61. The Princeton Mathematics Community In The 1930s (PMC08) and a year or two later hassler whitney, Hermann Weyl, and Marston Morse came . I used to walk around with—he was 6 61/2 tall—and hassler whitney. http://libweb.princeton.edu/libraries/firestone/rbsc/finding_aids/mathoral/pmc08

The Princeton Mathematics Community in the 1930s Transcript Number 8 (PMC8) © The Trustees of Princeton University, 1985 WILLIAM L. DUREN, NATHAN JACOBSON, and EDWARD J. McSHANE This is an interview of William L. Duren, Nathan Jacobson, and Edward J. McShane on 10 April 1984 at the University of Virginia. The interviewer is Karen Parshall. Jacobson: I'd like to start with my introduction to the Princeton mathematics department. I came there in 1930, in late September I believe is when the term started. I had come from the University of Alabama, and of course it was very exciting to go to Princeton, which had a reputation of being one of the three greatest centers of mathematics in the country. It probably was the greatest at that time. The department had a meeting of the new graduate students with all the faculty, which included James W. Alexander, Oswald Veblen, Solomon Lefschetz, and J.H.M. Wedderburn. I think all came to this meeting. We were introduced to them, and then they all offered us advice as to how we should conduct ourselves to become mathematicians. One of the things I remember most clearly was that Alexander's advice was to tell us how to get into the library in case the building was locked. We didn't have keys. The building was Palmer Laboratory, which was the building that was used before Fine Hall was completed a year after that in 1931. Anyway, his advice was that we could climb up to the second-story window. Alexander was a famous mountain climber; he even had a method of climbing Long's Peak (Colorado) named after him. He used to climb the Graduate School tower and do various other things of that sort. But that was his advice for us students. It started us out properly in our careers at Princeton.

62. Wolf Prize Recipients In Mathematics hassler whitney, Institute for Advanced Study, Princeton, USA, for his fundamentalwork in algebraic topology, differential geometry and differential http://www.jewishvirtuallibrary.org/jsource/Society_&_Culture/wolfmath.html

Wolf Prize Recipients in Mathematics IZRAIL M. GELFAND, Moscow State University, Moscow, U.S.S.R., for his work in functional analysis, group representation, and for his seminal contributions to many areas of mathematics and its applications, and CARL L. SIEGEL , Georg-August University, Gottingen, W. Germany, for his contributions to the theory of numbers, theory of several complex variables, and celestial mechanics. JEAN LERAY, College de France, Paris, France, for pioneering work on the development and application of topological methods to the study of differential equations; and ANDRE WEIL, Institute for Advanced Study, Princeton, U.S.A., for his inspired introduction of algebro-geometry methods to the theory of numbers. HENRI CARTAN, Universite de Paris, Paris, France, for pioneering work in algebraic topology, complex variables, homological algebra and inspired leadership of a generation of mathematicians; and ANDREI N. KOLMOGOROV, Moscow State University, Moscow, U.S.S.R., for deep and original discoveries in Fourier analysis, probability theory, ergodic theory and dynamical systems. LARS V. AHLFORS, Harvard University, Cambridge, U.S.A., for seminal discoveries and the creation of powerful new methods in geometric function theory; and OSCAR ZARISKI, Harvard University, Cambridge, U.S.A., creator of the modern approach to algebraic geometry, by its fusion with commutative algebra.

63. Old Papers © March-01-2000 BF. whitney, hassler SphereSpaces Proc. Natl. Acad. Sci. USA 21, 464-468, 1935.whitney.ps, 5M, Wed 21 Aug 2002 1427. whitney.tiff, 287k, Wed 21 Aug 2002 14 http://kaluza.physik.uni-konstanz.de/~fauser/P_old_papers.shtml

