ISBN: 978-1-118-85750-2
248 pages
March 2014
First published by Wiley in 1978, this book is being re-issued with a new Preface by the author. The roots of the book lie in the writings of RA Fisher both as concerns results and the general stance to statistical science, and this stance was the determining factor in the author's selection of topics. His treatise brings together results on aspects of statistical information, notably concerning likelihood functions, plausibility functions, ancillarity, and sufficiency, and on exponential families of probability distributions.
Galois geometry is the theory that deals with substructures living in projective spaces over finite fields, also called Galois fields.
This collected work presents current research topics in Galois geometry, and their applications. Presented topics include classical objects, blocking sets and caps in projective spaces, substructures in finite classical polar spaces, the polynomial method in Galois geometry, finite semifields, links between Galois geometry and coding theory, as well as links between Galois geometry and cryptography. (Imprint: Nova)
Preface
1. Constructions and characterizations of classical sets in PG(n,q)
(Frank De Clerck, Ghent University, Department of Mathematics, Ghent, Belgium; Nicola Durante, Dipartimento di Matematica e Applicazioni Caccioppoli, Universita di Napoli gFederico IIh, Complesso di Monte S. Angelo - Edificio T., via Cintia, Napoli, Italy) pp.1-34
2. Substructures of finite classical polar spaces
(Jan De Beule. Ghent University, Department of Mathematics, Gent, Belgium; Andreas Klein, Ghent University, Department of Mathematics, Gent, Belgium; Klaus Metsch, Universitat Giesen, Mathematisches Institut, Germany) pp.35-62
3. Blocking sets in projective spaces
(Aart Blokhuis, Eindhoven Univ. of Technology, Dept. of Mathematics and Computer Science, Eindhoven, the Netherlands, Peter Sziklai, Eotvos Lorand University, Institute of Mathematics, Pazmany Peter setany, Budapest, Hungary; Tamas Sz*nyi, Eotvos Lorand Univ., Institute of Mathematics, Pazmany Peter setany, Budapest, Hungary and Computer and Automation Research Inst., Hungarian Academy of Sciences, Budapest, Hungary) pp.63-86
4. Large caps in projective Galois spaces
(Jurgen Bierbrauer, Department of Mathematical Sciences, Michigan Technological University, Houghton, MI; Yves Edel, Ghent University, Department of Mathematics, Gent, Belgium) pp.87-104
5. The polynomial method in Galois geometries
(Simeon Ball, Departament de Matematica Aplicada IV, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Modul C3, Campus Nord, Barcelona, Spain) pp.105-130
6. Finite semifields
(Michel Lavrauw, Ghent University, Department of Mathematics, Gent, Belgium; Olga Polverino, Dipartimento di Matematica, Seconda Universita degli Studi di Napoli, Caserta) pp.131-160
7. Codes over rings and ring geometries
(Thomas Honold, Department of Information and Electronic Engineering, Zhejiang University, Hangzhou, China; Ivan Landjev, New Bulgarian University, Sofia, Bulgaria and Institute of Mathematics and Informatics, Sofia, Bulgaria)pp.161-186
8. Galois geometries and coding theory
(Ivan Landjev; (b) Leo Storme, Ghent University, Department of Mathematics, Ghent, Belgium) pp.187-214
9. Applications of Galois geometry to cryptology
(Wen-Ai Jackson, School of Mathematical Sciences, the University of Adelaide, Australia; Keith M. Martin, Information Security Group, Royal Holloway, University of London, Egham, U.K; Maura B. Paterson, Department of Economics, Mathematics and Statistics, Birkbeck, University of London, London, U.K) pp.215-244
10. Galois geometries and low-density parity-check codes
(Marcus Greferath, School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland; Cornelia Rosing, School of Mathematical Sciences, University College Dublin, Belfield, Dublin, Ireland; Leo Storme) pp.245-270
Index pp.271-276
Series:
Mathematics Research Developments
Binding: Softcover
Pub. Date: 2014 - 2nd Quarter
Pages: 7x10 - (NBC-C)
ISBN: 978-1-63117-340-0
Series: Springer Monographs in Mathematics
2015, X, 260 p. 10 illus.
Hardcover
ISBN 978-4-431-54918-5
Due: December 31, 2014
.This book can understand relations to special values of zeta functions
This book can meet the need of the relation between Bernoulli numbers and Riemann zeta functions
This book has a significant educational benefit for amateur math-lovers
Various topics on Bernoulli numbers and zeta functions. The purpose is to introduce readers to the elementary theories of Bernoulli numbers and zeta functions and to present several specific topics rather independent with each other. This is not a monograph, nor lecture notes. This may be used as a textbook but we do not expect systematic reading from the beginning till the end. This is rather a book of surveys on independent topics related to Bernoulli numbers and zeta functions. Also, the book contains numerous number theoretical formulas concerning Bernoulli numbers.
