DOCSLIB.ORG

Edwin Henry Spanier 1921

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Edwin Henry Spanier 1921 UC Berkeley UC Berkeley Previously Published Works Title Edwin Henry Spanier (1921-1996) Permalink https://escholarship.org/uc/item/1cv2r77d Journal Notices of the American Mathematical Society, 45(June-July) ISSN 1088-9477 Author Hirsch, MW Publication Date 1998 Peer reviewed eScholarship.org Powered by the California Digital Library University of California comm-spanier.qxp 6/2/98 2:32 PM Page 704 Edwin Henry Spanier (1921–1996) Morris W. Hirsch Edwin Henry a Miller Research Fellow at Berkeley in 1961–62. His Spanier died visiting appointments include positions in Ar- of cancer in gentina, Brazil, Canada, Chile, France, Germany, Scottsdale, Italy, Spain, and Switzerland, and at UCSD and Arizona, on UCLA. October 11, Spanier was appointed professor of math- 1996. Born in ematics at Berkeley in 1959 at the beginning of a Washington, period of rapid expansion of the mathematics de- D.C., on Au- partment. An internationally recognized authority gust 8, 1921, in the swiftly developing field of topology, he at- he was grad- tracted first-class mathematicians as visitors and uated from new faculty members. He played a major role in the Univer- organizing new programs in geometry and topol- sity of Min- ogy, subjects in which Berkeley soon achieved pre- nesota in eminence. He served several times as vice chair and 1941 and acting chair of the department and directed four- then spent teen doctoral dissertations at Berkeley in addition three years to three at Chicago. In 1991 he became professor as a math- emeritus. ematician in Photograph courtesy of Jerome Spanier. the U. S. From his doctoral dissertation through the mid- Edwin Spanier Army Signal 1960s, and again in the last fifteen years of his life, Corps. He re- Spanier’s research was concentrated in algebraic ceived his doctorate in mathematics in 1947 from topology. This subject, founded a century ago by the University of Michigan under the direction of Henri Poincaré to aid in the qualitative analysis of Norman Steenrod. After a postdoctoral fellowship differential equations, was little known to most at the Institute for Advanced Study in Princeton, mathematicians when Spanier started his career. New Jersey, he joined the faculty at the University His dissertation supervisor, Norman Steenrod, to- of Chicago in 1948. He was a Guggenheim Fellow gether with Samuel Eilenberg, had just set out sim- in Paris in the academic year 1952–53, a member ple and powerful axioms for the main tool, ho- of the Institute for Advanced Study in 1958–59, and mology theory; this cleared up much of the confusion endemic in a subject that combines Morris W. Hirsch is professor of mathematics at the Uni- geometry, algebra, and analysis. Spanier was at versity of California at Berkeley. His e-mail address is the forefront of the explosive development of al- [email protected]. He received his Ph.D. in gebraic topology during the next decade. The im- 1958 under the supervision of Ed Spanier. portance of his work was quickly recognized; in 704 NOTICES OF THE AMS VOLUME 45, NUMBER 6 comm-spanier.qxp 6/2/98 2:32 PM Page 705 1950 he gave an Invited Address to the Interna- languages from this viewpoint and obtained a tional Congress of Mathematicians at Harvard. number of impressive results. In another approach, Spanier’s interest in topology continued through- they investigated families of languages generated out his career. Both his first paper in 1948 and one from a single grammar, machine, or structure using of his last, published in 1992, dealt with the Eilen- simple substitution operations. berg-Steenrod axioms. The importance of their work can be seen from Spanier’s first major contribution in topology the review1 of a 1983 article [2] by Spanier, S. Gins- was the theory of cohomotopy groups, which gave burg, and J. Goldstine, “On the equality of gram- an algebraic classification of matical families”. The review maps