Contemporary Mathematics, Volume: 536
2011; 152 pp; softcover
ISBN-13: 978-0-8218-4975-0
Expected publication date is March 13, 2011.
This volume contains a collection papers, written by physicists, computer scientists, and mathematicians, from the Conference on Representation Theory, Quantum Field Theory, Category Theory, and Quantum Information Theory, which was held at the University of Texas at Tyler from October 1-4, 2009.
Quantum computing is a field at the interface of the physical sciences, computer sciences and mathematics. As such, advances in one field are often overlooked by practitioners in other fields. This volume brings together articles from each of these areas to make students, researchers and others interested in quantum computation aware of the most current advances. It is hoped that this work will stimulate future advances in the field.
Graduate students and research mathematicians interested in quantum computing.
A. D. Ballard and Y.-S. Wu -- Cartan decomposition and entangling power of braiding quantum gates
G. Chen, V. Ramakrishna, and Z. Zhang -- A unified approach to universality for three distinct types of 2-qubit quantum computing devices
S. Bravyi -- Efficient algorithm for a quantum analogue of 2-SAT
H. E. Brandt -- Quantum computational curvature and Jacobi fields
L. H. Kauffman -- A quantum model for the Jones polynomial, Khovanov homology and generalized simplicial homology
L. H. Kauffman and D. E. Radford -- Oriented quantum algebras and coalgebras, invariants of oriented 1-1 tangles, knots and links
P. Benioff -- Space and time lattices in frame fields of quantum representations of real and complex numbers
Student Mathematical Library, Volume: 57
2011; approx. 246 pp; softcover
ISBN-13: 978-0-8218-5261-3
Expected publication date is April 10, 2011.
This book explores four real-world topics through the lens of probability theory. It can be used to supplement a standard text in probability or statistics. Most elementary textbooks present the basic theory and then illustrate the ideas with some neatly packaged examples. Here the authors assume that the reader has seen, or is learning, the basic theory from another book and concentrate in some depth on the following topics: streaks, the stock market, lotteries, and fingerprints. This extended format allows the authors to present multiple approaches to problems and to pursue promising side discussions in ways that would not be possible in a book constrained to cover a fixed set of topics.
To keep the main narrative accessible, the authors have placed the more technical mathematical details in appendices. The appendices can be understood by someone who has taken one or two semesters of calculus.
Undergraduate students interested in the connections of mathematics (specifically, probability and statistics) and real-life stories.
Streaks
Modeling the stock market
Lotteries
Fingerprints
Answers to John Haigh's lottery questions
Bibliography
Index
Graduate Studies in Mathematics, Volume: 122
2011; approx. 232 pp; hardcover
ISBN-13: 978-0-8218-5318-4
Expected publication date is April 8, 2011.
Differential Galois theory has seen intense research activity during the last decades in several directions: elaboration of more general theories, computational aspects, model theoretic approaches, applications to classical and quantum mechanics as well as to other mathematical areas such as number theory.
This book intends to introduce the reader to this subject by presenting Picard-Vessiot theory, i.e. Galois theory of linear differential equations, in a self-contained way. The needed prerequisites from algebraic geometry and algebraic groups are contained in the first two parts of the book. The third part includes Picard-Vessiot extensions, the fundamental theorem of Picard-Vessiot theory, solvability by quadratures, Fuchsian equations, monodromy group and Kovacic's algorithm. Over one hundred exercises will help to assimilate the concepts and to introduce the reader to some topics beyond the scope of this book.
This book is suitable for a graduate course in differential Galois theory. The last chapter contains several suggestions for further reading encouraging the reader to enter more deeply into different topics of differential Galois theory or related fields.
Graduate students and research mathematicians interested in algebraic methods in differential equations, differential Galois theory, and dynamical systems.
Algebraic geometry
Affine and projective varieties
Algebraic varieties
Algebraic groups
Basic notions
Lie algebras and algebraic groups
Differential Galois theory
Picard-Vessiot extensions
The Galois correspondence
Differential equations over mathbb{C}(z)
Suggestions for further reading
Bibliography
Index
584 pages
Trim Size 6 1/8 X 9 1/5 in
Copyright 2011
Hardcover
Key Features
* Realistic applications from a variety of disciplines integrated throughout the text
* Plentiful, updated and more rigorous problems, including computer ''challenges''
* Revised end-of-chapter exercises sets*in all, 250 exercises with answers
* New chapter on Brownian motion and related processes
* Additional sections on Matingales and Poisson process
* Solutions manual available to adopting instructors
Serving as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus, Introduction to Stochastic Modeling, Third Edition, bridges the gap between basic probability and an intermediate level course in stochastic processes. The objectives of the text are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide exercises in the application of simple stochastic analysis to realistic problems.
Upper division undergraduate and graduate-level courses in stochastic processes and stochastic modeling, offered in statistics and mathematics departments at all major universities.
Conditional Probability and Conditional Expectation
Markov Chains: Introduction
The Long Run Behavior of Markov Chains
Poisson Processes
Continuous Time Markov Chains
Renewal Phenomena
Brownian Motion and Related Processes
Queueing Systems
ISBN13: 9780805382914 Hardcover
ISBN13: 9780321503367 Softcover
language: English
total pages: 550
pub.-date: Juli 2010
This best-selling classic provides a graduate-level, non-historical, modern introduction of quantum mechanical concepts. The author, J. J. Sakurai, was a renowned theorist in particle theory. This revision by Jim Napolitano retains the original material and adds topics that extend the text's usefulness into the 21st century. The introduction of new material, and modification of existing material, appears in a way that better prepares the student for the next course in quantum field theory. Students will still find such classic developments as neutron interferometer experiments, Feynman path integrals, correlation measurements, and Bell's inequality. The style and treatment of topics is now more consistent across chapters.
The chapter on scattering theory (Chapter 6 in this edition) is completely reorganized, with a new introduction based on time dependent perturbation theory.
Explicit solutions to the SchrodingerWave Equation have been added, including the linear potential, the simple harmonic oscillator using generating functions, and the derivation of spherical harmonics.
A discussion of SO(4) symmetry and its application to solving the hydrogen atom and approximation techniques based on extreme time dependences have been added to early chapters.
The chapter on identical particles (Chapter 7 in this edition) is now expanded to include the technique of second quantization and its application to electrons in solids and the quantized electromagnetic field.
A new chapter on relativistic wave mechanics has been added (Chapter 8).
Discussion, including literature references, of experimental demonstration of quantum mechanical phenomena is featured, including: the Stern-Gerlach experiment on cesium atoms, muon spin rotation and g-2, neutrino oscillations, gbouncingh ultracold neutrons, Berry's phase with neutrons, elastic scattering of protons from nuclei, the effects of exchange symmetry in nuclear decay, and the Casimir effect, among others.
Advanced mathematical techniques (for example generating functions and contour integrals) associated with quantum mechanical calculations appear throughout.