Mathematics Department
The City College of New York
160 Convent Avenue
New York, NY 10031
Biography
Back when dinosaurs roamed Manhattan, I was an undergraduate at City College, taking classes with Jesse Douglas, among others, and graduating in 1965. After my PhD at Princeton (1969), I taught at University of California, Berkeley from Fall, 1968 through Spring, 1970. In the Fall of 1970 I returned to City College where I have been teaching ever since, aging slightly.
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Currently Teaching: Spring, 2026
Math 34600 L (33201)
Elements of Linear Algebra
Tuesday, Thursday 9:30AM-10:45AM NAC 6/121.
Math 39100 K (33191)
Methods of Differential Equations
Tuesday, Thursday 8:00AM-9:15AM Marshak MR2.
Class Documents
Math 203
Math 346
- Math 34600L-Spring2026-Course Info
- Math 34600L-Spring2026-HWschedule
- Math 34600L-Spring2026-Post 01
- Math 34600L-Spring2026-Post 02
- Math 34600L-Spring2026-Homework Solutions
- Math 34600L-Spring2026-Test 1-Solutions
- Nicholson-Linear Algebra with Applications2018
Math 391
- Math 39100K-Spring2026-HWschedule
- Math 39100K-Spring2026-Course Info
- Math 39100K-Spring2026-Post 01
- Math 39100K-Spring2026-Post 02
- Math 39100K-Spring2026-Scrambled HW Problems
- Math 39100K-Spring2026-Scrambled Solutions
- Math 39100K-Spring2026-HW-Post 01
- Math 39100K-Spring2026-HW-Post 02
- Math 39100K-Spring2026-Test 1-Solutions
- Math 39100K-Spring2026-DeMoivre Examples
(In addition to those below, any papers listed in my CV are available upon request)
Especially important during my graduate school years were my friend and mentor, George Cooke, and my thesis advisor, Marshall Cohen. The article below contains some memories from that period.
Research
My primary research lies in the topological part of dynamical systems theory. Below is some introductory material describing two books, The General Topology of Dynamical Systems and Recurrence in Topological Dynamics: Furstenberg Families and Ellis Actions as well as three monographs Simplicial Dynamical Systems, Dynamics of Topologically Generic Homeomorphisms (with Michael Hurley and Judy Kennedy) and The Topological Dynamics of Ellis Actions (with Joseph Auslander and Eli Glasner). The survey of topological dynamics is my - rather idiosyncratic - view of the subject. It is in the Encyclopedia of Complexity and Systems Science (2009).
- 1993-General Topology of Dynamical Systems (a tourist's guide)
- 1997-Recurrence in Topological Dynamics (introduction)
- 1999-Simplicial Dynamical Systems (introduction)
- 2003-The Dynamics of Topologically Generic Homeomorphisms (introduction)
- 2005-The Topological Dynamics of Ellis Actions (introduction)
- 2007-Topological Dynamics: A Survey
My work in population genetics is represented by an old paper: Cycling in Simple Genetic Systems. Because of my research in biology, I became interested in the controversy about Intelligent Design. In Theses on Johnson I defend - at length - the view that the ID position is wrong but interesting, as opposed to wrong and stupid, which is the general opinion among biologists.
Of perhaps more general interest is Why the 3X+1 Problem Is Hard?. This is an introduction to the -simple to state, but unsolved, Collatz Problem.
The Spiteful Computer is a description of an odd determinism paradox.
Following the recent work of Press and Dyson there have been advances in the study of the Prisoner's Dilemma. My contributions are represented by The Iterated Prisoner's Dilemma: Good Strategies and Their Dynamics, and Good Strategies for the Iterated Prisoner’s Dilemma: Smale vs. Markov.
Some recent work on tournaments: Rock-Paper-Scissors.etc: The Theory of Regular Tournaments, and Topological Tournaments.
Miscellaneous: Some work in point-set topology: Trees and Homogeneous LOTS (with Karel Hrbacek).A paper on interest rates: The Simple Yield Curve Models (with Morton Davis).
Finally, some essays and letters on various political topics:
