David Wright, Washington University in St. Louis, MO

Mathematics and Music

Mathematical World, Volume: 28
2009; 161 pp; softcover
ISBN-13: 978-0-8218-4873-9
Expected publication date is September 23, 2009.

Many people intuitively sense that there is a connection between mathematics and music. If nothing else, both involve counting. There is, of course, much more to the association. David Wright's book is an investigation of the interrelationships between mathematics and music, reviewing the needed background concepts in each subject as they are encountered. Along the way, readers will augment their understanding of both mathematics and music.

The text explores the common foundations of the two subjects, which are developed side by side. Musical and mathematical notions are brought together, such as scales and modular arithmetic, intervals and logarithms, tone and trigonometry, and timbre and harmonic analysis. When possible, discussions of musical and mathematical notions are directly interwoven. Occasionally the discourse dwells for a while on one subject and not the other, but eventually the connection is established, making this an integrative treatment of the two subjects.

The book is a text for a freshman level college course suitable for musically inclined or mathematically inclined students, with the intent of breaking down any apprehension that either group might have for the other subject. Exercises are given at the end of each chapter. The mathematical prerequisites are a high-school level familiarity with algebra, trigonometry, functions, and graphs. Musically, the student should have had some exposure to musical staffs, standard clefs, and key signatures, though all of these are explained in the text.

Readership

Undergraduate students interested in math and/or music.

Table of Contents

Basic mathematical and musical concepts
Horizontal structure
Harmony and related numerology
Ratios and musical intervals
Logarithms and musical intervals
Chromatic scales
Octave identification and modular arithmetic
Algebraic properties of the integers
The integers as intervals
Timbre and periodic functions
The rational numbers as musical intervals
Tuning the scale to obtain rational intervals
Bibliography
Index

Edited by: Miguel Abreu, Instituto Superior Tecnico, Lisbon, Portugal, Francois Lalonde, Universite de Montreal, QC, Canada, and Leonid Polterovich, Tel Aviv University, Israel

New Perspectives and Challenges in Symplectic Field Theory

CRM Proceedings & Lecture Notes, Volume: 49
2009; approx. 345 pp; softcover

ISBN-13: 978-0-8218-4356-7
Expected publication date is September 30, 2009.

This volume, in honor of Yakov Eliashberg, gives a panorama of some of the most fascinating recent developments in symplectic, contact and gauge theories. It contains research papers aimed at experts, as well as a series of skillfully written surveys accessible for a broad geometrically oriented readership from the graduate level onwards. This collection will serve as an enduring source of information and ideas for those who want to enter this exciting area as well as for experts.

Readership

Graduate students and research mathematicians interested in geometry and topology.

Table of Contents

• P. Biran and O. Cornea -- A Lagrangian quantum homology
• F. Bourgeois -- A survey of contact homology
  
• Y. Chekanov, O. van Koert, and F. Schlenk -- Minimal atlases of closed contact manifolds
  
• K. Cieliebak and J. Latschev -- The role of string topology in symplectic field theory
  
• R. L. Cohen and M. Schwarz -- A Morse theoretic description of string topology
  
• T. Ekholm -- A version of rational SFT for exact Lagrangian cobordisms in 1-jet spaces
  
• K. Fukaya, Y.-G. Oh, H. Ohta, and K. Ono -- Canonical models of filtered A_\infty-algebras and Morse complexes
• R. E. Gompf -- Constructing Stein manifolds after Eliashberg
  
• S. Hohloch, G. Noetzel, and D. A. Salamon -- Floer homology groups in hyperkahler geometry
  
• M. Hutchings -- The embedded contact homology index revisited
  
• F. Laudenbach -- Positive Legendrian regular homotopies
  
• T.-J. Li and Y. Ruan -- Symplectic birational geometry
  
• R. Lipshitz -- Heegaard Floer homology, double points and nice diagrams
  

Edited by: Ricardo Baeza, University of Talca, Talca, Chile, Wai Kiu Chan, Wesleyan University, Middletown, CT, Detlev W. Hoffmann, University of Nottingham, England, and Rainer Schulze-Pillot, Universitat des Saarlandes, Saarbruecken, Germany

Quadratic Forms--Algebra, Arithmetic, and Geometry

Contemporary Mathematics, Volume: 493
2009; 408 pp; softcover
ISBN-13: 978-0-8218-4648-3
Expected publication date is September 13, 2009.

This volume presents a collection of articles that are based on talks delivered at the International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms held in Frutillar, Chile in December 2007.

