1. MacLane Saunders MacLane. Born Saunders MacLane graduated in 1926 from high schooland, in that year, he entered the University of Yale. MacLane's http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/MacLane.html

Saunders MacLane Born: 4 Aug 1909 in Taftville, Connecticut, USA Click the picture above to see four larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Saunders MacLane graduated in 1926 from high school and, in that year, he entered the University of Yale. MacLane's school education had been interrupted when he was 15 years old for, at that time, his father had died. His father had been a Congregational Minister and, after his death, MacLane moved to Leominster to live with his grandfather who was also a Congregational Minister. MacLane graduated from Yale in 1930 and took up a fellowship at Chicago. At the University of Chicago he was influenced by Eliakim Moore . By this time E H Moore Moore had himself studied in Germany as a young man and had created in Chicago an eminent research school of mathematics based on his experiences of German mathematics at that time. Bernays Abbreviated Proofs in the Logical Calculus , with Weyl On returning to the United States, MacLane spent the session 1933/34 at Yale and then the following two years at Harvard. He left Harvard to take up a post of instructor at Cornell for session 1936/37, he spent the following session back at Chicago before accepting an appointment as an assistant professor at Harvard.

2. Editions Jacques Gabay - Saunders MacLANE Translate this page Saunders MacLANE. Saunders MacLANE. Au catalogue des Editions JacquesGabay MacLANE et BIRKHOFF Algèbre, tome I, 1970 et tome http://www.gabay.com/sources/Liste_Bio.asp?NP=MacLANE Saunders

3. Saunders MacLane - Wikipedia Translate this page 216.239.46.104 Identification Aide. Saunders MacLane. Saunders MacLane est un mathématicienaméricain, l'un des créateurs de la théorie des catégories. http://fr.wikipedia.org/wiki/Saunders_MacLane

Accueil Modifications récentes Modifier cette page Historique Pages spéciales Préférences Liste de suivi Modifications récentes Copier un fichier Liste des images Liste des participants Statistiques Une page au hasard Pages orphelines Images orphelines Les plus populaires Les plus demandées Articles courts Articles longs Nouvelles pages Toutes les pages Adresses IP bloquées Page de Maintenance Librairies en ligne Version imprimable Discuter Identification Aide Saunders MacLane Un article de Wikipédia, l'encyclopédie libre. Saunders MacLane -) est un mathématicien américain , l'un des créateurs de la théorie des catégories Lien : http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/MacLane.html Modifier cette page Page de discussion Historique ... Modifications récentes Cette page a été consultée 29 fois. Dernière modification de cette page : 19:50 fév 23, 2003. All text is available under the terms of the GNU Free Documentation License Accueil Modifications récentes Une page au hasard ... Rapport d'erreurs

4. Structures Directory Email directory of logicians, algebraists, and programming linguists working primarily on structural Category Science Math Algebra Category Theory...... essex.stfx.ca (Wendy MacCaull) macdonald johnm@math.ubc.ca (John MacDonald) macleodrichardm@kean.ucs.mun.ca (Richard MacLeod) maclane saunders@math.uchicago http://boole.stanford.edu/pub/structdir

5. Seminar By Saunders MacLane Current extreme political pressures on scientific research saunders maclane (University of Chicago) Thursday, October 17, Abelson 131, 2 p.m. http://www.cs.brandeis.edu/~mairson/CS-seminar/maclane.html

Current extreme political pressures on scientific research Saunders MacLane (University of Chicago) Thursday, October 17, Abelson 131 2 p.m. The current pressures on research in the mathematical sciences are no longer just budgetary, but also have become programmatic. A brief selection of such pressures include the following: There are proposals to "reinvent the University" along engineering lines, as advocated at a recent conference at UCLA, proposing industrial ideas like total quality management and not tenure for faculty. There are criticisms of the Vannevar Bush report, Science, the endless frontier , from people who do not understand the origins of Bush's ideas. A recent conference on this topic at Columbia University represented science policy experts and not scientists-the two are not the same. There have been workshops on graduate work which emphasize training for industry, and wholly forget that a thesis is required for the Ph.D. Degree. There have been many reforms of the calculus, some tainted with substantial errors, and with irrelevant real world examples. These and related developments will be examined.

