ISBN: 978-0-470-41349-4
Paperback
62 pages
June 2008
Preface 0
Section 1: Introduction 1
Section 2: Mathematical Knots: What Are They? 5
A. The Basic Idea 5
B. Composition 9
C. Crossing Number 13
D. Reidemeister Moves 15
E. Links 19
F. Unknotting Number 27
G. How Many Knots Are There? 30
H. Denoting Pictures of Knots 34
Section 3: Knots, What Good Are They? 38
A. History 38
B. Knotted DNA 39
C. Knotted Molecules 41
D. Random Knotting 44
Section 4: The Future 45
Extra Fun 46
Appendix 1 48
Appendix 2 50
Further Reading 51
Some Answers to the Experiments 52
ISBN: 978-0-470-29466-6
Hardcover
360 pages
November 2008
* Focuses on the underlying mathematics, especially the concepts of finite-dimensional vector spaces and matrix methods, and provides a rigorous model for signals and images based on vector spaces and linear algebra methods
* Emphasizes discrete and digital methods and utilizes MATLAB(r) to illustrate these concepts
* Combines traditional methods such as discrete Fourier transforms and discrete cosine transforms with more recent techniques such as filter banks and wavelets
* Strikes an even balance in emphasis between the mathematics and the applications with the emphasis on linear algebra as a unifying theme
Contents
ISBN: 978-0-470-28073-7
Hardcover
416 pages
November 2008
There is a great need for a book on introductory probability applied to problems in computing. Probability with R serves as an introduction to probability and its application to computer disciplines and successfully convinces readers of the relevance of probability to computing. Most examples are related to computing and cover a wide range of computer science applications. This thoroughly classroom-tested, self-contained book encourages computing professionals and upper-undergraduates to perform the simulations in R in order to gain a firm understanding of the concepts discussed in the book.
Contents
ISBN-13: 978-0-19-536790-4
Estimated publication date: July 2009
256 pages, 50 halftones, 260 lines,
A must-have for puzzle fans - a fascinating account of Magic Squares and Sudoku, ranging from ancient history to helpful tips on creating and solving them
Offers a fascinating account of Sudoku and Magic Squares, ranging from ancient history to helpful tips on creating and solving these puzzles
Sudoku has become a vastly popular and even addictive game. But fans may not know that Sudoku is a recent offshoot of the venerable Magic Square, which dates back over 4,000 years to ancient China, where it was literally considered magical. Indeed, Magic Squares have fascinated centuries of mystics, astrologers, and some of the world's most brilliant thinkers, including Ben Franklin.
In Sudoku and Magic Squares , Seymour Block and Santiago Tavares offer a crystal clear and engaging tour tour of Magic Squares, tracing their footsteps through through ancient and medieval history and illuminating their uses in art and design, statistics and electronics. The book provides a delightful account of a mind-boggling variety of magical squares, ranging from simple 3 x 3 and squares, to magic cubes, magic circles, magic pyramids, and even "the Beastly Magical Square," whose magic sum is 666. Of course, the authors also cover Sudoku, describing how the game became a world-wide phenomenon and revealing various strategies for solving the puzzles. And along the way, the book offers readers many fascinating facts--for instance, Sudoku was invented in 1979 by an American architect living in Indianapolis and was originally called Number Place. Oddly enough, though the puzzle is known around the world by its Japanese name (which means "single numbers"), many Japanese still call it Number Place. We also learn that in a 4 x 4 magic square, there are 880 different solutions that will yield the magic sum of 34--a surprisingly large number until you remember that there are over 2.6 trillion possible combinations.
Filled with lots of original puzzles for gamers to solve, Sudoku and Magic Squares is an entertaining book that will delight anyone who loves a challenge, including all fans of Sudoku.
ISBN-13: 978-0-19-921843-1
Estimated publication date: January 2009
288 pages, Numerous B&W line diagrams, 196x129 mm
Networks are everywhere - wherever people and things relate and connect to one another: from social networks and the internet, to ancient mazes, secret codes, and even the genetic structure of life itself.
Peter Higgins explains how mathematics can give us rich and surprising insights into the workings of networks of all types.
Circular Sudoku and the 'Chinese Postman Problem' (can he deliver all his letters without traversing the same street twice?) are just some of the fascinating and classic mathematical puzzles that are explored here.
Uses a minimum of technical language - the mathematics emerges naturally and accessibly through the examples used.
What do road and railway systems, electrical circuits, mingling at parties, mazes, family trees, and the internet all have in common?
All are networks - either people or places or things that relate and connect to one another. Only relatively recently have mathematicians begun to explore such networks and connections, and their importance has taken everyone by surprise.
The mathematics of networks form the basis of many fascinating puzzles and problems, from tic-tac-toe and circular sudoku to the 'Chinese Postman Problem' (can he deliver all his letters without traversing the same street twice?). Peter Higgins shows how such puzzles as well as many real-world phenomena are underpinned by the same deep mathematical structure. Understanding mathematical networks can give us remarkable new insights into them all.
Readership: Anyone interested in mathematics, or in the mathematical basis of real-world networks (e.g. those interested in the internet, economists, social scientists, etc). General readers of popular mathematics books and mathematical puzzles.
Preface
1. Nets, trees and lies
2. Trees and games of logic
3. The nature of networks
4. Coloring and Planarity
5. How to traverse a network
6. One-way systems
7. Spanning networks
8. Going with the flow
9. Novel applications of nets
10. For Connoisseurs
ISBN-13: 978-0-19-923289-5(hard cover)
ISBN-13: 978-0-19-923290-1(soft cover)
Estimated publication date: February 2009
352 pages, 66 line illus., 234x156 mm
Comprehensive treatment of topics not generally covered in epidemiology texts
Extensive examples from the literature
Mathematical presentation at a level suitable for graduate students in epidemiology and biostatistics
Topical and timely work in a growing field
Author is a highly regarded researcher and expositor
Environmental epidemiology is the study of the environmental causes of disease in populations and how these risks vary in relation to intensity and duration of exposure and other factors like genetic susceptibility. As such, it is the basic science upon which governmental safety standards and compensation policies for environmental and occupational exposure are based. Profusely illustrated with examples from the epidemiologic literature on ionizing radiation and air pollution, this text provides a systematic treatment of the statistical challenges that arise in environmental health studies and the use epidemiologic data in formulating public policy, at a level suitable for graduate students and epidemiologic researchers.
After a general overview of study design and statistical methods for epidemiology generally, the book goes on to address the problems that are unique to environmental health studies, special-purpose designs like two-phase case-control studies and countermatching, statistical methods for modeling exposure-time-response relationships, longitudinal and time-series studies, spatial and ecologic methods, exposure measurement error, interactions, and mechanistic models. It also discusses studies aimed at evaluating the public health benefits of interventions to improve the environment, the use of epidemiologic data to establish environmental safety standards and compensation policy, and concludes with emerging problems in reproductive epidemiology, natural and man-made disasters like global warming, and the global burden of environmentally caused disease. No other book provides such a broad perspective on the methodological challenges in this field at a level accessible to both epidemiologists and statisticians.