The theory of quadratic forms is closely connected with a broad spectrum of areas in algebra and number theory. The articles in this volume deal mainly with questions from the algebraic, geometric, arithmetic, and analytic theory of quadratic forms, and related questions in algebraic group theory and algebraic geometry.

Readership

Graduate students and research mathematicians quadradic forms (and their applications in algebra), number theory, and algebraic geometry.

Table of Contents

Rick Gillman, Valparaiso University, IN, and David Housman, Goshen College, IN

Models of Conflict and Cooperation

2009; approx. 419 pp; hardcover
ISBN-13: 978-0-8218-4872-2
Expected publication date is October 15, 2009.

Models of Conflict and Cooperation is a comprehensive, introductory, game theory text for general undergraduate students. As a textbook, it provides a new and distinctive experience for students working to become quantitatively literate. Each chapter begins with a "dialogue" that models quantitative discourse while previewing the topics presented in the rest of the chapter. Subsequent sections develop the key ideas starting with basic models and ending with deep concepts and results. Throughout all of the sections, attention is given to promoting student engagement with the material through relevant models, recommended activities, and exercises. The general game models that are discussed include deterministic, strategic, sequential, bargaining, coalition, and fair division games. A separate, essential chapter discusses player preferences. All of the chapters are designed to strengthen the fundamental mathematical skills of quantitative literacy: logical reasoning, basic algebra and probability skills, geometric reasoning, and problem solving. A distinctive feature of this book is its emphasis on the process of mathematical modeling.

Readership

Undergraduate students interested in game theory.

Table of Contents

• Deterministic games
  
• Player preferences
  
• Strategic games
  
• Probabilistic strategies
  
• Strategic game cooperation
  
• Negotiation and arbitration
  
• Coalition games
  
• Fair division
  
• Epilogue
  
• Answers to selected exercises
  
• Bibliography
  
• Index

Edited by: John McCleary, Vassar College, Poughkeepsie, NY

Collected Papers of John Milnor: IV. Homotopy, Homology and Manifolds

Collected Works, Volume: 19
2009; approx. 357 pp; hardcover
ISBN-13: 978-0-8218-4475-5
Expected publication date is October 16, 2009.

The development of algebraic topology in the 1950's and 1960's was deeply influenced by the work of Milnor. In this collection of papers the reader finds those original papers and some previously unpublished works. The book is divided into four parts: Homotopy Theory, Homology and Cohomology, Manifolds, and Expository Papers. Introductions to each part provide some historical context and subsequent development. Of particular interest are the articles on classifying spaces, the Steenrod algebra, the introductory notes on foliations and the surveys of work on the Poincare conjecture.

Together with the previously published volumes I-III of the Collected Works by John Milnor, volume IV provides a rich portion of the most important developments in geometry and topology from those decades.

This volume is highly recommended to a broad mathematical audience, and, in particular, to young mathematicians who will certainly benefit from their acquaintance with Milnor's mode of thinking and writing.

Readership

Graduate students and research mathematicians interested in algebraic differential topology.

Table of Contents

Part 1: Homotopy theory

• Introduction to Part 1: homotopy theory
  
• Construction of universal bundles, I
  
• Construction of universal bundles, II
  
• The geometric realization of a semi-simplicial complex
  
• On spaces having the homotopy type of a CW-complex
  
• On the construction of FK

Part 2: Cohomology and homology

• Introduction to Part 2: cohomolgy and homology
  
• The Steenrod algebra and its dual
  
• On the Steenrod homology theory
  
• On axiomatic homology theory
  
• (with M. G. Barratt), An example of anomalous singular homology
  
• (with G. Lusztig and F. P. Peterson), Semi-characteristics and cobordism
  
• On the homology of Lie groups made discrete

Part 3: Manifolds

• Introduction to Part 3: Manifolds
  
• On the immersion of n-manifolds in (n+1)-space
  
• On simply connected 4-manifolds
  
• (with M. Kervaire), On 2-spheres in 4-manifolds
  
• (with E. Spanier), Two remarks on fiber homotopy type
  
• Microbundles and differentiable structures
  
• Topological manifolds and smooth manifolds
  
• Microbundles. I
  
• On characteristic classes for spherical fibre spaces

Part 4: Expository papers

• Introduction to Part 4: Expository papers
  
• The work of J. H. C. Whitehead
  
• Foliations and foliated vector bundles
  
• The work of M. H. Freedman
  
• Towards the Poincare conjecture and the classification of 3-manifolds
  
• The Poincare conjecture one hundred years later
  
• Fifty years ago: topology of manifolds in the 50's and 60's
  
• Bibliography
  
• Index