6. MacLane Biography of saunders maclane (19090BC) saunders maclane. Born 4 Aug 1909 in Taftville, Connecticut, USA http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/MacLane.html

Saunders MacLane Born: 4 Aug 1909 in Taftville, Connecticut, USA Click the picture above to see four larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Saunders MacLane graduated in 1926 from high school and, in that year, he entered the University of Yale. MacLane's school education had been interrupted when he was 15 years old for, at that time, his father had died. His father had been a Congregational Minister and, after his death, MacLane moved to Leominster to live with his grandfather who was also a Congregational Minister. MacLane graduated from Yale in 1930 and took up a fellowship at Chicago. At the University of Chicago he was influenced by Eliakim Moore . By this time E H Moore Moore had himself studied in Germany as a young man and had created in Chicago an eminent research school of mathematics based on his experiences of German mathematics at that time. Bernays Abbreviated Proofs in the Logical Calculus , with Weyl On returning to the United States, MacLane spent the session 1933/34 at Yale and then the following two years at Harvard. He left Harvard to take up a post of instructor at Cornell for session 1936/37, he spent the following session back at Chicago before accepting an appointment as an assistant professor at Harvard.

7. References For MacLane References for saunders maclane. Books I Kaplansky (ed.), saundersmaclane Selected Papers (New York Heidelberg, 1979). Articles http://www-gap.dcs.st-and.ac.uk/~history/References/MacLane.html

References for Saunders MacLane Books: I Kaplansky (ed.), Saunders MacLane : Selected Papers (New York - Heidelberg, 1979). Articles: S Eilenberg, Some remarks on the interface of algebra and geometry, in I Kaplansky (ed.), Saunders MacLane : Selected Papers (New York - Heidelberg, 1979), 525-526. I Kaplansky, The early work of Saunders MacLane on valuations and fields, in I Kaplansky (ed.), Saunders MacLane : Selected Papers (New York - Heidelberg, 1979), 519-524. M Kelly, Saunders MacLane and category theory, in I Kaplansky (ed.), Saunders MacLane : Selected Papers (New York - Heidelberg, 1979), 527-544. R Lyndon, Saunders MacLane as a shaper of mathematics and mathematicians, in I Kaplansky (ed.), Saunders MacLane : Selected Papers (New York - Heidelberg, 1979), 515-518. Notices of the American Mathematical Society A Putman, A biographical note, in I Kaplansky (ed.), Saunders MacLane : Selected Papers (New York - Heidelberg, 1979), ix-xii. Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR June 1997 School of Mathematics and Statistics University of St Andrews, Scotland

8. References For MacLane References for the biography of saunders maclane of algebra and geometry, in I Kaplansky (ed.), saunders maclane Selected Papers (New York Heidelberg, 1979), 525-526. http://www-history.mcs.st-and.ac.uk/References/MacLane.html

References for Saunders MacLane Books: I Kaplansky (ed.), Saunders MacLane : Selected Papers (New York - Heidelberg, 1979). Articles: S Eilenberg, Some remarks on the interface of algebra and geometry, in I Kaplansky (ed.), Saunders MacLane : Selected Papers (New York - Heidelberg, 1979), 525-526. I Kaplansky, The early work of Saunders MacLane on valuations and fields, in I Kaplansky (ed.), Saunders MacLane : Selected Papers (New York - Heidelberg, 1979), 519-524. M Kelly, Saunders MacLane and category theory, in I Kaplansky (ed.), Saunders MacLane : Selected Papers (New York - Heidelberg, 1979), 527-544. R Lyndon, Saunders MacLane as a shaper of mathematics and mathematicians, in I Kaplansky (ed.), Saunders MacLane : Selected Papers (New York - Heidelberg, 1979), 515-518. Notices of the American Mathematical Society A Putman, A biographical note, in I Kaplansky (ed.), Saunders MacLane : Selected Papers (New York - Heidelberg, 1979), ix-xii. Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR June 1997 School of Mathematics and Statistics University of St Andrews, Scotland

