The Geometry of Numbers

Author: C. D. Olds,Anneli Lax,Giuliana Davidoff,Giuliana P. Davidoff

Publisher: Cambridge University Press

ISBN: 9780883856437

Category: Mathematics

Page: 174

View: 2644


A self-contained introduction to the geometry of numbers.

Introductory Lectures on Knot Theory

Selected Lectures Presented at the Advanced School and Conference on Knot Theory and Its Applications to Physics and Biology, ICTP, Trieste, Italy, 11 - 29 May 2009

Author: Louis H. Kauffman

Publisher: World Scientific

ISBN: 9814313009

Category: Mathematics

Page: 519

View: 3856


More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book.


The Scientific Computation System

Author: Richard D. Jenks,Robert S. Sutor

Publisher: Springer

ISBN: 1461229405

Category: Mathematics

Page: 742

View: 8899


Recent advances in hardware performance and software technology have made possible a wholly different approach to computational mathematics. Symbolic computation systems have revolutionized the field, building upon established and recent mathematical theory to open new possibilities in virtually every industry. Formerly dubbed Scratchpad, AXIOM is a powerful new symbolic and numerical system developed at the IBM Thomas J. Watson Research Center. AXIOM's scope, structure, and organization make it outstanding among computer algebra systems. AXIOM: The Scientific Computation System is a companion to the AXIOM system. The text is written in a straightforward style and begins with a spirited foreword by David and Gregory Chudnovsky. The book gives the reader a technical introduction to AXIOM, interacts with the system's tutorial, accesses algorithms newly developed by the symbolic computation community, and presents advanced programming and problem solving techniques. Eighty illustrations and eight pages of color inserts accompany text detailing methods used in the 2D and 3D interactive graphics system, and over 2500 example input lines help the reader solve formerly intractable problems.