Book Reviews

• A Guide to Monte-Carlo Simulations in Statistical Physics (Third Edition)

  This is a graduate level text that deals primarily with Monte-Carlo simulation of complex physical systems encountered in condensed-matter physics and statistical mechanics. It also provides a very brief overview of some alternative computer simulation methods of use in statistical physics, such as molecular dynamics, quasi-classical spin dynamics, dissipative particle dynamics, lattice gas cellular automata and others. The emphasis however, is firmly on various Monte-Carlo simulation approaches to lattice based systems, especially Ising spin type models, and off-lattice systems, exemplified by binary fluids and polymer mixtures.

• Cows in the Maze – And Other Mathematical Explorations

  The book is an eclectic mix of mathematics selected from Ian Stewart’s columns in Scientific American. It is the third such collection he has written. The book offers a wonderful insight into the range of diverse topics that mathematics as a subject has to offer.

• Essential Math Skills for Engineers

  Mathematics is at the heart of engineering design. So states the author, Clayton R. Paul, a professor of electrical and computer engineering at Mercer University, in Macon, Georgia. I expect readers of this magazine are likely to agree, though I’ve known a few engineers who wouldn’t!

• How to Guard an Art Gallery and Other Discrete Mathematical Adventures

  ‘How to Guard an Art Gallery and Other Discrete Mathematical Adventures’ models solutions to a variety of problems - what is the largest number of pizza slices that we can make with n straight lines, how does a computer configure the best arrangement of pixels to represent a straight line, what is the minimum number of guards needed to guard an art gallery?

• Loving + Hating Mathematics: Challenging the Myths of Mathematical Life

  Mathematicians are different from other people, lacking emotional complexity. Mathematics is a solitary pursuit. Mathematics is a young man’s game. Mathematics is an effective filter for higher education.

• Mathematics of Social Choice: Voting, Compensation, and Division

  This book is an introduction to, as the title suggests, the mathematics of voting, compensation and division. Each section is self-contained, consisting of short and snappy chapters without being over-concise, and accompanied by mercifully doable exercises which not only tie in well with the text, but are mostly provided with that rare luxury of worked solutions in the back.

• Networks, Crowds, and Markets - Reasoning about a Highly Connected World

  The growth of connectedness in modern society in recent years seems to have escalated at a spectacular rate. The rapid technological growth of the internet and global communications, as well as the spread of epidemics and financial crises, affects the wholeworld with surprising speed and intensity.

• Numbers Rule: The Vexing Mathematics of Democracy, from Plato to the Present

  There are inherent problems and paradoxes when the choices of a number of individuals need to be combined to make one collective decision. With the recent referendum on voting reform such issues are topical today, but they actually go back to antiquity. Szpiro writes from a historical and mathematical perspective. He also looks at the principal characters and gives a short biography of each, putting their ideas into a social context.

• Quantum Field Theory

  This book provides a complete introduction to quantum field theory and the elementary particles. It is set at the level of graduate students who have covered special relativity and quantum mechanics. It covers, amongst other areas, the unification of forces, super symmetry, the renormalization group, quark and gluon scattering, and non-peturbative physics (magnetic monopoles and instantons).

• Routes of Learning: Highways, Pathways and Byways in the History of Mathematics

  In this volume Ivor Grattan-Guinness collects together a range of papers spanning forty years of his distinguished career as a historian of mathematics. The central theme linking chapters in the first two sections (the ‘Highways’ and ‘Pathways’ of the subtitle) is the place of history in mathematical education. The author criticises accounts which conflate ‘history’ (the development of a particular piece of work) with ‘heritage’ (the impact of that work on future mathematics).

• Soliton Equations and Their Algebro-Geometric Solutions (Volume II: (1 + 1) - Dimensional Discrete Models)

  One definition of the soliton is “a pulselike nonlinear wave (solitary wave) which emerges from a collision with a similar pulse having unchanged shape and speed”. More informally it is a “self-reinforcing solitary wave that maintains its shape while it travels at constant speed”. The name is derived from ‘solitary wave solutions’. The phenomenon was first described by John Scott Russell who observed such a wave on a Scottish canal in 1834.

• Structure and Randomness: Pages from Year One of a Mathematical Blog

  Terence Tao is a distinguished mathematician, perhaps best known for his work in combinatorics and number theory, linked especially to the theory of arithmetic progressions of prime numbers. In 2007, he turned his homepage into a weblog, and this book collects some of his online writings which first appeared there. In the book’s collection of some of these blogs, it sketches out unusual proofs for classical theorems, the texts of three of his invited lectures, a selection of discussions of open problems, and a few number curiosities.

• Symmetry in Chaos: A Search for Pattern in Mathematics, Art and Nature (Second Edition)

  Symmetry and chaos seem unlikely bedfellows; yet Field, from the University of Houston, and Golubitsky, from Ohio State University, have produced a book full of beautiful pictures by combining the two. To quote from the Introduction: “Our pictures are created by merging symmetry and chaos. At first sight this seems paradoxical: a merging of order and disorder or yin and yang”.

• The Num8er My5teries - A Mathematical Odyssey through Everyday Life

  Marcus du Sautoy’s latest book The Num8er My5teries is written for the general reader. The book bursts with creativity, analysis and explanation in a clear non-specialist style. Complex issues in the subject become accessible as he exposes readers to the big ideas in mathematics.

• What's Luck Got to Do with It? The History, Mathematics, and Psychology of the Gambler's Illusion

  Joseph Mazur’s book takes us on a fascinating journey looking at the misconceptions involved in gambling. The reader learns the history of gambling, the way mathematicians analyse luck and the psychology that affects gamblers.