Lecture Notes of the Les Houches Summer School: Volume 103,
August 2014
Published: 12 January 2017 (Estimated)
608 Pages
246x171mm
ISBN: 9780198785781
Presents a modern view on topological matter
Pedagogical presentation
Covers a wide spectrum of topics
Provides basic and advanced lectures
Contributions from leading scientists in the field
This book contains lecture notes by world experts on one of the most rapidly growing fields of research in physics. Topological quantum phenomena are being uncovered at unprecedented rates in novel material systems. The consequences are far reaching, from the possibility of carrying currents and performing computations without dissipation of energy, to the possibility of realizing platforms for topological quantum computation.The pedagogical lectures contained in this book are an excellent introduction to this blooming field. The lecture notes are intended for graduate students or advanced undergraduate students in physics and mathematics who want to immerse in this exciting XXI century physics topic.
This Les Houches Summer School presents an overview of this field, along with a sense of its origins and its placement on the map of fundamental physics advancements. The School comprised a set of basic lectures (part 1) aimed at a pedagogical introduction of the fundamental concepts, which was accompanied by more advanced lectures (part 2) covering individual topics at the forefront of today's research in condensed-matter physics.
Published: 26 January 2017 (Estimated)
544 Pages
246x189mm
Hardback
ISBN: 9780198747826
Paperback
ISBN: 9780198747833
A complete guide to one of the greatest scientists of the 20th century
Covers aspects of Turing's life and the wide range of his intellectual activities
Aimed at a wide readership
This carefully edited resource written by a star-studded list of contributors
Around 100 illustrations
Alan Turing has long proved a subject of fascination, but following the centenary of his birth in 2012, the code-breaker, computer pioneer, mathematician (and much more) has become even more celebrated with much media coverage, and several meetings, conferences and books raising public awareness of Turing's life and work.
This volume will bring together contributions from some of the leading experts on Alan Turing to create a comprehensive guide to Turing that will serve as a useful resource for researchers in the area as well as the increasingly interested general reader. The book will cover aspects of Turing's life and the wide range of his intellectual activities, including mathematics, code-breaking, computer science, logic, artificial intelligence and mathematical biology, as well as his subsequent influence.
April 3, 2017
Textbook - 872 Pages - 893 B/W Illustrations
ISBN 9781498730655
Series: Textbooks in Mathematics
Emphasizes proofs, which will appeal to a subset of this course market
Links examples to exercise sets
Offers edition that has been heavily reviewed and developed
Focuses on graph theory
Covers trees and algorithms
This book is intended for a one-semester course in discrete mathematics. Such a course is typically taken by mathematics, mathematics education, and computer science majors, usually in their sophomore year. Calculus is not a prerequisite to use this book. Part one focuses on how to write proofs, then moves on to topics in number theory, employing set theory in the process. Part two focuses on computations, combinatorics, graph theory, trees, and algorithms.
PROOFS. Logic and Sets. Basic Proof Writing. Elementary Number Theory. Indexed by Integers. Relations. COMPUTATIONS AND PROBLEM SOLVING. Basic Counting. More Counting. Basic Graph Theory. Graph Properties. Trees and Algorithms. Answers to Selected Exercises. Appendices.
A Graduate Course in Algebra: Volume 1
A Graduate Course in Algebra: Volume 2
700pp May 2017
ISBN: 978-981-3142-60-2 (hardcover)
ISBN: 978-981-3142-61-9 (softcover)
This comprehensive two-volume book deals with algebra, broadly conceived. Volume 1 (Chapters 1?6) comprises material for a first year graduate course in algebra, offering the instructor a number of options in designing such a course. Volume 1, provides as well all essential material that students need to prepare for the qualifying exam in algebra at most American and European universities. Volume 2 (Chapters 7?13) forms the basis for a second year graduate course in topics in algebra. As the table of contents shows, that volume provides ample material accommodating a variety of topics that may be included in a second year course. To facilitate matters for the reader, there is a chart showing the interdependence of the chapters.
Volume 1:
Introduction and Fundamentals
Groups
Further Topics in Group Theory
Vector Spaces
Inner Product Spaces
Rings, Fields and Algebras
Modules
Volume 2:
Multilinear Algebra
Symplectic Geometry
Commutative Algebra
Valuations and p-adic Numbers
Galois Theory
Representations of Finite Groups
Representations of Associative Algebras
Readership: Graduate students and researchers in Algebra and related areas.
300pp Jul 2017
ISBN: 978-981-4713-58-0 (hardcover)
We propose a new direction for stochastic analysis. Starting with a noise which is a system of i.i.d. idealized elemental random variables, we form polynomials in the noise and come to the space of generalized functionals of the noise with special emphasis on the Gaussian noise. New tools of analyzing these functionals are introduced. We further establish a harmonic analysis arising from the infinite dimensional rotation group which plays significant roles in white noise analysis. Many applications, in particular to quantum dynamics, have been shown.
Functionals of other kind of noises are discussed. As a new approach, we discuss functionals of a space noise. There one can find similarity and dissimilarity as well as duality to the analysis of Poisson noise functionals.
White Noise (Gaussian Noise)
New Noise Depending on the Space Variable
Generalized Functionals of a Noise
Harmonic Analysis Arising from Infinite Dimensional Rotation Group
Operators Acting on the Space of Functionals of a Noise
Topics in the Related Fields
Applications
Readership: Researchers in stochastic analysis, probability and statistics and mathematical physics.