**Professor Jonathan L. Gross**

### Professional Biography:

Jonathan Gross is Professor of Computer Science at Columbia University. His research in topology, graph theory, and cultural sociometry has earned him an Alfred P. Sloan Fellowship, an IBM postdoctoral fellowship, and various research grants from the Office of Naval Research, the National Science Foundation, and the Russell Sage Foundation.
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His best-known mathematical invention, the voltage graph, is widely used in the construction of minimum-genus graph imbeddings and of symmetric graph imbeddings. He and Thomas Tucker proved that every covering graph can be realized as a voltage graph construction. He also wrote the pioneering papers on enumerative techniques in topological graph theory, with various co-authors. His biography appears in *Who's Who in America*.
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Professor Gross has created and delivered numerous software-development short courses for Bell Laboratories and for IBM. These include mathematical methods for performance evaluation at the advanced level and for developing reusable software at a basic level. He has received several awards for outstanding teaching at Columbia University, including the career Great Teacher Award from the Society of Columbia Graduates.
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His most recent books are *Topics in Topological Graph Theory* (co-edited with Tom Tucker and series editors Lowell Beineke and Robin Wilson) and *Combinatorial Methods with Computer Applications*. Other books include *Topological Graph Theory* (co-authored with Thomas W. Tucker), *Graph Theory and Its Applications* (co-authored with Jay Yellen), and the *Handbook of Graph Theory* (co-edited with Jay Yellen). Another previous book, *Measuring Culture* (co-authored with Steve Rayner) constructs network-theoretic tools for measuring sociological phenomena.
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Prior to Columbia University, Professor Gross was in the Mathematics
Department at Princeton University, where he worked with Ralph Fox. His undergraduate work was at the Massachusetts Institute of Technology. His Ph.D. thesis on 3-dimensional topology at Dartmouth College solved a published problem of Fields Medalist John Milnor.
### Research Interests:

Topological graph theory --- especially genus distribution; knot theory --- especially Celtic knots; computer graphics --- especially woven shapes; covering-space methods: especially voltage graphs; mathematical models for social anthropology --- especially the grid-group theory of Mary Douglas; topology of 3-manifolds.

### Research Publications

Journal Publications
Supplementary Research Material

### Current Graduate Students

Imran F. Khan
Mehvish I. Poshni

### Miscellaneous Resources

graph theory
Genus Distribution Calculator

### Monographs and Edited Volumes

*Topological Graph Theory*, (with T. W. Tucker), Wiley-Interscience, 1987. Paperback edition by Dover Publications, 2001.
*Graph Theory and Its Applications* (with J. Yellen), CRC Press, 1999. Second edition, 2006.
*Handbook of Discrete and Combinatorial Mathematics* (Associate Editor, with R.H. Rosen and D. Shier), CRC Press, 2000.
*Handbook of Graph Theory* (co-Editor with Jay Yellen), CRC Press, 2004.
*Combinatorial Methods with Computer Applications*, CRC Press, 2008.
*Topics in Topological Graph Theory* (co-Editor with T. W. Tucker; series editors L. W. Beineke, R. J. Wilson), Cambridge University Press, 2009.
*Measuring Culture: A Paradigm for the Analysis of Social Organization*, (with Steve Rayner; Introduction by Mary Douglas), Columbia University Press, 1985.
### Courses at Columbia

COMS 4203: Graph Theory
COMS 4205: Combinatorial Theory

COMS 3203: Discrete Mathematics

COMS 6204: Topics in Graph Theory

### Some Things I Said in Class

Things I Said
### Contact Information

- Phone: (212) 939-7015
- Office: 458 CSB
- e-mail:
*gross at cs dot columbia dot edu*

- Mailing address:
- Department of Computer Science
- Columbia University
- 458 Computer Science Building
- 1214 Amsterdam Avenue, Mailcode 0401
- New York, NY 10027-7003

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