Fields Institute Communications, Volume: 55
2009; approx. 247 pp; hardcover
ISBN-13: 978-0-8218-4485-4
Expected publication date is June 19, 2009.
A large number of mathematical models in many diverse areas of science and engineering have lead to the formulation of optimization problems where the best solution (globally optimal) is needed. Due to the interdisciplinary nature of global optimization, there has been astonishing progress in this field during the last few decades. Many powerful computational algorithms and new theoretical developments have been introduced to solve a spectrum of hard problems in several disciplines.
This book covers a small subset of recent important topics in global optimization with emphasis on recent theoretical developments and scientific applications. The chapters are based on the talks presented at the workshop on "Global Optimization: Methods and Applications" that was held at the Fields Institute from May 11-12, 2007. The target audience includes graduate students in mathematics, engineering, and sciences, academic researchers, as well as practitioners, who use global optimization for their specific needs and applications.
Graduate students and research mathematicians interested in global optimization.
C. Audet, P. Hansen, and F. Messine -- Extremal problems for convex polygons--an update
X. Bao and N. V. Sahinidis -- Finite algorithms for global minimization of separable concave programs
J. Carlsson, D. Ge, A. Subramaniam, and Y. Ye -- Solving min-max multi-depot vehicle routing problem
H.-D. Chiang, J.-H. Chen, and C. Reddy -- Trust-tech-based global optimization methodology for nonlinear programming
V. Dua, K. Kouramas, and S. Pistikopoulos -- Global optimization issues in parametric programming and control
C. A. Floudas and C. E. Gounaris -- An overview of advances in global optimization during 2003-2008
O. E. Kundakcioglu and P. M. Pardalos -- Optimization in biomedical research
J. D. Pinter -- Software developement for global optimization
L. Li, X. Zhu, D.-Z. Du, P. M. Pardalos, and W. Wu -- Connected dominating set in hypergraph
A. Tsoukalas, W. Wiesemann, and B. Rustem -- Global optimisation of pessimistic bi-level problems
Mathematical World, Volume: 27
2009; approx. 176 pp; softcover
ISBN-13: 978-0-8218-4473-1
Expected publication date is July 9, 2009.
This text should not be viewed as a comprehensive history of algebra before 1600, but as a basic introduction to the types of problems that illustrate the earliest forms of algebra. It would be particularly useful for an instructor who is looking for examples to help enliven a course on elementary algebra with problems drawn from actual historical texts.
--Warren Van Egmond about the French edition for MathSciNet
This book does not aim to give an exhaustive survey of the history of algebra up to early modern times but merely to present some significant steps in solving equations and, wherever applicable, to link these developments to the extension of the number system. Various examples of problems, with their typical solution methods, are analyzed, and sometimes translated completely. Indeed, it is another aim of this book to ease the reader's access to modern editions of old mathematical texts, or even to the original texts; to this end, some of the problems discussed in the text have been reproduced in the appendices in their original language (Greek, Latin, Arabic, Hebrew, French, German, Provencal, and Italian) with explicative notes.
Undergraduate students, graduate students, and research mathematicians interested in the history of mathematics.
Algebra in Mesopotamia
Algebra in ancient Greece
Algebra in the Islamic world
Algebra in medieval Europe
Algebra in the Renaissance
Appendix A. Mesopotamian texts in translation
Appendix B. Greek and Latin texts
Appendix C. Arabic texts
Appendix D. Hebrew text
Appendix E. French, German, Italian, and Provencal texts
Index
Contemporary Mathematics, Volume: 487
2009; 206 pp; softcover
ISBN-13: 978-0-8218-4716-9
Expected publication date is July 11, 2009.
This volume contains the proceedings of the 11th conference on \mathrm{AGC^{2}T}, held in Marseilles, France in November 2007. There are 12 original research articles covering asymptotic properties of global fields, arithmetic properties of curves and higher dimensional varieties, and applications to codes and cryptography. This volume also contains a survey article on applications of finite fields by J.-P. Serre.
mathrm{AGC^{2}T} conferences take place in Marseilles, France every 2 years.
These international conferences have been a major event in the area of
applied arithmetic geometry for more than 20 years.
Graduate students and research mathematicians interested in arithmetic geometry and its applications.
Contemporary Mathematics, Volume: 488
2009; 285 pp; softcover
ISBN-13: 978-0-8218-4706-0
Expected publication date is July 12, 2009.
This book is the first of two volumes, which represent leading themes of current research in automorphic forms and representation theory of reductive groups over local fields. Articles in this volume mainly represent global aspects of automorphic forms. Among the topics are the trace formula; functoriality; representations of reductive groups over local fields; the relative trace formula and periods of automorphic forms; Rankin-Selberg convolutions and L-functions; and p-adic L-functions. The articles are written by leading researchers in the field, and bring the reader, advanced graduate students and researchers alike, to the frontline of the vigorous research in these deep, vital topics. The companion volume (Contemporary Mathematics, Volume 489) is devoted to local aspects of automorphic forms.
Graduate students and research mathematicians interested in representation theory and automorphic forms.
Contemporary Mathematics,Volume: 489
2009; 313 pp; softcover
ISBN-13: 978-0-8218-4708-4
Expected publication date is August 8, 2009.
This book is the second of two volumes, which represent leading themes of current research in automorphic forms and representation theory of reductive groups over local fields. Articles in this volume mainly represent global aspects of automorphic forms. Among the topics are the trace formula; functoriality; representations of reductive groups over local fields; the relative trace formula and periods of automorphic forms; Rankin-Selberg convolutions and L-functions; and p-adic L-functions. The articles are written by leading researchers in the field, and bring the reader, advanced graduate students and researchers alike, to the frontline of the vigorous research in these deep, vital topics. The companion volume (Contemporary Mathematics, Volume 488) is devoted to global aspects of automorphic forms.
Graduate students and research mathematicians interested in representation theory and automorphic forms.
Student Mathematical Library, Volume: 49
2009; approx. 391 pp; softcover
ISBN-13: 978-0-8218-4816-6
Expected publication date is August 5, 2009.
The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathematics of 3-dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments.
Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. However, the ultimate goal is to describe the very recently completed geometrization program for 3-dimensional manifolds. The journey to reach this goal emphasizes examples and concrete constructions as an introduction to more general statements. This includes the tessellations associated to the process of gluing together the sides of a polygon. Bending some of these tessellations provides a natural introduction to 3-dimensional hyperbolic geometry and to the theory of kleinian groups, and it eventually leads to a discussion of the geometrization theorems for knot complements and 3-dimensional manifolds.
This book is illustrated with many pictures, as the author intended to share his own enthusiasm for the beauty of some of the mathematical objects involved. However, it also emphasizes mathematical rigor and, with the exception of the most recent research breakthroughs, its constructions and statements are carefully justified.
Undergraduate students interested in topology and/or geometry of low-dimensional manifolds, particularly 3-manifolds.
The euclidean plane
The hyperbolic plane
The 2-dimensional sphere
Gluing constructions
Gluing examples
Tessellations
Group actions and fundamental domains
The Farey tessellation and circle packing
The 3-dimensional hyperbolic space
Kleinian groups
The figure-eight knot complement
Geometrization theorems in dimension 3
Tool kit
Bibliography and references
Index