open 1/15/96
updated 9/26/98


Scott W. Williams' Resumé Page










Scott Williams' home page





Scott W. Williams
Professor of Mathematics
State University of New York at Buffalo
Buffalo NY 14214 USA

DATE AND PLACE OF BIRTH: April 22, 1943, Staten Island, NY


Offspring: RACHAEL (22), REBEKAH (20), and EVE (12)




1964, B.S. Morgan State College (Baltimore, MD)

1967, M.S. Lehigh University (Bethlehem, PA)

1969, Ph.D. Lehigh University (Bethlehem, PA)


1964 International Business Machines, Product Testing Department, Kingston NY

1968-1969 Instructor, Pennsylvania State University, Allentown PA

1969-1971 Research Associate, Pennsylvania State University, College Park PA

1971-1977 Assistant Professor, State University of New York at Buffalo, Buffalo NY

1977-1985 Associate Professor, State University of New York at Buffalo, Buffalo NY

1980-1981 Visiting Associate Professor, Institute for Medicine and Mathematics, Athens, OH

1985-PRESENT Professor, State University of New York at Buffalo, Buffalo NY

1986-1987 Fulbright Lecturer, Charles University, Prague, Czechoslovakia

1988-1991 Adjunct Professor, Beijing Teacher's College, Beijing, China

1992-1997 Summer School on Mathematical Biology for Young Scholars, Villanova University, Philadelphia PA



Teaching Awards:

1982 Chancellor's Award for Excellence in Teaching, State University of New York

1986-1987 Fulbright-Lecturer (Prague Czechoslovakia)

Research Grants:

1980-1981 Ford Foundation Senior Minority Postdoctoral Fellowship

1983-1988 NSF #R118219633, Two Topics in Topology: Box Products and Co-absolutes

I have given 80 invited conference lectures, colloquia, and seminar lectures at 55 institutions in 7 countries; e.g, Univerisity of Toronto (Canada), Beijing Normal University (China), Charles University (Czech Republic), Oxford University (England), University of Warsaw (Poland).

Invited Lecures since January 96:

University of North Carolina, Wilmington NC, More Dynamics on the irrationals, Colloquium, February 1996

University of North Carolina, Wilmington NC, Sly Fox Approach to Racism, Lecture to student body&community, February 1996

2nd Conference of African American Research in the Mathematical Sciences, DIMACS at Rutgers University, More Dynamics on the irrationals, New Brunswick, New Jersey, June 1996

University of Toronto, Mo' better dynamics on the rrationals, Logic Seminar, October 1996

Conference on Black History, Queens University, Kingston, Ontario, Sly Fox Approach to Racism, Keynote Address, February 1997

Seminar on Topology and Applications, New York, New York, Dynamics on the Irationals, May 1997



General Topology, Set-theoretic Topology, Set Theory, Topological Dynamics. For the mathematics field of Topology in general, browse Topology Atlas.

PUBLICATIONS (Look me up in MATHEMATICAL REVIEWS for observations by peers.)

Completeness for all , Proceedings of the Washington State University Conference on Topology, (1970), 127-136.

Liberation of the Q - Gap , Proceedings of the University of Houston Point Set Topology Conference, (1972), 179-186.

The transfinite cardinal covering dimension and separability , Portugaliae Mathematicae 32, No. 3 (1973), 139-145.

(with William Fleischman) The Gdelta -topology on compact spaces , Fundamenta Mathematicae 83 (1974), 143-149.

A technique for reducing certain covers on certain L.O.T.S. and their products , TOPO 72 (1974), 586-590.

Paracompactness and products , General Topology and its applications 9, (1976), 117-125.

Is box omega omega+1 Paracompact? , Topology Proceedings 1 (1976), 141-146.

Boxes of compact ordinals , Topology Proceedings 2 (1977), 631-642.

An application of trees to topology , Topology Proceedings 3 (1978), 523-525.

Recent results in the theory of co-absolutes , N.A.M. Proceedings (1981), 2-7.

Spaces wth dense orderable subspaces, Topology and Order Structures I, Math. Cent. Tracts 142 (1981) , 27-49.

(with Marlene Gewand) Covering properties of linearly ordered topological spaces and their products</I> , Topology and Order I, Math Cent. Tracts 142 (1981), 119-132.

Co-absolutes and homeomorphic dense subspaces , Canadian Journal of Mathematics 33 (1981), 857-861.

