Ce volume contient la seconde partie des notes de cours de l'Ecole d'ete franco-asiatique de geometrie algebrique et de theorie des nombres, qui s'est tenue a l'Institut des Hautes Etudes Scientifiques (Bures-sur-Yvette) et a l'universite Paris-Sud XI en juillet 2006. Cette ecole etait consacree a la theorie des motifs et a ses recents developpements, ainsi qu'a des sujets voisins, comme la theorie des varietes de Shimura et des representations automorphes. Cette seconde partie est constituee de versions developpees des cours de M. Levine consacres aux categories triangulees de motifs et a la theorie homotopique des schemas (Six lectures on motives) et des lecons de J. Wildeshaus sur les motifs bords et leurs applications (Boundary motives, relative motives and extensions of motives) et de B. Kahn sur une version triangulee des conjectures de Tate et Beilinson sur les cycles algebriques sur les corps finis (The full faithfullness conjectures in characteristic p).
This volume contains the second part of the lectures notes of the Asian-French summer school on algebraic geometry and number theory, which was held at the Institut des Hautes Etudes Scientifiques (Bures-sur-Yvette) and the universite Paris-Sud XI (Orsay) in July 2006. This summer school was devoted to the theory of motives and its recent developments, and to related topics, notably Shimura varieties and automorphic representations. The contributions in this second part are expanded versions of the series of lectures by M. Levine on triangulated categories of motives and motivic homotopy of schemes (Six lectures on motives), and of the additional lectures by J. Wildeshaus on boundary motives and their applications (Boundary motives, relative motives and extensions of motives) and by B. Kahn on a triangulated version of the conjectures of Tate and Beilinson on algebraic cycles over a finite field (The full faithfullness conjectures in characteristic p).
Keywords: Motives, automorphic forms, Shimura varieties
ISBN : 978-2-85629-784-1
Asterisque 362 (2014), vi + 134 pages
Theory of H_p-spaces for continuous filtrations in von Neumann algebras
Nous introduisons des espaces de Hardy pour des martingales relatives a des filtrations continues d'algebres de von Neumann. Nous demontrons en particulier les inegalites de Burkholder-Gundy et de Burkholder-Rosenthal dans ce cadre. Les arguments usuels bases sur des temps d'arret dans le cas commutatif sont remplaces par des outils de la theorie des fonctions non commutatives, qui nous permettent d'obtenir l'analogue de la dualite de Fefferman-Stein et de prouver une decomposition de Davis non commutative.
We introduce Hardy spaces for martingales with respect to continuous filtration for von Neumann algebras. In particular we prove the analogues of the Burkholder-Gundy and Burkholder-Rosenthal inequalities in this setting. The usual arguments using stopping times in the commutative case are replaced by tools from noncommutative function theory and allow us to obtain the analogue of the Feffermann-Stein duality and prove a noncommutative Davis decomposition.
Keywords: Noncommutative L_p-spaces, noncommutative martingales, Hardy spaces, continuous filtration
ISBN : 978-2-85629-789-6
432 pages | 113 b/w line drawings | 216x138mm
978-0-19-870644-1 | Hardback | March 2015 (estimated)
978-0-19-870643-4 | Paperback | March 2015 (estimated)
Explicitly suggests to the student ways they can increase their understanding.
Explains the motivation behind otherwise abstract foundational material in mathematics.
Guides the reader from an informal to a formal, axiomatic approach.
Extremely well-known bestselling authors.
New edition of a widely used book.
Highly illustrated.
The new edition of The Foundations of Mathematics is a major update, with four entirely new chapters and the remainder of the book updated as necessary.
The original opening chapter on ・ Mathematical Thinking will be completely rewritten and significantly expanded.
A brand new Part IV of the book on Using Axiomatic Systems will contain three further new chapters on ・ Axiomatic Structures and Structure Theorems ・ Permutations and Groups ・ Infinitesimals
The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory.
The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas.
This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups.
While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The approach here is not the conventional one of 'nonstandard analysis', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward.
This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.
