Education

Graduate Education: University of California at Berkeley
Ph.D. June 1972 in Mathematics; Thesis Advisor: Alfred Tarski

Undergraduate Education: Harvey Mudd College, Claremont, California
B.S. June 1967 in Mathematics with Distinction and Departmental Honors

Experience

Permanent Positions

1986--present	Professor	University of South Carolina
1991--1994	Department Chair	University of South Carolina
1979--1986	Associate Professor	University of South Carolina
1975--1979	Assistant Professor	University of South Carolina

 

Visiting Positions

1995--1996	Visiting Professor	University of Hawai`i, Honolulu, HI
1994 (Summer)	Visiting Researcher	LaTrobe University, Bundoora, Australia
1985 (Fall)	Visiting Professor	University of Colorado, Boulder, CO
1982--1983	Visiting Fulbright Professor	University of The Philippines
1982 (Spring)	Visiting Associate Professor	University of Hawai`i, Honolulu, HI
1979 (Fall)	Visiting Associate Professor	University of California, La Jolla, CA
1975 (Summer)	Visiting Research Mathematician	Technische Hochschule, Darmstadt,Germany

 

Post-doctoral Positions

1973--1975	J. W. Young Research Instructor	Dartmouth College, Hanover, NH
1973 (Summer)	Visiting Assistant Researcher	University of California,Berkeley
1972--1973	NRC Postdoctorate Fellow	University of Manitoba, Winnipeg, Canada

Awards

2013 Fellow of the American Mathematical Society
1998 Stanislaw Ulam Lectureship, University of Colorado, Boulder
1994 Hour Invited Address, American Mathematical Society, Lexington, KY
1983 Alexander von Humboldt Research Fellowship, Darmstadt, Germany
1982--1983 Fulbright-Hays Professorship, Manila, Philippines
1967--69, 71--72 National Science Foundation Graduate Fellowship, UC Berkeley
1967--68 Honorary Woodrow Wilson Graduate Fellowship, UC Berkeley

Courses Taught

I have taught almost all of the undergraduate mathematics courses as well as many of the graduate course, particularly those is algebra and mathematical logic. For Fall 2019 I am teaching two sections of MATH 141 to students in the South Carolina Honors College.

Research

Most of my research lies at the confluence of algebra, mathematical logic, discrete mathematics, and computer science. I also have some papers lying outside this confluence including five in psychological journals that results from two decades of collaboration with psychologists working at the Medical School and the state mental hospitals.

Selected Publications

• (With R. McKenzie and W. Taylor), 
  Algebras, Lattices, Varieties, Volume I
  Wadsworth & Brooks/Cole,  Monterey, CA,
  1987, 361 + xii,
  AMS Chelsea Edition,  American Mathematical Society,
  Providence, RI, 2018, pp. 367+xiii
  R. Freese has joined as a collaborator for volumes II and III, which should appear shortly.
• Decision problems for equational bases of algebras,
  
  Annals of Mathematical Logic,vol 11 (1976) 193--259.
• (With Dwight Bean and Andrzej Ehrenfeucht)
  Avoidable patterns in strings of symbols,
  Pacific Journal of Mathematics, vol. 84 (1979)  261--294.
•  (With Kirby and Baker and Heinrich Werner)
  Shift automorphism methods for inherently nonfinitely based varieties of algebras,
  Czechoslovak Journal Mathematics, vol. 39 (1989) 53-69.
•  (With R. Freese and J.B.~Nation)
  Inherently nonfinitely based lattices,
  Annals of Pure and Applied Logic. vol. 115} (2002) 177--195.
• (With Kirby Baker and Ju Wang)
  An extension of Willard's Finite Basis Theorem: Congruence
  meet-semidistributive varieties of finite critical depth
  Algebra Universalis. vol. 52 (2004)  289--302.
•  (With Ralph  Howard and Virginia Johnson)
  A characterization of real closed fields that are Archimedean by way of Cauchy's functional equation,
  American Mathematical Monthly vol. 125 (2018) 169--172.
• The computational complexity of deciding whethera finite algebra generates a minimal variety. 
  In''Don Pigozzi on Abstract Algebraic Logic, Universal Algebra and Computer Science.'' In volume 16 of the Springer-Verlag series ``Outstanding contributions to logic'', Janusz Celakowski editor, (2018) 233-256.
• (with Ross Willard)
  Congruence meet-semidistributive locally finite varieties and a finite basis theorem,
  Algebra Universalis,  vol. 79 (2018), no. 2, Art. 44, 20 pp.