9. Editions Jacques Gabay - LAVOISIER : Traité élémentaire De Chimie Translate this page saunders maclane et Garrett BIRKHOFF. Corps par J. WEIL et J. HOCQUEMILLER Préfacede saunders maclane et Garrett Birkhoff Paris, Gauthier-Villars, 1972. http://www.gabay.com/sources/Liste_Fiche.asp?CV=103

10. MATHEMATICAL STRUCTURES RESEARCH Research topics include mathematical models and theories in the empirical sciences, models and theories Category Society Philosophy Philosophy of Mathematics...... maclane, saunders. Mathematics Form and Function. SpringerVerlag CambridgeUniversity Press,1986; maclane, saunders. Categories for http://www.mmsysgrp.com/mathstrc.htm

MATHEMATICAL STRUCTURES Research topics include mathematical models and theories in the empirical sciences, models and theories in mathematics, category theory, and the use of mathematical structures in theoretical computer science. Research Bibliography Mathematical Theories and Models Scientific Theories and Models Category Theory Theoretical Computer Science ... WWW Research Sites Mathematical Theories and Models Agazzi and Darvas. Philosophy of Mathematics Today. Kluwer Academic Publishers, 1997 Anglin and Lambek. The Heritage of Thales. Springer-Verlag, 1995 Akin, Ethan. The General Topology of Dynamical Systems. American Mathematical Society, 1993 Barwise, Jon. (ed) Handbook of Mathematical Logic. North-Holland,1977 Barwise, Jon. "Axioms for Abstract Model Theory" ,Annals of Mathematical Logic 7(1974) 221-265. Bell, John and Machover,Moshe. A Course in Mathematical Logic. North-Holland, 1977 Bridge, Jane. Beginning Model Theory. Clarendon Press, 1977 Burgess, John and Rosen, Gifeon. A Subject with No Object Oxford Press, 1997

11. Seminar By Saunders MacLane Current political pressures on mathematical research and education saunders maclane (University of Chicago) Thursday, October 17, Abelson 131, 2 p.m. http://www.cs.brandeis.edu/~mairson/CS-seminar/maclane-old.html

Current political pressures on mathematical research and education Saunders MacLane (University of Chicago) Thursday, October 17, Abelson 131 2 p.m. Until recently, budgetary constraints presented the chief difficulties for the support of mathematical research. But now deeper "policy" concerns and pressures for industrial relevance enter. There are stentorian calls to "reinvent" the university, as in a recent conference under this title, held at UCLA. The slogan is an engineering device, often propounded by individuals who do not understand the university traditions, with intent to make the university more like industry, complete with "total quality management." At the end of World War II, Vannevar Bush wrote Science, the Endless Frontier to record the varied ways in which science could help in peace as well as in war. Today, it has become the fashion to end the endless-usually in order to propose scientific initiative by mindless planning. A recent example is a conference on such endings, held at Columbia University in September 1996, attended by policy experts but not scientists, and in blissful ignorance of the effective wartime research at that university, "Workshops" are in fashion as a means of imposing policy changes. The NSF recently held such a shop on graduate education. It emphasized gimmicks and industrial internships, ignoring the fact that the Ph.D. involves a thesis presenting an original contribution to knowledge. Similar ignorance has been amply displayed by an earlier COSEPUP report on graduate education, chaired by Phillip Griffiths. A recent NRC workshop proposed to instruct all departments of mathematical sciences on "actions needed" to meet the so-called changing environment. This shop was notable for agitation for publicity of math, adjustments to ideas from industry, and subservience to Congress.

