Combinatorics Through Guided Discovery, 2004a

About the Author
Kenneth Paul Bogart was born on October 6, 1943 in Cincinnati, OH. He graduated
from Marietta College in Ohio in 1965, and earned his Ph.D. in mathematics
from the California Institute of Technology in 1968. He married Ruth Tucker in
1966, and they moved to Hanover in 1968 where Ken was appointed an Assistant
Professor of Mathematics. Ken remained in the job that he loved for 37 years being
promoted to Associate Professor in 1974, and to Full Professor in 1980. Ken’s
career was characterized by a love of mathematics and scholarship, and a passion
for teaching and mentoring at all levels within the mathematics curriculum. His
passion for research is evidenced by over 60 journal articles and nine textbooks in
his field of combinatorics. Ken’s research covered a wide spectrum of topics within
combinatorics.
Ken’s mathematical roots were in algebra and lattice theory, and his earliest
papers developed structural results for Noether lattices. One of the main topics in
his research was partial orders, about which he wrote more than two dozen papers.
This line of research started in the early 1970’s with contributions to the theory of
dimension for partial orders. A number of his papers treated applications of partial
orders to the social sciences; for instance, he contributed to social choice theory by
examining the optimal way to develop a consensus based on rankings that are
partial orders. Interval orders and interval graphs played the most prominent role
in Ken’s research; his papers in this field span roughly thirty years, starting in the
mid 1970’s, and about half of his Ph.D. students worked in this area. Among his
contributions in this area are the introduction and investigation of new concepts
related to interval orders and graphs, the development of new and simpler proofs of
key results, and the exploration of a number of structures that are natural variations
or interesting special types of interval orders and graphs. Ken also contributed to
the theory of error-correcting codes; in particular, he constructed a class of codes
from partial orders. He collaborated on several papers in matroid theory, to which
he contributed valuable insights from lattice theory and geometry.
Throughout the later part of his career, Ken became increasing interested in how
students learn mathematics. His NSF-sponsored project of "guided-discovery" in
combinatorics is an element that lives on in the math department. Ken also devoted
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