of polyhedra into states: “This paper presents spheres [4]. Together with Ph.D. Students of Edwin Spanier a major and difficult decid- S. S. Chern he pioneered the Clair Miller (1951) ability result in grammar form analysis of the homology Morris W. Hirsch (1958) theory. It is proved that, given groups of fibre spaces [1]. Elon Lima (1958) two arbitrary context-free In a series of papers with Alphonse Thomas Vasquez (1962) grammar forms, it is decid- the English topologist J. H. C. able whether or not the fam- Robert Emmett Williamson Jr. (1963) Whitehead, Spanier devel- ily of one is contained in the oped the new algebraic tool Samuel Feder (1964) other. This leads immediately of duality in homotopy the- John Ucci (1964) to the decidability of the ory [5]. In 1966 his long- Benson Brown (1965) equality of two context-free awaited book Algebraic Jose Alves (1965) grammar forms.” This result Topology [3] was published. is based on an earlier paper, David Kraines (1965) The first comprehensive “A prime decomposition the- modern treatment of the Denis Sjerve (1967) orem for grammatical fami- subject, it is still a funda- Jon Goldstine (1970) lies”, in which the same au- mental source. John Paul Alexander (1971) thors obtained a prime In all, Spanier published Mark Luker (1975) decomposition for formal lan- more than forty papers in Kenneth Klingenstein (1975) guage families, closely analo- gous in form to the decom- algebraic topology, con- Gerald Eisman (1977) tributing to most of the position of whole numbers Richard B. Hull (1980) major research areas in the into prime factors. field, including cohomology Spanier’s publications, as operations, obstruction the- were his lectures, are charac- ory, homotopy theory, imbeddability of polyhe- terized by unusual lucidity and precision and an dra in Euclidean spaces, and topology of function even rarer quality of naturalness and simplicity. No spaces. Many of his results are now standard tools matter how complex the subject, at the end the in all fields that utilize global geometrical rea- reader feels the theorems are the right ones, the soning. These include not only various subjects in hypotheses natural, and the methods as simple as pure mathematics, but also diverse areas in applied possible. mathematics, including computer science, math- Ed Spanier will be remembered as a gifted re- ematical physics, economic models, and game the- searcher, an inspiring teacher, an able adminis- ory. Interestingly, one of Spanier’s theories, now trator, and as a modest, friendly, wise, and help- called Alexander-Spanier homology, is currently ful colleague. being applied to analyze differential equations— References a return to Poincaré’s original use of algebraic topology. [1] S. S. CHERN and E. SPANIER, The homology structure of sphere bundles, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), In 1961 Spanier began a fruitful collaboration 248–255. with Seymour Ginsburg of the University of South- [2] S. GINSBURG, J. GOLDSTINE, and E. SPANIER, On the equal- ern California, resulting in more than a score of pa- ity of grammatical families, J. Comput. System Sci. pers on the structure of formal languages. This sub- 26 (1983), 171–196. ject is of importance in several mathematical [3] E. SPANIER, Algebraic topology, McGraw-Hill, New disciplines, including theoretical computer sci- York, 1966. ence and foundations of mathematics. Recently it [4] E. SPANIER, Borsuk’s cohomotopy groups, Ann. Math. 50 (1949), 203–245. has been applied in dynamical systems theory. [5] E. SPANIER AND J. H. C. WHITEHEAD, Duality in homotopy Their work was driven by an operational perspec- theory, Mathematika 2 (1955), 56–80. tive on formal languages: What formal operations on these objects are reasonable, and what are their effects? This view led them to abstract and study families of languages closed under specific oper- ations. They also investigated abstract families of 1Mathematical Reviews 85g:68037. JUNE/JULY 1998 NOTICES OF THE AMS 705.