Site of Extensions : Old Papers 3/3/99 BF. Start Page Cookeville 2002 Conf. Registration Pre-Registered Persons ... Konstanz, Lake Mail to BF. Debug This page presents scaned versions of some papers which are of historic interest to reasearchers working in geometric algebra. You can download and print out these works. However, be aware that the files are extraordinary large! There are ps-files included in tgz-archives or tiff pictures in zip-archives available. If you have scaned versions of importand historic papers, you are welcome to send them as email (attached) to be incorporated into this list. How to unpack: Authors in lexicographical order Eckmann, Beno Comentarii mathematici Helvetici, 15, 358-366, 1943 Eckmann.ps.gz Wed 21 Aug 2002 14:27 Eckmann.tiff Wed 21 Aug 2002 14:27 Einstein, A.; Mayer, W. Semi-Vektoren und Spinoren Sitzungsbericht der Preussischen Akademie der Wissenschaften (1932) 522-550 EinsteinMayer.tgz Wed 21 Aug 2002 14:26 EinsteinMayer.zip Wed 21 Aug 2002 14:26 Zur Theorie der Farbenmischung Poggendorffs Annalen der Physik und Chemie Bd. 89 (1853) 69-84 (i.e. Annalen der Physik)

64. [Psu-math-spppart] Fwd: NCLB: Benezet/Whitney Thinking Dr. hassler whitney, a distinguished mathematician at the Institute for AdvancedStudy in Princeton, says that for several decades mathematics teaching http://toto.plymouth.edu/pipermail/psu-math-spppart/2004-September/000022.html

[Psu-math-spppart] Fwd: NCLB: Benezet/Whitney Thinking Brian Beaudrie bpbeaudrie at mail.plymouth.edu Mon Sep 6 14:51:48 EDT 2004 Previous message: [Psu-math-spppart] Fwd: NCLB: Benezet/Whitney Thinking Next message: [Psu-math-spppart] Cognitive Tutor Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] If anyone is interested, I have copies of the original articles by L. P. Benezet concerning the experiment. They make for some very fascinating reading! Dr. Brian Beaudrie Assistant Professor of Mathematics Plymouth State University (603) 535-3116 -Original Message- From: psu-math-spppart-bounces at toto.plymouth.edu [mailto: psu-math-spppart-bounces at toto.plymouth.edu ] On Behalf Of Richard Evans Sent: Monday, September 06, 2004 10:57 AM To: msp participants; impact teachers; msp participants; NHMATHED at toto.plymouth.edu Subject: [Psu-math-spppart] Fwd: NCLB: Benezet/Whitney Thinking This article reminds us that the emphasis needs to be on "thinking" and not on memorizing and using procedures without understanding. And, it happened here in NH!! Dick Begin forwarded message: > jbecker at siu.edu

65. Professor Jenny Harrison the Institute for Advanced Study, hassler whitney became my postdoc adviser.I had been assigned to be Milnor s assistant, but whitney took on the role. http://math.berkeley.edu/~harrison/more/background/

@import url("http://math.berkeley.edu/~harrison/css/iemac.css") screen; @import url("http://math.berkeley.edu/~harrison/css/good.css") screen; font + font - Professor Jenny Harrison home courses about vita ... research more pictures background the settlement I started off at the University of Alabama as a music major in 1967. It was not until my senior year that I realized music was not well suited for me. In my five years of training, I had had few chances to perform and I suffered from bone grinding stage fright. The point of bifurcation in my life occurred the day that Julliard's Jeanine Dowis accepted me as a student. The thought of practicing seven hours a day for the rest of my life, when I was so uncomfortable performing, gave me pause. I decided to give up piano after that first lesson, when she both accepted me and asked me to prepare a Chopin Ballade and Beethoven's Emperor Piano Concerto, music of my dreams. I had finally come to a point of accomplishment where I felt free to leave. The Princeton math department offered me a position as Instructor. The tea room conversations about mathematics were similar to those at Warwick. They were simply thrilling, and I learned about cutting edge mathematics as it was evolving in the seminars given by visitors, postdocs, and Princeton faculty. It was there that I learned about the Seifert Conjecture. This was Michael Handel's favorite problem and a common topic of conversation at Princeton. The problem is a three dimensional version of the Hairy Ball Theorem which says that every vector field on the two-sphere must have a zero. The Seifert Conjecture asserts that every vector field on the three-sphere must have a zero or a closed orbit. I had no idea of the powerful political forces from several directions that I would come up against in my quest for a solution and was almost swept away by them.

