Juilliard Graduate School: Diploma in piano 1938.
Columbia University: BS in mathematics 1942, MA 1945, PhD 1953; PhD dissertation, On Intervals of Ordered Sets, Annals of Mathematics 56 (1952), 440--459.
Columbia University, Assistant and Lecturer, 1941--43.
Tufts College 1943--1945 and MIT 1945--52, Naval operations analyst.
Purdue University, Instructor 1952--53, Assistant Professor 1953--56, Associate Professor 1956--60.
University of Rochester, Professor 1960--1969 (chairman).
University of Texas at Austin, Professor 1969--87 (chairman 1969--73), Professor Emeritus 1987--.
30+ articles, primarily in set theory and topology, most of them in Annals of Mathematics, Bull. Amer. Math. Soc., Proc. Amer. Math. Soc., Trans. Amer. Math. Soc, Fundamenta Mathematicae, Michigan Math. J., Illinois Math. J., or Comptes Rendus Acad. Sci. Paris; the others in symposium proceedings or various smaller journals.
About 200 reviews in Mathematical Reviews (AMS) (1954--74) and several in American Mathematical Monthly (MAA) (1974--).
BookletsMathematical Analysis of Ordinary and Deviated Pursuit Curves (declassified), Special Devices Section, Training Division, Bureau of Aeronautics, Navy Department, with Harry H. Goode, 264 pp. 1944.Rings of Continuous Functions (a graduate text), with Meyer Jerison, Van Nostrand 1960, Springer 1976, ix + 300 pp. Rings of Quotients of Rings of Functions (a research monograph), with N. J. Fine and J. Lambek, McGill University Press, 1966, v + 97 pp. Calculus, (an undergraduate text), with Robert H. McDowell, Norton 1973, 674 pp., 1978, xiv + 899 pp. Czech translation Matematicka Analyze, Prague, 2nd edition 1983, 630 pp.
You'll Need Math, addressed to high school and junior high school students, Math. Assoc. Amer. 1967, 16 pp. Writing Mathematics Well, addressed to professionals, Math. Assoc. Amer. 1987, ix + 49 pp.
Memberships
Fellowships and grantsAmer. Math. Soc. Summer Institute in Topology, Madison WI, 1955 Institute for Advanced Study, Princeton NJ, 1958--60.
PrizesFellow, Juilliard Graduate School (piano), 1933--38. Fellow, Carnegie Corporation (Mathematical Statistics), 1942--43. Fellow, Guggenhiem Memorial Foundation (Mathematics), 1958--59. (silver anniversary of Juilliard) Fellow, National Science Foundation (Mathematics, Senior Post--Doctoral), 1959--60. National Science Foundation Research Grants, 1953--69 (continuously).
Invited addresses at international conferences.Lester R. Ford Award, Mathematical Association of America, 1994, for the article An Axiomatic Approach to the Integral. Amer. Math. Monthly, 100 (1993), 16--25. Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to Mathematics (1999)
ListingsSymposium on General Topology and Its Relations to Modern Analysis and Algebra, Czechoslovak Academy of Sciences, Prague 1961, 1966. Colloquium, Polish Academy of Sciences, Warsaw 1961, 1966. Covegno sugli Anelli di Funzioni Continue, Istituto Nazionale di Alta Matematica, Rome, 1973.
American Men and Women in Science, 1954--. Who's Who in America 1963--. Who's Who in the World 1980--
Mathematical Association of AmericaRegional Institute in Topology, University of Rochester, Summer 1962 (Director). Committee to Monitor Problems in Communication, 1972--77. (Chairman, 1975--77). Committee on Post-Doctoral Fellowships, 1974--77. Committee on Publication Policy, 1977--78. Committee on Professional Ethics, 1982--84. Associate Secretary 1969--71
Committee on the Undergraduate Program in Mathematics (CUPM), 1965--68. CUPM Panel on Pre-Graduate Training, 1965--68. CUPM Panel on College Teacher Preparation, 1966--68 (Chair). Board of Governors, 1973--95. Committee on Publications, 1973--87. Staff and Services Committee, 1973--87 (Chairman). Program Committees for six national meetings (chair of four), 1965--95. Committee on Minority Participation in Mathematics since its inception in 1989. Treasurer 1973--86. President-Elect 1986--87, President 1987--89, Past-President 1989--90.
Industrial
DeFlorez Engineering Co. (for Texaco), 1947--51. MELPAR, inc. (For Navy Dept.), 1951--52. Willow Run Research Center (for Navy Dept.), 1951--52. W. Henschel Engineering Consultants (for New Jersey Highway Dept.), 1968.
Wesleyan University, Outside Examiner, College of Quantitative Studies, 1963. Franklin and Marshall College, Evaluation Committee for the Mathematics Dept., 1965. National Science Foundation, site visitor, UC San Diego, 1965--66. W. W. Norton Co. (Publishers), Editorial Advisor, 1967--80. Harvard University, Outside Advisory Committee on a Candidate for Mathematics and Logic without Limit of Time, 1968. Woodrow Wilson National Fellowship Foundation, Evaluating Panel, 1968--69. Hampshire College, Consultant, Mathematics Program, 1968--75. Graduate Record Examination, Consultant, Advanced Mathematics Committee, 1969. Topology and Its Applications (a journal), Member of Editorial Board, 1971--1994. National Humanities Faculty, Lecturer and Consultant, 1976.
Scientist in Residence (2 weeks)School MathematicsCarleton College, Northfield MN, Scientist in Residence, April 1966. Hope College, Holland MI, Visiting Lecturer, July 1968. St. Andrews Presbyterian College, Laurinburg NC, Scientist in Residence, November 1968. Bar Ilan University, Ramat Gan, Israel, Professor of Mathematics, January 1979. School Mathematics Study Group Writing team, K--12, Summer 1964. Writing team, Probability, Grades 4--12, Summers 1965, 66 (Director). Advisory Panel on Secondary School Mathematics, 1965--71. Advisory Panel, 1967--71. Musical activities
Piano soloist with university and civic orchestras in concertos by Bach, Mozart, Chopin, Brahms, Liszt, Grieg, and Tschaikovsky, on occasions during 1938--69. Eastman School of Music, Two doctoral committees, (theory, musicology), 1961, 1964. University of Texas at Austin, doctoral committee (theory), about 1980. The Gilbert & Sullivan Society of Austin: Leading role of the Lord Chancellor in Iolanthe 1978, musical director for Trial by Jury 1982 and The Gondoliers 1983. Pianist at four national AMS--MAA meetings, two with Louis Rowen, cello, 1976 (Bach, Brahms, Beethoven, Chopin), 1980 (Bach, Franck, Beethoven, Rachmaninoff, Chopin), and two with William Browder, flute, 1989 [AMS--MAA Presidents' Concert] (Bach, Poulenc, Schubert, Gluck) and 1992 [AMS--MAA Past--Presidents' Concert] (Bach, Schubert, Franck, Mozart). AMS Centennial Banquet (1988): conducted 1900 mathematicians singing Happy Birthday Dear American Mathematical Society.