The word "algebra" has several related meanings in mathematics, as a single word or with qualifiers. Milnor's current interest is dynamics, especially holomorphic dynamics. His work in dynamics is summarised by Peter Makienko in his review of [ 9 ]:- By a link homotopy is meant a deformation of one link onto another, during which each component of the link is allowed to cross itself, but such that no two components are allowed to intersect. The purpose of this paper is to study links under the relation of homotopy. The fundamental tool in this study will be the link group. The link group of a link is a factor group of the fundamental group of its complement, which is invariant under homotopy. ... I am indebted to R H Fox for assistance in the preparation of this paper. Imagine that he is hugely enthusiastic and charming, and that his thoughtful analyses of contemporary human politics range from the individual to the mass, from theory to action, from ideology to consequence. For the kind of algebraic structure, see Algebra over a field. For other uses, see Algebra (disambiguation).

The Algebraist - Iain M. Banks - Google Books The Algebraist - Iain M. Banks - Google Books

The references [ 4 ] to [ 18 ] give a good indication of the wide influence of Milnor's work up to 1992 (when these articles were written ). The article [ 4 ] is a survey of Milnor's work in algebra, particularly in algebraic K K K-theory, where his work continues to have important influences. The article [ 17 ] looks at nine papers which Milnor had written on differential geometry. It discusses Milnor's theorem, which shows that the total curvature of a knot is at least 4. Among other results discussed are Milnor's result showing that we cannot necessarily "hear the shape" of a 16-dimensional torus, and another result giving upper and lower bounds on the number of distinct words of a given length in a finitely generated subgroup of the fundamental group. J Milnor, Differential Topology Forty-six Years Later, Notices Amer. Math. Soc. 58 (6) (2011), 804- 809.S S Khare, On Abel Prize 2011 to John Willard Milnor: a brief description of his significant work, Math. Student 82 (1- 4) (2013), 247- 279. This was only one of several papers that Milnor published in 1953. The others were: The characteristics of a vector field on the two-sphere; On total curvatures of closed space curves; and (with Israel Herstein ) An axiomatic approach to measurable utility. Another paper, Link groups, was published in 1954 but it had been submitted for publication in March 1952, over a year before the first of the 1953 papers just mentioned. Milnor writes in the Introduction to Link groups:- The Algebraist marks a return to the happy hunting grounds of Banks's early SF, replete with all the whizzy boys' toys, wildly improbable extreme sports, damning character assassinations and good-humoured condemnation of all that's wearying about humanity. The Culture, the great civilisation of many of his previous SF novels, is absent, but it's been replaced by a baroque sweep of aliens in capitalist overdrive, providing more than adequate fuel for the author's twin obsessions of sociopolitics and having fun, the two always riding hand in glove, switching with enviable effortlessness between the intimate and the cosmic. H Bass, John Milnor, the algebraist, in Topological methods in modern mathematics (Houston, TX, 1993), 45- 84.

The Algebraist by Iain M. Banks | Goodreads

M Raussen and J Milnor, Interview with John Milnor, Notices Amer. Math. Soc. 59 (3) (2012), 400- 408.. J Sondow, An aroma of paradox and audacity : Milnor's work in differential topology, in Topological methods in modern mathematics (Houston, TX, 1993), 23- 30. Milnor has written eight important books: Morse theory (1963); Lectures on the h-cobordism theorem (1965); Topology from the differentiable viewpoint (1965); Singular points of complex hypersurfaces (1968); Introduction to algebraic K-theory (1971); (with Dale Husemoller ) Symmetric bilinear forms (1973); (with James D Stasheff ) Characteristic classes (1974); and Dynamics in one complex variable (1999).For a good overview of Milnor's mathematics, see the citations for the various prizes which he has won at THIS LINK. E H Spanier, Review: Characteristic classes, by John Willard Milnor and James D Stasheff, Bull. Amer. Math. Soc. 81 (5) (1975), 862- 866. In the 1950s Milnor did a substantial amount of work on algebraic topology which is discussed in [ 18 ]. He constructed the classifying space of a topological group and gave a geometric realisation of a semi-simplicial complex. He also studied the Steenrod algebra and its dual, investigated the structure of Hopf algebras, and studied characteristic classes and their relation to mathematical physics.

Algebra - Wikipedia Algebra - Wikipedia

The word algebra comes from the Arabic: الجبر, romanized: al-jabr, lit.'reunion of broken parts, [1] bonesetting [2]' from the title of the early 9th century book ʿIlm al-jabr wa l-muqābala "The Science of Restoring and Balancing" by the Persian mathematician and astronomer al-Khwarizmi. In his work, the term al-jabr referred to the operation of moving a term from one side of an equation to the other, المقابلة al-muqābala "balancing" referred to adding equal terms to both sides. Shortened to just algeber or algebra in Latin, the word eventually entered the English language during the 15th century, from either Spanish, Italian, or Medieval Latin. It originally referred to the surgical procedure of setting broken or dislocated bones. The mathematical meaning was first recorded (in English) in the 16th century. [6] Different meanings of "algebra" Sometimes both meanings exist for the same qualifier, as in the sentence: Commutative algebra is the study of commutative rings, which are commutative algebras over the integers.

He was promoted to professor in 1960 then, in 1962, Milnor was appointed to the Henry Putman chair. Imagine that the storyteller has a well-educated and thoughtful mind with which he fills you in on all the details of these new worlds and peculiar personalities, and that he has the skill to paint in words the most breathtaking portraits of our universe on levels from the chemical to the personal. Milnor has received many awards and honours for his extraordinarily important contributions. He received the National Medal of Science in 1967 and was elected a member of the National Academy of Sciences, the American Academy of Arts and Science. He is a member of the American Philosophy Society and has played a major role in the American Mathematical Society. In August 1982 Milnor received the Leroy P Steele Prize:- Much high-calibre espionage, imaginative intellectualising and mega-ordnance goes off in spectacular fashion during Fassin's travails. So big, so good - Banks even takes on the opportunities to examine the humane and not so humane angles of his characters, revealing their self-deceptions, weakness and complexity.