Load more

Recommended publications
  • The Arf-Kervaire Invariant Problem in Algebraic Topology: Introduction
    THE ARF-KERVAIRE INVARIANT PROBLEM IN ALGEBRAIC TOPOLOGY: INTRODUCTION MICHAEL A. HILL, MICHAEL J. HOPKINS, AND DOUGLAS C. RAVENEL ABSTRACT. This paper gives the history and background of one of the oldest problems in algebraic topology, along with a short summary of our solution to it and a description of some of the tools we use. More details of the proof are provided in our second paper in this volume, The Arf-Kervaire invariant problem in algebraic topology: Sketch of the proof. A rigorous account can be found in our preprint The non-existence of elements of Kervaire invariant one on the arXiv and on the third author’s home page. The latter also has numerous links to related papers and talks we have given on the subject since announcing our result in April, 2009. CONTENTS 1. Background and history 3 1.1. Pontryagin’s early work on homotopy groups of spheres 3 1.2. Our main result 8 1.3. The manifold formulation 8 1.4. The unstable formulation 12 1.5. Questions raised by our theorem 14 2. Our strategy 14 2.1. Ingredients of the proof 14 2.2. The spectrum Ω 15 2.3. How we construct Ω 15 3. Some classical algebraic topology. 15 3.1. Fibrations 15 3.2. Cofibrations 18 3.3. Eilenberg-Mac Lane spaces and cohomology operations 18 3.4. The Steenrod algebra. 19 3.5. Milnor’s formulation 20 3.6. Serre’s method of computing homotopy groups 21 3.7. The Adams spectral sequence 21 4. Spectra and equivariant spectra 23 4.1.
    [Show full text]
  • Combinatorial Topology and Applications to Quantum Field Theory
    Combinatorial Topology and Applications to Quantum Field Theory by Ryan George Thorngren A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Mathematics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Vivek Shende, Chair Professor Ian Agol Professor Constantin Teleman Professor Joel Moore Fall 2018 Abstract Combinatorial Topology and Applications to Quantum Field Theory by Ryan George Thorngren Doctor of Philosophy in Mathematics University of California, Berkeley Professor Vivek Shende, Chair Topology has become increasingly important in the study of many-body quantum mechanics, in both high energy and condensed matter applications. While the importance of smooth topology has long been appreciated in this context, especially with the rise of index theory, torsion phenomena and dis- crete group symmetries are relatively new directions. In this thesis, I collect some mathematical results and conjectures that I have encountered in the exploration of these new topics. I also give an introduction to some quantum field theory topics I hope will be accessible to topologists. 1 To my loving parents, kind friends, and patient teachers. i Contents I Discrete Topology Toolbox1 1 Basics4 1.1 Discrete Spaces..........................4 1.1.1 Cellular Maps and Cellular Approximation.......6 1.1.2 Triangulations and Barycentric Subdivision......6 1.1.3 PL-Manifolds and Combinatorial Duality........8 1.1.4 Discrete Morse Flows...................9 1.2 Chains, Cycles, Cochains, Cocycles............... 13 1.2.1 Chains, Cycles, and Homology.............. 13 1.2.2 Pushforward of Chains.................. 15 1.2.3 Cochains, Cocycles, and Cohomology.........
    [Show full text]
  • Groups St. Andrews 2009 in Bath. Volume 1
    This page intentionally left blank LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES Managing Editor: Professor M. Reid, Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom The titles below are available from booksellers, or from Cambridge University Press at www.cambridge.org/mathematics 234 Introduction to subfactors, V. JONES & V.S. SUNDER 235 Number theory: Seminaire´ de theorie´ des nombres de Paris 1993–94, S. DAVID (ed) 236 The James forest, H. FETTER & B. GAMBOA DE BUEN 237 Sieve methods, exponential sums, and their applications in number theory, G.R.H. GREAVES et al (eds) 238 Representation theory and algebraic geometry, A. MARTSINKOVSKY & G. TODOROV (eds) 240 Stable groups, F.O. WAGNER 241 Surveys in combinatorics, 1997, R.A. BAILEY (ed) 242 Geometric Galois actions I, L. SCHNEPS & P. LOCHAK (eds) 243 Geometric Galois actions II, L. SCHNEPS & P. LOCHAK (eds) 244 Model theory of groups and automorphism groups, D.M. EVANS (ed) 245 Geometry, combinatorial designs and related structures, J.W.P. HIRSCHFELD et al (eds) 246 p-Automorphisms of finite p-groups, E.I. KHUKHRO 247 Analytic number theory, Y. MOTOHASHI (ed) 248 Tame topology and O-minimal structures, L. VAN DEN DRIES 249 The atlas of finite groups - Ten years on, R.T. CURTIS & R.A. WILSON (eds) 250 Characters and blocks of finite groups, G. NAVARRO 251 Grobner¨ bases and applications, B. BUCHBERGER & F. WINKLER (eds) 252 Geometry and cohomology in group theory, P.H. KROPHOLLER, G.A. NIBLO & R. STOHR¨ (eds) 253 The q-Schur algebra, S. DONKIN 254 Galois representations in arithmetic algebraic geometry, A.J.
