Philip Martin Whitman | |
---|---|
Nationality | American |
Education | Haverford College |
Alma mater | Harvard University |
Known for | Free lattice word problem |
Awards | AMS Honorary Member |
Scientific career | |
Fields | Lattice theory |
Institutions | UPenn, [1] Tufts [2] |
Thesis | Free Lattices (1941) |
Doctoral advisor | Garrett Birkhoff |
Philip Martin Whitman is an American mathematician who contributed to lattice theory, particularly the theory of free lattices.
Living in Pittsburgh, [3] he attended the Haverford College, where he earned a corporation scholarship for 1936–37, [4] and a Clementine Cope fellowship for 1937–38, [5] and was awarded highest honors in mathematical astronomy in 1937. [6] He was elected to the college's chapter of the Phi Beta Kappa Society. [7] In June 1937, he was conferred the Bachelor of Science degree from Haverford. [8] According to Garrett Birkhoff, Whitman was an undergraduate Harvard student in 1937, [9] and an outstanding graduate student not later than 1940, one of the first who taught elementary courses to freshmen in the mathematics department. [10] In 1938 he earned his AM, [11] and in June 1941 he obtained his Ph.D. degree from Harvard University. [12] He was a member of the AMS not later than 1947, [13] and was awarded an AMS honorary membership not later than 1995. [14]
In mathematics, a distributive lattice is a lattice in which the operations of join and meet distribute over each other. The prototypical examples of such structures are collections of sets for which the lattice operations can be given by set union and intersection. Indeed, these lattices of sets describe the scenery completely: every distributive lattice is—up to isomorphism—given as such a lattice of sets.
Saunders Mac Lane, born Leslie Saunders MacLane, was an American mathematician who co-founded category theory with Samuel Eilenberg.
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum and a unique infimum. An example is given by the power set of a set, partially ordered by inclusion, for which the supremum is the union and the infimum is the intersection. Another example is given by the natural numbers, partially ordered by divisibility, for which the supremum is the least common multiple and the infimum is the greatest common divisor.
Norman Levinson was an American mathematician. Some of his major contributions were in the study of Fourier transforms, complex analysis, non-linear differential equations, number theory, and signal processing. He worked closely with Norbert Wiener in his early career. He joined the faculty of the Massachusetts Institute of Technology in 1937. In 1954, he was awarded the Bôcher Memorial Prize of the American Mathematical Society and in 1971 the Chauvenet Prize of the Mathematical Association of America for his paper A Motivated Account of an Elementary Proof of the Prime Number Theorem. In 1974 he published a paper proving that more than a third of the zeros of the Riemann zeta function lie on the critical line, a result later improved to two fifths by Conrey.
Garrett Birkhoff was an American mathematician. He is best known for his work in lattice theory.
Bernard Osgood Koopman was a French-born American mathematician, known for his work in ergodic theory, the foundations of probability, statistical theory and operations research.
Holbrook Mann MacNeille was an American mathematician who worked for the United States Atomic Energy Commission before becoming the first Executive Director of the American Mathematical Society.
In mathematics, the lattice of subgroups of a group is the lattice whose elements are the subgroups of , with the partial ordering being set inclusion. In this lattice, the join of two subgroups is the subgroup generated by their union, and the meet of two subgroups is their intersection.
James Burton Ax was an American mathematician who made groundbreaking contributions in algebra and number theory using model theory. He shared, with Simon B. Kochen, the seventh Frank Nelson Cole Prize in Number Theory, which was awarded for a series of three joint papers on Diophantine problems.
William Fogg Osgood was an American mathematician.
James Gilbert Glimm is an American mathematician, former president of the American Mathematical Society, and distinguished professor at Stony Brook University. He has made many contributions in the areas of pure and applied mathematics.
Leonidas (Leon) Alaoglu was a mathematician best known for Alaoglu's theorem on the weak-star compactness of the closed unit ball in the dual of a normed space, also known as the Banach–Alaoglu theorem.
Toshiyuki Kobayashi is a Japanese mathematician known for his original work in the field of Lie theory, and in particular for the theory of discontinuous groups (lattice in Lie groups) and the application of geometric analysis to representation theory. He was a major developer in particular of the theory of discontinuous groups for non-Riemannian homogeneous spaces and the theory of discrete breaking symmetry in unitary representation theory.
George Daniel Mostow was an American mathematician, renowned for his contributions to Lie theory. He was the Henry Ford II (emeritus) Professor of Mathematics at Yale University, a member of the National Academy of Sciences, the 49th president of the American Mathematical Society (1987–1988), and a trustee of the Institute for Advanced Study from 1982 to 1992.
Paul Roesel Garabedian was a mathematician and numerical analyst. Garabedian was the Director-Division of Computational Fluid Dynamics at the Courant Institute of Mathematical Sciences, New York University. He is known for his contributions to the fields of computational fluid dynamics and plasma physics, which ranged from elegant existence proofs for potential theory and conformal mappings to the design and optimization of stellarators. Garabedian was elected a member of the National Academy of Sciences in 1975.
George David Birkhoff was one of the top American mathematicians of his generation. He made valuable contributions to the theory of differential equations, dynamical systems, the four-color problem, the three-body problem, and general relativity. Today, Birkhoff is best remembered for the ergodic theorem. The George D. Birkhoff House, his residence in Cambridge, Massachusetts, has been designated a National Historic Landmark.
In mathematics, continuous geometry is an analogue of complex projective geometry introduced by von Neumann, where instead of the dimension of a subspace being in a discrete set , it can be an element of the unit interval . Von Neumann was motivated by his discovery of von Neumann algebras with a dimension function taking a continuous range of dimensions, and the first example of a continuous geometry other than projective space was the projections of the hyperfinite type II factor.
Joseph Lawrence Taylor was an American mathematician, specializing in Banach algebras and non-commutative harmonic analysis.
Lois Wilfred Griffiths was an American mathematician and teacher. She served as a researcher, mathematician, and professor for 37 years at Northwestern University before retiring in 1964. She is best known for her work in polygonal numbers. She published multiple papers and wrote a textbook, Introduction to the Theory of Equations, published in 1945.
In the mathematical disciplines of in functional analysis and order theory, a Banach lattice(X,‖·‖) is a complete normed vector space with a lattice order, , such that for all x, y ∈ X, the implication holds, where the absolute value |·| is defined as