Adolph Winkler Goodman (July 20, 1915 – July 30, 2004) was an 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 ...
who contributed to
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...
,
graph theory
In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ...
and to the theory of
univalent functions
In mathematics, in the branch of complex analysis, a holomorphic function on an open subset of the complex plane is called univalent if it is injective.
Examples
The function f \colon z \mapsto 2z + z^2 is univalent in the open unit disc, ...
:
[See the brief obituary on him published on the newsletter of the department of Mathematics of the ]University of South Florida
The University of South Florida (USF) is a public research university with its main campus located in Tampa, Florida, and other campuses in St. Petersburg and Sarasota. It is one of 12 members of the State University System of Florida. USF is ...
. The conjecture on the coefficients of multivalent functions named after him is considered the most interesting challenge in the area after the
Bieberbach conjecture In complex analysis, de Branges's theorem, or the Bieberbach conjecture, is a theorem that gives a necessary condition on a holomorphic function in order for it to map the open unit disk of the complex plane injectively to the complex plane. It was ...
, proved by
Louis de Branges in 1985.
[According to .]
Life and work
In 1948, he made a mathematical conjecture on coefficients of -valent functions, first published in his
Columbia University
Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...
dissertation thesis and then in a closely following paper. After the proof of the Bieberbach conjecture by Louis de Branges, this conjecture is considered the most interesting challenge in the field,
and he himself and coauthors answered affirmatively to the conjecture for some classes of -valent functions. His researches in the field continued in the paper ''Univalent functions and nonanalytic curves'', published in 1957: in 1968, he published the survey ''Open problems on univalent and multivalent functions'', which eventually led him to write the two-volume book ''Univalent Functions''.
Apart from his research activity, He was actively involved in teaching: he wrote several college and high school textbooks including ''Analytic Geometry and the Calculus'', and the five-volume set ''Algebra from A to Z''.
He retired in 1993, became a Distinguished Professor Emeritus in 1995, and died in 2004.
Selected works
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Notes
Biographical references
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References
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Additional sources
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{{DEFAULTSORT:Goodman, Adolph Winkler
20th-century American mathematicians
21st-century American mathematicians
Complex analysts
American mathematical analysts
American number theorists
Graph theorists
1915 births
2004 deaths