12. The Theory Of Everything maclane, saunders. Categories for the Working Mathematician.SpringerVerlag,1971; maclane, saunders and Birkhoff, Garrett. Algebra http://www.mmsysgrp.com/QIS/category.htm

Category Theory and Homological Algebra John C. Baez (University of California, Riverside): Categorification 'Categorification' is the process of finding category-theoretic analogs of set-theoretic concepts by replacing sets with categories, functions with functors, and equations between functions by natural isomorphisms between functors, which in turn should satisfy certain equations of their own, called `coherence laws'. Iterating this process requires a theory of `n-categories', algebraic structures having objects, morphisms between objects, 2-morphisms between morphisms and so on up to n-morphisms. After a brief introduction to n-categories and their relation to homotopy theory, we discuss algebraic structures that can be seen as iterated categorifications of the natural numbers and integers. John C. Baez (University of California, Riverside): From Finite Sets to Feynman Diagrams John C. Baez (University of California, Riverside): Higher-Dimensional Algebra and Planck-Scale Physics This is a nontechnical introduction to recent work on quantum gravity using ideas from higher-dimensional algebra. We argue that reconciling general relativity with the Standard Model requires a `background-free quantum theory with local degrees of freedom propagating causally'. We describe the insights provided by work on topological quantum field theories such as quantum gravity in 3-dimensional spacetime. These are background-free quantum theories lacking local degrees of freedom, so they only display some of the features we seek. However, they suggest a deep link between the concepts of `space' and `state', and similarly those of `spacetime' and `process', which we argue is to be expected in any background-free quantum theory. We sketch how higher-dimensional algebra provides the mathematical tools to make this link precise. Finally, we comment on attempts to formulate a theory of quantum gravity in 4-dimensional spacetime using `spin networks' and `spin foams'.

13. MacLane Portraits Portraits of saunders maclane saunders maclane. JOC/EFR August 2001 http://www-history.mcs.st-and.ac.uk/history/PictDisplay/MacLane.html

Saunders MacLane JOC/EFR August 2001 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/PictDisplay/MacLane.html

14. Pareigis: Advanced Algebra 73. New York, Heidelberg, Berlin Springer. (1980). maclane, saunders Categories for the working mathematician. http://www.mathematik.uni-muenchen.de/~pareigis/algebra_adv.html

B. Pareigis: Advanced Algebra Time: Tu. 11:15 - 13:00, Fr. 14:15 - 16:00 Room: HS E27 Problem sessions: Tu. 16:15 - 18:00 Room: HS E06 Contents: This course is an introduction to the major techniques used in algebra. It is to be considered as a basis for subsequent courses on quantum groups and noncommutative geometry. The main concepts that will be introduced and studied are Tensor products of vector spaces and modules, Algebras and coalgebras, Projective modules, Simple and semisimple rings and modules, Categories and functors, Morita theorems, Local rings and localization, Functors, limits, the Yoneda Lemma, Monoidal categories, Hopf algebras. (This course is obligatory for all those wishing to take more advanced courses and seminars in algebra during their second and higher semesters.) This course will be continued by the course Quantum Groups and Noncommutative Geometry planned for the summer term 2002. Lecture Notes: (will be updated in irregular intervalls) Prerequisites: Thorough knowledge of abstract linear algebra and the basic concepts of algebra, like groups, monoids, rings, algebras, and modules. Literature: Hungerford, Thomas W.:

15. References Of derivation of quantum logic. maclane, saunders (1990) Originality,Novelty and Fashion , in Proc. 8th Int. Congress on Systems and http://www.c3.lanl.gov/~joslyn/refs/refs_m.html

