Promotions - Choice's Outstanding Academic Titles 2014 -

The Institute of Mathematics and Its Applications (United Kingdom) celebrated its 50th anniversary in 2014.  Visions of Mathematicsis its celebratory publication.  But it is no flimsy pamphlet.  This book is a collection of 50 four-page essays by mathematicians worldwide.  The chapters are diverse: e.g., infinite series ("Proof by Pizza"); drag on soccer balls ("Dimples, Grooves, and Knuckleballs"); epidemic modeling ("Pigs Didnt Fly but Swine Flu"); forensic science ("How Does Mathematics Help at a Murder Scene?"); the Kalman filter ("Finding Apollo"); Kaprekars operation ("The Mysterious Number 6174"); and meteorological modeling ("Leapfrogging into the Future").  The captivating essays are successfully written for a general audience, and the topics selected show the pervasiveness of mathematics in our lives.  Other valuable features of the book include 50 photographs of our mathematics-filled world; tidbits on Pythagorass theorem, from serious to whimsical; and a clever and humble foreword not to be missed by would-be mathematics scholars.  This is no boring recreational mathematics book.  It is exactly as intended by the Institute: a gleaming celebration of mathematics, c.2014and it is a smashing success.  Bookstores must stock it; libraries must keep it on their shelves; and people must buy it for their own personal collections.Summing Up: Essential. All mathematics collections.

This unique work represents the most thorough discussion to date of the history of permutation statistical methods from 1920 to the present.  Previous research on permutation statistical methods was often done by researchers trained in other fields (economics, chemistry, etc.); however, with the introduction of high-speed computing, researchers in highly quantitative areas, including computer science and medicine, have made significant contemporary contributions to the field.  Though several earlier books may have discussed this topic, e.g., Andrew DalesA History of Inverse Probability(CH, Apr'92, 29-4569), no one book has focused solely on permutation statistical methods.  Berry and Mielke (both, Colorado State) and Johnston (US government) consulted numerous biographies, dissertations, manuscripts, theses, etc. to compile this extensive, detailed account.  The numerous permutation statistical tests discussed are organized chronologically and grouped in 20-year increments.  Many well-known and not-so-well-known statistical tests are addressed, e.g., correlation and regression, analysis of variance, Olmstead-Tukey and the quadrant-sum test, Kamats rank test for dispersion, Ghent and the Fisher-Yates exact test, and more.  This clearly written book is a succinct compilation of those tests associated with the history of permutation statistical methods and their impact on the field of statistics.  Its nonmathematical coverage makes it accessible to most readers.Summing Up: Highly recommended. Upper-division undergraduates through professionals/practitioners.

Succeeding in his earnest quest to explore the intersections of mathematics and poetry, Aharoni (Technion/Israel Institute of Technology, Haifa) concludes that the answer lies in the aesthetics of beauty.  He examines many common elements of poetry and mathematics, such as the diversion of attention, the search for hidden patterns and deep order, the uncovering of hidden truths, communication via pictures, compression of information, interplay between the concrete and the abstract, and the sense of magic both mathematics and poetry inspire.  Amid discussions of illustrative poems as a context, the author does not shy away from examining significant mathematics, ranging from number theory to topology to geometry to set theory to discrete mathematics to the infinite to Gödels theorem to the role of mathematical proofs.  Every page offers a new delight as readers are gently convinced by the authors arguments.  To help readers from both worlds, appendixes provide brief summaries of various mathematical fields, different sets of numbers, and poetic devices.  Though an index would have improved the book, one needs to read the full book, front to back, to appreciate the argument that mathematical and poetic techniques evoke the same sense of beauty.  A great book and a fascinating journey.Summing Up: Essential. All readers.

This extraordinary, extravagantApologia pro Vita Suathe title more deliberately echoes G. H. Hardys renowned 1940 memoirA Mathematicians Apologyheads off in many directions and is all the more admirable for it.  The book is part memoir, part account of the arcane research that brought number theorist Harris (Univ. Paris Diderot; Columbia Univ.) a measure of fame, and part sociological/economic study of academic mathematics.  Together with interspersed chapters amusingly titled How to Explain Number Theory at a Dinner Party, the work offers erudition, panache, and an intriguing authorial voice.  It even contains a deconstruction of the Thomas Pynchon novelAgainst the Day (2006) combined with reproaches to the New Yorker and theNew York Review of Books for assigning reviewers who boasted their mathematical ignorance!  Another digression, labeled mind-body problem, is an analysisnot always easy to followof the celebrated Mishima-influenced erotic film short Rites of Love and Math, by mathematician Edward Frenkel (Univ. of California, Berkeley).  Harris is polyglot, deeply learned.  Threading through his remarkable book, unifying it, is Hardys lament regarding whether a pure mathematician can make a claim that the vocation has a philosophically useful purpose.  Harriss reply is multivalent, persuasive, and profound.  A book to be read and then read again.Summing Up: Highly recommended. Upper-division undergraduates and above.

