Kluwer, Dordrecht, 1998, p. 85-99.

Patenting Mathematics, New Scientist, October 30, 1999.

Fair Legislative Representation, UMAP Journal, 21 (2000) 55-71.

Mathematics and the Human Genome, Parts I-IV, Consortium (Newsletter of COMAP, the Consortium for Mathematics and Its Applications, Numbers 75, 76, 77, 78, 2000-2001.

Theory and Applications in the Teaching of Linear Algebra: Evolution over Time (with Walter Meyer), in History of Undergraduate Mathematics in America, Proceedings of a Conference held at the United States Military Academy, West Point, New York, June 21-24, 2001, (ed.) A. Shell-Gellasch, United States Military Academy, West Point, 2002, p. 295-310.

Teaching Mathematical Biology in High School (Talk at Dimacs/Rutgers, Spring 2005) Teaching Mathematical Biology in High School (Slides for DIMACS/Rutgers presentation). Can be downloaded in pdf format.

Drugs and Blocks, Consortium (Newsletter of COMAP, the Consortium for Mathematics and Its Applications, Number 91, Fall-Winter, 2006, pp. 7-9.

The Geometry of Urban Services: Theorems, Algorithms, and Proofs. (Math For America workshop, Oct. 2007) The Geometry of Urban Services: Theorems, Algorithms and Proofs. (Minimal slides for a Math for America workshop.) Can be downloaded in pdf format.

Mathematical Modeling. (This is a collection of urban operations research problems with a geometrical (graph theory) flavor. The problems raised involve the concepts of Euler circuits, the chinese postman problem, matchings, the traveling salesman problem, and minimial cost spanning trees.) Math for America workshop, Oct.2007. Mathematical Modeling. Notes for a Math for America Workshop. Can be downloaded in pdf format. An on-line version is here.

Content Matters. (This pdf document conists of the sides that I used for a recent conference, sponsored by Math is More, dealing with content issues for mathematics in high school.

What is Geometry? in Understanding Geometry for a Changing World, 71 First Yearbooks, eds. T. Craine, R. Rubenstein, NCTM, Reston, VA., 2009, pp. 3-17.

Learning Objectives For the New Community College Mathematics Progeam. (This document provides some thoughts on an innovative freshman mathematics program for the New Community College that CUNY proposes to establish.

The "New Math" and claims discrete mathematics is the New "New Math," Mathematics in School, 40 (2011) 8-11.

Arithmetic and algebra to solve fairness problems, Journal of Mathematics Education at Teachers College, Spring-Summer, 2011, pp. 68-69.

Representing 3-Dimensional Polyhedra in the Plane. (Here is a pdf file of the slides I used for giving a talk to the Differential Geometry Seminar at the CUNY Graduate Center (July, 2011). The talk dealt with Steinitz's Theorem, unfolding of convex polyhedra (Shephards' conjecture), and folding polygons (Alexandrov's Theorem).

At the Mathfest in Madison (Aug. 2012) I participated in a panel discussion dealing with educational issues:

Mathfest Panel

My slides for the Mathfest presentation I gave are available as a pdf file.

Here are some notes that I produced in conjunction with a workshop about Mathematical Modeling which was run by Math For America's PDO in August, 2011.

Modeling Problems Inspired by Hurricane Irene

Here are two other tasks which were produced in conjunction with the Math For America PDO events in the Fall of 2011. The first is related to the Gale-Shapley stable marriage model and the second is related to bin packing.

Stable Marriage Model

Packaging Advertisements

These questions deal with some modeling problems from "transportation science" and operations research, in particular with scheduling.

Exploring Modeling

Here is an essay (prepared in conjunction with some of my work for Math for America) that deals with issues related to problem solving, exercises, models, and mathematical modeling. These terms are compared and contrasted.

Exercises, Problem Solving and Modeling

Modeling Problems:

I have authored a variety of Mathematical Modeling Problems which have been used by COMAP (Consortium for Mathematics and Its Applications) in its Mathematical Modeling Competition. More recently, I have contributed some problems to Mathmodels.org, which is also sponsored by COMAP.

Hotel Charges

School Quality and Class Size

Shaking Marbles

Heat Transfer Fan

Leaf Problem

I enjoying making presentations to high school students about mathematics, particularly at my high school alma mater, Stuyvesant High School. Here are the pdf file slides for a talk I gave (June, 2012) there about partitions and compositions and the ties between these ideas and binary strings and d-cubes.

Book Reviews:

Nexus: Architecture and Mathematics, Kim Williams (ed.), Edizioni Dell'Erba, Fucecchio, Italy, 1996, in Humanistic Mathematics Network Jounal # 16, p. 52-53. November, 1997.

Wonders of Numbers, Clifford Pickover, Oxford, New York, 2001, in the New Scientist.

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