Series: Springer Monographs in Mathematics
1st ed. 2017, X, 206 p. 146 illus.
Hardcover
ISBN 978-981-10-4090-0
* Is the first undergraduate textbook on surface knots, quandles, and
two-dimensional braids
* Includes a quick course on classical knot theory
* Contains techniques for the motion picture method and quandle
theory that are not only useful but essential for research
This introductory volume provides the basics of surface-knots and related topics, not only
for researchers in these areas but also for graduate students and researchers who are not
familiar with the field.
Knot theory is one of the most active research fields in modern mathematics. Knots and
links are closed curves (one-dimensional manifolds) in Euclidean 3-space, and they are
related to braids and 3-manifolds. These notions are generalized into higher dimensions.
Surface-knots or surface-links are closed surfaces (two-dimensional manifolds) in
Euclidean 4-space, which are related to two-dimensional braids and 4-manifolds. Surfaceknot
theory treats not only closed surfaces but also surfaces with boundaries in 4-
manifolds. For example, knot concordance and knot cobordism, which are also important
objects in knot theory, are surfaces in the product space of the 3-sphere and the interval.
Included in this book are basics of surface-knots and the related topics of classical knots,
the motion picture method, surface diagrams, handle surgeries, ribbon surface-knots,
spinning construction, knot concordance and 4-genus, quandles and their homology
theory, and two-dimensional braids.
564pp Mar 2017
ISBN: 978-981-3202-11-5 (hardcover)
ISBN: 978-981-3202-12-2 (softcover)
The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret "non-commutative analysis" broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.)
A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras.
The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.
Foreword
Preface
Acknowledgments
Abbreviations, Notation, Some Core Theorems
Introduction and Motivation:
Subjects and User's Guide
Topics from Functional Analysis and Operators in Hilbert Space: A Selection:
Elementary Facts
Unbounded Operators in Hilbert Space
Spectral Theory
Applications:
GNS and Representations
Completely Positive Maps
Brownian Motion
Lie Groups, and Their Unitary Representations
The Kadison-Singer Problem
Extension of Operators:
Selfadjoint Extensions
Unbounded Graph-Laplacians
Reproducing Kernel Hilbert Space
Appendices:
An Overview of Functional Analysis Books (Cast of Characters)
Terminology from Neighboring Areas
Often Cited
Prizes and Fame
List of Exercises
Definitions of Frequently Occurring Terms
List of Figures
List of Tables
Bibliography
Index
Undergraduates, graduate students and researchers in operator theory, functional
analysis, mathematical physics, complex analysis, stochastic analysis,
quantum mechanics.
World Century Mathematical Olympiad Series: Volume 2200pp Aug 2017
ISBN: 978-1-938134-95-1 (hardcover)
ISBN: 978-1-938134-92-0 (softcover)
The focus of this book is algebraic inequalities. Not only is it the current Mathematical Olympiad hot topic, it is also the basis of geometric inequalities. In addition, the book involves some analysis on inequality.
This book serves as a good reference in the field of algebraic inequalities as faced in problems found in a Mathematical Olympiad.
Inequalities and Equalities
Transformation
Homogenizations and Normalizations
Inequalities of Sequences
Convex Function and Some Complex Inequalities
Inequality Skills of Arqady
Answer Sheet and Hints
School students keen to learn more of mathematics and specifically mathematics related to the IMO; coaches and instructors of mathematical competitions.