Bagaria, Joan; Todorcevic, Stevo (Eds.)

Set Theory
Centre de Recerca Matematica Barcelona, 2003-2004

Series: Trends in Mathematics
2006, Approx. 415 p., Hardcover
ISBN: 3-7643-7691-0

About this book

This volume has its origins in the Research Programme on Set Theory and its Applications that took place at the CRM Barcelona from September 2003 to July 2004. It consists of two parts. The first contains survey papers on some of the mainstream areas of set theory, such as Omega-logic, complexity of sets, selection theory, or real-valued measurable cardinals. The second part contains original research articles.

Written for:

Postgraduates and researchers in set theory

Table of contents

Foreword.- Contributions by J. Bagaria, T. Banakh, M. Bekkali, A. Blass, R. Bosch, A.E. Caicedo, N. Castells, S.-D. Friedman, G. Hjorth, P. Koepke, P. Larson, A. Marcone, P. Matet, A.R.D. Mathias, C. Morgan, R. Schindler, B. Tsaban, P. Welch, D. Zhani.

Chenciner, Alain

Courbes algebriques planes, 2ieme ed.

2006, Approx. 200 p., Broche
ISBN: 3-540-33707-5

A propos de ce livre

Issu d’un cours de maitrise de l’Universite Paris VII, ce livre est republie tel qu’il etait paru en 1978. A propos du theoreme de Bezout sont introduits divers outils necessaires au developpement de la notion de multiplicite d’intersection de deux courbes algebriques dans le plan projectif complexe. Partant des notions elementaires sur les sous-ensembles algebriques affines et projectifs, on definit les multiplicites d’intersection et interprete leur somme entermes du resultant de deux polynomes. L’etude locale est pretexte a l’introduction des anneaux de serie formelles ou convergentes ; elle culmine dans le theoreme de Puiseux dont la convergence est ramenee par des eclatements a celle du theoreme des fonctions implicites. Diverses figures eclairent le texte: on y "voit" en particulier que l’equation homogene x3+y3+z3 = 0 definit un tore dans le plan projectif complexe.

Sommaire

Sous-ensembles algebriques de C.- Ensembles algebriques affines.- Courbes planes affines.- Ensembles algebriques projectifs.- Courbes projectives planes : le theoreme de Bezout.- Le resultant.- Point de vue local : anneaux de series formelles.- Anneaux de series convergentes.- Le theoreme de Puiseux.- Theorie locale des intersections de courbes.

Gartner, Bernd, Matousek, Jiri

Understanding and Using Linear Programming

Series: Universitext
2006, Approx. 200 p., Softcover
ISBN: 3-540-30697-8

About this textbook

The book is an introductory textbook mainly for students of computer science and mathematics. Our guiding phrase is "what every theoretical computer scientist should know about linear programming". A major focus is on applications of linear programming, both in practice and in theory. The book is concise, but at the same time, the main results are covered with complete proofs and in sufficient detail, ready for presentation in class. The book does not require more prerequisites than basic linear algebra (which is summarized in an appendix). One of its main goals is to help the reader to see linear programming "behind the scenes".

Table of contents

Preliminary.- 1 What Is It, and What For?- 2 Examples.- 3 Integer Programming and LP Relaxation.- 4 Theory of Linear Programming: First Steps.- 5 The Simplex Method.- 6 Duality of Linear Programming.- 7 Not Only the Simplex Method.- 8 More Applications.- 9 Software and Further Reading.

Martzloff, Jean-Claude

A History of Chinese Mathematics, Corr. 2nd printing

2006, Approx. 505 p. 185 illus., Softcover
ISBN: 3-540-33782-2

About this book

The book is made up of two mutually explanatory parts, the first devoted to the general, historical and cultural background, and the second to the development of each subdiscipline that together comprise Chinese mathematics. This section is organised topically rather than chronologically, and is enriched in each case by examples, guides on how to intepret the contextual setting and by exhaustive references - both mathematical and sinological. This makes the book uniquely accessible, both as a topical reference work, and also as an overview that can be read and reread at many levels of sophistication by both sinologists and mathematicians alike. Indeed anyone with an interest in Chinese culture or the history of ideas will derive great benefit from this book.

Table of contents

Part I: The Historiographical Context, The Historical Context, The Notion of Chinese Mathematics, Applications of Chinese Mathematics, The Structure of Mathematical Works, Mathematical Terminology, Modes of Reasoning, Chinese Mathematicians, The Transmission of Knowledge, Influences and Transmission, Main Works and Main Autors (from Origins to 1600) Part II: Numbers and Numeration, Calculating Instruments, Techniques for Numerical Computation, Geometry, Indeterminate Problems, Approximation Formulae, Li Shanlan's Summation Formulae, Infinite Series, Magic Squares and Other Magic Figures Appendix I: Adaptations of European Mathematical Works Appendix II: Adaptations of European Mathematical Works (17th-19th Centuries).

Seibt, Peter

Algorithmic Information Theory
Mathematics of Digital Information Processing

Series: Signals and Communication Technology
2006, Approx. 600 p., Hardcover
ISBN: 3-540-33218-9

About this book

This book treats the Mathematics of many important areas in digital information processing.

It covers, in a unified presentation, five topics: Data Compression, Cryptography, Sampling (Signal Theory), Error Control Codes, Data Reduction. The thematic choices are practice-oriented. So, the important final part of the book deals with the Discrete Cosine Transform and the Discrete Wavelet Transform, acting in image compression. The presentation is dense, the examples and numerous exercises are concrete. The pedagogic architecture follows increasing mathematical complexity. A read-and-learn book on Concrete Mathematics, for teachers, students and practitioners in Electronic Engineering, Computer Science and Mathematics.

Table of contents

Data Compaction.- Cryptography.- Information Theory and Signal Theory: Sampling and Reconstruction.- Error Control Codes.- Data Reduction: Lossy Compression.

Basu, Saugata, Pollack, Richard, Roy, Marie-Francoise

Algorithms in Real Algebraic Geometry, 2nd ed.

Series: Algorithms and Computation in Mathematics , Vol. 10
2006, Approx. 670 p. 40 illus., Hardcover
ISBN: 3-540-33098-4

About this textbook

In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. This self-contained book is accessible to graduate and undergraduate students.

Table of contents

Introduction.- 1 Algebraically Closed Fields.- 2 Real Closed Fields.- 3 Semi-Algebraic Sets.- 4 Algebra.- 5 Decomposition of Semi-Algebraic Sets.- 6 Elements of Topology.- 7 Quantitative Semi-Algebraic Geometry.- 8 Complexity of Basic Algorithms.- 9 Cauchy Index and Applications.- 10 Real Roots.- 11 Cylindrical Decomposition Algorithm.- 12 Polynomial System Solving.- 13 Existential Theory of the Reals.- 14 Quantifier Elimination.- 15 Computing Roadmaps and Connected Components of Algebraic Sets.- 16 Computing Roadmaps and Connected Components of Semi-Algebraic Sets.- References.- Index of Notation.- Index.