The Algebraist

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Algebra (from Arabic ‏ الجبر‎ ( al-jabr)'reunion of broken parts, [1] bonesetting' [2]) [ʔldʒbr] ( listen ⓘ) is the study of variables and the rules for manipulating these variables in formulas; [3] it is a unifying thread of almost all of mathematics. [4] M Raussen and J Milnor, Interview with John Milnor, Notices Amer. Math. Soc. 59 (3) (2012), 400- 408.. It's not the word count that's the problem, although the glut of information dilutes the emotional impact of some of the dramatic turns, but that the author's personality - cheery, optimistic, absurd-aware - is so strong it drowns out chances for genuine pathos. Even in the face of some truly awful atrocities the reader remains aware that events are completely subject to the cosy demands of the narrative, not the other way around. Without an article, it means a part of algebra, such as linear algebra, elementary algebra (the symbol-manipulation rules taught in elementary courses of mathematics as part of primary and secondary education), or abstract algebra (the study of the algebraic structures for themselves).

The Algebraist - Iain Banks - Google Books The Algebraist - Iain Banks - Google Books

He was promoted to professor in 1960 then, in 1962, Milnor was appointed to the Henry Putman chair.

al·ge·bra

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:- 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. N H Kuiper, Review: Morse theory, by John Willard Milnor, Bull. Amer. Math. Soc. 71 (1) (1965), 136- 137. The word algebra is not only used for naming an area of mathematics and some subareas; it is also used for naming some sorts of algebraic structures, such as an algebra over a field, commonly called an algebra. Sometimes, the same phrase is used for a subarea and its main algebraic structures; for example, Boolean algebra and a Boolean algebra. A mathematician specialized in algebra is called an algebraist. It is evident now that low-dimensional dynamics, to a large extent initiated by Milnor's work, is a fundamental part of general dynamical systems theory. Milnor cast his eye on dynamical systems theory in the mid- 1970s. By that time the Smale program in dynamics had been completed. Milnor's approach was to start over from the very beginning, looking at the simplest nontrivial families of maps. The first choice, one-dimensional dynamics, became the subject of his joint paper with Thurston. Even the case of a unimodal map, that is, one with a single critical point, turns out to be extremely rich. This work may be compared with Poincaré's work on circle diffeomorphisms, which 100 years before had inaugurated the qualitative theory of dynamical systems. Milnor's work has opened several new directions in this field, and has given us many basic concepts, challenging problems and nice theorems.

The Algebraist - Wikiwand

Algebra began with computations similar to those of arithmetic, with letters standing for numbers. [7] This allowed proofs of properties that are true no matter which numbers are involved. For example, in the quadratic equation a x 2 + b x + c = 0 , {\displaystyle axfor a paper of fundamental and lasting importance, 'On manifolds homeomorphic to the 7-sphere', Annals of Mathematics 64 (1956), 399- 405. 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. J Milnor, Differential Topology Forty-six Years Later, Notices Amer. Math. Soc. 58 (6) (2011), 804- 809. J Milnor, Growing up in the old Fine Hall, in Prospects in Mathematics (Amer. Math. Soc., Providence, RI, 1999), 1- 11, H Bass, John Milnor, the algebraist, in Topological methods in modern mathematics (Houston, TX, 1993), 45- 84.

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The first time that I developed a particular interest in mathematics was as a freshman at Princeton University. I had been rather socially maladjusted and did not have too many friends, but when I came to Princeton, I found myself very much at home in the atmosphere of the mathematics common room. People were chatting about mathematics, playing games, and one could come by at any time and just relax. I found the lectures very interesting. I felt more at home there than I ever had before and I have stayed with mathematics ever since. The quadratic formula expresses the solution of the equation ax 2 + bx + c = 0, where a is not zero, in terms of its coefficients a, b and c. 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. 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. 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.

He began research at Princeton after graduating with his B.A. and, in 1953, before completing his doctoral studies, he was appointed to the faculty in Princeton. While undertaking research he enjoyed playing games in the common room. In particular he played Kriegspiel (a game of blindfold chess ), Go and Nash (a game invented by John Nash and now called Hex ). In fact John Nash was at Princeton during these years and Milnor and Nash often talked about game theory. Milnor's next paper, written while he was undertaking research, was Sums of positional games (1953). Milnor writes in the Introduction:- E H Spanier, Review: Characteristic classes, by John Willard Milnor and James D Stasheff, Bull. Amer. Math. Soc. 81 (5) (1975), 862- 866. 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:- For the kind of algebraic structure, see Algebra over a field. For other uses, see Algebra (disambiguation). E H Brown, Review: Topology from the differentiable viewpoint, by John Willard Milnor, Amer. Math. Monthly 74 (4) (1967), 461.

The Algebraist - Wikipedia

For a good overview of Milnor's mathematics, see the citations for the various prizes which he has won at THIS LINK. He received the Wolf Prize (1989), the Leroy P Steele Prize for Mathematical Exposition (2004), the Leroy P Steele Prize for Lifetime Achievement (2011), the Abel Prize (2011) and in 2014 was made a Fellow of the American Mathematical Society.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.