Featured Reviews
http://www.maa.org/maa-reviews/rss.xml
enTextbooks, Testing, Training: How We Discourage Thinking
http://www.maa.org/publications/maa-reviews/textbooks-testing-training-how-we-discourage-thinking
<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/9781614448037_MAAR.png" 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">09/14/2014</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"><blockquote>
<p>This short book recounts many specific true stories from my fifty-nine years of teaching that I believe cast some light on what is wrong with American education and perhaps some clues as to what might improve it. (p. 1)</p>
</blockquote>
<p>This is an incisive yet readable critique of the American education system. Willoughby writes from the perspective of six decades of experience. He knows that the best way to persuade someone is to tell them a story. The author illustrates his points with anecdotes from his own experience and those of his colleagues.</p></div></div></div>Sun, 14 Sep 2014 21:13:44 +0000fqgouvea476925 at http://www.maa.orghttp://www.maa.org/publications/maa-reviews/textbooks-testing-training-how-we-discourage-thinking#commentsCalculus for the Ambitious
http://www.maa.org/publications/maa-reviews/calculus-for-the-ambitious
<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/CalcAmbitious.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">09/11/2014</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>How does T. W. Körner do it?</p></div></div></div>Thu, 31 Jul 2014 18:07:57 +0000fqgouvea453232 at http://www.maa.orghttp://www.maa.org/publications/maa-reviews/calculus-for-the-ambitious#commentsA Historian Looks Back: The Calculus as Algebra and Selected Writings
http://www.maa.org/publications/maa-reviews/a-historian-looks-back-the-calculus-as-algebra-and-selected-writings
<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/HistorianLooksBack14229.jpg" width="90" height="130" 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">09/11/2014</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>Looking back is, of course, what historians do. The title of this book is a play on that, because in addition to looking back on history it also gives us a “look back” at the author’s own history as one of our best historians of mathematics. It contains an updated version of her first book, <em>The Calculus as Algebra</em>, plus several articles on the history of calculus, mostly focused on the crucial transition to “rigor” in the late eighteenth and early nineteenth centuries.</p></div></div></div>Mon, 11 Oct 2010 14:44:14 +0000newton_admin111222 at http://www.maa.orghttp://www.maa.org/publications/maa-reviews/a-historian-looks-back-the-calculus-as-algebra-and-selected-writings#commentsAdvanced Calculus: A Differential Forms Approach
http://www.maa.org/publications/maa-reviews/advanced-calculus-a-differential-forms-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/EdwardsDiffForms.jpg" width="99" 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">09/9/2014</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>As I suppose is the case for many of us, I first encountered H. M. Edwards as the author of the wonderful book <a href="http://www.maa.org/publications/maa-reviews/riemanns-zeta-function"><em>Riemann’s Zeta Function</em></a>, a marvelous work of historical scholarship and an exposition of the inner life of the zeta function, with <em>the</em> hypothesis on center stage. Edwards wrote the book in 1974, pretty early in his career as a prolific author of books with a heavy historical dimension to them.</p></div></div></div>Fri, 06 Dec 2013 19:54:48 +0000fqgouvea252080 at http://www.maa.orghttp://www.maa.org/publications/maa-reviews/advanced-calculus-a-differential-forms-approach#commentsPearls from a Lost City: The Lvov School of Mathematics
http://www.maa.org/publications/maa-reviews/pearls-from-a-lost-city-the-lvov-school-of-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/PearlsLostCity.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">09/14/2014</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 focus of this book is on the mathematical activity and the mathematicians in the city of Lvov during the period 1920 to 1940, especially at Lvov University. The author refers to this period in Lvov as “The Golden Age.” Useful historical background is given concerning Lvov University and mathematical developments in Lvov and in Poland in general. Three chapters are devoted to the period from 1940 through early 1946, when Lvov was occupied and ruled sequentially by the Soviet Union, Nazi Germany, and then again by the Soviets.</p></div></div></div>Thu, 21 Aug 2014 10:27:17 +0000fqgouvea464813 at http://www.maa.orghttp://www.maa.org/publications/maa-reviews/pearls-from-a-lost-city-the-lvov-school-of-mathematics#commentsLimits, Limits Everywhere: The Tools of Mathematical Analysis
http://www.maa.org/publications/maa-reviews/limits-limits-everywhere-the-tools-of-mathematical-analysis
