Sriram Pemmaraju / Indian Institute of Technology, Bombay, and University of Iowa
Steven Skiena / State University of New York, Stony Brook

Computational Discrete Mathematics
Combinatorics and Graph Theory with Mathematica R

Paperback (ISBN-13: 9780521121460)
Page extent: 496 pages

This book was first published in 2003. Combinatorica, an extension to the popular computer algebra system MathematicaR, is the most comprehensive software available for teaching and research applications of discrete mathematics, particularly combinatorics and graph theory. This book is the definitive reference/userfs guide to Combinatorica, with examples of all 450 Combinatorica functions in action, along with the associated mathematical and algorithmic theory. The authors cover classical and advanced topics on the most important combinatorial objects: permutations, subsets, partitions, and Young tableaux, as well as all important areas of graph theory: graph construction operations, invariants, embeddings, and algorithmic graph theory. In addition to being a research tool, Combinatorica makes discrete mathematics accessible in new and exciting ways to a wide variety of people, by encouraging computational experimentation and visualization. The book contains no formal proofs, but enough discussion to understand and appreciate all the algorithms and theorems it contains.

* The definitive guide to the latest version of the Combinatorica software, included with every copy of Mathematica, with new functionality, significantly improved performance, and advanced graphics * Unique experimental approach to teaching/learning combinatorics and graph theory * Steven Skiena is the best-selling author of the books The Algorithm Design Manual and Calculated Bets

Contents

1. Combinatorica: an explorer's guide; 2. Permutations and combinations; 3. Algebraic combinatorics; 4. Partitions, compositions and Young tableaux; 5. Graph representation; 6. Generating graphs; 7. Properties of graphs; 8. Algorithmic graph theory.

Jeff Suzuki / Brooklyn College, City University of New York

Mathematics in Historical Context

Series: Spectrum
Hardback (ISBN-13: 9780883855706)
Page extent: 420 pages

What would Newton see if he looked out his bedroom window* This book describes the world around the important mathematicians of the past, and explores the complex interaction between mathematics, mathematicians, and society. It takes the reader on a grand tour of history from the ancient Egyptians to the twentieth century to show how mathematicians and mathematics were affected by the outside world, and at the same time how the outside world was affected by mathematics and mathematicians. Part biography, part mathematics, and part history, this book provides the interested layperson the background to understand mathematics and the history of mathematics, and is suitable for supplemental reading in any history of mathematics course.

* Ideal as a supplement to a history of mathematics course * Moves from the ancient world to the Second World War * Conveys how famous mathematical figures such as Newton and Archimedes affected and were affected by the political events, cultural development and artistic conventions of their time

Contents

Introduction; 1. The ancient world; 2. The classical world; 3. China and India; 4. The Islamic world; 5. The Middle Ages; 6. Renaissance and Reformation; 7. Early modern Europe; 8. The eighteenth century; 9. The nineteenth century; 10. The United States; 11. The modern world; Epilogue; Bibliography.

Editors:
Alain Connes (IHES, Bures-sur-Yvette, France)
Frederic Fauvet (IRMA, Strasbourg, France )
Jean-Pierre Ramis (Institut de Mathematiques de Toulouse, France)

Renormalization and Galois Theories

IRMA Lectures in Mathematics and Theoretical Physics Vol. 15
ISBN 978-3-03719-073-9
September 2009, 279 pages, softcover, 17 x 24 cm.

This volume is the outcome of a CIRM Workshop on Renormalization and Galois Theories held in Luminy, France, in March 2006. The subject of this workshop was the interaction and relationship between four currently very active areas: renormalization in quantum field theory (QFT), differential Galois theory, noncommutative geometry, motives and Galois theory.

The last decade has seen a burst of new techniques to cope with the various mathematical questions involved in QFT, with notably the development of a Hopf-algebraic approach and insights into the classes of numbers and special functions that systematically appear in the calculations of perturbative QFT (pQFT). The analysis of the ambiguities of resummation of the divergent series of pQFT, an old problem, has been renewed, using recent results on Gevrey asymptotics, generalized Borel summation, Stokes phenomenon and resurgent functions.

The purpose of the present book is to highlight, in the context of renormalization, the convergence of these various themes, orchestrated by diverse Galois theories. It contains three lecture courses together with five research articles and will be useful to both reseachers and graduate students in mathematics and physics.

