It includes worked solutions to all exercises and problems in the associated textbook. This is an invaluable handbook for students and teachers attending or giving courses in probability
It contains more than 1300 exercises across a range of difficulty and topic. It is an essential aid for teachers compiling examinations and seeking exercises to illuminate lecture courses.
New to this Edition:
The number of exercises and problems has been increased by around 300 to a total of about 1317
There are sections on coupling from the past, Levy processes, self-similarity and stability, time changes, and the holding-time/jump-chain construction of continuous-time Markov chains
This third edition is a revised, updated, and greatly expanded version of previous edition of 2001. The 1300+ exercises contained within are not merely drill problems, but have been chosen to illustrate the concepts, illuminate the subject, and both inform and entertain the reader. A broad range of subjects is covered, including elementary aspects of probability and random variables, sampling, generating functions, Markov chains, convergence, stationary processes, renewals, queues, martingales, diffusions, Levy processes, stability and self-similarity, time changes, and stochastic calculus including option pricing via the Black-Scholes model of mathematical finance.
The text is intended to serve students as a companion for elementary, intermediate, and advanced courses in probability, random processes and operations research. It will also be useful for anyone needing a source for large numbers of problems and questions in these fields. In particular, this book acts as a companion to the authors' volume, Probability and Random Processes, fourth edition (OUP 2020).
1:Events and their probabilities
2:Random variables and their distributions
3:Discrete random variables
4:Continuous random variables
5:Generating functions and their applications
6:Markov chains
7:Convergence of random variables
8:Random processes
9:Stationary processes
10:Renewals
11:Queues
12:Martingales
13:Diffusion processes
Paperback
Published: 16 July 2020
592 Pages
246x171mm
ISBN: 9780198847618
Integrated approach that uses several up-to-date notions allows for improved understanding of topics
An original bridge between physics and mathematics, contributing to clarify the mathematical foundations of field theory
Helps to cement a firm understanding of the basic ideas involved in quantum particle physics
Gauge Field theory in Natural Geometric Language addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a brief, integrated approach that exploits standard and non-standard notions, as well as recent advances, in a natural geometric language in which the role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves.
In proposing an original bridge between physics and mathematics, this text will appeal not only to mathematicians who wish to understand some of the basic ideas involved in quantum particle physics, but also to physicists who are not satisfied with the usual mathematical presentations of their field.
1:Bundle prolongations and connections
2:Special algebraic notions
3:Spinors and Minkowski space
4:Spinor bundles and spacetime geometry
5:Classical gauge field theory
6:Gauge field theory and gravitation
7:Optical geometry
8:Electroweak geometry and fields
9:First-order theory of fields with arbitrary spin
10:Infinitesimal deformations of ECD fields
11:Generalised maps
12:Special generalised densities on Minkowski spacetime
13:Multi-particle spaces
14:Bundles of quantum states
15:Quantum bundles
16:Quantum fields
17:Detectors
18:Free quantum fields
19:Electroweak extensions
20:Basic notions in particle physics
21:Scattering matrix computations
22:Quantum electrodynamics
23:On gauge freedom and interactions
Hardback
Published: 05 October 2020
368 Pages
234x156mm
ISBN: 9780198861492
Psychologically natural introduction to the subject, informed by research in undergraduate mathematics education
In-depth exploration of examples via tables and diagrams
Focus on why: why definitions are sensible, why key results hold for some mathematical objects but not others, and why mathematicians care about what they care about
How to Think about Abstract Algebra provides an engaging and readable introduction to its subject, which encompasses group theory and ring theory. Abstract Algebra is central in most undergraduate mathematics degrees, and it captures regularities that appear across diverse mathematical structures - many people find it beautiful for this reason. But its abstraction can make its central ideas hard to grasp, and even the best students might find that they can follow some of the reasoning without really understanding what it is all about.
This book aims to solve that problem. It is not like other Abstract Algebra texts and is not a textbook containing standard content. Rather, it is designed to be read before starting an Abstract Algebra course, or as a companion text once a course has begun. It builds up key information on five topics: binary operations, groups, quotient groups, isomorphisms and homomorphisms, and rings. It provides numerous examples, tables and diagrams, and its explanations are informed by research in mathematics education.
The book also provides study advice focused on the skills that students need in order to learn successfully in their own Abstract Algebra courses. It explains how to interact productively with axioms, definitions, theorems and proofs, and how research in psychology should inform our beliefs about effective learning.
Cover
How to Think About Abstract Algebra
Lara Alcock
Table of Contents
1:What is Abstract Algebra?
2:Axioms and Denitions
3:Theorems and Proofs
4:Studying Abstract Algebra
5:Binary Operations
6:Groups and Subgroups
7:Quotient Groups
8:Isomorphisms and Homomorphisms
9:Rings
References
Paperback
Published: 29 January 2021 (Estimated)
256 Pages
196x129mm
ISBN: 9780198843382
Presents for the first time all works of Eugenio Calabi, one of the most
influencial geometers of the last century
Includes scholarly comments on Calabifs work and impact by leading
differential geometers
While Eugenio Calabi is best known for his contributions to the theory of Calabi-Yau manifolds,
this Steele-Prize-winning geometerfs fundamental contributions to mathematics have been far
broader and more diverse than might be guessed from this one aspect of his work. His works
have deep influence and lasting impact in global differential geometry, mathematical physics
and beyond. By bringing together 47 of Calabifs important articles in a single volume, this book
provides a comprehensive overview of his mathematical oeuvre, and includes papers on
complex manifolds, algebraic geometry, Kahler metrics, affine geometry, partial differential
equations, several complex variables, group actions and topology. The volume also includes
essays on Calabifs mathematics by several of his mathematical admirers, including S.K.
Donaldson, B. Lawson and S.-T. Yau, Marcel Berger; and Jean Pierre Bourguignon.This book is
intended for mathematicians and graduate students around the world. Calabifs visionary
contributions will certainly continue to shape the course of this subject far into the future.
Mathematics : Differential Geometry
Due 2020-11-26
1st ed. 2021, Approx. 840 p.
Hardcover
ISBN 978-3-662-62133-2
Product category ] Collected works
A very readable introduction to modern mathematical topics in quantum
mechanics
Solves the problem of how to teach quantum mechanics to mathematically
oriented students in an optimal way
Shows how the mathematical treatment of quantum mechanics brings
insights to physics
Useful guide to the literature
The book gives a streamlined introduction to quantum mechanics while describing the basic
mathematical structures underpinning this discipline. Starting with an overview of key physical
experiments illustrating the origin of the physical foundations, the book proceedswith a
description of the basic notions of quantum mechanics and their mathematical content. It then
makes its way to topics of current interest, specifically those in which mathematics plays an
important role. The more advanced topics presented include:many-body systems, modern
perturbation theory, path integrals, the theoryof resonances, adiabatic theory,geometrical
phases, Aharonov-Bohm effect, density functional theory, open systems,the theoryof radiation
(non-relativistic quantum electrodynamics), and the renormalizationgroup. With different
selections of chapters, the book can serve as a text for an introductory,intermediate, or
advanced course in quantum mechanics. Some of the sections could be used for introductions
to geometrical methods in Quantum Mechanics, to quantum information theory and to
quantum electrodynamics and quantum field theory.
Mathematics : Functional Analysis
Due 2020-11-26
3rd ed. 2020, XIV, 456 p.33 illus.
Softcover
ISBN 978-3-030-59561-6
Product category : Graduate/advanced undergraduate textbook
Series : Universitext