    [Show full text]
  • NORMAN EARL STEENROD April 22, 1910-October 14, 1971
    NATIONAL ACADEMY OF SCIENCES N ORMAN EARL S TEENROD 1910—1971 A Biographical Memoir by G E O R G E W . W HITEHEAD Any opinions expressed in this memoir are those of the author(s) and do not necessarily reflect the views of the National Academy of Sciences. Biographical Memoir COPYRIGHT 1985 NATIONAL ACADEMY OF SCIENCES WASHINGTON D.C. NORMAN EARL STEENROD April 22, 1910-October 14, 1971 BY GEORGE W. WHITEHEAD HE SUBJECT OF ALGEBRAIC TOPOLOGY has undergone a Tspectacular development in the years since World War II. From a position of minor importance, as compared with the traditional areas of analysis and algebra, its concepts and methods have come to exert a profound influence over the older fields, and it is now commonplace that a mathematical problem is "solved" by reducing it to a homotopy-theoretic one. And, to a great extent, the success of this development can be attributed to the influence of Norman Steenrod. Norman Earl Steenrod was born in Dayton, Ohio, April 22, 1910, the youngest of three surviving children of Earl Lindsay Steenrod and his wife Sarah (nee Rutledge). The Steenrods, reputedly of Norwegian origin, came to this country by way of Holland before the Revolutionary War, and Norman's great-great-great-grandfather, Cornelius Steenrod, raised a company of soldiers who fought in that war. Both his parents were teachers—his mother for two years before her marriage, his father for some forty years as a high school instructor in manual training and mechanical drawing (and occasionally other subjects). Neither parent had any special interest in mathematics, though Earl Steen- rod had a keen interest in astronomy, which he communicat- ed to his son.
    [Show full text]
  • Graduate Texts in Mathematics 61
    Graduate Texts in Mathematics 61 Editorial Board J.H. Ewing F.w. Gehring P.R. Halmos Graduate Texts in Mathematics 1 TAKEUTl/ZARING. Introduction to Axiomatic Set Theory. 2nd. ed. 2 OXTOBY. Measure and Category. 2nd ed. 3 SCHAEFFER. Topological Vector Spaces. 4 HILTON/STAMMBACH. A Course in Homological Algebra. 5 MAC LANE. Categories for the Working Mathematician. 6 HUGHES/PIPER. Projective Planes. 7 SERRE. A Course in Arithmetic. 8 TAKEUTl/ZARING. Axiometic Set Theory. 9 HUMPHREYS. Introduction to Lie Algebras and Representation Theory. 10 COHEN. A Course in Simple Homotopy Theory. 11 CONWAY. Functions of One Complex Variable. 2nd ed. 12 BEALS. Advanced Mathematical Analysis. 13 ANOERSON!FULLER. Rings and Categories of Modules. 14 GOLUBITSKY GUILEMIN. Stable Mappings and Their Singularities. 15 BERBERIAN. Lectures in Functional Analysis and Operator Theory. 16 WINTER. The Structure of Fields. 17 ROSENBLATT. Random Processes. 2nd ed. 18 HALMos. Measure Theory. 19 HALMos. A Hilbert Space Problem Book. 2nd ed., revised. 20 HUSEMOLLER. Fibre Bundles 2nd ed. 21 HUMPHREYS. Linear Algebraic Groups. 22 BARNES!MACK. An Algebraic Introduction to Mathematical Logic. 23 GREUB. Linear Algebra. 4th ed. 24 HOLMES. Geometric Functional Analysis and its Applications. 25 HEWITT/STROMBERG. Real and Abstract Analysis. 26 MANES. Algebraic Theories. 27 KELLEY. General Topology. 28 ZARISKI/SAMUEL. Commutative Algebra. Vol. I. 29 ZARISKI/SAMUEL. Commutative Algebra. Vol. II. 30 JACOBSON. Lectures in Abstract Algebra I. Basic Concepts. 31 JACOBSON. Lectures in Abstract Algebra II. Linear Algebra. 32 JACOBSON. Lectures in Abstract Algebra Ill. Theory of Fields and Galois Theory. 33 HIRSCH. Differential Topology. 34 SPITZER. Principles of Random Walk.
