Anderson, James W

Hyperbolic Geometry

Series: Springer Undergraduate Mathematics Series
2nd ed., 2005, XII, 276 p. 21 illus., Softcover
ISBN: 1-85233-934-9

About this textbook

The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, providing the reader with a firm grasp of the concepts and techniques of this beautiful area of mathematics. Topics covered include the upper half-space model of the hyperbolic plane, Mobius transformations, the general Mobius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincare disc model, convex subsets of the hyperbolic plane, and the Gauss-Bonnet formula for the area of a hyperbolic polygon and its applications.

Table of contents

Preamble to the Second Edition
Preamble to the First Edition
The Basic Spaces
The General Mobius Group
Length and Distance in H
Planar Models of the Hyperbolic Plane
Convexity, Area and Trigonometry
Non-planar models
Solutions to Exercises
References;
List of Notation
Index

Akulin, Vladimir M.

Coherent Dynamics of Complex Quantum Systems

Series: Texts and Monographs in Physics
2005, X, 471 p. 140 illus., Hardcover
ISBN: 3-540-21052-0

About this textbook

A large number of modern problems in physics, chemistry, and quantum electronics require a consideration of population dynamics in complex multilevel quantum systems. The purpose of this book is to provide a systematic treatment of these questions and to present a number of exactly solvable problems. It considers the different dynamical problems frequently encountered in different areas of physics from the same perspective, based mainly on the fundamental ideas of group theory and on the idea of ensemble average. Also treated are concepts of complete quantum control and correction of decoherence induced errors that are complementary to the idea of ensemble average. Coherent Dynamics of Complex Quantum Systems is aimed at senior-level undergraduate students in the areas of atomic, molecular, and laser physics, physical chemistry, quantum optics and quantum informatics. It should help them put particular problems in these fields into a broader scientific context and thereby take advantage of the well-elaborated technique of the adjacent fields.

Table of contents

Complex Systems and Statistical Description.- Examples of Complex Systems.- Two-Level and Level-Band Systems.- Two-Band System.- Soluble Time-Dependent Systems.- Time-Dependent Complex Systems.- Dynamics of 1-D Relay Type System.- Composed Complex Quantum Systems.- Bibliography and Problems.- References.

by Stephen G. Simpson (Editor)

Reverse Mathematics 2001
Lecture Notes in Logic 21

Summary

Reverse Mathematics is a program of research in the foundations of mathematics, motivated by the foundational questions of what are appropriate axioms for mathematics, and what are the logical strengths of particular axioms and particular theorems. The book contains 24 original papers by leading researchers. These articles exhibit the exciting recent developments in reverse mathematics and subsystems of second order arithmetic.

Details
ISBN: 1-56881-263-9
Year: 2005
Format: Hardcover
Pages: 416

***************************************************