Hardback
Series: Cambridge Tracts in Mathematics (No. 190)
ISBN: 9781107016170
Dimensions: 228 x 152 mm
available from December 2011
Jordan theory has developed rapidly in the last three decades, but very few books describe its diverse applications. Here, the author discusses some recent advances of Jordan theory in differential geometry, complex and functional analysis, with the aid of numerous examples and concise historical notes. These include: the connection between Jordan and Lie theory via the Tits?Kantor?Koecher construction of Lie algebras; a Jordan algebraic approach to infinite dimensional symmetric manifolds including Riemannian symmetric spaces; the one-to-one correspondence between bounded symmetric domains and JB*-triples; and applications of Jordan methods in complex function theory. The basic structures and some functional analytic properties of JB*-triples are also discussed. The book is a convenient reference for experts in complex geometry or functional analysis, as well as an introduction to these areas for beginning researchers. The recent applications of Jordan theory discussed in the book should also appeal to algebraists
Preface
1. Jordan and Lie theory
2. Jordan structures in geometry
3. Jordan structures in analysis
Bibliography
Index.
Paperback
Series: London Mathematical Society Lecture Note Series (No. 393)
ISBN: 9781107648852
5 b/w illus.
Dimensions: 228 x 152 mm
available from December 2011
Number theory currently has at least three different perspectives on non-abelian phenomena: the Langlands programme, non-commutative Iwasawa theory and anabelian geometry. In the second half of 2009, experts from each of these three areas gathered at the Isaac Newton Institute in Cambridge to explain the latest advances in their research and to investigate possible avenues of future investigation and collaboration. For those in attendance, the overwhelming impression was that number theory is going through a tumultuous period of theory-building and experimentation analogous to the late 19th century, when many different special reciprocity laws of abelian class field theory were formulated before knowledge of the Artin?Takagi theory. Non-abelian Fundamental Groups and Iwasawa Theory presents the state of the art in theorems, conjectures and speculations that point the way towards a new synthesis, an as-yet-undiscovered unified theory of non-abelian arithmetic geometry.
List of contributors
Preface
1. Lectures on anabelian phenomena in geometry and arithmetic Florian Pop
2. On Galois rigidity of fundamental groups of algebraic curves Hiroaki Nakamura
3. Around the Grothendieck anabelian section conjecture Mohamed Saidi
4. From the classical to the noncommutative Iwasawa theory (for totally real number fields) Mahesh Kakde
5. On the ĻH(G)-conjecture J. Coates and R. Sujatha
6. Galois theory and Diophantine geometry Minhyong Kim
7. Potential modularity - a survey Kevin Buzzard
8. Remarks on some locally Qp-analytic representations of GL2(F) in the crystalline case Christophe Breuil
9. Completed cohomology - a survey Frank Calegari and Matthew Emerton
10. Tensor and homotopy criteria for functional equations of l-adic and classical iterated integrals Hiroaki Nakamura and Zdzis?aw Wojtkowiak.
Hardback
ISBN: 9781107014992
35 b/w illus. 35 tables 90 exercises
Dimensions: 247 x 174 mm
available from January 2012
Pseudo-random sequences are essential ingredients of every modern digital communication system including cellular telephones, GPS, secure internet transactions and satellite imagery. Each application requires pseudo-random sequences with specific statistical properties. This book describes the design, mathematical analysis and implementation of pseudo-random sequences, particularly those generated by shift registers and related architectures such as feedback-with-carry shift registers. The earlier chapters may be used as a textbook in an advanced undergraduate mathematics course or a graduate electrical engineering course; the more advanced chapters provide a reference work for researchers in the field. Background material from algebra, beginning with elementary group theory, is provided in an appendix.
1. Introduction
Part I. Algebraically Defined Sequences: 2. Sequences
3. Linear feedback shift registers and linear recurrences
4. Feedback with carry shift registers and multiply with carry sequences
5. Algebraic feedback shift registers
6. d-FCSRs
7. Galois mode, linear registers, and related circuits
Part II. Pseudo-Random and Pseudo-Noise Sequences: 8. Measures of pseudo-randomness
9. Shift and add sequences
10. M-sequences
11. Related sequences and their correlations
12. Maximal period function field sequences
13. Maximal period FCSR sequences
14. Maximal period d-FCSR sequences
Part III. Register Synthesis and Security Measures: 15. Register synthesis and LFSR synthesis
16. FCSR synthesis
17. AFSR synthesis
18. Average and asymptotic behavior of security measures
Part IV. Algebraic Background: A. Abstract algebra
B. Fields
C. Finite local rings and Galois rings
D. Algebraic realizations of sequences
Bibliography
Index.
Hardback
Series: Dolciani Mathematical Expositions
ISBN: 9780883853528
Publication date: August 2011
346 pages
Dimensions: 247 x 174 mm
Weight: 0.6 kg
Certain geometric diagrams play a crucial role in visualizing mathematical proofs. Twenty of these icons of mathematics are presented in this book, where the authors explore the mathematics within them and the mathematics that can be created from them. A chapter is devoted to each icon, illustrating its presence in real life, its primary mathematical characteristics and how it plays a central role in visual proofs of a wide range of mathematical facts. Among these are classical results from plane geometry, properties of the integers, means and inequalities, trigonometric identities, theorems from calculus and puzzles from recreational mathematics. Each chapter concludes with a selection of challenges for the reader to explore further properties and applications of the icon. Those teaching undergraduate mathematics will find material here for problem solving sessions, as well as enrichment material for courses on proofs and mathematical reasoning.
Preface
Twenty key icons of mathematics
1. The Bride's Chair
2. Zhou Bi Suan Jing
3. Garfield's trapezoid
4. The semicircle
5. Similar figures
6. Cevians
7. The right triangle
8. Napoleon's triangles
9. Arcs and angles
10. Polygons with circles
11. Two circles
12. Venn diagrams
13. Overlapping figures
14. Yin and yang
15. Polygonal lines
16. Star polygons
17. Self-similar figures
18. Tatami
19. The rectangular hyperbola
20. Tiling
Solutions to the challenges
References
Index
About the authors.
Hardback
Series: Dolciani Mathematical Expositions
ISBN: 9780883853535
Dimensions: 228 x 152 mm
available from April 2012
This is an informal and accessible introduction to plane algebraic curves that also serves as a natural entry point to algebraic geometry. There is a unifying theme to the book: give curves enough living space and beautiful theorems will follow. This book provides the reader with a solid intuition for the subject, while at the same time keeping the exposition simple and understandable, by introducing abstract concepts with concrete examples and pictures. It can be used as the text for an undergraduate course on plane algebraic curves, or as a companion to algebraic geometry at graduate level. This book is accessible to those with a limited mathematical background. This is because for those outside mathematics there is a growing need for an entree to algebraic geometry, a need created by the ever-expanding role algebraic geometry is playing in areas ranging from biology to chemistry and robotics to cryptology.
Preface
1. A gallery of algebraic curves
2. Points at infinity
3. From real to complex
4. Topology of algebraic curves in P2.C/
5. Singularities
6. The big three: C, K, S
Bibliography.