Crm Proceedings Lecture Notes
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Number Theory
Author | : Canadian Number Theory Association. Conference |
Publisher | : American Mathematical Soc. |
Total Pages | : 588 |
Release | : 1999 |
Genre | : Number theory |
ISBN | : 9780821809648 |
This book contains papers presented at the Fifth Canadian Number Theory Association (CNTA) conference held at Carleton University Ottawa, Ontario. The invited speakers focused on arithmetic algebraic geometry and elliptic curves, diophantine problems, analytic number theory, and algebraic and computational number theory. The contributed talks represented a wide variety of areas in number theory. David Boyd gave an hour-long talk on Mahler's Measure and Elliptic Curves. This lecture was open to the public and attracted a large audience from outside the conference.
Elliptic Curves and Related Topics
Author | : H. Kisilevsky |
Publisher | : American Mathematical Soc. |
Total Pages | : 208 |
Release | : 1994-01-01 |
Genre | : Mathematics |
ISBN | : 9780821870358 |
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.
Theta Functions
Author | : Maruti Ram Murty |
Publisher | : American Mathematical Soc. |
Total Pages | : 188 |
Release | : 1993-01-01 |
Genre | : Mathematics |
ISBN | : 9780821870112 |
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.
Algebraic Structures and Moduli Spaces
Author | : Jacques Hurtubise and Eyal Markman |
Publisher | : American Mathematical Soc. |
Total Pages | : 268 |
Release | : |
Genre | : Algebra, Abstract |
ISBN | : 9780821870334 |
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.
Anatomy of Integers
Author | : |
Publisher | : |
Total Pages | : 297 |
Release | : 2008 |
Genre | : Integrals |
ISBN | : 9781470439606 |
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.
Additive Combinatorics
Author | : Andrew Granville |
Publisher | : American Mathematical Soc. |
Total Pages | : 348 |
Release | : |
Genre | : Mathematics |
ISBN | : 9780821870396 |
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.
Data Mining and Mathematical Programming
Author | : Panos M. Pardalos |
Publisher | : American Mathematical Soc. |
Total Pages | : 252 |
Release | : 2008-04-09 |
Genre | : Computers |
ISBN | : 9780821870402 |
Data mining aims at finding interesting, useful or profitable information in very large databases. The enormous increase in the size of available scientific and commercial databases (data avalanche) as well as the continuing and exponential growth in performance of present day computers make data mining a very active field. In many cases, the burgeoning volume of data sets has grown so large that it threatens to overwhelm rather than enlighten scientists. Therefore, traditional methods are revised and streamlined, complemented by many new methods to address challenging new problems. Mathematical Programming plays a key role in this endeavor. It helps us to formulate precise objectives (e.g., a clustering criterion or a measure of discrimination) as well as the constraints imposed on the solution (e.g., find a partition, a covering or a hierarchy in clustering). It also provides powerful mathematical tools to build highly performing exact or approximate algorithms. This book is based on lectures presented at the workshop on "Data Mining and Mathematical Programming" (October 10-13, 2006, Montreal) and will be a valuable scientific source of information to faculty, students, and researchers in optimization, data analysis and data mining, as well as people working in computer science, engineering and applied mathematics.