Cliff Joslyn , Letter: M References of Cliff Joslyn , Letter: M Date: Filter: Ma, Ming; Friedman, Menahem; and Kandel, Abraham: (1997) "A Note on Fuzzy Universal Approximator", Information Sciences MacColl, Ewan: (1965) Folk Songs and Ballads of Scotland , Oak Publications, New York, MacDonald, Steven W. and Grebogi, Celso: (1985) "Fractal Basin Boundaries", Physica , v. Prince , Penguin, MacKay, Donald M: (1969) Information, Mechanism, and Meaning , MIT Press, Cambridge, Mackey, G: (1963) Mathematical Foundations of Quantum Mechanics , Benjamin Publishers, New York, [ Aximoatic derivation of quantum logic. ] MacLane, Saunders: (1990) "Originality, Novelty and Fashion", in: Proc. 8th Int. Congress on Systems and Cybernetics [ Bogus intellectual fads, examples from fuzzy, algebra, category theory, and Nat. Academy of Sciences ] MacLane, Saunders and Birkhoff, G: (1979) Algebra , MacMillan, New York, [ Good non-abstract algebra text. ] Macphail, Euan M.: "Comparative Psychology of Intelligence", Behavioral and Brain Science MacPherson, PK: (1980)

16. Untitled (Mathematics in Science and Engineering ; Volume 68). maclane, saunders MA 160 http://www.gwdg.de/gwdg/standort/bibliothek/autko2.htm

[Top] [Prev] [Next] [Bottom] Maarssen, L. A. WA 153 Machine Oriented Higher Level Languages / W.L. Van der Poel; Maarssen, L. A. [Hrsg.]. - Amsterdam; London: North-Holland Publishing Company, 1974. - XE 50 Zur Anpassung virtueller Mensch-Rechnerschnittstellen an Benutzererfordernisse im Dialog - dargestellt am Beispiel von Hamburg, 1978. - XA 110 The Adaptation of Virtual Man-Computer Interfaces to User Requirements in Berlin; Heidelberg; New York: Springer, 1981. - (Lecture Notes in Computer Science ; Vol. 110) XE 104 Mensch-Rechner-Kommunikation - Herkunft und Chancen eines neuen Paradigmas - Hamburg, 1984. - XE 170 Hamburg, 1994. - MacCallum, Malcolm A.H. NC 104 Algebraic Computing with REDUCE Lecture Notes from the First Brazilian School on Computer Algebra / Malcolm A.H. MacCallum; Wright, Francis J. - Oxford: Clarendon Press, 1991. - (Oxford Science Publications) Macchia, Ilaria YY 958 Virtual Realities: Researches and Applications all over the World / Ilaria Macchia. -

17. Biography-center - Letter M gpe/drvmaclan.html; maclane, saunders www-history.mcs.st-and.ac.uk/~history/Mathematicians/maclane.html;Maclaurin, Colin www-history http://www.biography-center.com/m.html

Visit a random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish M 749 biographies www-history.mcs.st-and.ac.uk/~history/Mathematicians/Meray.html www-history.mcs.st-and.ac.uk/~history/Mathematicians/Mobius.html MacArthur, Douglas www.pbs.org/wgbh/pages/amex/macarthur/peopleevents/pandeAMEX106.html Macarthur, Elizabeth www.abc.net.au/btn/australians/macarthu.htm MacArthur, Mary P.H. www.pbs.org/wgbh/pages/amex/macarthur/peopleevents/pandeAMEX109.html Macaulay, Francis www-history.mcs.st-and.ac.uk/~history/Mathematicians/Macaulay.html Macaulay, Eunice www.nfb.ca/e/highlights/eunice_macaulay.html MacBride, Seán www.nobel.se/peace/laureates/1974/macbride-cv.html Macció, Rómulo www.proa.org.ar/exhibicion/maccio/exhibi-fr.html MacCullagh, James www-history.mcs.st-and.ac.uk/~history/Mathematicians/MacCullagh.html MacCurtain, Margaret

18. BIBCYT Autor: Alejandría BE 4.7.1.7r Translate this page Autor maclane, saunders, (Comienzo). Sólo un registro cumplióla condición especificada en la base de información BIBCYT. http://bibcyt.ucla.edu.ve/cgi-win/be_alex.exe?Autor=Maclane, Saunders&Nombrebd=B

