Hardback
April 26, 2018 Forthcoming by Chapman and Hall/CRC
Textbook - 464 Pages - 10 B/W Illustrations
ISBN 9780815353010 - CAT# K346056
Series: Discrete Mathematics and Its Applications
No direct competition--first book of its kind
Can be used for undergraduates as basis for research projects
Moves gradually through five distinct parts--suitable for beginners with no prerequesitves and also for more advanced students
Includes extensive proofs of propositions and theorems
This book deals with additive combinatorics, a vibrant area of current mathematical research. Additive combinatorics ? an offspring of combinatorial number theory and additive number theory ? can be described as the study of combinatorial properties of sumsets in additive structures. It is a rather new field that is just now coming to its own; although some of its results have been known for centuries, many of its fundamental questions have only been settled recently or are still unsolved. For this and many other reasons, additive combinatorics provides an excellent area for research by students of any background: it has intriguing and promising questions for everyone.
Preface, Notations, I Ingredients, 1 Number Theory, 2 Combinatorics, 3 Graph Theory; II Appetizers: Spherical Designs and More; III Sides, Functions; IV. Entres, A Maximum Supset Size, B Spanning Sets, C Sidon Sets; D Minimum Subset Size, E The Critical Number, F Zero-Sum-Free Sets, G Sum-Free Sets; V. Pudding: Proof of Propositions and Theorems; Bibilography; Index
Series:Inverse and Ill-Posed Problems Series 61
Hardcover
Publication Date: 2018
To be published: February 2018
ISBN 978-3-11-055630-8
Presents the state of the art on algorithms and methods for the regularization of ill-posed problems.
Utilizes modern functional analytic techniques.
Of interest to researchers and graduate students working in inverse and ill-posed problems.
This specialized and authoritative book presents the state of the art on iterative algorithms and methods for the regularization of a variety of ill-posed problems. Topics covered include iterative regularization of linear and nonlinear operator equations in Hilbert and Banach spaces, regularization of ill-posed Cauchy problems for operator differential equations, and regularization of nonlinear variational inequalities and optimization problems.
Details
24.0 x 17.0 cm
xvi, 326 pages
2 Fig.
Language:
English
Type of Publication:
Monograph
Subjects
Mathematics > Analysis
Mathematics > Numerical and Computational Mathematics
Mathematics > Applied Mathematics
Series:De Gruyter Textbook
A detailed presentation of nonlinear functional analysis.
Includes advanced but well-selected material for new and experienced researchers alike.
Covers the parts of the theory needed for conducting both mathematical and applied research.
The aim of this book is to provide a concise but complete introduction to the main mathematical tools of nonlinear functional analysis, which are also used in the study of concrete problems in economics, engineering, and physics. This volume gathers the mathematical background needed in order to conduct research or to deal with theoretical problems and applications using the tools of nonlinear functional analysis.
Details
24.0 x 17.0 cm
Approx. xii, 550 pages
5 Fig.
Language:
English
Type of Publication:
Textbook
Subjects
Mathematics > Analysis
Asterisque Volume: 393
2017; 143 pp; Softcover
MSC: Primary 55;
Print ISBN: 978-2-85629-868-8
Unstable coalgebras over the Steenrod algebra form a natural target category for singular homology with prime field coefficients. The realization problem asks whether an unstable coalgebra is isomorphic to the homology of a topological space. The authors study the moduli space of such realizations and give a description of this in terms of cohomological invariants of the unstable coalgebra. This is accomplished by a thorough comparative study of the homotopy theories of cosimplicial unstable coalgebras and of cosimplicial spaces.
Graduate students and research mathematicians.
ISBN: 978-1-118-74208-2
Jul 2018
736 pages
Select type: Hardcover
Fibonacci and Lucas numbers have intrigued amateurs and professionals for centuries, and for the first time under one cover, this book unifies advanced properties, applications, and occurrences of the extended Fibonacci-related family. In addition, the book offers analysis of these famous integers, complete with a wealth of exciting applications, enlightening examples, and fun exercises that provide numerous opportunities for exploration and experimentation. Fibonacci and Lucas numbers, Pell and Pell-Lucas numbers, Jacobsthal and Jacobsthal-Lucas numbers, and the corresponding univariate and bivariate polynomials are discussed. The author also details the close link between univariate Fibonacci and Lucas polynomials using differential and integral calculus and between Pell and Pell-Lucas polynomials and numbers. Extensive combinatorial interpretations of the bivariate polynomials using linear and circular tilings are provided as well as the inclusion of Fibonacci-Pell and Lucas-Pell-Lucas hybridities. Most of the chapters end with exercise sets, and brief solutions/proofs of odd-numbered exercises appear at the end of the book. Solutions to the even-numbered problems can be obtained via written request to the Publisher. The Appendix contains three tables covering the first 100 Fibonacci and Lucas numbers; the first 100 Pell and Pell-Lucas numbers; and the first 100 Jacobsthal and Jacobsthal-Lucas numbers. Topical coverage includes: Fibonacci trees; Fibonacci quadratics; Fibonacci and Lucas identities; advanced applications; Fibonacci and Lucas determinants; univariate Fibonacci and Lucas polynomials; bivariate Fibonacci and Lucas families; bivariate Pell and Jacobsthal families; combinatorial interpretations of bivariate Fibonacci and Lucas polynomials; links with Pascal's Triangle; Pell trees; Fibonacci-Pell hybridities; Pellnomial numbers; and advanced Fibonometry.