The Art of Mathematics

Coffee Time in Memphis

Author: Béla Bollobás

Publisher: Cambridge University Press

ISBN: 0521872286

Category: Mathematics

Page: 359

View: 4691

A collection of mathematical problems chosen to illustrate the mathematician's art.
Posted in Mathematics

Mathematical Mind-Benders

Author: Peter Winkler

Publisher: CRC Press

ISBN: 1568815077

Category: Mathematics

Page: 160

View: 5934

Peter Winkler is at it again. Following the enthusiastic reaction to Mathematical Puzzles: A Connoisseur's Collection, Peter has compiled a new collection of elegant mathematical puzzles to challenge and entertain the reader. The original puzzle connoisseur shares these puzzles, old and new, so that you can add them to your own anthology. This book is for lovers of mathematics, lovers of puzzles, lovers of a challenge. Most of all, it is for those who think that the world of mathematics is orderly, logical, and intuitive-and are ready to learn otherwise! A pdf with errata is updated by the author and can be accessed here
Posted in Mathematics

Combinatorics

Set Systems, Hypergraphs, Families of Vectors, and Combinatorial Probability

Author: Béla Bollobás

Publisher: Cambridge University Press

ISBN: 9780521337038

Category: Mathematics

Page: 177

View: 5891

Combinatorics is a book whose main theme is the study of subsets of a finite set. It gives a thorough grounding in the theories of set systems and hypergraphs, while providing an introduction to matroids, designs, combinatorial probability and Ramsey theory for infinite sets. The gems of the theory are emphasized: beautiful results with elegant proofs. The book developed from a course at Louisiana State University and combines a careful presentation with the informal style of those lectures. It should be an ideal text for senior undergraduates and beginning graduates.
Posted in Mathematics

50th IMO - 50 Years of International Mathematical Olympiads

Author: Hans-Dietrich Gronau,Hanns-Heinrich Langmann,Dierk Schleicher

Publisher: Springer Science & Business Media

ISBN: 9783642145650

Category: Mathematics

Page: 297

View: 3797

In July 2009 Germany hosted the 50th International Mathematical Olympiad (IMO). For the very first time the number of participating countries exceeded 100, with 104 countries from all continents. Celebrating the 50th anniversary of the IMO provides an ideal opportunity to look back over the past five decades and to review its development to become a worldwide event. This book is a report about the 50th IMO as well as the IMO history. A lot of data about all the 50 IMOs are included. We list the most successful contestants, the results of the 50 Olympiads and the 112 countries that have ever taken part. It is impressive to see that many of the world’s leading research mathematicians were among the most successful IMO participants in their youth. Six of them gave presentations at a special celebration: Bollobás, Gowers, Lovász, Smirnov, Tao and Yoccoz. This book is aimed at students in the IMO age group and all those who have interest in this worldwide leading competition for highschool students.
Posted in Mathematics

Linear Analysis

An Introductory Course

Author: Béla Bollobás

Publisher: Cambridge University Press

ISBN: 9780521655774

Category: Mathematics

Page: 240

View: 902

Revised and updated introduction to functional analysis.
Posted in Mathematics

Handbook of Mathematical Induction

Theory and Applications

Author: David S. Gunderson

Publisher: CRC Press

ISBN: 1420093657

Category: Mathematics

Page: 921

View: 3078

Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics. In the first part of the book, the author discusses different inductive techniques, including well-ordered sets, basic mathematical induction, strong induction, double induction, infinite descent, downward induction, and several variants. He then introduces ordinals and cardinals, transfinite induction, the axiom of choice, Zorn’s lemma, empirical induction, and fallacies and induction. He also explains how to write inductive proofs. The next part contains more than 750 exercises that highlight the levels of difficulty of an inductive proof, the variety of inductive techniques available, and the scope of results provable by mathematical induction. Each self-contained chapter in this section includes the necessary definitions, theory, and notation and covers a range of theorems and problems, from fundamental to very specialized. The final part presents either solutions or hints to the exercises. Slightly longer than what is found in most texts, these solutions provide complete details for every step of the problem-solving process.
Posted in Mathematics

Topics in Fixed Point Theory

Author: Saleh Almezel,Qamrul Hasan Ansari,Mohamed Amine Khamsi

Publisher: Springer Science & Business Media

ISBN: 3319015869

Category: Mathematics

Page: 304

View: 1101

The purpose of this contributed volume is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The book presents information for those wishing to find results that might apply to their own work and for those wishing to obtain a deeper understanding of the theory. The book should be of interest to a wide range of researchers in mathematical analysis as well as to those whose primary interest is the study of fixed point theory and the underlying spaces. The level of exposition is directed to a wide audience, including students and established researchers. Key topics covered include Banach contraction theorem, hyperconvex metric spaces, modular function spaces, fixed point theory in ordered sets, topological fixed point theory for set-valued maps, coincidence theorems, Lefschetz and Nielsen theories, systems of nonlinear inequalities, iterative methods for fixed point problems, and the Ekeland’s variational principle.
Posted in Mathematics

Enumerative Combinatorics:

Author: Richard P. Stanley

Publisher: Cambridge University Press

ISBN: 9780521663519

Category: Mathematics

Page: 340

View: 1062

This book is the first of a two-volume basic introduction to enumerative combinatorics at a level suitable for graduate students and research mathematicians. It concentrates on the theory and application of generating functions, a fundamental tool in enumerative combinatorics. The book covers those parts of enumerative combinatorics of greatest applicability to other areas of mathematics. The four chapters are devoted to an introduction to enumeration (suitable for advanced undergraduates), sieve methods (including the Principle of Inclusion-Exclusion), partially ordered sets, and rational generating functions. There are a large number of exercises, almost all with solutions, which greatly augment the text and provide entry into many areas not covered directly. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference.
Posted in Mathematics

Algorithmic Puzzles

Author: Anany Levitin,Maria Levitin

Publisher: Oxford University Press

ISBN: 0199911770

Category: Mathematics

Page: 280

View: 8095

While many think of algorithms as specific to computer science, at its core algorithmic thinking is defined by the use of analytical logic to solve problems. This logic extends far beyond the realm of computer science and into the wide and entertaining world of puzzles. In Algorithmic Puzzles, Anany and Maria Levitin use many classic brainteasers as well as newer examples from job interviews with major corporations to show readers how to apply analytical thinking to solve puzzles requiring well-defined procedures. The book's unique collection of puzzles is supplemented with carefully developed tutorials on algorithm design strategies and analysis techniques intended to walk the reader step-by-step through the various approaches to algorithmic problem solving. Mastery of these strategies--exhaustive search, backtracking, and divide-and-conquer, among others--will aid the reader in solving not only the puzzles contained in this book, but also others encountered in interviews, puzzle collections, and throughout everyday life. Each of the 150 puzzles contains hints and solutions, along with commentary on the puzzle's origins and solution methods. The only book of its kind, Algorithmic Puzzles houses puzzles for all skill levels. Readers with only middle school mathematics will develop their algorithmic problem-solving skills through puzzles at the elementary level, while seasoned puzzle solvers will enjoy the challenge of thinking through more difficult puzzles.
Posted in Mathematics

Building a Masterpiece

The Sydney Opera House

Author: Anne Watson

Publisher: N.A

ISBN: 9781863171526

Category: Architecture

Page: 215

View: 8182

Building a masterpiece explores some of the untold chapters in the long history of the Opera House's gestation, development and completion -- of individuals whose careers were made or broken by the Opera House, the companies whose reputations were secured through their association with the building, and the pioneering construction methods, innovative technologies and methodologies developed to meet the demands of its unprecedented design and challenging construction. The workers who built the building, the politicians, architects and members of the public who championed it and its often beleaguered architect are discussed as is its current world status as a symbol of Australia.To coincide with the 40th anniversary of the opening of the Sydney Opera House, this new edition of Building a Masterpiece will include a new chapter on another little known and much misunderstood story: the architect who took over from Utzon and completed the project.
Posted in Architecture

Percolation

Author: Bela Bollobás,Oliver Riordan

Publisher: Cambridge University Press

ISBN: 0521872324

Category: Mathematics

Page: 323

View: 8434

This book, first published in 2006, is an account of percolation theory and its ramifications.
Posted in Mathematics

Einstein's Dreams

Author: Alan Lightman

Publisher: Vintage

ISBN: 0307789748

Category: Fiction

Page: 144

View: 4354

A modern classic, Einstein’s Dreams is a fictional collage of stories dreamed by Albert Einstein in 1905, about time, relativity and physics. As the defiant but sensitive young genius is creating his theory of relativity, a new conception of time, he imagines many possible worlds. In one, time is circular, so that people are fated to repeat triumphs and failures over and over. In another, there is a place where time stands still, visited by lovers and parents clinging to their children. In another, time is a nightingale, sometimes trapped by a bell jar. Now translated into thirty languages, Einstein’s Dreams has inspired playwrights, dancers, musicians, and painters all over the world. In poetic vignettes, it explores the connections between science and art, the process of creativity, and ultimately the fragility of human existence.
Posted in Fiction

Fuzzy Modeling and Fuzzy Control

Author: Huaguang Zhang,Derong Liu

Publisher: Springer Science & Business Media

ISBN: 081764539X

Category: Technology & Engineering

Page: 416

View: 3785

Fuzzy logic methodology has proven effective in dealing with complex nonlinear systems containing uncertainties that are otherwise difficult to model. Technology based on this methodology is applicable to many real-world problems, especially in the area of consumer products. This book presents the first comprehensive, unified treatment of fuzzy modeling and fuzzy control, providing tools for the control of complex nonlinear systems. Coverage includes model complexity, model precision, and computing time. This is an excellent reference for electrical, computer, chemical, industrial, civil, manufacturing, mechanical and aeronautical engineers, and also useful for graduate courses in electrical engineering, computer engineering, and computer science.
Posted in Technology & Engineering

