Elliptic Curves and Related Topics
Elliptic Curves and Related Topics

Author: H. Kisilevsky

Publisher: American Mathematical Soc.

Published: 1994-01-01

Total Pages: 208

ISBN-13: 9780821870358

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This book represents the proceedings of a workshop on elliptic curves held in St. Adele, Quebec, in February 1992. Containing both expository and research articles on the theory of elliptic curves, this collection covers a range of topics, from Langlands's theory to the algebraic geometry of elliptic curves, from Iwasawa theory to computational aspects of elliptic curves. This book is especially significant in that it covers topics comprising the main ingredients in Andrew Wiles's recent result on Fermat's Last Theorem.

Additive Combinatorics
Additive Combinatorics

Author: Andrew Granville

Publisher: American Mathematical Soc.

Published:

Total Pages: 348

ISBN-13: 9780821870396

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This book, based in part on lectures delivered at the 2006 CRM-Clay School on Additive Combinatorics, brings together some of the top researchers in one of the hottest topics in analysis today. This new subject brings together ideas from many different areas to prove some extraordinary results. The book encompasses proceedings from the school, articles on open questions in additive combinatorics, and new research.

Theta Functions
Theta Functions

Author: Maruti Ram Murty

Publisher: American Mathematical Soc.

Published: 1993-01-01

Total Pages: 188

ISBN-13: 9780821870112

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This book contains lectures on theta functions written by experts well known for excellence in exposition. The lectures represent the content of four courses given at the Centre de Recherches Mathematiques in Montreal during the academic year 1991-1992, which was devoted to the study of automorphic forms. Aimed at graduate students, the book synthesizes the classical and modern points of view in theta functions, concentrating on connections to number theory and representation theory. An excellent introduction to this important subject of current research, this book is suitable as a text in advanced graduate courses.

Analysis and Geometry of Metric Measure Spaces
Analysis and Geometry of Metric Measure Spaces

Author: Galia Devora Dafni

Publisher: American Mathematical Soc.

Published: 2013

Total Pages: 241

ISBN-13: 0821894188

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Contains lecture notes from most of the courses presented at the 50th anniversary edition of the Seminaire de Mathematiques Superieure in Montreal. This 2011 summer school was devoted to the analysis and geometry of metric measure spaces, and featured much interplay between this subject and the emergent topic of optimal transportation.

Anatomy of Integers
Anatomy of Integers

Author:

Publisher:

Published: 2008

Total Pages: 297

ISBN-13: 9781470439606

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The book is mostly devoted to the study of the prime factors of integers, their size and their quantity, to good bounds on the number of integers with different properties (for example, those with only large prime factors) and to the distribution of divisors of integers in a given interval. In particular, various estimates concerning smooth numbers are developed. A large emphasis is put on the study of additive and multiplicative functions as well as various arithmetic functions such as the partition function. More specific topics include the Erdős-Kac Theorem, cyclotomic polynomials, combinat.

Number Theory
Number Theory

Author: H. Kisilevsky

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 329

ISBN-13: 0821833316

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Collects articles from the meeting of the Canadian Number Theory Association held at the Centre de Recherches Mathematiques (CRM) at the University of Montreal. This book covers topics such as algebraic number theory, analytic number theory, arithmetic algebraic geometry, computational number theory, and Diophantine analysis and approximation.

Algebraic Structures and Moduli Spaces
Algebraic Structures and Moduli Spaces

Author: Jacques Hurtubise and Eyal Markman

Publisher: American Mathematical Soc.

Published:

Total Pages: 268

ISBN-13: 9780821870334

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This book contains recent and exciting developments on the structure of moduli spaces, with an emphasis on the algebraic structures that underlie this structure. Topics covered include Hilbert schemes of points, moduli of instantons, coherent sheaves and their derived categories, moduli of flat connections, Hodge structures, and the topology of affine varieties. Two beautiful series of lectures are a particularly fine feature of the book. One is an introductory series by Manfred Lehn on the topology and geometry of Hilbert schemes of points on surfaces, and the other, by Hiraku Nakajima and Kota Yoshioka, explains their recent work on the moduli space of instantons over ${\mathbb R 4$. The material is suitable for graduate students and researchers interested in moduli spaces in algebraic geometry, topology, and mathematical physics.

High-Dimensional Partial Differential Equations in Science and Engineering
High-Dimensional Partial Differential Equations in Science and Engineering

Author: André D. Bandrauk

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 210

ISBN-13: 0821838539

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High-dimensional spatio-temporal partial differential equations are a major challenge to scientific computing of the future. Up to now deemed prohibitive, they have recently become manageable by combining recent developments in numerical techniques, appropriate computer implementations, and the use of computers with parallel and even massively parallel architectures. This opens new perspectives in many fields of applications. Kinetic plasma physics equations, the many body Schrodinger equation, Dirac and Maxwell equations for molecular electronic structures and nuclear dynamic computations, options pricing equations in mathematical finance, as well as Fokker-Planck and fluid dynamics equations for complex fluids, are examples of equations that can now be handled. The objective of this volume is to bring together contributions by experts of international stature in that broad spectrum of areas to confront their approaches and possibly bring out common problem formulations and research directions in the numerical solutions of high-dimensional partial differential equations in various fields of science and engineering with special emphasis on chemistry and physics. Information for our distributors: Titles in this series are co-published with the Centre de Recherches Mathematiques.

Stable Marriage and Its Relation to Other Combinatorial Problems
Stable Marriage and Its Relation to Other Combinatorial Problems

Author: Donald Ervin Knuth

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 90

ISBN-13: 0821806033

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Uses the theory of stable marriage to introduce and illustrate a variety of important concepts and techniques of computer science and mathematics: data structures, control structures, combinatorics, probability, analysis, algebra, and especially the analysis of algorithms.