Book: Sue Kay, Vaughan Jones «New Inside Out: Upper-Intermediate: Student's Book (+ CD-ROM)»

New Inside Out: Upper-Intermediate: Student's Book (+ CD-ROM)

What's new in New Inside Out Upper Intermediate? There are now 8 pages of 'core' content per unit, plus extra pages which comprise the additional syllabus. Useful phrases - a language bank of practical English, built up unit-by-unit, to provide students with the key language they need outside the classroom. Vocabulary Extra pages - These are linked to the Macmillan English Dictionary, and develop dictionary skills. They focus on language features such as collocation, synonyms, word families and more. In the Upper Intermediate level these pages are alternated with Writing Extra sections, which focus on writing skills. Grammar sections - New Inside Out provides the support teachers need for the effective teaching of grammar. There are two comprehensive grammar sections in every unit. In addition, students are referred to the Grammar Extra section at the back of the student's book for extended explanations and practice. Clear signposting - New design features...

Издательство: "Macmillan Publishers Limited" (2009)

Формат: 210x295, 160 стр.

ISBN: 978-0-230-00914-1

Купить за 2039 руб на Озоне

Vaughan Jones

Infobox Scientist
box_width =
name = Vaughan Frederick Randal Jones



image_size =
caption = Vaughan Jones in 2007
birth_date = Birth date and age|1952|12|31
birth_place = Gisborne, New Zealand
death_date =
death_place =
residence =
citizenship =
nationality =
ethnicity =
fields = Mathematics
workplaces = University of California, Berkeley
alma_mater = University of Geneva
University of Auckland
doctoral_advisor = André Haefliger
academic_advisors =
doctoral_students =
notable_students =
known_for = Von Neumann algebras, knot polynomials,
conformal field theory
author_abbrev_bot =
author_abbrev_zoo =
influences =
influenced =
awards = Fields Medal (1990)
religion =


footnotes =

Vaughan Frederick Randal Jones DCNZM (born 31 December 1952) is a New Zealand mathematician, known for his work on von Neumann algebras, knot polynomials and conformal field theory. He was awarded a Fields Medal in 1990, and famously wore a New Zealand rugby jersey when he accepted the prize. Jones is a professor at the University of California, Berkeley and a Distinguished Alumni Professor at the University of Auckland.

Jones was born in Gisborne, New Zealand and brought up in Cambridge, New Zealand, completing secondary school at Auckland Grammar School. His undergraduate studies were at the University of Auckland, from where he obtained a B.Sc. in 1972 and an M.Sc. in 1973. For his graduate studies, he went to Switzerland, where he completed his Ph.D. at the University of Geneva in 1979. His thesis, titled "Actions of finite groups on the hyperfinite II1 factor", was written under the supervision of André Haefliger. In 1980, he moved to the United States, where he taught at the University of California, Los Angeles (1980-1981) and the University of Pennsylvania (1981-1985), before being appointed as Professor of Mathematics at the University of California, Berkeley.

His work on knot polynomials, with the discovery of what is now called the Jones polynomial, was from an unexpected direction with origins in the theory of von Neumann algebras, an area of analysis already much developed by Alain Connes. It led to the solution of a number of the classical problems of knot theory, and to increased interest in low-dimensional topology.

He was awarded Distinguished Companionship of the New Zealand Order of Merit in 2002 (an equivalent of a Knighthood under the old honours system).

ee also

*Subfactor

External links

*MacTutor Biography|id=Jones_Vaughan
*MathGenealogy |id=25056
* [http://math.berkeley.edu/~vfr/ Jones' home page]
* [http://www.math.auckland.ac.nz/Careers/vaughan/vaughan.htm Career profile page at the University of Auckland]

Persondata
NAME= Jones, Vaughan Frederick Randal
ALTERNATIVE NAMES=
SHORT DESCRIPTION=New Zealand mathematician and Fields Medalist
DATE OF BIRTH= December 31, 1952
PLACE OF BIRTH= Gisborne, New Zealand
DATE OF DEATH=
PLACE OF DEATH=

Источник: Vaughan Jones

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