Paperback
Hardback
Published June 17, 2019
Reference - 340 Pages - 15 B/W Illustrations
ISBN 9781138381414 - CAT# K398461
Series: Discrete Mathematics and Its Applications
The reach of algebraic curves in cryptography goes far beyond elliptic curve or public key cryptography yet these other application areas have not been systematically covered in the literature. Addressing this gap, Algebraic Curves in Cryptography explores the rich uses of algebraic curves in a range of cryptographic applications, such as secret sharing, frameproof codes, and broadcast encryption.
Suitable for researchers and graduate students in mathematics and computer science, this self-contained book is one of the first to focus on many topics in cryptography involving algebraic curves. After supplying the necessary background on algebraic curves, the authors discuss error-correcting codes, including algebraic geometry codes, and provide an introduction to elliptic curves. Each chapter in the remainder of the book deals with a selected topic in cryptography (other than elliptic curve cryptography). The topics covered include secret sharing schemes, authentication codes, frameproof codes, key distribution schemes, broadcast encryption, and sequences. Chapters begin with introductory material before featuring the application of algebraic curves.
Hardback
October 16, 2019 Forthcoming
Textbook - 280 Pages - 12 B/W Illustrations
ISBN 9780367336936 - CAT# 318514
Series: Textbooks in Mathematics
This text is intended to help students move from introductory courses to those where rigor and proof play a much greater role. The emphasis is on precise definitions of mathematical objects and rigorous proofs of properties. The text contains four parts. The first reviews earlier concepts more rigorously and covers methods to make a correct argument. In the second part, concepts and objects are introduced including induction, sets, functions, cardinality, complex numbers, permutations, and matrices. The third part covers number theory including applications to cryptography. In the final part, important objects from abstract algebra are introduced at a relatively elementary level.
1 A Look Back: Precalculus Math 2 A Look Back: Calculus 3 About Proofs and Proof Strategies 4 Mathematical Induction 5 The Well-ordering Principle 6 Sets 7 Equivalence Relations 8 Functions 9 Cardinality of Sets 10 Permutations 11 Complex Numbers 12 Matrices and Sets with Algebraic Structure 13 Divisibility in Z and Number Theory 14 Primes and Unique Factorization 15 Congruences and the Finite Sets Zn 16 Solving Congruences 17 Fermat’s Theorem 18 Diffie-Hellman Key Exchange 19 Euler’s Function and Euler’s Theorem
Hardback
October 8, 2019 Forthcoming
Reference - 416 Pages
ISBN 9780367334895 - CAT# 317688
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Inverse Scattering Problems and their Application to Non-Linear Integrable Equations is devoted to inverse scattering problems (ISPs) for differential equations and their application to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, partial differential equations, equations of mathematical physics, and functions of a complex variable. This book is intended for a wide community working with inverse scattering problems and their applications, in particular, there is a traditional community in mathematical physics.
In this monograph, the problems are solved step-by-step, and detailed proofs are given for the problems to make the topics more accessible for students who are approaching them for the first time.
Hardback
November 19, 2019 Forthcoming
Textbook - 906 Pages - 131 B/W Illustrations
ISBN 9781138605831 - CAT# K388558
Series: Textbooks in Mathematics
The Second Edition of this successful text builds upon over ten years of in-class use. The text is unique in its approach to motivation, precision, explanations and methods. A layered approach offers an opportunity for flexible coverage and depth. Topics are introduced in a more accessfible way before subsequent sections develop these further. Motivating and giving reasons for the concepts and computations is an important part of the text. The author offers an emphasis on modeling and technology use. Guides for carrying out some of the lengthier computational procedures are given with illustrative examples integrated into the discussion. An engaging writing style appeals to students.
Hardback
October 28, 2019 Forthcoming
Textbook - 416 Pages - 67 B/W Illustrations
ISBN 9780367338237 - CAT# 318961
Series: Textbooks in Mathematics
This book contains an introduction to mathematical proofs. The topics appearing in Parts I through VII constitute the standard core material in proofs course. Part VIII develops properties of the real numbers from the ordered field axioms. The book maintains a targeted focus on helping students master key skills needed for later work, as opposed to giving a dry treatment of logic and set theory. A friendly conversational style couples with the necessary level of precision and rigor. The lecture format facilitates a continual cycle of examples, summaries, and review of previous material. Every lecture ends with an immediate review of the main points just covered. Three review lectures give detailed summaries. The essential core material is supplemented by more advanced topics in optional sections. Heavy emphasis is placed on proof templates, creating proof outlines for complex statements based on the logical structure. Many sample proofs are accompanied by annotations. Our coverage of induction is more extensive than some other texts. A careful distinction between the graph of a function and the function itself is made.
Arranged by fifty one-hour lectures. The lecture format facilitates a continual cycle of examples, summaries, and
review of previous material.
Parts I and VII cover all the essential topics for a Transition to Advanced Mathematics course.
Part VIII offers advanced topics typcially found in an Advanced Calculus course.
Heavy emphasis is placed on proof templates, which create proof outlines for complex statements.
Induction is covered more than in other texts.
1st Edition
Hardcover ISBN: 9780444640031
Published Date: 6th January 2020
Page Count: 500
series: Handbook of Numerical Analysis,Volume 21
1. Numerical methods for the Laplace-Beltrami operator
Andrea Bonito, Alan Demlow and R. H. Nochetto
2. Nonlinear plates
S. Bartels
3. Phase field methods and geometric PDEs
Qiang Du
4. Level-set methods and geometric PDEs
James Sethian
5. Parametric Finite Element Approximations of Curvature Driven Interface Evolution
Harald Garcke, John W. Barrett and Robert Nurnberg
6. Fully nonlinear PDEs
Michael Neilan
7. Free Boundary Problems in Fluids and Materials
Eberhard Baensch
8. Computational Geometry
Max Wardetzky
Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. It includes basic ideas, analysis and applications of state-of-the-art fundamental algorithms for the approximation of geometric PDEs together with their impacts in a variety of fields within mathematics, science, and engineering.