Featured Reviews
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enThe Princeton Companion to Applied Mathematics
http://www.maa.org/press/maa-reviews/the-princeton-companion-to-applied-mathematics
<div class="field field-name-field-cover-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img src="http://www.maa.org/sites/default/files/CompanionAppMarh.jpg" width="100" height="128" alt="" /></div></div></div><div class="field field-name-field-review-date field-type-datetime field-label-inline clearfix"><div class="field-label">Review Date: </div><div class="field-items"><div class="field-item even"><span class="date-display-single">09/15/2016</span></div></div></div><div class="field field-name-field-maa-review field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>The editor behind <i>The Princeton Companion to Applied Mathematics</i> (PCAM) is Nicholas J. Higham, a numerical analyst who has been recognized with multiple awards for his contributions to the accuracy and stability of numerical algorithms. He is assisted by more than 150 experts in applied mathematics. The book is an excellent reference that successfully compiles into a readable and engaging form the broad range of topics that an applied mathematician might encounter in their career.</p>
<p><b>Organization</b></p></div></div></div>Fashion, Faith and Fantasy in the New Physics of the Universe
http://www.maa.org/press/maa-reviews/fashion-faith-and-fantasy-in-the-new-physics-of-the-universe
<div class="field field-name-field-cover-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img src="http://www.maa.org/sites/default/files/FashionFaith.jpg" width="94" height="140" alt="" /></div></div></div><div class="field field-name-field-review-date field-type-datetime field-label-inline clearfix"><div class="field-label">Review Date: </div><div class="field-items"><div class="field-item even"><span class="date-display-single">09/15/2016</span></div></div></div><div class="field field-name-field-maa-review field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Roger Penrose has had a long career as one of the most original thinkers in the field of mathematical physics. His early work included ground-breaking results on general relativity and singularity theorems for solutions of Einstein’s equations. He later went on to invent “twistor theory”, which is based on a radically different approach to the geometry of space-time, one that describes Minkowski space and spinor fields in terms of the classical geometry of the Grassmanian of complex two-planes in \(\mathbf C^4\).</p></div></div></div>Causal Inference in Statistics: A Primer
http://www.maa.org/press/maa-reviews/causal-inference-in-statistics-a-primer
<div class="field field-name-field-cover-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img src="http://www.maa.org/sites/default/files/CasualInferStats.jpg" width="98" height="140" alt="" /></div></div></div><div class="field field-name-field-review-date field-type-datetime field-label-inline clearfix"><div class="field-label">Review Date: </div><div class="field-items"><div class="field-item even"><span class="date-display-single">09/14/2016</span></div></div></div><div class="field field-name-field-maa-review field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>If you have taught an introductory statistics course, you have probably uttered the phrase “correlation is not causation” many times. While most textbooks include that idea, fewer explain when it is relevant. Generally, a carefully designed experiment in which we control extraneous variables and randomly assign subjects to treatments allows us to reach causal conclusions, at least for the subjects at hand. The mantra is relevant primarily to situations where we take a survey of a randomly selected sample, or to observational studies where no randomization is applied.</p></div></div></div>Elementary Point-Set Topology: A Transition to Advanced Mathematics
http://www.maa.org/press/maa-reviews/elementary-point-set-topology-a-transition-to-advanced-mathematics
<div class="field field-name-field-cover-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img src="http://www.maa.org/sites/default/files/ElemPtSetTopolYandl.jpg" width="94" height="140" alt="" /></div></div></div><div class="field field-name-field-review-date field-type-datetime field-label-inline clearfix"><div class="field-label">Review Date: </div><div class="field-items"><div class="field-item even"><span class="date-display-single">09/14/2016</span></div></div></div><div class="field field-name-field-maa-review field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>This is a back-to-basics introductory text in point-set topology that can double as a transition to proofs course. The writing is very clear, not too concise or too wordy. The book was developed from many years of lectures at Seattle University and the authors recommend it for a one-semester course, or possibly two semesters, depending on the background and interests of the students.</p></div></div></div>Tipping Points: Modelling Social Problems and Health
http://www.maa.org/press/maa-reviews/tipping-points-modelling-social-problems-and-health
<div class="field field-name-field-cover-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img src="http://www.maa.org/sites/default/files/TippingPts.jpg" width="91" height="140" alt="" /></div></div></div><div class="field field-name-field-review-date field-type-datetime field-label-inline clearfix"><div class="field-label">Review Date: </div><div class="field-items"><div class="field-item even"><span class="date-display-single">09/16/2016</span></div></div></div><div class="field field-name-field-maa-review field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>This book is not really about tipping points: the book’s subtitle, “Modelling Social Problems in Health”, should have been the title. Each chapter is based on a different paper originally presented at a conference which was funded as part of the so-called “Tipping Points Project” — so that the authors of each paper apparently had to find some way to jump on the “tipping point” bandwagon. Although tipping points do appear in various ways in the different chapters, they are in general not the major focus.</p></div></div></div>Advanced Modern Algebra:Third Edition, Part 1