19. TOPCOM,Samuel Eilenberg By Saunders Mac Lane Samuel Eilenberg (19141998). saunders maclane. Department of MathematicsThe University of Chicago Memorial from Volume 3, 1, of TopCom http://at.yorku.ca/t/o/p/c/52.htm

Topology Atlas Samuel Eilenberg (1914-1998) Saunders MacLane Department of Mathematics The University of Chicago Memorial from Volume 3, #1 , of TopCom Samuel Eilenberg, who made decisive contributions to topology and other areas of mathematics, died on Friday, Feb. 6 in New York City. He had been a leading member of the department of mathematics at Columbia University since 1947. His mathematical books, ideas and papers had a major influence. Eilenberg was born in Poland in 1914. At the University of Warsaw he was a student of Borsuk in the active school of Polish Topology. His thesis, concerned with the topology of the plane, was published in Fundamenta Mathematica in 1936. Its results were well received both in Poland and in the USA. In 1938 he published there another influential paper on the action of the fundamental group on the higher homotopy groups of a space. Algebra was not foreign to his topology! Early in 1939 Sammy's father told him "ammy, it doesn't look good here in Poland, Get out." He did, arriving in New York on April 23, 1939, and going at once to Princeton. At that University, Oswald Veblen and Solomon Lefschetz efficiently welcomed refugee mathematicians and found them suitable positions at American Universities. Sammy's work in topology was well known, so a position for him was found at the University of Michigan. There Ray Wilder had an active group of Topologists, including Norman Steenrod, then a recent Princeton Ph.D. Sammy immediately fitted in, did collaborative research (for example, with Wilder, O.G. Harrold and Dean Montgomery). His 1940 paper in the Annals formulated and codified the ideas of the "obstructions" recently introduced by Hassler Whitney. He also argued with Lefschetz. Finding the Lefschetz book obscure in its treatment of singular homology he provided an elegant and definitive treatment in the Annals (1949).

20. TOPCOM, Volume 3, #1 Memorial for Samuel Eilenberg by saunders maclane; The Discovery Learning Project; Memorialfor J. Roberts. 5.MEMORIAL FOR SAMUEL EILENBERG. by saunders maclane http://at.yorku.ca/t/o/p/c/47.htm

Topology Atlas Document # topc-47.htm TOPOLOGICAL COMMENTARY Volume 3, #1, March 15, 1998 edited by Melvin Henriksen commentary@mail.mathatlas.yorku.ca I continue to invite commentary on any article in any issue of TopCom or on any topic of general interest to topologists, including news about topologists or topological activity. TABLE OF CONTENTS Editorial Remarks by Melvin Henriksen Leonard Gillman; an Interview (Part II) by Melvin Henriksen The Catalog of the Hausdorff Edition Memorial for J. Roberts by Richard E. Hodel and Jerry E. Vaughan Memorial for Samuel Eilenberg by Saunders MacLane The Discovery Learning Project More Conference Photos A Book Review by William Goldman Qualifying Exams in Topology by Scott Williams Federal Support for Basic Research in the Mathematical Sciences Letter to the Editor Mystery Topologist 1. EDITORIAL REMARKS by Melvin Henriksen In this editorial, the editor argues for keeping papers reasonably self-contained in mathematical journals. For Whom Are We Writing Papers? 2. LEONARD GILLMAN; AN INTERVIEW by Melvin Henriksen Leonard Gillman has a long and distinguished career as a concert pianist who earned a diploma in piano from the Julliard School of Music, an applied mathematician working for the United States Navy during the second world war, a set-theorist and topologist who wrote many research papers as well as being a co-author with Meyer Jerison of the definitive text "Rings of Continuous Functions" that set the tone for research in this area for the next quarter century, the builder of an excellent mathematics department at the University of Rochester, chairman of the mathematics department at the University of Texas, Secretary-Treasurer of the MAA for many years, and finally its President, author of many excellent expository articles for the American Mathematical Monthly as well as a monograph on how to write mathematics. He consented to summarize his career in a lengthy interview. The first part of the interview has appeared in

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