This book is a fun and interesting tour of graph theory, leaving each visitor with a feeling of accomplishment and a satisfying understanding of this unusual mathematical world.  As it should, the tour focuses on classical problems, which become the basis and motivation for introducing the graph theoretic methods needed to explore those problems.  As part of the journey, Benjamin (Harvey Mudd College), Chartrand (emer., Western Michigan Univ.), and Zhang (Western Michigan) introduce readers to the ideas of graphs, distance, and trees surrounded by all the active procedures and ideas involving graphsclassifying, traversing, encircling, factoring, decomposing, orienting, drawing, coloring, and synchronizing.  Important theorems are stated and proven at times, all amid some of the relevant history and mathematicians involved.  But the best part is the large collection of ordered problems that not only are accessible to any motivated reader but also reveal the power of graph theory.  In addition to suggested further readings for each chapters content, the book has a useful index involving both graph theoretic ideas and associated mathematicians.  This is an entertaining book for those who enjoy solving problems, plus readers will learn about some powerful mathematical ideas along the way!Summing Up: Highly recommended. All levels/libraries.

Math is big.  Really big.  People just will not believe how vastly, hugely, mind-bogglingly big it is.  This slight revision of Douglas Adamss words holds true, so although this reviewer had already read a great many books on mathematics aimed at general audiences, this one by Bellos (curator-in-residence, Science Museum, London) provided enough new material to keep him entertained.  Even sections on extremely familiar topics, such as conic sections, Benfords law, and Zipfs laws, contained nuggets he had not previously encountered.  History, presented with the mathematics, provides context and helps enliven the book.  Bellos obtained his material both through print sources and by interviewing mathematicians.  This is of great benefit to early undergraduate readers, who are typically familiar almost exclusively with work from the 17th century and earlier and do not realize that mathematics is very much alive today.  Some pages are devoted to teaching trigonometry and basic ideas in calculus, but most of the book deals with interesting topics that are not seen in a typical undergraduate mathematics program.  The book is appropriate for both the math curious and enthusiasts who wish to supplement their formal education.Summing Up: Highly recommended. All levels/libraries.

Astatistic means one number computed from a complex of raw experimental data.  When experiments produce a sequence ofn distinct readings, statisticians may first rank those values from 1 ton.  Any value computed from the derived sequence of ranks then constitutes apermutation statistic.  The subject of random permutations concerns permutation statistic behavior under the null hypothesis of independent, uncorrelated readings.  Romik (Univ. of California, Davis) studies one basic permutation statistic with a famously subtle theory, namely the maximum length among all increasing subsequences; a subsequence of not necessarily consecutive readings increases whenever each reading exceeds the previous one.  That the asymptotic formula for the mean value involves a constant associated with the Painleve equation of type II shows intrinsic depth.  Undergraduates will find here an exciting testament to the unity of mathematics, where verification of answers to elementary questions leads into, as the author notes, combinatorics, probability, analysis, linear algebra, operator theory, differential equations, special functions, and representation theory.  Random matrix theory, a hot topic for physicists as well, also has an important role.  Timely, authoritative, and unique in its coverage, this book will synergize well with Bruce Sagan'sThe Symmetric Group (CH, Jun'92, 29-5737) and David Bressoud'sProofs and Confirmations(CH, Jun'00, 37-5714).Summing Up: Highly recommended. General readers, upper-division undergraduates, graduate students, researchers/faculty, and professionals/practitioners.

A mathematics teacher in Australia and more recently in the UK, Parker also spends time popularizing his subject as a comedian.  However, Things to Make and Do in the Fourth Dimension is no comedy act.  It is a serious exposition on pure mathematics: primes, knots, graphs, algorithms, shapes, higher dimensions, data, and orders of infinity.  To illustrate, he devotes one chapter to number classifications.  Not only does the author take readers through the progression from counting numbers to complex numbers, with stops in between, he goes beyond to octonions.  He then develops another less well-known categorization  of numbers: whole numbers, constructibles, algebraics, and computables.  These progressions include historic motivations, giving readers an appreciation for the evolution of our number systems.  The book is not just recreational mathematics, though the topic is treated in one chapter as part of mathematics.  The book educates and enriches.  Historic context is generous.  The style is conversational.  Parker misses no opportunity to include witticisms, clever analogies, blunt truths, and humor to accomplish his life goal: to bring mathematics to people and people to mathematics.  Type style and graphics are excellent.  This book has much to offer readers at all levels.Summing Up: Highly recommended. All levels/libraries.

Quaternions have proven useful in a number of academic disciplines, including physics (quantum mechanics), engineering (control systems), and computer science (graphics).  As a result, the research papers utilizing quaternions appear in a wide spectrum of journals.  Rodman (College of William & Mary) fills a void in the monographic literature with this work, part of the "Princeton Series in Applied Mathematics."  Although most of the included material has never appeared in a book before, it is accessible to those with a background in linear algebra and some knowledge of complex analysis.  The first part of the book covers the fundamentals of quaternions in matrix analysis, including canonical forms and invariant subspaces.  The second part is essentially a research monograph on quaternions with an emphasis on matrix pencils with symmetries.  There are plenty of exercises and open questions in the text that will encourage research even at the undergraduate level.  As the first book in the field, it also serves as an excellent resource for anyone with an interest in doing linear algebra and matrix analysis over the skew field of quaternions.Summing Up: Highly recommended. Upper-division undergraduates, graduate students, and researchers/faculty.