66. Parapluie De Whitney Translate this page PARAPLUIE DE whitney whitney umbrella, whitneyscher Regenschirm. hassler whitney (1907 -1989) mathématicien américain. http://www.mathcurve.com/surfaces/whitney/whitney.shtml

surface suivante courbes 2D courbes 3D surfaces ... fractals PARAPLUIE DE WHITNEY Whitney umbrella, Whitneyscher Regenschirm Surface ou Le parapluie de Whitney est un Oz points-pince r (la transformation le transforme en surface suivante courbes 2D courbes 3D surfaces ... fractals

67. COLLECTED PAPERS whitney, hassler, Collected Papers, 2, QA611/W455 1992. Witt, Ernest, 19111991.Collected Papers Gesammelte Abhandlungen, 1, QA3/W57 1998 http://www.matmor.unam.mx/acervo/OBRAS_COMPLETAS_EN_MATEMATICAS.html

OBRAS COMPLETAS EN MATEMATICAS a nivel Internacional, este material se puede consultar en nuestra Unidad AUTOR TITULO VOLUMENES CLASIFICACION Adams, J. Frank, 1930-1997. The Selected papers works of J. Frank Adams Albert, Abraham Adrian, 1905-1972. Collected Mathematical Papers Anderson, T. W. Collected papers of T. W. Anderson : 1943-1985 QA276/A12A53 1990 v.2 Artin, Emil 1898-1962 Collected Papers Auslander, Maurice, 1926-1994 Selected Works Archimedes The Works of Archimedes Atiyah, Michael Francis 1929- Collected Papers Beurling, Arne Collected Works QA331.7/B487 1989 v.2 Bishop, Errett, 1928-1983 Selected Papers Bochner, Salomon, 1899-1982 Collected Papers Borel, Armand, 1923- Oeuvres = Collected Papers QA3/B5787 1983 v. 4 Bott, Raoul, 1924- Collected Papers Brauer, Richard, 1901-1977 Collected Papers QA3/B693 1980 v. 1-2 Collected Works Cartan, Henri, 1904- Oeuvres : Collected Works Coxeter, H.S.M., 1907-2003 Kaleidoscopes : selected writting Chen, K. T. Collected Papers C hern, Shiing-Shen, 1911- Mathematician and his Mathematical Work Chowla, Sarvadaman

68. Obras Daniel (Graduate Texts in Mathematics, 61) BDBH QA593 whitney, hassler W618c Complex (AddisonWesley Series in Mathematics) BDBH QA586 whitney, hassler W618g http://www.ime.usp.br/bib/daniel.html

Coleção Professor Daniel Henry Livros Termodinâmica. Transversal mappings and flows. Almost periodic functions and functional equations. New York, Van Nostrand, 1971. 184p. (The University Series in Higher Mathematics) BDBH QA336 ARNOLD, V. I. A759dF Chapitres supplémentaires de la théorie des équations différentielles ordinaires. Moscou, Mir, c1980. 323p. BDBH QA338 ARNOLD, V. I. A759oP Equações diferenciais ordinárias.

69. "Matroid Theory", AMS, 1996. properties of linear dependence, hassler whitney founded the theory of matroids.The richness of whitney s work can be attributed in part to the variety http://users.wpi.edu/~bservat/cmbook.html

Title: Matroid Theory Editors: Joseph Bonin, James Oxley and Brigitte Servatius Publisher: Contemporary Math., AMS, 1996. ISBN 0-8218-0508-8 Preface to Text: With his 1935 paper On the abstract properties of linear dependence, Hassler Whitney founded the theory of matroids. The richness of Whitney's work can be attributed in part to the variety of fields from which he drew inspiration, including algebra, geometry, and graph theory. Since Whitney's paper, numerous authors have recognized the natural occurrence of matroids in a wide diversity of areas, and the interplay between matroid theory and other fields has flourished. This volume, the proceedings of the 1995 AMSIMSSIAM Summer Research Conference Matroid Theory, features three comprehensive surveys that bring the reader to the forefront of research in matroid theory. Joseph Kung 's encyclopedic treatment of the critical problem traces the development of this problem from its origins through its numerous links with other branches of mathematics to the current status of its many aspects. James Oxley 's survey of the role of connectivity and structure theorems in matroid theory stresses the influence of the Wheels and Whirls Theorem of Tutte and the Splitter Theorem of Seymour.