Trees, Gleason spaces, and co-abolutes of betaN\N , Transactions of the American Mathematical Society 271 (1982), 83-100.

(with Jan van Mill) A compact F-space not co-absolute with betaN\N , Topology and its Applications 15 (1983), 59-64.

Orderable subspaces of Cech-Stone remainders , Topology Proceedings 7 (1982), 301-327.

Co-absolute of Cech-Stone Remainders and Orderable Spaces , General Topology and relations to Modern Analysis and Algebra 5 (1982), 699-705.

Orderable subspaces of compact F-spaces , Topology and Order Structures II, Math. Cent. Tracts 169 (1983), 91-105.

Box Products , The Handbook for Set-theoretic Topology, North-Holland (1984), 169-200.

Paracompactness in box products , Proceedings of the 12th Winter School on Abstract Analysis, Rend. del Cir. Mat. Palermo series II.6 (1984), 314-328.

More realcompact spaces , Rings of Continuous Functions , Lecture Notes Pure and Applied Mathematics 95 (1985), 289-300.

(with B. Balcar and P. Kalasek) Multiple recurrence in dynamical systems , Comment. Math. Univ. Carolina 28 (1987), 607-612.

Mapping the ordinal function depth , Interim Reports of the Prague Topological Symposium 1 (1987), p. 24.

(with L. Friedler and H. Martin) Paracompact C-scattered spaces , Pacific Journal of Mathematics 129 (1987), 277-296.

Special points arising from self-maps , General Topology and relations to Modern Analysis 6, (1988), 629-638.

(with Yang Shou-lian) On the countable box products of compact ordinal spaces , Topology Proceedings 12 (1987), 159-172.

(with Yang Shou-lian) On the box products of small ordinal spaces (chinese), Kexue Tong bao 33 (1987), 1051-1053.

(with J. Roitman) The Paracompactness of spaces related to uncountable box products</I> , Topology Proceedings 15 (1990), 135-142.

(with Haoxuan Zhou) Strong versions of normality , General Topology and Applications, lecture notes in pure and applied mathematics 134 (1991), 379-390.

(with J. Pelant) Examples of Recurrence , Papers on General Toplogy and Applications, Annals of the New York Academy of Sciences 806 (1996), 316-332.

Dynamics on the irrationals , African Americans in Mathematics, Series in Discrete Math and Theor. Comp. Sci. 34 (1997), N. Dean ed., 83-103.

(with Haoxuan Zhou) The order-like structure of compact monotonically normal spaces , Comment. Math. Univ. Carolinae, 39,1 (1998), 207-217.

World Wide Web Publications


1. On Affirmative Action, Topology Atlas 1 #1, (1996)

2. Are our students worse?, Topology Atlas 1 #2, (1996)

3. Moore karma ran over my dogma, Topology Atlas 1 #3, (1996)

4. Keep your hands from beans, Topology Atlas 2 #2, (1997)

5. A Column Concerned with Qualifying Exams in Topology, Topology Atlas 3 #1, 1998

Mathematicians of the African Diaspora:


Modern General Topology with Dynamics and Homotopy (working title), previously known as The Black Arts of Topology with Homotopy - an undergraduate/graduate textbook (Ms. 600 pp.) accepted for publication John Wiley & Sons - projected appearance fall 1996.


More dynamics on the irrationals (Ms. 11pp.)

Some compact monotonically normal spaces (Ms. 18 pp.)

(with Stephen Watson) Resolving to the Absolute


Exercises into the mathematics of the glass bead game (1972). (Ms. 6 pp.)

The big intervals (1974). (Ms. 3 pp.)

On first countable ordered spaces (1974). (Ms. 18 pp.)

(with Marlene Gewand) Products with Lindelof Spaces (1975). (Ms. 19 pp.)

Countable box topologies (1976). (Ms. 14 pp.)

Paracompact products and cardinal functions (1977). (Ms. 9 pp.)

A survey letter on the theory of co-absolutes (1979). (Ms. 6 pp.)

A simple exercise in forcing (1981). (Ms. 15 pp.)

Paracompactness and realcompactness in finer topologies (1983). (Ms. 44 pp.)

Maps from compact X to itself (1984). (Ms. 31 pp.)

General dynamics (1986). (Ms. 72 pp.)

China Lectures on set theory in topololgical dynamics (1988). (Ms. 60 pp.)

