Alexandre V. Borovik (born 1956) is a Professor of Pure Mathematics at the University of Manchester, United Kingdom. He was born in Russia and graduated from Novosibirsk State University in 1978. His principal research lies in algebra, model theory, and combinatorics—topics on which he published several monographs and a number of papers.He also has an interest in mathematical practice: his book Mathematics under the Microscope: Notes on Cognitive Aspects of Mathematical Practice examines a mathematician's outlook on psychophysiological and cognitive issues in mathematics.
Mathematical logic, also called formal logic, is a subfield of mathematics exploring the applications of formal logic to mathematics. It bears close connections to metamathematics, the foundations of mathematics, philosophy, and theoretical computer science. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems.
Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups act.
Jean, Baron Bourgain was a Belgian mathematician. He was awarded the Fields Medal in 1994 in recognition of his work on several core topics of mathematical analysis such as the geometry of Banach spaces, harmonic analysis, ergodic theory and nonlinear partial differential equations from mathematical physics.
Ben Joseph Green FRS is a British mathematician, specialising in combinatorics and number theory. He is the Waynflete Professor of Pure Mathematics at the University of Oxford.
In geometry, the center of curvature of a curve is found at a point that is at a distance from the curve equal to the radius of curvature lying on the normal vector. It is the point at infinity if the curvature is zero. The osculating circle to the curve is centered at the centre of curvature. Cauchy defined the center of curvature C as the intersection point of two infinitely close normal lines to the curve. The locus of centers of curvature for each point on the curve comprise the evolute of the curve. This term is generally used in physics regarding to study of lenses and mirrors.
In model theory, a stable group is a group that is stable in the sense of stability theory. An important class of examples is provided by groups of finite Morley rank.
In theoretical particle physics, the non-commutative Standard Model, is a model based on noncommutative geometry that unifies a modified form of general relativity with the Standard Model.
Oded Schramm was an Israeli-American mathematician known for the invention of the Schramm–Loewner evolution (SLE) and for working at the intersection of conformal field theory and probability theory.
Victor Ginzburg is a Russian American mathematician who works in representation theory and in noncommutative geometry. He is known for his contributions to geometric representation theory, especially, for his works on representations of quantum groups and Hecke algebras, and on the geometric Langlands program. He is currently a Professor of Mathematics at the University of Chicago.
Georg Gottlob FRS is an Austrian computer scientist who works in the areas of database theory, logic, and artificial intelligence and is Professor of Informatics at the University of Oxford.
Nonstandard analysis and its offshoot, nonstandard calculus, have been criticized by several authors, notably Errett Bishop, Paul Halmos, and Alain Connes. These criticisms are analyzed below.
Elementary Calculus: An Infinitesimal approach is a textbook by H. Jerome Keisler. The subtitle alludes to the infinitesimal numbers of the hyperreal number system of Abraham Robinson and is sometimes given as An approach using infinitesimals. The book is available freely online and is currently published by Dover.
David Orme Tall is Emeritus Professor in Mathematical Thinking at the University of Warwick. One of his early influential works is the joint paper with Vinner "Concept image and concept definition in mathematics with particular reference to limits and continuity". The "concept image" is a notion in cognitive theory. It consists of all the cognitive structure in the individual's mind that is associated with a given concept. Tall and Vinner point out that the concept image may not be globally coherent, and may have aspects which are quite different from the formal concept definition. They study the development of limits and continuity, as taught in secondary school and university, from the cognitive viewpoint, and report on investigations which exhibit individual concept images differing from the formal theory, and containing factors which cause cognitive conflict.
Steve Shnider is a retired professor of mathematics at Bar Ilan University. He received a PhD in Mathematics from Harvard University in 1972, under Shlomo Sternberg. His main interests are in the differential geometry of fiber bundles; algebraic methods in the theory of deformation of geometric structures; symplectic geometry; supersymmetry; operads; and Hopf algebras. He retired in 2014.
Simon Antoine Jean L'Huilier was a Swiss mathematician of French Hugenot descent. He is known for his work in mathematical analysis and topology, and in particular the generalization of Euler's formula for planar graphs.
David M. Sherry is a philosopher and professor at Northern Arizona University in Flagstaff, Arizona. He teaches History of Philosophy, History of Logic, as well as Philosophy of Mathematics. He has published on Logic, Philosophy of Mathematics and Philosophy of Science.
Joel David Hamkins is an American mathematician and philosopher based at the University of Oxford. He has made contributions in mathematical and philosophical logic, set theory and philosophy of set theory, in computability theory, and in group theory.
Alexandre Mikhailovich Vinogradov was a Russian and Italian mathematician. He made important contributions to the areas of differential calculus over commutative algebras, the algebraic theory of differential operators, homological algebra, differential geometry and algebraic topology, mechanics and mathematical physics, the geometrical theory of nonlinear partial differential equations and secondary calculus.
Ivan Vadimovich Loseu is a Belarusian-American mathematician, specializing in representation theory, symplectic geometry, algebraic geometry, and combinatorial algebra.