70. INSTITUTO ARGENTINO DE MATEMÁTICA whitney, hassler. whitney, hassler. Complex analytic varieties. AddisonWesley . whitney, hassler. Geometry integration theory. University Press. http://www.iam.conicet.gov.ar/Biblioteca/BD-LIBROS-W.html

INSTITUTO ARGENTINO DE MATEMÁTICA BIBLIOTECA LIBRARY Base de Datos de Libros Books Data Base - W - Wadderburn, J.H.M. Wadderburn, J.H.M. Lectures on Matrices Dover Publications Inc. N.York 1964-00-00 Wade, Thomas L. Wade, Thomas L. The algebra of vectors and matrices Addison-Wesley. Cambridge 1951 Wadsworth, George P. Wadsworth, George P.; Bryan, Joseph G. Introduction to probability and Random variables McGraw-Hill. New York 1960 Waerden, B. L. van der Waerden, B. L. van der Moderne algebra Ungar. New York 1943 Waerden, B. L. van der Einführung in die algebraische gemmetrie Dover. New York 1945 Waerden, B. L. van der Statistique mathématique Dunod. Paris 1967 Waerden, B. L. van der Modern algebra Ungar. New York 1949, 50 Waerden, B. L. van der Algebra Hayka. Moscú 1976 Waerden, Bartel van der Waerden, Bartel van der; Gross, Herbert Studien theorie der quadratischen formen Birkhäuser. Bassel 1968 Wagner, Frank O. Wagner, Frank O. Stable groups Wagner 1997 Wainstein, L. A. Wainstein, L. A.; Zubakov, V. D. Extraction of signals from noise Prentice-Hall. Englewood Cliffs, N. J. 1962

71. Theme4_Cours1 hassler whitney des années 1960 (hassler whitney - 1968), mais aussi plus récents (Klaus http://www-leibniz.imag.fr/EEDDM11/Theme4/Cours1.html

Cours 1 Grandeurs et mesures : d'Euclide, les The American Mathematical Monthly La mesure des grandeurs Linear Algebra e e Bibliographie Euclide, 1993, , Librairie Albert Blanchard, Paris. Euclide, 1994, Traduction et commentaires par Bernard Vitrac , Presses Universitaires de France. Goblot R., 1998, Hartshorne Robin, 2000, Geometry : Euclid and beyond, Springer. Linear Algebra Hilbert D., 1971, , Dunod, Paris. Klain D. A., Rota G-C, 1997, Introduction to Geometric Probability , Cambridge University Press. *Lebesgue H., 1975, La mesure des grandeurs , Librairie scientifique et technique Albert Blanchard, Paris. Stillwell J., 1998, Numbers and geometry , collection Readings in Mathematics, Springer. Whitney Hassler, 1968, The mathematics of physical quantities, Part II : Quantity structures and dimensional analysis, The American Mathematical Monthly

72. Finite Fields And Applications Plenary Talk The problem we wish to discuss was addressed by David Slepian in the 60s and,earlier and more generally, by hassler whitney. http://www.lehigh.edu/efa0/public/www-data/watab.html

