Jan Mycielski (born February 7, 1932 in
Wiśniowa,
Podkarpackie Voivodeship,
Poland
Poland, officially the Republic of Poland, is a country in Central Europe. It is divided into 16 administrative provinces called voivodeships, covering an area of . Poland has a population of over 38 million and is the fifth-most populou ...
)
[Curriculum vitae](_blank)
from Mycielski's web site, retrieved 2010-03-10. is a
Polish-American
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
, a professor emeritus of mathematics at the
University of Colorado at Boulder
The University of Colorado Boulder (CU Boulder, CU, or Colorado) is a public research university in Boulder, Colorado. Founded in 1876, five months before Colorado became a state, it is the flagship university of the University of Colorado sy ...
.
Academic career
Mycielski received his Ph.D. in mathematics from the
University of Wrocław
, ''Schlesische Friedrich-Wilhelms-Universität zu Breslau'' (before 1945)
, free_label = Specialty programs
, free =
, colors = Blue
, website uni.wroc.pl
The University of Wrocław ( pl, Uniwersytet Wrocławski, U ...
in 1957 under the supervision of . His dissertation was entitled "Applications of
Free Group
In mathematics, the free group ''F'S'' over a given set ''S'' consists of all words that can be built from members of ''S'', considering two words to be different unless their equality follows from the group axioms (e.g. ''st'' = ''suu''−1' ...
s to Geometrical Constructions". Following positions at the
Centre National de la Recherche Scientifique
The French National Centre for Scientific Research (french: link=no, Centre national de la recherche scientifique, CNRS) is the French state research organisation and is the largest fundamental science agency in Europe.
In 2016, it employed 31,63 ...
in
Paris
Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. Si ...
, the Institute of Mathematics of the
Polish Academy of Sciences
The Polish Academy of Sciences ( pl, Polska Akademia Nauk, PAN) is a Polish state-sponsored institution of higher learning. Headquartered in Warsaw, it is responsible for spearheading the development of science across the country by a society o ...
, the
University of California, Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant un ...
, and
Case Western Reserve University
Case Western Reserve University (CWRU) is a private research university in Cleveland, Ohio. Case Western Reserve was established in 1967, when Western Reserve University, founded in 1826 and named for its location in the Connecticut Western Reser ...
, he took a permanent faculty position at Colorado in 1969.
Contributions
Among the mathematical concepts named after Mycielski are:
*The
Ehrenfeucht–Mycielski sequence, a sequence of binary digits with
pseudorandom
A pseudorandom sequence of numbers is one that appears to be statistically random, despite having been produced by a completely deterministic and repeatable process.
Background
The generation of random numbers has many uses, such as for rand ...
properties
*The
Mycielskian
In the mathematical area of graph theory, the Mycielskian or Mycielski graph of an undirected graph is a larger graph formed from it by a construction of . The construction preserves the property of being triangle-free but increases the chromatic ...
, a construction for embedding any
undirected graph
In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called '' ve ...
into a larger graph with strictly higher
chromatic number
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices ...
without creating any additional triangles.
*The
Mycielski–Grötzsch graph, the Mycielskian of the 5-cycle, an 11-vertex
triangle-free graph
In the mathematical area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. Triangle-free graphs may be equivalently defined as graphs with clique number ≤ 2, graphs with g ...
that is the smallest possible triangle-free graph requiring four colors.
*
Mycielski's theorem
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices o ...
that there exist triangle-free graphs with arbitrarily large chromatic number.
Awards and honors
In 2012 he became a fellow of the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meeting ...
.
List of Fellows of the American Mathematical Society
retrieved 2013-02-10.
Selected works
* 1991. ''A Note on S. M. Ulam's Mathematics''.
: A note in ''Adventures of a Mathematician''. Stanislaw Ulam
Stanisław Marcin Ulam (; 13 April 1909 – 13 May 1984) was a Polish-American scientist in the fields of mathematics and nuclear physics. He participated in the Manhattan Project, originated the Teller–Ulam design of thermonuclear weapon ...
. University of California Press, 1991.
See also
* List of Poles
This is a partial list of notable Polish or Polish-speaking or -writing people. People of partial Polish heritage have their respective ancestries credited.
Science
Physics
* Czesław Białobrzeski
* Andrzej Buras
* Georges Charpa ...
References
External links
Mycielski's personal web page
at the Univ. of Colorado.
{{DEFAULTSORT:Mycielski, Jan
1932 births
Living people
Polish set theorists
Polish logicians
University of Colorado Boulder faculty
Polish emigrants to the United States
University of Wrocław alumni
20th-century American mathematicians
21st-century American mathematicians
Fellows of the American Mathematical Society
Jan
20th-century Polish philosophers