Littlewood's Miscellany

Author: John Edensor Littlewood,Béla Bollobás

Publisher: Cambridge University Press

ISBN: 9780521337021

Category: Mathematics

Page: 200

View: 5847

Academic life in Cambridge especially in Trinity College is viewed through the eyes of one of its greatest figures. Most of Professor Littlewood's earlier work is presented along with a wealth of new material.
Posted in Mathematics

The God Problem

How a Godless Cosmos Creates

Author: Howard Bloom

Publisher: Prometheus Books

ISBN: 1616145528

Category: Religion

Page: 708

View: 4429

God’s war crimes, Aristotle’s sneaky tricks, Einstein’s pajamas, information theory’s blind spot, Stephen Wolfram’s new kind of science, and six monkeys at six typewriters getting it wrong. What do these have to do with the birth of a universe and with your need for meaning? Everything, as you’re about to see. How does the cosmos do something it has long been thought only gods could achieve? How does an inanimate universe generate stunning new forms and unbelievable new powers without a creator? How does the cosmos create? That’s the central question of this book, which finds clues in strange places. Why A does not equal A. Why one plus one does not equal two. How the Greeks used kickballs to reinvent the universe. And the reason that Polish-born Benoît Mandelbrot—the father of fractal geometry—rebelled against his uncle. You’ll take a scientific expedition into the secret heart of a cosmos you’ve never seen. Not just any cosmos. An electrifyingly inventive cosmos. An obsessive-compulsive cosmos. A driven, ambitious cosmos. A cosmos of colossal shocks. A cosmos of screaming, stunning surprise. A cosmos that breaks five of science’s most sacred laws. Yes, five. And you’ll be rewarded with author Howard Bloom’s provocative new theory of the beginning, middle, and end of the universe—the Bloom toroidal model, also known as the big bagel theory—which explains two of the biggest mysteries in physics: dark energy and why, if antimatter and matter are created in equal amounts, there is so little antimatter in this universe. Called "truly awesome" by Nobel Prize–winner Dudley Herschbach, The God Problem will pull you in with the irresistible attraction of a black hole and spit you out again enlightened with the force of a big bang. Be prepared to have your mind blown. From the Hardcover edition.
Posted in Religion

A Primer for Mathematics Competitions

Author: Alexander Zawaira,Gavin Hitchcock

Publisher: OUP Oxford

ISBN: 0191561703

Category: Mathematics

Page: 368

View: 867

The importance of mathematics competitions has been widely recognised for three reasons: they help to develop imaginative capacity and thinking skills whose value far transcends mathematics; they constitute the most effective way of discovering and nurturing mathematical talent; and they provide a means to combat the prevalent false image of mathematics held by high school students, as either a fearsomely difficult or a dull and uncreative subject. This book provides a comprehensive training resource for competitions from local and provincial to national Olympiad level, containing hundreds of diagrams, and graced by many light-hearted cartoons. It features a large collection of what mathematicians call "beautiful" problems - non-routine, provocative, fascinating, and challenging problems, often with elegant solutions. It features careful, systematic exposition of a selection of the most important topics encountered in mathematics competitions, assuming little prior knowledge. Geometry, trigonometry, mathematical induction, inequalities, Diophantine equations, number theory, sequences and series, the binomial theorem, and combinatorics - are all developed in a gentle but lively manner, liberally illustrated with examples, and consistently motivated by attractive "appetiser" problems, whose solution appears after the relevant theory has been expounded. Each chapter is presented as a "toolchest" of instruments designed for cracking the problems collected at the end of the chapter. Other topics, such as algebra, co-ordinate geometry, functional equations and probability, are introduced and elucidated in the posing and solving of the large collection of miscellaneous problems in the final toolchest. An unusual feature of this book is the attention paid throughout to the history of mathematics - the origins of the ideas, the terminology and some of the problems, and the celebration of mathematics as a multicultural, cooperative human achievement. As a bonus the aspiring "mathlete" may encounter, in the most enjoyable way possible, many of the topics that form the core of the standard school curriculum.
Posted in Mathematics

Extremal Graph Theory

Author: Bela Bollobas

Publisher: Courier Corporation

ISBN: 0486317587

Category: Mathematics

Page: 512

View: 1994

The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory. Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. Although geared toward mathematicians and research students, much of Extremal Graph Theory is accessible even to undergraduate students of mathematics. Pure mathematicians will find this text a valuable resource in terms of its unusually large collection of results and proofs, and professionals in other fields with an interest in the applications of graph theory will also appreciate its precision and scope.
Posted in Mathematics

Cambridge IGCSE® and O Level Additional Mathematics Coursebook

Author: Sue Pemberton

Publisher: Cambridge University Press

ISBN: 1108411665

Category: Education

Page: N.A

View: 7530

These resources have been created for the Cambridge IGCSE® and O Level Additional Mathematics syllabuses (0606/4037), for first examination from 2020. This coursebook gives clear explanations of new mathematical concepts followed by exercises. This allows students to practise the skills required and gain the confidence to apply them. Classroom discussion exercises and extra challenge questions have been designed to deepen students' understanding and stimulate interest in Mathematics. Answers to coursebook questions are in the back of the book.
Posted in Education