The Category of Linear Codes by E. F. Assmus, Jr. Abstract of a plenary talk at Fq4 in Waterloo, Canada The problem we wish to discuss was addressed by David Slepian in the 60s and, earlier and more generally, by Hassler Whitney. It is the problem of ``classifying'' the k x n matrices of rank k over a field F - which we take, given our setting at this conference, to be finite. The classification sought is under the following equivalence relation: two such matrices, G and H, are equivalent if H = MGP, where M is a k x k non-singular matrix and P an n x n monomial matrix (i.e., a matrix with precisely one non-zero entry in every row and column). Clearly, from the point of view of the coding theorist, we wish to classify the k-dimensional ``row spaces'' of n-tuples from the field F, under the equivalence given by permuting the coordinates and possibly multiplying each coordinate by a non-zero scalar. This was Slepian's point of view. For Whitney it was the collection of columns and their linear dependencies that was of interest - a dual point of view. Both authors proved the same decomposition theorem showing that any k x n matrix over F of rank k was equivalent to a block-diagonal matrix (G1,G2,...,Gr) where the Gi are ``indecomposable'' and have uniquely determined row spaces - up to order, of course.

73. Quantum Books : Engineering Author whitney, hassler ISBN 0486445658 Publisher Dover Publications Pub DateDec 12, 2005 Status Not Yet Published/Back Ordered. List Price $18.95 http://www.quantumbooks.com/Merchant2/merchant.mvc?Screen=CTGY&Store_Code=qb&Cat

74. A Guide To The Princeton Mathematics Community In The 1930s Oral History Collect Snapper, Ernst. Taub, Abraham H. Taylor, Angus E. Tucker, Albert W. Tukey, John.Walker, Robert. whitney, hassler. Wigner, Eugene. Wylie, Shaun http://www.lib.utexas.edu/taro/utcah/00206/cah-00206.html

TARO Repository Browse List Print Version Raw XML File (10k) ... Accessing Materials Described Here TABLE OF CONTENTS Descriptive Summary Scope and Contents Restrictions Index Terms ... Interview transcripts: A Guide to the Princeton Mathematics Community in the 1930s Oral History Collection, 1984-1985 Descriptive Summary Title Princeton Mathematics Community in the 1930s Oral History Collection Dates: Abstract Transcripts of oral history interviews with 43 individuals concerning their memories of mathematics at Princeton University during the 1930s. Accession No. Extent 3 in. Language English. Repository Center for American History,The University of Texas at Austin Scope and Contents Transcripts of oral history interviews with 43 individuals concerning their memories of mathematics at Princeton University during the 1930s. The interviews focus on the institutional and social context of the Princeton graduate program and the Institute for Advanced Study as they developed, as well as the personalities of the people involved. Prominent individuals involved with Princeton in the 1930s included James Alexander, Albert Einstein, Luther Eisenhart, Solomon Lefschetz, Marston Morse, Oswald Veblen, John von Neumann, Hermann Weyl and Eugene Wigner. Most of these individuals had died at the time of these interviews, however several faculty members as well as graduate students, visitors and permanent researchers took part in the oral history project. Arranged alphabetically by interviewee.

75. A Guide To The Princeton Mathematics Community In The 1930s Oral History Collect Rosser, J. Barkley. Singleton, Robert. Snapper, Ernst. Taub, Abraham H. Taylor,Angus E. Tucker, Albert W. Tukey, John. Walker, Robert. whitney, hassler http://www.lib.utexas.edu/taro/utcah/00206/00206-P.html

Main Version Raw XML File (10k) A Guide to the Princeton Mathematics Community in the 1930s Oral History Collection, 1984-1985 Descriptive Summary Title Princeton Mathematics Community in the 1930s Oral History Collection Dates: Abstract Transcripts of oral history interviews with 43 individuals concerning their memories of mathematics at Princeton University during the 1930s. Accession No. Extent 3 in. Language English. Repository Center for American History,The University of Texas at Austin Scope and Contents Transcripts of oral history interviews with 43 individuals concerning their memories of mathematics at Princeton University during the 1930s. The interviews focus on the institutional and social context of the Princeton graduate program and the Institute for Advanced Study as they developed, as well as the personalities of the people involved. Prominent individuals involved with Princeton in the 1930s included James Alexander, Albert Einstein, Luther Eisenhart, Solomon Lefschetz, Marston Morse, Oswald Veblen, John von Neumann, Hermann Weyl and Eugene Wigner. Most of these individuals had died at the time of these interviews, however several faculty members as well as graduate students, visitors and permanent researchers took part in the oral history project. Arranged alphabetically by interviewee. Forms part of the Archives of American Mathematics Restrictions Access Restrictions Unrestricted access.

