Книга: Jones Vaughan «Focus 3. Student's Book»

Focus 3. Student's Book

Серия: "Focus"

Focus is a rich, varied, carefully levelled course for upper secondary students. Specially designed to motivate older teens, it helps them to track their level and achieve the exam results they need. With its unique blended learning package, Focus is the flexible course that gets results.

Издательство: "Pearson Education (Longman)" (2015)

ISBN: 978-1-4479-9809-9

Купить за 1283 руб в My-shop

Другие книги автора:

КнигаОписаниеГодЦенаТип книги
Focus BRE 3. Student's Book&MyEnglishLab PackFocus is a rich, varied, carefully levelled course for upper secondary students. Specially designed to motivate older teens, it helps them to track their level and achieve the exam results they need… — Pearson Education (Longman), Focus Подробнее...20162115бумажная книга
Focus BRE 2. Student's Book&MyEnglishLab PackFocus is a rich, varied, carefully levelled course for upper secondary students. Specially designed to motivate older teens, it helps them to track their level and achieve the exam results they need… — Pearson Education (Longman), Focus Подробнее...20162115бумажная книга
Focus 3. Student's Book with Practice Tests Plus Preliminary Booklet Pack (количество томов: 2)Five-level upper secondary course. Exams oriented learning path for state and private school students. A course structured to promote motivation, memory and meaning. A unique approach to teaching and… — Pearson Education (Longman), Focus Подробнее...20162361бумажная книга
Focus 5. Student's Book&MyEnglishLab PackFocus is a rich, varied, carefully leveled course for upper secondary students. Specially designed to motivate older teens, it helps them to track their level and achieve the exam results they need… — Pearson Education (Longman), Focus Подробнее...20172115бумажная книга
Focus 4. Student's Book + Practice Tests Plus First Booklet PackFocus is a rich, varied, carefully levelled course for upper secondary students. Specially designed to motivate older teens, it helps them to track their level and achieve the exam results they need… — Pearson Education (Longman), Focus Подробнее...20162019бумажная книга
New Inside Out. Intermediate. Student's Pack (+ CD-ROM)The Student’s Book Pack consists of a visually engaging, 16 unit Student’s Book that develops the core skills through challenging and fun activities. Special ‘Extra’ sections further develop… — Macmillan Publishers, - Подробнее...20161968бумажная книга
New Inside Out. Intermediate. Student`s Pack (+ CD-ROM)The Student s Book Pack consists of a visually engaging, 16 unit Student s Book that develops the core skills through challenging and fun activities. Special Extra sections further develop student… — Macmillan Publishers, (формат: 296x210x10мм, 128 стр.) Подробнее...20162917бумажная книга

Jones, Vaughan

▪ New Zealand mathematician
in full  Vaughan Frederick Randal Jones 
born December 31, 1952, Gisborne, New Zealand

      New Zealand mathematician who was awarded the Fields Medal in 1990 for his study of functional analysis (analysis) and knot theory.

      Jones attended the University of Geneva's school of mathematics (Ph.D., 1979) and became a professor at the University of California, Berkeley, U.S., in 1985. He was awarded the Fields Medal at the International Congress of Mathematicians in Kyōto, Japan, in 1990.

      In his study of von Neumann algebras (algebras of bounded operators acting on a Hilbert space), Jones came across polynomials that were invariant for knots and links—simple closed curves in three-dimensional space. Initially it was suspected that these were essentially Alexander polynomials (named after the work of the American mathematician James W. Alexander (Alexander, James Waddell, II) in 1928), but this turned out not to be the case. For any topological displacement (without cutting the loop), the associated Alexander polynomial is unchanged, or invariant. Both Alexander's polynomials and the new polynomials are specializations of the more general two-variable Jones polynomials. The Jones polynomials do have an advantage over the earlier Alexander polynomials in that they distinguish knots from their mirror images. Further, while these polynomials are useful in knot theory, they are also of interest in the study of statistical mechanics, Dynkin diagrams in the representation theory of simple Lie algebras, and quantum groups. (For further information, see mathematics, history of: Mathematical physics and the theory of groups (mathematics).)

      Jones's publications include Actions of Finite Groups on the Hyperfinite Type II 1 Factor (1980); with Frederick M. Goodman and Pierre de la Harpe, Coxeter Graphs and Towers of Algebras (1989); and Subfactors and Knots (1991).

* * *

Источник: Jones, Vaughan

См. также в других словарях:

  • Student life at Brigham Young University — is heavily influenced by the fact that 98% of its students are members of the Church of Jesus Christ of Latter day Saints. The school is privately owned by the church and aims to create an atmosphere in which secular and religious principles are… …   Wikipedia

  • Student activism — is work done by students to effect political, environmental, economic, or social change. It has often focused on making changes in schools, such as increasing student influence over curriculum or improving educational funding. In some settings,… …   Wikipedia

  • Student prank — University students have a long association with pranks and japes. [ [http://www.princeton.edu/mudd/news/faq/topics/pranks.shtml Seeley G. Mudd Manuscript Library : FAQ Student pranks ] ] [ [http://www.kiwiblog.co.nz/2006/10/student pranks.html… …   Wikipedia

  • Student — For other uses, see Student (disambiguation). Students attending a lecture on linear algebra at the Helsinki University of Technology …   Wikipedia

  • Book of Mormon — This article is about the religious book. For the Broadway musical, see The Book of Mormon (musical). For other uses, see Book of Mormon (disambiguation). Part of a series on …   Wikipedia

  • Behemoth (book) — Behemoth, full title Behemoth: the history of the causes of the civil wars of england, and of the counsels and artifices by which they were carried on from the year 1640 to the year 1660 , also known as The Long Parliament , is a book written by… …   Wikipedia

Поделиться ссылкой на выделенное

Прямая ссылка:
… Нажмите правой клавишей мыши и выберите «Копировать ссылку»