Readership: ・ First-year mathematics undergraduates ・ Advanced school students contemplating further study in mathematics ・ Anyone seeking a firmer grasp of mathematical foundations and thought processes
I: The Intuitive Background
1: Mathematical Thinking
2: Number Systems
II: The Beginnings of Formalisation
3: Sets
4: Relations
5: Functions
III: The Development of Axiomatic Systems
8: Natural Numbers and Proof by Induction
9: Real Numbers
10: Real Numbers as a Complete Ordered Field
11: Complex Numbers and Beyond
IV: Using Axiomatic Systems
12: Axiomatic Structures and Structure Theorems
13: Permutations and Groups
14: Infinite Cardinal Numbers
15: Infinitesimals
V: Strengthening the Foundations
16: Axioms for Set Theory
Series: Springer Monographs in Mathematics
2014, XVI, 487 p. 22 illus.
Hardcover
ISBN 978-3-319-10740-0
Due: November 14, 2014
Includes many insights into diophantine approximation by one of the field's leading contributors
Covers both classical results and recent research developments
Provides detailed and well-motivated proofs, enabling the reader to grasp key ideas behind difficult arguments
This book gives a comprehensive treatment of random phenomena and distribution results in diophantine approximation, with a particular emphasis on quadratic irrationals. It covers classical material on the subject as well as many new results developed by the author over the past decade. A range of ideas from other areas of mathematics are brought to bear with surprising connections to topics such as formulae for class numbers, special values of L-functions, and Dedekind sums. Care is taken to elaborate difficult proofs by motivating major steps and accompanying them with background explanations, enabling the reader to learn the theory and relevant techniques.
Written by one of the acknowledged experts in the field, Probabilistic Diophantine Approximation is presented in a clear and informal style with sufficient detail to appeal to both advanced students and researchers in number theory.
Preface.- 1 What is "probabilistic" diophantine approximation?.- 2 Expectation, and its connection with quadratic fields.- 3 Variance, and its connection with quadratic fields.- 4 Proving randomness.- 5 Pell equation, super irregularity and randomness.- 6 More on randomness.- References.- Index.
Series: Springer Series in Statistics
2014, XIV, 346 p.
Hardcover
ISBN 978-1-4939-2136-2
Due: November 14, 2014
Primary audience is researchers and graduate students in statistics and social sciences or applied statistics research areas, but chapters 1-3 could also be used in advanced undergraduate courses
This is the first book in longitudinal categorical data analysis with parametric correlation models developed based on dynamic relationships among repeated categorical responses. This book is a natural generalization of the longitudinal binary data analysis to the multinomial data setup with more than two categories. Thus, unlike the existing books on cross-sectional categorical data analysis using log linear models, this book uses multinomial probability models both in cross-sectional and longitudinal setups. A theoretical foundation is provided for the analysis of univariate multinomial responses, by developing models systematically for the cases with no covariates as well as categorical covariates, both in cross-sectional and longitudinal setups. In the longitudinal setup, both stationary and non-stationary covariates are considered. These models have also been extended to the bivariate multinomial setup along with suitable covariates. For the inferences, the book uses the generalized quasi-likelihood as well as the exact likelihood approaches.
The book is technically rigorous, and, it also presents illustrations of the statistical analysis of various real life data involving univariate multinomial responses both in cross-sectional and longitudinal setups. This book is written mainly for the graduate students and researchers in statistics and social sciences, among other applied statistics research areas. However, the rest of the book, specifically the chapters from 1 to 3, may also be used for a senior undergraduate course in statistics.
Brajendra Sutradhar is a University Research Professor at Memorial University in St. John's, Canada. He is author of the book Dynamic Mixed Models for Familial Longitudinal Data, published in 2011 by Springer, New York. Also, he edited the special issue of the Canadian Journal of Statistics (2010, Vol. 38, June Issue, John Wiley) and the Lecture Notes in Statistics (2013, Vol. 211, Springer), with selected papers from two symposiums: ISS-2009 and ISS-2012, respectively.
Introduction.- Overview of Regression Models for Cross-sectional Univariate Categorical Data.- Regression Models for Univariate Longitudinal Stationary Categorical Data.- Regression Models for Univariate Longitudinal Non-stationary Categorical Data.- Multinomial Models for Cross-sectional Bivariate Categorical Data.- Multinomial Models for Longitudinal Bivariate Categorical Data.- Index.