76. From Rusin@vesuvius.math.niu.edu (Dave Rusin) Newsgroups Sci In 1935, hassler whitney showed that every C^infinity manifold M of dimension nmay be embedded in R^N as long as N 2n, that is, there is a submanifold of http://www.math.niu.edu/~rusin/known-math/96/diff.geom

From: rusin@vesuvius.math.niu.edu (Dave Rusin) Newsgroups: sci.math Subject: Re: Question about non-euclidian geometry Date: 19 Aug 1996 22:01:50 GMT In article , Greg Moriarty , Greg Moriarty wrote: >Usually to grasp the concept of non-euclidian geometry the student is told >to imagine a 2 dimensional plane wrapped around into a 3 dimensional >sphere. To the ant living on the plane, to which the 3rd dimension is a >foreign concept, parallel lines seem to intersect and triangles add up to >>180 degrees and other such silliness. To the god-like observer, those >things aren't odd at all since the god-like creature has an understanding >of the 3rd dimesion. My question is thus: > >Can one go from a non-euclidian geometry to a euclidian geometry by >introducing a new dimension? Is this something that is done? If so, can >one ALWAYS do so? I responded to this (and some later points) in a post which might appear to be at variance with another follow-up, which I feel sort of misses the point. In article , Kevin Anthony Scaldeferri

77. Earliest Known Uses Of Some Of The Words Of Mathematics (M) hassler whitney coined the term matroid and introduced it in his fundamentalpaper On the abstract properties of linear independence, Amer. J. Math. http://members.aol.com/jeff570/m.html

Earliest Known Uses of Some of the Words of Mathematics (M) Last revision: March 20, 2005 MACLAURIN'S SERIES is named for Colin Maclaurin Maclaurin's theorem appears in 1820 in Collection of Examples of the Applications of the Differential and Integral Calculus by G. Peacock [Mark Dunn]. In 1849, An Introduction to the Differential and Integral Calculus, 2nd ed., by James Thomson has: "A particular case of this formula is commonly called Maclaurin's theorem, because it was first made generally known by that writer. It had been given previously, however, by Stirling, another Scotch mathematician; and therefore, if a particular case of Taylor's general theorem should be named after any other mathematician, this ought to be called Stirling's theorem. " Thomson subsequently uses the term Stirling's theorem throughout the book. McLaurin's formula is found in English in 1855 in Elements of the differential and integral calculus by Albert Ensign Church [University of Michigan Digital Library]. Nouv. Ann. Maclaurin's series is found in English in 1831 in the second edition of Elements of the Differential Calculus (1836) by John Radford Young: "All that is meant is, that the function in

78. Samuel Eilenberg, September 30, 1913—January 30, 1998 | By Hyman Bass, Henri Ca and codified the ideas of the obstructions recently introduced by hasslerwhitney. for example, JHC Whitehead, hassler whitney, Saunders Mac Lane, http://stills.nap.edu/html/biomems/seilenberg.html

BIOGRAPHICAL MEMOIRS National Academy of Sciences Courtesy of Columbia University Samuel Eilenberg By Hyman Bass, Henri Cartan, Peter Freyd, Alex Heller, and Saunders Mac Lane S AMUEL EILENBERG DIED IN New York, January 30, 1998, after a two-year illness brought on by a stroke. He left no surviving family, except for his wide family of friends, students, and colleagues, and the rich legacy of his life's work, in both mathematics and as an art collector. "Sammy", as he has long been called by all who had the good fortune to know him, was one of the great architects of twentieth-century mathematics and definitively reshaped the ways we think about topology. The ideas that accomplished this were so fundamental and supple that they took on a life of their own, giving birth first to homological algebra and in turn to category theory, structures that now permeate much of contemporary mathematics. Born in Warsaw, Poland, Sammy studied in the Polish school of topology. At his father's urging, he fled Europe in 1939. On his arrival in Princeton, Oswald Veblen and Solomon Lefschetz helped him (as they had helped other refugees) find a position at the University of Michigan, where Ray Wilder was building up a group in topology. Wilder made Michigan a center of topology, bringing in such figures as Norman Steenrod, Raoul Bott, Hans Samelson, and others. Saunders Mac Lane's invited lecture there on group extensions precipitated the long and fruitful Eilenberg-Mac Lane collaboration. In 1947 Sammy came to the Columbia University mathematics department, which he twice chaired and where he remained till his retirement. In 1982 he was named a University professor, the highest faculty distinction that the university confers.

