Jacob E. Goodman

Jacob E. Goodman
Born	November 15, 1933 Lynn, Massachusetts
Nationality	United States
Fields	Mathematics, Music
Institutions	City College of New York
Alma mater	New York University Columbia University
Doctoral advisor	Heisuke Hironaka[1]
Known for	Open affine subsets of algebraic varieties Allowable sequences and wiring diagrams Geometric transversal theory Discrete and Computational Geometry Handbook of Discrete and Computational Geometry New York Composers Circle
Notable awards	Lester R. Ford Award (Mathematical Association of America, 1990)

Jacob Eli Goodman (born November 15, 1933) is an American geometer who has spent most of his career at the City College of New York, where he is now Professor Emeritus.^[2] In 1986 he and Richard Pollack were the founding co-editors-in-chief of the journal Discrete and Computational Geometry.^[3]

Together, he and Pollack (his long-term collaborator) introduced concepts such as "allowable sequence of permutations" and "wiring diagram" ^[4] which have played a major role in discrete geometry, specifically in the study of arrangements of pseudolines and (more generally) oriented matroids. His work with Pollack includes such results as the first nontrivial bounds on the number of order types and polytopes, ^[5] and a generalization of the Hadwiger transversal theorem to higher dimensions ^[6] In addition to the work above, Goodman is also known as the originator of the "pancake problem," an elementary question on permutations which he published under the pseudonym Harry Dweighter (sounds like "harried waiter"), ^[7] and which gave rise to the concept of pancake sorting, ^{[8] [9]} which turns out to play a role in DNA rearrangements in molecular biology ^[10]

Among Goodman's best-known work is the Handbook of Discrete and Computational Geometry, which he co-edited with Joseph O'Rourke. ^[11] In 1999 Goodman returned to an old love, musical composition, and in 2002 was founding president of the New York Composers Circle.^{[12] [13]}

In 2012 he became a fellow of the American Mathematical Society.^[14]

Selected publications

• Dweighter, Harry; Garey, Michael R.; Johnson, David S.; Lin, Shen (1977), "Solutions of Elementary Problem E2569", Amer. Math. Monthly 84: 296, doi:10.2307/2318878.
• Goodman, Jacob E. (1980), "Proof of a conjecture of Burr, Grünbaum, and Sloane", Discrete Math. 32: 27–35, doi:10.1016/0012-365x(80)90096-5.
• Goodman, Jacob E.; Pollack, Richard (1983), "Multidimensional sorting", SIAM J. Comput. 12: 484–507, doi:10.1137/0212032.
• Goodman, Jacob E.; Pollack, Richard (1984), "Semispaces of configurations, cell complexes of arrangements", J. Combinatorial Theory Ser. A 37: 257–293, doi:10.1016/0097-3165(84)90050-5.
• Goodman, Jacob E.; Pollack, Richard (1995), "Foundations of a theory of convexity on affine Grassmann manifolds", Mathematika 42: 305–328, doi:10.1112/s0025579300014613.
• Goodman, Jacob E.; Pollack, Richard; Sturmfels, Bernd (1990), "The intrinsic spread of a configuration in R^d", J. Amer. Math. Soc. 3: 639–651, doi:10.1090/s0894-0347-1990-1046181-2
• Cappell, Sylvain; Goodman, Jacob E.; Pach, János; Pollack, Richard; Sharir, Micha; Wenger, Rephael (1994), "Common tangents and common transversals", Advances in Math. 106: 198–215, doi:10.1006/aima.1994.1056.
• Goodman, Jacob E.; Pach, János; Pollack, Richard, eds. (2008), Surveys on Discrete and Computational Geometry: Twenty Years Later, Contemporary Mathematics 453, Amer. Math. Soc..

References

1. Jacob Eli Goodman at the Mathematics Genealogy Project
2. http://math.sci.ccny.cuny.edu/person/list
3. http://www.springer.com/journal/454
4. Bjorner, Anders; Las Vergnas, Michel; Sturmfels, Bernd; White, Neil; Ziegler, Günter M. (1999), Oriented Matroids, 2nd Ed., Encyclopedia of Mathematics and its Applications 46, Cambridge University Press
5. Goodman, Jacob E.; Pollack, Richard (1986), "There are asymptotically far fewer polytopes than we thought", Bull. Amer. Math. Soc. 46: 127–129, doi:10.1090/s0273-0979-1986-15415-7
6. .Goodman, Jacob E.; Pollack, Richard (1988), "Hadwiger's transversal theorem in higher dimensions", J. Amer. Math. Soc. (1): 301–309
7. Dweighter, Harry (1975), "Elementary Problem E2569", Amer. Math. Monthly 82: 1010, doi:10.2307/2318260
8. http://www.maa.org/mathtourist/mathtourist_10_9_08.html
9. http://mathworld.wolfram.com/PancakeSorting.html
10. http://sites.google.com/site/ivarspeterson/pancakesorting.
11. Goodman, Jacob E.; O'Rourke, Joseph (2004), Handbook of Discrete and Computational Geometry, Encyclopedia of Mathematics and its Applications, 2nd Ed. 46, CRC Press
12. http://nycomposerscircle.org/about
13. http://nycomposerscircle.org/2010/08/05/jacob-e-goodman
14. List of Fellows of the American Mathematical Society, retrieved 2013-01-19.