    [Show full text]
  • Algebraic Topology I: Lecture 11 the Eilenberg Steenrod Axioms and The
    11. THE EILENBERG STEENROD AXIOMS AND THE LOCALITY PRINCIPLE 25 o // / 11 The Eilenberg Steenrod axioms and the locality principle Before we proceed to prove the excision theorem, let’s review the properties ofsingular homology as we have developed them. They are captured by a set of axioms, due to Sammy Eilenberg and Norman Steenrod [5]. Definition 11.1. A homology theory (on Top) is: • a sequence of functors hn : Top2 ! Ab for all n 2 Z and • a sequence of natural transformations @ : hn(X; A) ! hn−1(A; ?) such that: • If f0; f1 :(X; A) ! (Y; B) are homotopic, then f0∗ = f1∗ : hn(X; A) ! hn(Y; B). • Excisions induce isomorphisms. • For any pair (X; A), the sequence @ @ ···! hq+1(X; A) −! hq(A) ! hq(X) ! hq(X; A) −!· · · is exact, where we have written hq(X) for hq(X; ?). 26 CHAPTER 1. SINGULAR HOMOLOGY • (The dimension axiom): The group hn(∗) is nonzero only for n = 0. We add the following “Milnor axiom” [8] to our definition. To state it, let I be a set and suppose ` that for each i 2 I we have a space Xi. We can form their disjoint union or coproduct Xi. The ` ` inclusion maps Xi ! Xi induce maps hn(Xi) ! hn( Xi), and these in turn induce a map from the direct sum, or coproduct in Ab: ! M a α : hn(Xi) ! hn Xi : i2I i2I Then: • The map α is an isomorphism for all n. Ordinary singular homology satisfies these, with h0(∗) = Z. We will soon add “coefficents” to homology, producing a homology theory whose value on a point is any prescribed abelian group.
    [Show full text]
  • Fifty Years of Homotopy Theory
    BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 8, Number 1, January 1983 FIFTY YEARS OF HOMOTOPY THEORY BY GEORGE W. WHITEHEAD The subject of homotopy theory may be said to have begun in 1930 with the discovery of the Hopf map. Since I began to work under Norman Steenrod as a graduate student at Chicago in 1939 and received my Ph.D. in 1941, I have been active in the field for all but the first ten years of its existence. Thus the present account of the development of the subject is based, to a large extent, on my own recollections. I have divided my discussion into two parts, the first covering the period from 1930 to about 1960 and the second from 1960 to the present. Each part is accompanied by a diagram showing the connections among the results dis­ cussed, and one reason for the twofold division is the complication of the diagram that would result were we to attempt to merge the two eras into one. The dating given in this paper reflects, not the publication dates of the papers involved, but, as nearly as I can determine them, the actual dates of discovery. In many cases, this is based on my own memory; this failing, I have used the date of the earliest announcement in print of the result (for example, as the abstract of a paper presented to the American Mathematical Society or as a note in the Comptes Rendus or the Proceedings of the National Academy). Failing these, I have used the date of submission of the paper, whenever available.