<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/LimitsEverywhere.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">09/11/2014</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>There is no doubt that the concept of “limit” is fundamental in calculus and analysis. Many other essential topics, such as derivative and integral, are defined as limits of some kind, as are topics in analysis like sequences and series. The notion of limit is also hidden in heart of some primordial matters such as the notion of a “number”. These are some facts that the author of the book under review is focused on.</p></div></div></div>Tue, 11 Feb 2014 18:19:29 +0000fqgouvea328360 at http://www.maa.orghttp://www.maa.org/publications/maa-reviews/limits-limits-everywhere-the-tools-of-mathematical-analysis#commentsPath Integrals and Hamiltonians: Principles and Methods
http://www.maa.org/publications/maa-reviews/path-integrals-and-hamiltonians-principles-and-methods
<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/PathIntegralsBaaquie.jpg" width="100" 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">09/11/2014</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>My own path to, or through, quantum mechanics has been heavily influenced by the fact that I am a pure mathematician and don’t speak physics. I find physics books written for physicists by physicists very difficult to read. This was brought home to me in spades when I started all this ecumenical work in the cause of what are ultimately analytic number theoretic concerns. (See below for a hint.) Happily, I hit upon the book by Prugovečki, <em>Quantum Mechanics in Hilbert Space</em>, which is in my opinion, unsurpassed.</p></div></div></div>Wed, 09 Jul 2014 14:54:11 +0000fqgouvea438853 at http://www.maa.orghttp://www.maa.org/publications/maa-reviews/path-integrals-and-hamiltonians-principles-and-methods#commentsArithmetic Geometry of Toric Varieties: Metrics, Measures and Heights
http://www.maa.org/publications/maa-reviews/arithmetic-geometry-of-toric-varieties-metrics-measures-and-heights
<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/ArithGeomToric.jpg" width="100" height="135" 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">09/9/2014</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>Toric varieties are a family of algebraic varieties that are classical, naturally defined, and a natural testing ground for conjectures on algebraic geometry. Toric varieties include affine and projective spaces. Originally defined in Demazure’s paper “Sous-grupes algébriques de rang maximum du group de Cremona” (<em>Ann. Sci. École Norm. Sup,</em> <strong>3</strong> (1970), 507–588) very soon they were at the center of research by virtue of their ubiquity and the variety of techniques that could be used to study them.</p></div></div></div>Fri, 13 Jun 2014 18:45:40 +0000fqgouvea427318 at http://www.maa.orghttp://www.maa.org/publications/maa-reviews/arithmetic-geometry-of-toric-varieties-metrics-measures-and-heights#commentsThe Emperor's New Mathematics: Western Learning and Imperial Authority During the Kangxi Reign (1662-1722)
http://www.maa.org/publications/maa-reviews/the-emperors-new-mathematics-western-learning-and-imperial-authority-during-the-kangxi-reign-1662
<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/EmperorMarh.jpg" width="100" height="130" 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">09/7/2014</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 the anecdotal account, King Ptolemy (323–283 BCE) would have liked to skip the hard work of learning mathematics and was told “there is no royal road to geometry.” By contrast, geometry and other mathematical subjects, including astronomy, were studied diligently by Emperor Kangxi (b. 1654, reigned 1662–1722) in China, who used the technical knowledge as part of statecraft in his long reign.</p></div></div></div>Wed, 14 Aug 2013 17:18:08 +0000fqgouvea156531 at http://www.maa.orghttp://www.maa.org/publications/maa-reviews/the-emperors-new-mathematics-western-learning-and-imperial-authority-during-the-kangxi-reign-1662#commentsMathematics in 20th-Century Literature and Art
http://www.maa.org/publications/maa-reviews/mathematics-in-20th-century-literature-and-art
<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/MathLitArtTubbs.jpg" width="92" 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">09/6/2014</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>Various artists, such as Piet Mondrian and Theo van Doesburg, produced many paintings based upon plane geometric shapes. Naum Gabo, who trained as an engineer, is known for his 3-d constructions of ruled surfaces. Another sculptor, Man Ray, constructed a visual equivalent of Enneper’s surface of constant negative curvature (derived from the pseudo-sphere).</p></div></div></div>Wed, 09 Jul 2014 14:41:05 +0000fqgouvea438846 at http://www.maa.orghttp://www.maa.org/publications/maa-reviews/mathematics-in-20th-century-literature-and-art#comments