Table of contents

Edited by:
David Jerison (MIT); Barry Mazur (Harvard University); Tomasz Mrowka (MIT);
Wilfried Schmid (Harvard University); Richard P. Stanley (MIT); Shing-Tung Yau (Harvard University)

Current Developments in Mathematics, 2008

Softcover. 454 pages.
ISBN-13: 978-1-57146-139-1
Published: October 2009

Table of Contents

* The Evolution Problem in General Relativity
Mihalis Dafermos
* Very Large Graphs
Lazlo Lovasz
* On the Classification of Topological Field Theories
Jacob Lurie
* Properly embedded minimal planar domains with infinite topology are
Riemann minimal examples
William H. Meeks III and Joaquin Perez
* Unearthing the Visions of a Master: Harmonic Maass Forms and Number Theory
Ken Ono

About the series

The Current Developments in Mathematics (CDM) conference is an annual
seminar, jointly hosted by Harvard University and the Massachusetts
Institute of Technology, and devoted to surveying the most recent
developments in mathematics. In choosing speakers, the hosts take a broad
look at the field of geometry, and select geometers who transcend classical
perceptions within their field. All speakers are prominent specialists in
the fields of algebraic geometry, mathematical physics, and other areas.
International Press is pleased to bring the full contents of these
proceedings to you in their Current Developments in Mathematics book series.



Ivor Grattan-Guinness

Routes of Learning
Highways, Pathways, and Byways in the History of Mathematics

HARDBACK / 9780801892479
PAPERBACK / 9780801892486

2009 392 pp., 31 line drawings

This seminal collection gathers together many general writings of one of the world's leading historians of mathematics. Organized thematically, these essays ponder the intellectual underpinnings of the field, examine the major topics in the history of mathematics, and recount the bizarre history of pseudomath.

Ivor Grattan*Guinness explores how people understand mathematics -- the routes of learning they take as they make important discoveries and study mathematical concepts and theories. The essays in the first part of the book discuss the history of mathematics as a field and its central philosophical issues. Those in the next part address the history of mathematics education and its importance to current modes of teaching. In the last section Grattan*Guinness investigates various understudied aspects of math, including numerology, Masonic symbols in classical music, and the links between mathematics and Christianity.

This collection includes several essays that are difficult to find anywhere else. All historians of mathematics and students of the field will want a copy of this remarkable resource on their bookshelves.

"Ivor Grattan*Guinness has been a leader in the field for decades. His ideas are at times contentious, which is all the more reason to have them all together in one volume. There is nothing else available like this, because there is no other researcher like Grattan*Guinness. This volume is a must for math historians, math philosophers, and all collegiate libraries." -- Amy Shell*Gellasch, editor of From Calculus to Computers: Using the Last 200 Years of Mathematics History in the Classroom

Ivor Grattan*Guinness is a professor emeritus of the history of mathematics and logic at Middlesex University. He is author of Convolutions in French Mathematics, 1800*1840: From the Calculus and Mechanics to Mathematical Analysis and Mathematical Physics and editor of the Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, also published by Johns Hopkins.


Emil Simiu

Chaotic Transitions in Deterministic and Stochastic Dynamical Systems:
Applications of Melnikov Processes in Engineering, Physics, and Neuroscience

Paper | 2009 | 978-0-691-14434-4
246 pp. | 6 x 9 | 94 line illus

The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the applicability of the Melnikov method to physically realizable stochastic planar systems with additive, state-dependent, white, colored, or dichotomous noise. The extended Melnikov method yields the novel result that motions with transitions are chaotic regardless of whether the excitation is deterministic or stochastic. It explains the role in the occurrence of transitions of the characteristics of the system and its deterministic or stochastic excitation, and is a powerful modeling and identification tool.

The book is designed primarily for readers interested in applications. The level of preparation required corresponds to the equivalent of a first-year graduate course in applied mathematics. No previous exposure to dynamical systems theory or the theory of stochastic processes is required. The theoretical prerequisites and developments are presented in the first part of the book. The second part of the book is devoted to applications, ranging from physics to mechanical engineering, naval architecture, oceanography, nonlinear control, stochastic resonance, and neurophysiology.

Emil Simiu is a NIST Fellow, National Institute of Standards and Technology, and Research Professor, Whiting School of Engineering, The Johns Hopkins University. A specialist in flow-structure interaction, he is the coauthor of Wind Effects on Structures and was the 1984 recipient of the Federal Engineer of the Year award.

Review:

"Highly readable, elegant, and concise. . . . Emil Simiu has succeeded in putting together a highly stimulating book that proposes a promising, unifying approach to various aspects of chaos theory. While encompassing a wide swath of topics, traditionally found only on scattered sources, the book is succinctly written, exhibiting a quality reserved to the best of review works."--Daniel ben-Avraham, Journal of Statistical Physics

Endorsement:

"The author has chosen an excellent subject, which will probably become a main direction of research in the field of stochastic differential equations. This book is addressed to a wide readership: specialists in dynamical systems and stochastic processes, mathematicians, engineers, physicists, and neuroscientists. The author succeeds in making the material interesting to all these groups of researchers."--Florin Diacu, Pacific Institute for the Mathematical Sciences, University of Victoria

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