    [Show full text]
  • Introduction to 3-Manifolds
    Introduction to 3-Manifolds Jennifer Schultens Graduate Studies in Mathematics Volume 151 American Mathematical Society https://doi.org/10.1090//gsm/151 Introduction to 3-Manifolds Jennifer Schultens Graduate Studies in Mathematics Volume 151 American Mathematical Society Providence, Rhode Island EDITORIAL COMMITTEE David Cox (Chair) Daniel S. Freed Rafe Mazzeo Gigliola Staffilani 2010 Mathematics Subject Classification. Primary 57N05, 57N10, 57N16, 57N40, 57N50, 57N75, 57Q15, 57Q25, 57Q40, 57Q45. For additional information and updates on this book, visit www.ams.org/bookpages/gsm-151 Library of Congress Cataloging-in-Publication Data Schultens, Jennifer, 1965– Introduction to 3-manifolds / Jennifer Schultens. pages cm — (Graduate studies in mathematics ; v. 151) Includes bibliographical references and index. ISBN 978-1-4704-1020-9 (alk. paper) 1. Topological manifolds. 2. Manifolds (Mathematics) I. Title. II. Title: Introduction to three-manifolds. QA613.2.S35 2014 514.34—dc23 2013046541 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294 USA. Requests can also be made by e-mail to [email protected]. c 2014 by the author.
    [Show full text]
  • Samuel Eilenberg and Categories
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Journal of Pure and Applied Algebra 168 (2002) 127–131 www.elsevier.com/locate/jpaa Samuel Eilenberg and Categories Saunders Mac Lane University of Chicago, 5734 University Ave. Chicago, IL 60637-1514, USA Received 1 October 1999; accepted 4 May 2001 Eilenberg’s wide understanding of mathematics was a decisive element in the origin and in the development of category theory. He was born in Poland in 1913 and learned mathematics in the very active school of topology in Poland, where he studied with K. Borsuk and with C. Kuratowski; there he wrote an important paper on the topology of the plane and, with Borsuk, studied the homology of special spaces such as the solenoids (to appear also below). Because of the looming political troubles, he left Poland and came to the United States, arriving in Princeton on April 23, 1939. In the mathematics department at Princeton, Oswald Veblen and Soloman Lefschetz welcomed many mathematical refugees from Europe and found them suitable positions in the United States. This e;ective work made a major contribution to the development of American mathematics. In the case of Sammy, his work in topology was well known so they found for hima junior position at the University of Michigan, where Raymond Wilder, Norman Steenrod and others encouraged research in topology. There Sammy prospered. At this period, the uses of algebra in topology were expanding. In 1930, Emmy Noether had emphasized the idea that homology was not just about Betti numbers, but about abelian groups (homology); the Betti numbers were just invariants of those homology groups.
    [Show full text]
  • Daniel M. Kan (1927–2013)
    DANIEL M. KAN (1927{2013) CLARK BARWICK, MICHAEL HOPKINS, HAYNES MILLER, AND IEKE MOERDIJK 1. Life In Holland. Daniel (or Daan in Dutch) Marinus Kan was born on August 4, 1927, and grew up as the only child in a liberal Jewish fam- ily in the southern quarter of Amsterdam, where his father worked as a lawyer. In 1939 he entered the Barlaeus Gymnasium, a secondary school in the center of Amsterdam, then and to this day one of the best schools in Amsterdam. He was only able to stay there for two years, because after the school year 1940/41, under German occupation, Jew- ish children were no longer allowed at that school. Instead, he went to the Jewish Lyceum (Joods lyceum). In the summer of 1943 a very difficult time for Kan and his family began. Together with his parents, he was picked up and sent to Westerbork, a transition camp near the eastern Dutch border. They stayed there for half a year, and were next sent to Bergen-Belsen where they remained for fifteen months. Both of his parents died of typhus soon after liberation. Dan himself barely survived, and he stayed in Germany for another three months to recover. In the summer of 1945 Kan returned to Amsterdam, where he entered the last year of high school at the Barleaus Gymnasium. He was inter- ested in mathematics, but the prospect of becoming a school teacher or having a job in an insurance firm did not appeal to him. It was the Dutch topologist L.E.J.