1. Bernoulli Numbers 2. Stirling Numbers and Bernoulli Numbers 3. Theorem of Clausen and von Staudt, and Kummerfs Congruence 4. Generalized Bernoulli Numbers 5. Summation Formula of Euler-Maclaurin and Riemann Zeta Function 6. Quadratic Forms and Ideal Theory of Quadratic Fields 7. Congruence Between Bernoulli Numbers and Class Numbers of Imaginary Quadratic Fields 8. Character Sums and Bernoulli Numbers 9. Special Values and Complex Integral Representation of L-functions 10. Class Number Formula and an Easy Zeta Function of a Prehomogeneous Vector Space 11. p-adic Measure and Kummerfs Congruence 12. Hurwitz Numbers 13. The Barnes Multiple Zeta Function 14. Poly-Bernoulli NumbersReferencesIndex
Chapman and Hall/CRC 2014 500 pages
Series: Discrete Mathematics and Its Applications
Hardback:
978-1-48-223772-6
15th August 2014
This best-selling, classic textbook continues to provide a complete one-semester introduction to mathematical logic. The sixth edition incorporates recent work on Godelfs second incompleteness theorem as well as an appendix on consistency proofs for first-order arithmetic. It also offers historical perspectives and many new exercises of varying difficulty, which motivate and lead students to an in-depth, practical understanding of the material.
The Propositional Calculus. First-Order Logic and Model Theory. Formal Number Theory. Axiomatic Set Theory. Computability. Appendices.
Chapman and Hall/CRC 2014 450 pages
Hardback:
978-1-48-222074-2
15th October 2014
Most related textbooks transition students from the mathematics of calculations to the concept of proofs through intuition. This introduction to pure mathematics minimizes the amount of intuition built into the subject. Suitable for a one-semester undergraduate course, the text also addresses the central question of determining the certainty provided by pure mathematics. Written by a well-known author and mathematician, the book includes "check your understanding" sections and many examples.
Number Systems. Sequences. Series of Numbers. Basic Topology. Limits and Continuity of Functions. Differentiation of Functions. The Integral. Sequences and Series of Functions
The book constitutes a basic, concise, yet rigorous course in complex analysis, for students who have studied calculus in one and several variables, but have not previously been exposed to complex analysis. The textbook should be particularly useful and relevant for undergraduate students in joint programmes with mathematics, as well as engineering students. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy*Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series expansions.
Each section contains several problems, which are not purely drill exercises, but are rather meant to reinforce the fundamental concepts. Detailed solutions to all the exercises appear at the end of the book, making the book ideal also for self-study.
*Complex Numbers and Their Geometry
*Complex Differentiability
*Cauchy Integral Theorem and Consequences
*Taylor and Laurent Series
*Harmonic Functions
Readership: Undergraduate students in complex analysis.
Series on Knots and Everything: Volume 54
This book is a Festschrift for the 90th birthday of the physicist Pierre Noyes. The book is a representative selection of papers on the topics that have been central to the meetings over the last three decades of ANPA, the Alternative Natural Philosophy Association. ANPA was founded by Pierre Noyes and his colleagues the philosopher-linguist-physicist Frederick Parker-Rhodes, the physicist Ted Bastin, and the mathematicians Clive Kilmister, John Amson.
Many of the topics in the book center on the combinatorial hierarchy discovered by the originators of ANPA. Other topics explore geometrical, cosmological and biological aspects of those ideas, and foundational aspects related to discrete physics and emergent quantum mechanics.
The book will be useful to readers interested in fundamental physics, and particularly to readers looking for new and important viewpoints in Science that contain the seeds of futurity.
*Unital Homogeneous Polynomial Operators on Hilbert Space (John C Amson)
*Towards a Generalised Combinatorial Hierarchy (Keith G Bowden)
*Quantum Cosmology and Special Mersenne Primes (Geoffrey F Chew)
*BiEntropy * the Measurement and Algebras of Order and Disorder in Finite Binary Strings (Grenville J Croll)
*Constraints Theory Brief (Anthony M Deakin)
*An Elegance First Approach to looking for the Universe in Finite Geometry (Herb Doughty)
*Boolean Geometry and Non-boolean Change (Thomas Etter)
*Speculation on Consciousness as Relative Existence (Louis Gidney)
*A Management View of ANPA (East) 1979 to 2012 (Michael Horner)
*Critical Stability of Few-Body Systems (V A Karmanov and J Carbonell)
*Non-Commutative Worlds and Classical Constraints (Louis H Kauffman)
*Report on ANPA to the ANPA Advisory Board, 2008 (Clive W Kilmister)
*Reflections on Fundamentals and Foundations of Physics (James Lindesay)
*Ordering Operators (David McGoveran)
*Information, Entropy, and the Combinatorial Hierarchy: Calculations (Michael Manthey and Douglas Matzke)
*Spacetime, Dirac and Bit-Strings (G N Ord)
*Fractal Large-Scale Structure in the Universe (D F Roscoe)
*A Dual Space as the Basis of Quantum Mechanics and Other Aspects of Physics (Peter Rowlands)
*Discrete Motion and the Emergence of Space and Time (Richard Shoup)
*Expanding*Contracting Universes (Irving Stein)
*Development of a New Approach to Systems Biology and Therapy Design (Fredric S Young)
Readership: Researchers in mathematical physics, theoretical physics and history of science.