79. The Institute Letter At the Institute for Advanced Study, where he occupies the office of the lateProfessor hassler whitney (1907–1989)—one of the leading geometers of the http://www.ias.edu/the-institute-letter/archive/04Fall/04Fall.php

From the Director Trustees Directory Publications ... How to Apply Institute For Advanced Study ARNOLD LEVINE APPOINTED FACULTY MEMBER IN THE SCHOOL OF NATURAL SCIENCES Arnold J. Levine is a graduate of Harpur College, State University of New York, and earned his Ph.D. in microbiology from the University of Pennsylvania School of Medicine. Subsequently, he was postdoctoral fellow of the Public Health Service at the California Institute of Technology. He holds honorary degrees from, among other institutions, Rider University, the University of Medicine and Dentistry of New Jersey, the Weizmann Institute of Science, and the University Pierre and Marie Curie in Paris. Among the numerous scientific organizations and educational institutions for which Professor Levine has served as board member or adviser, are the N.J. Biotechnology Institute, the American Cyanamid Corporation, the SUNY Health Sciences Center in Brooklyn, Albert Einstein College of Medicine, the Weizmann Institute, the Huntsman Cancer Center of the University of Utah, and the Institute for Cancer Research in Lausanne, Switzerland. A CONFERENCE ON THE OCCASION OF THE SIXTIETH BIRTHDAY OF ROBERT MACPHERSON Since the 1970s, intersection homology theory has been further developed and extended through the efforts of many talented, dedicated mathematicians. It is now such a rich, burgeoning field that the American Mathematical Society has designated a classification number (55N33) for papers dealing with intersection homology. It has been especially important in representation theory, where many of the naturally occurring objects have singularities.

80. Four Color Theorem The history of this approach going back to hassler whitney and other referencesto this approach are in the book. The MacTutor History of Mathematics http://grail.cba.csuohio.edu/~somos/4ct.html

Four Color Theorem Around 1998 Paul Kainen and I worked on an approach to the Four Color Theorem. He is a co-author of a book on this topic reprinted by Dover Publications. AUTHOR Saaty, Thomas L. TITLE The four-color problem : assaults and conquest / Thomas L. Saaty and Paul C. Kainen. PUBLISH INFO New York : Dover Publications, 1986. DESCRIPT'N vi, 217 p. : ill. ; 21 cm. NOTE Includes bibliographical references (p. 197-211) and index. SUBJECTS Four-color problem. LC NO QA612.19 .S2 1986. DEWEY NO 511/.5 19. OCLC # 12975758. ISBN 0486650928 (pbk.) : $6.00. AUTHOR Saaty, Thomas L. TITLE The four-color problem : assaults and conquest / Thomas L. Saaty and Paul C. Kainen. PUBLISHER New York : McGraw-Hill International Book Co., c1977. DESCRIPTION ix, 217 p. : ill. ; 25 cm. NOTES Bibliography: p. 197-211. Includes index. OCLC NO. 3186236. ISBN 0070543828 : $23.00. We take a pair of triangulations of a polygon and four color the vertices such that no two of the same color are connected by an edge of the triangulations. Polygon triangulations are easy to represent using data structures and the topological considerations of planarity are avoided. This turns the problem into a combinatorial one. The planarity reduces to circular order along the polygon and the non-crossing of diagonals. The history of this approach going back to Hassler Whitney and other references to this approach are in the book.

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