http://www.maa.org/press/maa-reviews/advanced-modern-algebrathird-edition-part-1
<div class="field field-name-field-cover-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img src="http://www.maa.org/sites/default/files/AdvModAlgOneRotman.jpg" width="97" height="140" alt="" /></div></div></div><div class="field field-name-field-review-date field-type-datetime field-label-inline clearfix"><div class="field-label">Review Date: </div><div class="field-items"><div class="field-item even"><span class="date-display-single">09/15/2016</span></div></div></div><div class="field field-name-field-maa-review field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>The third edition of this book is very different from the previous ones. As the reviews of the <a href="http://www.maa.org/press/maa-reviews/advanced-modern-algebra">first</a> and <a href="http://www.maa.org/press/maa-reviews/advanced-modern-algebra-0">second</a> editions indicate, Rotman is a very good writer. Those editions were masterful reference works presenting most of graduate-level algebra.</p></div></div></div>The Subjectivity of Scientists and the Bayesian Approach
http://www.maa.org/press/maa-reviews/the-subjectivity-of-scientists-and-the-bayesian-approach
<div class="field field-name-field-cover-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img src="http://www.maa.org/sites/default/files/SubjectScientists.jpg" width="95" height="140" alt="" /></div></div></div><div class="field field-name-field-review-date field-type-datetime field-label-inline clearfix"><div class="field-label">Review Date: </div><div class="field-items"><div class="field-item even"><span class="date-display-single">09/14/2016</span></div></div></div><div class="field field-name-field-maa-review field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>In his book <em>Clinical vs. Statistical Prediction: A Theoretical Analysis and a Review of the Evidence</em> (University of Minnesota, 1954), psychoanalyst Paul Meehl gave evidence that statistical models almost always yield better predictions and diagnoses than trained professionals. The authors here examine the cases of selected pioneers in science and how bias-driven subjectivity played a significant role in directing their advances. That role of subjectivity is the main thrust of this book.</p></div></div></div>UK Success Stories in Industrial Mathematics
http://www.maa.org/press/maa-reviews/uk-success-stories-in-industrial-mathematics
<div class="field field-name-field-cover-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img src="http://www.maa.org/sites/default/files/UKSuccessStories.jpg" width="95" height="140" alt="" /></div></div></div><div class="field field-name-field-review-date field-type-datetime field-label-inline clearfix"><div class="field-label">Review Date: </div><div class="field-items"><div class="field-item even"><span class="date-display-single">09/16/2016</span></div></div></div><div class="field field-name-field-maa-review field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Even veteran mathematicians will be impressed by the breadth of applications of mathematics included in this book. It is a conclusive item of evidence of how valuable a large set of applied mathematicians is to the modern industrial state. In fact they are essential to its continuance.</p>
<p>The papers are organized into eight parts:</p></div></div></div>Plain Plane Geometry
http://www.maa.org/press/maa-reviews/plain-plane-geometry
<div class="field field-name-field-cover-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img src="http://www.maa.org/sites/default/files/PlanePlain.jpg" width="95" height="140" alt="" /></div></div></div><div class="field field-name-field-review-date field-type-datetime field-label-inline clearfix"><div class="field-label">Review Date: </div><div class="field-items"><div class="field-item even"><span class="date-display-single">09/5/2016</span></div></div></div><div class="field field-name-field-maa-review field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Amol Sasane states on p. viii:</p>
<blockquote>
<p>The aim of this book is to cover the basics of the wonderful subject of Planar Geometry, at high school level, requiring no prerequisites beyond arithmetic, and hopefully to convey the sense of joy which I had when I was taught geometry.</p></blockquote></div></div></div>Algebra, Logic, and Combinatorics
http://www.maa.org/press/maa-reviews/algebra-logic-and-combinatorics
<div class="field field-name-field-cover-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img src="http://www.maa.org/sites/default/files/AlgLogicComb.jpg" width="95" height="140" alt="" /></div></div></div><div class="field field-name-field-review-date field-type-datetime field-label-inline clearfix"><div class="field-label">Review Date: </div><div class="field-items"><div class="field-item even"><span class="date-display-single">09/5/2016</span></div></div></div><div class="field field-name-field-maa-review field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>About 45 years ago, when I was an undergraduate in my senior year, a professor named George W. Booth, the best teacher I ever had from kindergarten through graduate school, pointed out to me a set of books titled <em>Lectures on Modern Mathematics</em>. Edited by Thomas Saaty, this is a three-volume set of expository articles on various branches of mathematics, written by experts in those areas: Coxeter on geometry, Halmos on Hilbert spaces, Kaplansky on Lie algebras, Nirenberg on partial differential equations, Brauer on group representation theory, and many others.</p></div></div></div>