Jacob E. Goodman

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]

Jacob E. Goodman
Born (1933-11-15) November 15, 1933 (age 87)
Nationality United States
Alma materNew York University
Columbia University
Known forOpen 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
AwardsLester R. Ford Award (Mathematical Association of America, 1990)
Scientific career
FieldsMathematics, Music
InstitutionsCity College of New York
Doctoral advisorHeisuke Hironaka[1]

Together, he and Pollack (his long-term collaborator) introduced concepts such as "allowable sequences of permutations" and "wiring diagrams",[4] which have played an important 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 of 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 publicationsEdit

  • 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, JSTOR 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 (3): 484–507, doi:10.1137/0212032.
  • Goodman, Jacob E.; Pollack, Richard (1984), "Semispaces of configurations, cell complexes of arrangements", Journal of Combinatorial Theory, Series A, 37 (3): 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 (2): 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 Mathematics, 106 (2): 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..

ReferencesEdit

  1. ^ Jacob Eli Goodman at the Mathematics Genealogy Project
  2. ^ http://math.sci.ccny.cuny.edu/person/list
  3. ^ "Discrete & Computational Geometry".
  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, JSTOR 2318260
  8. ^ http://www.maa.org/mathtourist/mathtourist_10_9_08.html
  9. ^ "Pancake Sorting".
  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. ^ "About NYCC".
  13. ^ http://newyorkcomposerscircle.org/2010/08/05/jacob-e-goodman
  14. ^ List of Fellows of the American Mathematical Society, retrieved 2013-01-19.