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enTilings and Patterns
http://www.maa.org/press/maa-reviews/tilings-and-patterns
<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/TilingsPatterns.jpg" width="100" height="125" 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">11/29/2016</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><em>Tilings and Patterns</em>, first published in 1987, has recently been re-published by Dover. Although it got outstanding reviews following its appearance, the original publisher chose to discontinue it in 1998. Dover has once again done the mathematical community a service in bringing back such a notable volume.</p></div></div></div>Geometric Measure Theory: A Beginner's Guide
http://www.maa.org/press/maa-reviews/geometric-measure-theory-a-beginners-guide
<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/GeomMeasureThyMorgan.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">11/29/2016</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 the fifth edition of an introductory text for graduate students. Morgan describes geometric measure theory as “differential geometry, generalized through measure theory to deal with maps and surfaces that are not necessarily smooth, and applied to the calculus of variations”. He calls the book an illustrated introduction, and his treatment is friendly enough (though still rigorous) that it does not intimidate. (Immediate intimidation was the effect on me some years ago by Federer’s book on the same subject.)</p></div></div></div>The Geometry of Celestial Mechanics
http://www.maa.org/press/maa-reviews/the-geometry-of-celestial-mechanics
<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/GeomCelestMechan.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">11/23/2016</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><em>The Geometry of Celestial Mechanics </em>offers a fresh look at one of the most celebrated topics of mathematics. In this text, the author attempts to introduce the topic in an elementary setting compared to Siegel and Moser’s <em>Lectures on Celestial Mechanics,</em> which he describes as taking a more mathematically mature approach. Nonetheless, this text contains more than enough content for a semester’s course, as detailed below.</p></div></div></div>Applications of Algebra and Geometry to the Work of Teaching
http://www.maa.org/press/maa-reviews/applications-of-algebra-and-geometry-to-the-work-of-teaching
<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/AppsAlgTeaching.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">11/29/2016</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><em>Applications of Algebra and Geometry to the Work of Teaching</em> is based on the 2008 Summer School Teacher Program (SSTP) at the Park City Mathematics Institute (PCMI) and the PROMYS for Teachers Program (PfT) at Boston University. As pointed out in the preface, PCMI is sponsored by the Institute for Advanced Study and is a three-week summer program for a wide range of people involved in mathematics: research mathematicians, graduate students, undergraduate faculty, undergraduate students, and precollege teachers. The SSTP has been a part of PCMI since 2001.</p></div></div></div>Mathematical Analysis and Its Inherent Nature
http://www.maa.org/press/maa-reviews/mathematical-analysis-and-its-inherent-nature
<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/MathAnalNature.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">11/21/2016</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 text in undergraduate single-variable analysis with metric spaces. The term “inherent nature” as used in the title refers to what the author calls the “essence” of the subject.</p></div></div></div>Theory of Functions of a Real Variable
http://www.maa.org/press/maa-reviews/theory-of-functions-of-a-real-variable
<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/ThyRealVariable.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">11/23/2016</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 very traditional text in measure and integration on the real line and on \(\mathbb{R}^n\) — traditional partly because it was deliberately written this way, and partly because it was originally written in 1941. It assumes the student has already had a good rigorous course in real analysis up to the Lebesgue integral. This would include the construction of the real numbers, uniform convergence, and the theory of derivatives and of the Riemann integral. The Russian work was aimed at third-year university students, and the English translation at graduate students.</p></div></div></div>The Mathematics that Power Our World: How is It Made?
http://www.maa.org/press/maa-reviews/the-mathematics-that-power-our-world-how-is-it-made
<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/MathPowerWorld.jpg" width="93" 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">11/29/2016</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 authors state in the preface that <em>The Mathematics That Power Our World: How Is It Made?</em> is an attempt at a mathematical version of the popular show <em>How it’s Made</em> intended to bridge the gap between two common (as defined by the authors) groups of mathematics students: the group that studies pure mathematics to further academic pursuits, and the group that views math simply as a tool or a means to an end. This reader is unconvinced as to how well the text does at bridging this supposed academic divide.</p></div></div></div>Philosophy of Science for Scientists
http://www.maa.org/press/maa-reviews/philosophy-of-science-for-scientists
<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/PhiloSciScientists.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">11/23/2016</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>Many years ago my wife and I hosted a married couple we didn’t know for dinner. He was a law school student but she was a local Ph.D. student studying the philosophy of science. Having recently obtained my doctorate in engineering I commented that there was no such thing as a philosophy to science. Rather, I naively said, science flowed from observations of facts, logical and mathematical arguments, or simply from one’s own thoughts of how the world behaved. Was I wrong!</p></div></div></div>Leibniz on the Parallel Postulate and the Foundations of Geometry
http://www.maa.org/press/maa-reviews/leibniz-on-the-parallel-postulate-and-the-foundations-of-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/LeibnizFoundGeom.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">11/9/2016</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 surveys Leibniz’s frustrated attempts to prove Euclid’s famous fifth postulate, while unable and even unwilling to explore the non-Euclidean geometries that lay at hand. The first of two parts is an overview of Leibniz’s idiosyncratic epistemology of geometry in the context of his time. It also provides a detailed commentary on his writings from correspondence, unpublished pieces, and marginalia on the theory of parallels.</p></div></div></div>Number Theory: An Introduction via the Density of Primes
http://www.maa.org/press/maa-reviews/number-theory-an-introduction-via-the-density-of-primes
<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/NumberThyFine.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">11/9/2016</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 an interesting take on an introductory number theory course, one that is heavily slanted toward the prime numbers. As such, it omits or mentions only briefly many topics that would normally appear in an introductory course, such as Diophantine equations, partitions, and continued fractions. It squeezes in a little bit on irrational numbers and on quadratic reciprocity, but these are given as isolated results that don’t go anywhere.</p></div></div></div>