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Showing posts with label Mathematical Foundations. Show all posts
Showing posts with label Mathematical Foundations. Show all posts

The Selected Correspondence of L.E.J. Brouwer by Dirk van Dalen

Posted by Mr Dragon at Thursday, October 27, 2011 , 0 Comments

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Book Details :
Title : The Selected Correspondence of L.E.J. Brouwer (Sources and Studies in the History of Mathematics and Physical Sciences)
Author : Dirk van Dalen
Paperback : 536 pages
Publisher : Springer; 1st Edition. edition (August 9, 2011)
Language : English
ISBN-10 : 0857295276
ISBN-13 : 978-0857295279
Size : 2.29 MB.
Type : Pdf.
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Book Description :

L.E.J. Brouwer (1881-1966) is best known for his revolutionary ideas on topology and foundations of mathematics (intuitionism). The present collection contains a mixture of letters; university and faculty correspondence has been included, some of which shed light on the student years, and in particular on the exchange of letters with his PhD adviser, Korteweg. Acting as the natural sequel to the publication of Brouwer’s biography, this book provides instrumental reading for those wishing to gain a deeper understanding of Brouwer and his role in the twentieth century. Striking a good balance of biographical and scientific information, the latter deals with innovations in topology (Cantor-Schoenflies style and the new topology) and foundations. The topological period in his research is well represented in correspondence with Hilbert, Schoenflies, Poincaré, Blumenthal, Lebesgue, Baire, Koebe, and foundational topics are discussed in letters exchanged with Weyl, Fraenkel, Heyting, van Dantzig and others. There is also a large part of correspondence on matters related to the interbellum scientific politics. This book will appeal to both graduate students and researchers with an interest in topology, the history of mathematics, the foundations of mathematics, philosophy and general science.


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Foundations of Optimization by Osman Güler

Posted by Mr Dragon at Friday, October 21, 2011 , 0 Comments

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Book Details :
Title : Foundations of Optimization (Graduate Texts in Mathematics)
Author : Osman Güler
Hardcover : 457 pages
Publisher : Springer; 1st Edition. edition (August 25, 2010)
Language : English
ISBN-10 : 0387344314
ISBN-13 : 978-0387344317
Size : 2.3 MB.
Type : Pdf.
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Book Description :

The book gives a detailed and rigorous treatment of the theory of optimization (unconstrained optimization, nonlinear programming, semi-infinite programming, etc.) in finite-dimensional spaces. The fundamental results of convexity theory and the theory of duality in nonlinear programming and the theories of linear inequalities, convex polyhedra, and linear programming are covered in detail. Over two hundred, carefully selected exercises should help the students master the material of the book and give further insight. Some of the most basic results are proved in several independent ways in order to give flexibility to the instructor. A separate chapter gives extensive treatments of three of the most basic optimization algorithms (the steepest-descent method, Newton’s method, the conjugate-gradient method). The first chapter of the book introduces the necessary differential calculus tools used in the book. Several chapters contain more advanced topics in optimization such as Ekeland’s epsilon-variational principle, a deep and detailed study of separation properties of two or more convex sets in general vector spaces, Helly’s theorem and its applications to optimization, etc. The book is suitable as a textbook for a first or second course in optimization at the graduate level. It is also suitable for self-study or as a reference book for advanced readers. The book grew out of author’s experience in teaching a graduate level one-semester course a dozen times since 1993. Osman Guler is a Professor in the Department of Mathematics and Statistics at University of Maryland, Baltimore County. His research interests include mathematical programming, convex analysis, complexity of optimization problems, and operations research.

This book is an advanced graduate level text on the mathematical theory of optimization. … filled with many useful examples and counterexamples that provide intuition to support the more formal theorems and proofs. … There are also numerous exercises for the student. … The book will also be useful as a reference for researchers working in various areas of optimization.


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Invariant Factors, Julia Equivalences and the (Abstract) Mandelbrot Set by Karsten Keller

Posted by Mr Dragon at Thursday, September 22, 2011 , 0 Comments

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Book Details :
Title : Invariant Factors, Julia Equivalences and the (Abstract) Mandelbrot Set (Lecture Notes in Mathematics)
Author : Karsten Keller
Paperback : 216 pages
Publisher : Springer; 1 edition (June 8, 2000)
Language : English
ISBN-10 : 3540674349
ISBN-13 : 978-3540674344
Size : 5.22 MB.
Type : Djvu.
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Book Description :

This book is mainly devoted to the combinatorics of quadratic holomorphic dynamics. The conceptual kernel is a self-contained abstract counterpart of connected quadratic Julia sets which is built on Thurston's concept of a quadratic invariant lamination and on symbolic descriptions of the angle-doubling map. The theory obtained is illustrated in the complex plane. It is used to give rigorous proofs of some well-known and some partially new statements on the structure of the Mandelbrot set. The text is intended for graduate students and researchers. Some elementary knowledge in topology and in functions of one complex variable is assumed.


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The Monty Hall Problem by Jason Rosenhouse

Posted by Mr Dragon at Thursday, August 25, 2011 , 0 Comments

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Book Details :
Title : The Monty Hall Problem: The Remarkable Story of Math's Most Contentious Brain Teaser
Author : Jason Rosenhouse
Hardcover : 208 pages
Publisher : Oxford University Press, USA; 1 edition (June 4, 2009)
Language : English
ISBN-10 : 0195367898
ISBN-13 : 978-0195367898
Size : 5.02 MB.
Type : Pdf.
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Book Description :

Mathematicians call it the Monty Hall Problem, and it is one of the most interesting mathematical brain teasers of recent times. Imagine that you face three doors, behind one of which is a prize. You choose one but do not open it. The host--call him Monty Hall--opens a different door, always choosing one he knows to be empty. Left with two doors, will you do better by sticking with your first choice, or by switching to the other remaining door? In this light-hearted yet ultimately serious book, Jason Rosenhouse explores the history of this fascinating puzzle. Using a minimum of mathematics (and none at all for much of the book), he shows how the problem has fascinated philosophers, psychologists, and many others, and examines the many variations that have appeared over the years. As Rosenhouse demonstrates, the Monty Hall Problem illuminates fundamental mathematical issues and has abiding philosophical implications. Perhaps most important, he writes, the problem opens a window on our cognitive difficulties in reasoning about uncertainty.

"Those intrigued by the original Monty Hall problem will find that this book is a superb source of variants of the problem, pays careful attention to the hidden assumptions behind the problems, and is written in a witty accessible style that never lapses into flippancy. This is a model of how to accessibly introduce mathematical material at an elementary level that is not a mere popularization of the material. A virtue of the book is that it goes beyond mere exposition to make some serious contributions to the discussion, including a proof that the strategy of switching at the last minute in the progressive version is uniquely optimal and a discussion of some philosophical treatments on the topic."-- Mathematical Reviews

About author :

Jason Rosenhouse is an Associate Professor of Mathematics at James Madison University in Virginia.


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