Paracompact subsets of uncountable box products (1992)





1969 Founder, National Association of Mathematicians (formerly known as Black and Third World Mathematicians)

1967-1976 Member, Mathematical Association of America

1969-present Member, National Association of Mathematicians

1969-1979 Member, American Mathematical Society

1971 Local Organizing Committee for American Mathematical Society Summer Meeting at Pennsylvania State University -University Park

1975-1976 Appointed to the Committee on Editorial Policy of the Notices of the American Mathematical Society

1976-1979 Editorial Board of the Notices of the American Mathematical Society

1976-1978 Founded the Great Lakes Seminar on General Topology and its Applications (A group of approximately 20 active topologists and another 10 to 20 students within a 200 mile radius of Buffalo, NY).

1976-present I have refereed articles for numerous journals, among them are: Bulletin Canadian Mathematical Society, Topology Proceedings, Proceedings American Mathematical Society, Topology and its Applications, Real Analysis Exchange, Indian Journal of Mathematics

1977-1978 Directed Meetings of the Great Lakes Seminar on General Topology and its Applications: April 1977, October 1977, April 1978

1980-1982 Appinted to the American Mathematical Society Committee on Opportunities in Mathematics for Disadvantaged Groups

1983-1986 National Science Foundation Panel on Minority Graduate Fellowships

1985 National Science Foundation Panel on Minorities in Science

1985-1986 Served as mentor to Yang Shou-lian, Exchange visitor from Beijing Teacher's College

1989-1993 Referee of Grant Applications to the National Science Foundation, grants in Topology and Foundations section

1990 National Association of Mathematicians, Book Review Editor

1991-1996 Advisory Committee of the Summer Conference on Topology and its Applications

1993-1994 National Research Council/Ford Foundation Panel on Minority Graduate Fellowships


1969-present I have given numerous lectures to high school students in Buffalo and elsewhere. The most significant of these were 30 lectures on Group Theory and Applications in the summer of 1981 to high ability minority students in Ohio while I was visiting the Institute for Medicine and Mathematics, and lectures in 1990 to Upward Bound Students at the State University of New York at Buffalo

1981-1988 Member, Bennett Park Montesori Public School Steering Committee

1984-1986 Chairman , Humanities Committee, Bennett Park Steering Committee

1989-1990 Made numerous visits to and talks at The Buffalo Public School Board Meetings

1992-1996 Advisory Board of WBFO (a National Public Radio member radio station)

1994-1995 Friends of Public Broadcasting (a volunteer support organization for the Corporation of Public Broadcasting)

1995-PRESENT Member of the Circle Association, a group of African-American men practicing and dedicated to the quality of life, successful manhood and parenting, economic growth and development, and the pursuit of excellence and spiritual development.

1996 Black Male Summit, member on a panel on opportunities for youth and young adults.

1996-present member of Profesional Macintosh Users Group

1996-present Newsletter Coodinator of Profesional Macintosh Users Group



PH.D THESIS DIRECTION at The State University of New York at Buffalo:

Student/Dissertation Title: Degree Awarded:

Gewand, Marlene 1978 Cardinal functions

Qi, Jincheng 1993 Normality in finer topologies

Li, Jingquan Co-absolutes of Orderable Spaces In progress


at Pennsylvania State University: 2 students

at The State University of New York at Buffalo: 2 students

at Ohio University: 1 student

at Beijing Teachers' College: 1 student

Other Activities in Teaching:

From 1972-1992, I've been the principal lecturer in a seminar not a part of my teaching duties.

I Designed and taught the following graduate courses :

1972-1973 (Fall Semester) Paracompact Spaces (Spring Semester) Dimension Theory (Spring Semester) Linearly Ordered Topological Spaces

1973 (Summer) Linearly Ordered Topological Spaces

1973-1974 (Spring Semester) Cardinal Functions in Topology

1974-1975 (Fall Semester) Box Topologies (Spring Semester) Category Theory

1975 (Summer Session) Category Theory

1977-1978 (with Nicolas Goodman) Applied Set Theory

1978 (Fall Semester) Boolean Algebras and the Theory of Ultrafilters

1982-1983 Product Spaces

1985-1986 Applications of Set Theory to Topology and Topological Dynamics

1990-94 Topology for Undergraduates and Graduates

1995-96 Resolutions and Elementary Submodels

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