Date Published: July 2017
format: Hardback
isbn: 9781107160019
Since its conception in the 1960s, string theory has been hailed as one of the most promising routes we have to unify quantum mechanics and general relativity. This book provides a concise introduction to string theory explaining central concepts, mathematical tools and covering recent developments in physics including compactifications and gauge/string dualities. With string theory being a multidisciplinary field interfacing with high energy physics, mathematics and quantum field theory, this book is ideal for both students with no previous knowledge of the field and scholars from other disciplines who are looking for an introduction to basic concepts.
A self-contained text which keeps advanced mathematical background to a minimum, making it easy to follow
Provides a modern treatment of string theory which builds foundations to enable understanding of important recent developments
An excellent text for self-study, providing concrete calculations and exercises, and covering topics from undergraduate level to topical research in mathematical physics
Part of London Mathematical Society Lecture Note Series
Date Published: June 2017
format: Paperback
isbn: 9781108413138
This volume contains nine survey articles which provide expanded accounts of plenary seminars given at the British Combinatorial Conference at the University of Strathclyde in July 2017. This biennial conference is a well-established international event attracting speakers from around the world. Written by internationally recognised experts in the field, these articles represent a timely snapshot of the state of the art in the different areas of combinatorics. Topics covered include the robustness of graph properties, the spt-function of Andrews, switching techniques for edge decompositions of graphs, monotone cellular automata, and applications of relative entropy in additive combinatorics. The book will be useful to researchers and advanced graduate students, primarily in mathematics but also in computer science and statistics.
Provides nine survey articles by world-leading researchers in combinatorics
Summarises the current state of the field
Accessible to non-experts
Publication planned for: November 2017
format: Hardback
isbn: 9781107109353
Peter L. Montgomery has made significant contributions to computational number theory, introducing many basic tools such as Montgomery multiplication, Montgomery simultaneous inversion, Montgomery curves, and the Montgomery ladder. This book features state-of-the-art research in computational number theory related to Montgomery's work and its impact on computational efficiency and cryptography. Topics cover a wide range of topics such as Montgomery multiplication for both hardware and software implementations; Montgomery curves and twisted Edwards curves as proposed in the latest standards for elliptic curve cryptography; and cryptographic pairings. This book provides a comprehensive overview of integer factorization techniques, including dedicated chapters on polynomial selection, the block Lanczos method, and the FFT extension for algebraic-group factorization algorithms. Graduate students and researchers in applied number theory and cryptography will benefit from this survey of Montgomery's work.
Provides a comprehensive overview of Peter L. Montgomery's contributions to number field and cryptography
Serves as a textbook for a wide range of computational number theory topics
Includes contributions by leading experts on each topic
1. Introduction Joppe W. Bos, Arjen K. Lenstra, Herman te Riele and Daniel Shumow
2. Montgomery arithmetic from a software perspective Joppe W. Bos and Peter L. Montgomery
3. Hardware aspects of Montgomery modular multiplication Colin D. Walter
4. Montgomery curves and the Montgomery ladder Daniel J. Bernstein and Tanja Lange
5. General purpose integer factoring Arjen K. Lenstra
6. Polynomial selection for the number field sieve Thorsten Kleinjung
7. The block lanczos algorithm Emmanuel Thome
8. FFT extension for algebraic-group factorization algorithms Richard P. Brent, Alexander Kruppa and Paul Zimmerman
9. Cryptographic pairings Kristin Lauter and Michael Naehrig.
Publication planned for: December 2017
format: Paperback
isbn: 9781316615102
This introduction to finite difference and finite element methods is aimed at graduate students who need to solve differential equations. The prerequisites are few (basic calculus, linear algebra, and ODEs) and so the book will be accessible and useful to readers from a range of disciplines across science and engineering. Part I begins with finite difference methods. Finite element methods are then introduced in Part II. In each part, the authors begin with a comprehensive discussion of one-dimensional problems, before proceeding to consider two or higher dimensions. An emphasis is placed on numerical algorithms, related mathematical theory, and essential details in the implementation, while some useful packages are also introduced. The authors also provide well-tested MATLABR codes, all available online.
Offers a concise and practical introduction to finite difference and finite element methods
Well-tested MATLABR codes are free to download
Teaches students how to use computers to solve linear ODEs and PDEs in one and two dimensions
1. Introduction
Part I. Finite Difference Methods:
2. Finite difference methods for 1D boundary value problems
3. Finite difference methods for 2D elliptic PDEs
4. FD methods for parabolic PDEs
5. Finite difference methods for hyperbolic PDEs
Part II. Finite Element Methods:
6. Finite element methods for 1D boundary value problems
7. Theoretical foundations of the finite element method
8. Issues of the FE method in one space dimension
9. The finite element method for 2D elliptic PDEs
Appendix. Numerical solutions of initial value problems
References
Index.
Part of Cambridge Texts in Applied Mathematics
Publication planned for: January 2018
format: Hardback
isbn: 9781107147133
format: Paperback
isbn: 9781316601174
This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject. It includes standard material such as direct methods for solving linear systems and least-squares problems, error, stability and conditioning, basic iterative methods and the calculation of eigenvalues. Later chapters cover more advanced material, such as Krylov subspace methods, multigrid methods, domain decomposition methods, multipole expansions, hierarchical matrices and compressed sensing. The book provides rigorous mathematical proofs throughout, and gives algorithms in general-purpose language-independent form. Requiring only a solid knowledge in linear algebra and basic analysis, this book will be useful for applied mathematicians, engineers, computer scientists, and all those interested in efficiently solving linear problems.
A comprehensive yet concise introduction to the topic
Includes rigorous mathematical proofs and numerous algorithms
Covers important new topics, including methods for dense matrices and underdetermined systems
Part I. Preliminaries:
1. Introduction
2. Error, stability and conditioning
Part II. Basic Methods:
3. Direct methods for solving linear systems
4. Iterative methods for solving linear systems
5. Calculation of eigenvalues
Part III. Advanced Methods:
6. Methods for large sparse systems
7. Methods for large dense systems
8. Preconditioning
9. Compressed sensing
References
Index.