    [Show full text]
  • Etale Cohomology Princeton Mathematical Series
    Etale Cohomology Princeton Mathematical Series Editors: Luis A. Cakearelli, John N. M a th f.r , a n d E lia s M. S te in 1. The Classical Groups by Hermann Weyl 3. An Introduction to Differential Geometry by Luther Pfahler Eisenhart 4. Dimension Theory by W. Hurewicz and H. Wallman 8. Theory of Lie Groups: I by C. Chevalley 9. Mathematical Methods of Statistics by Harald Cramer 10. Several Com plex V ariables by S. Bochner and W. T. Martin 11. Introduction to Topology by S. Lefschetz 12. Algebraic Geometry and Topology edited by R. H. Fox, D. C. Spencer, and A. IV. Tucker 14. The Topology o f Fibre B undles by Norman Steenrod 15. Foundations o f A lgebraic T opology by Samuel Eilenberg and Norman Steenrod 16. Functionals of Finite Riemann Surfaces by Menahem Schijfer and Donald C. Spencer 17. Introduction to Mathematical Logic, Vol. I by Alonzo Church 19. H om ological A lgebra by H. Cartan and S. Eilenberg 20. The Convolution Transform by 1.1. Hirschman and D. V. Widder 21. Geometric Integration Theory by H. Whitney 22. Qualitative Theory of Differential Equations by V. V. Nemytskii and V. V. Stepanov 23. Topological Analysis by Gordon T. Whyburn (revised 1964) 24. Analytic Functions by Ahlfors, Behnke, Bers, Grauert etal. 25. Continuous Geometry by John von Neumann 26. Riemann Surfaces by L. Ahlfors and L. Sario 27. Differential and Combinatorial Topology edited by S. S. Cairns 28. Convex Analysis by R. T. Rockafellar 29. Global Analysis edited by D. C. Spencer and S.
    [Show full text]
  • A Century in Books:Princeton University Press 1905-2005 Is Published by Princeton University Press and Copyrighted, © 2005, by Princeton University Press
    COPYRIGHT NOTICE: A Century in Books:Princeton University Press 1905-2005 is published by Princeton University Press and copyrighted, © 2005, by Princeton University Press. All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher, except for reading and browsing via the World Wide Web. Users are not permitted to mount this file on any network servers. For COURSE PACK and other PERMISSIONS, refer to entry on previous page. For more information, send e-mail to [email protected] ACentury in Books Princeton University Press 1905–2005 princeton university press princeton and oxford Copyright © by Princeton University Press Daniel Kevles essay copyright © by Daniel Kevles Requests for permission to reproduce material from this work should be sent to Permissions, Princeton University Press Published by Princeton University Press, William Street, Princeton, New Jersey, In the United Kingdom: Princeton University Press, Market Place, Woodstock, Oxfordshire OX SY All Rights Reserved ISBN: ---X Printed on acid-free paper. pup.princeton.edu Printed in the United States of America Contents Chronological List of Books vii Introduction xiii Walter Lippincott books, 1920–1943 1 Fragments of Modernity 13 Michael Wood books, 1943–1950 19 P. J. Conkwright and Book Design 33 books, 1950–1955 37 History, Politics, and Culture 43 Anthony Grafton books, 1956–1963 51 Economics at the Center of the Mathematical Universe 65 Sylvia Nasar books, 1963–1974 71 Bollingen Series, 1943–2002 85 books, 1975–1987 91 Albert Einstein: Relativity, War, and Fame 115 Daniel J.
    [Show full text]