Arthur Milgram
Encyclopedia
Arthur Norton Milgram was an American mathematician. He made contributions in functional analysis
, combinatorics
, differential geometry, topology
, partial differential equations, and Galois theory
. Perhaps one of his more famous contributions was the Lax–Milgram theorem—a theorem in functional analysis that is particularly applicable in the study of partial differential equations. In Emil Artin
's book Galois Theory http://books.google.com/books?id=BdS1D5mymwYC&dq=Galois+Theory+artin&printsec=frontcover&source=bn&hl=en&sa=X&oi=book_result&resnum=4&ct=result#PPA3,M1, Milgram also discussed some applications of Galois theory. Milgram also co-authored Verallgemeinerung eines graphentheoretischen Satzes von Rédei (a result in graph theory
) with Tibor Gallai
in 1960.
In 1937, Milgram received his Ph.D. from the University of Pennsylvania
. He worked under the supervision of John Kline
http://genealogy.math.ndsu.nodak.edu/id.php?id=287 (a student of Robert Lee Moore
). His dissertation was titled Decompositions and Dimension of Closed Sets in Rn.
Milgram advised 2 students at Syracuse University
in the 1940s and 1950s (Robert M. Exner http://genealogy.math.ndsu.nodak.edu/id.php?id=361 and Adnah Kostenbauder http://genealogy.math.ndsu.nodak.edu/id.php?id=362). In the 1950s, Milgram moved to the University of Minnesota at Minneapolis and helped found Minnesota's well-known PDE
group (http://www.math.umn.edu/grad/areas/pde.html). At Minnesota, Milgram was also the Ph.D. advisor for Robert Duke Adams http://genealogy.math.ndsu.nodak.edu/id.php?id=15778. It is also worth noting that Milgram's son R. James (Richard) Milgram http://genealogy.math.ndsu.nodak.edu/id.php?id=18610 (Professor Emeritus at Stanford http://math.stanford.edu/directory/faculty.html) also studied mathematics and received his Ph.D. from Minnesota.
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
, differential geometry, topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, partial differential equations, and Galois theory
Galois theory
In mathematics, more specifically in abstract algebra, Galois theory, named after Évariste Galois, provides a connection between field theory and group theory...
. Perhaps one of his more famous contributions was the Lax–Milgram theorem—a theorem in functional analysis that is particularly applicable in the study of partial differential equations. In Emil Artin
Emil Artin
Emil Artin was an Austrian-American mathematician of Armenian descent.-Parents:Emil Artin was born in Vienna to parents Emma Maria, née Laura , a soubrette on the operetta stages of Austria and Germany, and Emil Hadochadus Maria Artin, Austrian-born of Armenian descent...
's book Galois Theory http://books.google.com/books?id=BdS1D5mymwYC&dq=Galois+Theory+artin&printsec=frontcover&source=bn&hl=en&sa=X&oi=book_result&resnum=4&ct=result#PPA3,M1, Milgram also discussed some applications of Galois theory. Milgram also co-authored Verallgemeinerung eines graphentheoretischen Satzes von Rédei (a result in graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
) with Tibor Gallai
Tibor Gallai
Tibor Gallai was a Hungarian mathematician. He worked in combinatorics, especially in graph theory, and was a lifelong friend and collaborator of Paul Erdős. He was a student of Dénes König and an advisor of László Lovász...
in 1960.
In 1937, Milgram received his Ph.D. from the University of Pennsylvania
University of Pennsylvania
The University of Pennsylvania is a private, Ivy League university located in Philadelphia, Pennsylvania, United States. Penn is the fourth-oldest institution of higher education in the United States,Penn is the fourth-oldest using the founding dates claimed by each institution...
. He worked under the supervision of John Kline
John Robert Kline
John Robert Kline was a US-American Professor of Mathematics at the University of Pennsylvania from 1920 to 1955. A Ph.D. student of Robert Lee Moore, he was Guggenheim Fellow in 1925, later Chairman of the Department of Mathematics from 1933 to 1954 and Thomas A...
http://genealogy.math.ndsu.nodak.edu/id.php?id=287 (a student of Robert Lee Moore
Robert Lee Moore
Robert Lee Moore was an American mathematician, known for his work in general topology and the Moore method of teaching university mathematics.-Life:...
). His dissertation was titled Decompositions and Dimension of Closed Sets in Rn.
Milgram advised 2 students at Syracuse University
Syracuse University
Syracuse University is a private research university located in Syracuse, New York, United States. Its roots can be traced back to Genesee Wesleyan Seminary, founded by the Methodist Episcopal Church in 1832, which also later founded Genesee College...
in the 1940s and 1950s (Robert M. Exner http://genealogy.math.ndsu.nodak.edu/id.php?id=361 and Adnah Kostenbauder http://genealogy.math.ndsu.nodak.edu/id.php?id=362). In the 1950s, Milgram moved to the University of Minnesota at Minneapolis and helped found Minnesota's well-known PDE
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
group (http://www.math.umn.edu/grad/areas/pde.html). At Minnesota, Milgram was also the Ph.D. advisor for Robert Duke Adams http://genealogy.math.ndsu.nodak.edu/id.php?id=15778. It is also worth noting that Milgram's son R. James (Richard) Milgram http://genealogy.math.ndsu.nodak.edu/id.php?id=18610 (Professor Emeritus at Stanford http://math.stanford.edu/directory/faculty.html) also studied mathematics and received his Ph.D. from Minnesota.