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enFunctional Analysis
http://www.maa.org/publications/maa-reviews/functional-analysis-3
<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/FunctAnalMuscat.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">09/23/2014</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>Back around 45 years ago, as an undergraduate, I took a course in point-set topology based on the first part of Simmons’ book <a href="http://www.maa.org/publications/maa-reviews/introduction-to-topology-and-modern-analysis"><em>Introduction to Topology and Modern Analysis</em></a>. The second half of this book was a gentle introduction to the rudiments of functional analysis: Banach and Hilbert spaces, Banach algebras and a glimpse of spectral theory.</p></div></div></div>Differential Forms: Theory and Practice
http://www.maa.org/publications/maa-reviews/differential-forms-theory-and-practice
<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/DiffFormsWeintraub.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">09/24/2014</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>Differential forms have been moving into the undergraduate curriculum starting at least as early as Edwards’s <a href="http://www.maa.org/publications/maa-reviews/advanced-calculus-a-differential-forms-approach"><em>Advanced Calculus</em></a> in 1969 or so, just about the time I was taking advanced calculus myself. There are now at least a few advanced calculus textbooks that introduce differential forms in two and three dimensions as part of their treatment of vector calculus.</p></div></div></div>Classical Mechanics with Calculus of Variations and Optimal Control: An Intuitive Introduction
http://www.maa.org/publications/maa-reviews/classical-mechanics-with-calculus-of-variations-and-optimal-control-an-intuitive-introduction
<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/ClassMechLevi.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">09/24/2014</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>Mathematics and classical mechanics have had something of an off-and-on relationship over the last century of so. At one point mechanics was a standard part of the mathematics curriculum, but for some time it has been no more than an elective. For the most part, mathematicians have been happy to consign mechanics to physicists. Every now and again it will stage a mathematical comeback, most recently in a relatively abstract form involving symplectic and Poisson structures, moment maps and the machinery of Lie groups and Lie algebras.</p></div></div></div>Algebra
http://www.maa.org/publications/maa-reviews/algebra-0
<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/HungerfordAlgebra_0.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">09/24/2014</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>This is a text for a first-year graduate course in abstract algebra. It covers all the standard topics and has more than enough material for a year course. It is self-contained, but assumes the student has already had an undergraduate modern algebra course. The present volume is a 2003 corrected reprint of the 1974 Holt, Rinehart and Winston volume.</p></div></div></div>Mathematical Curiosities: A Treasure Trove of Unexpected Entertainments
http://www.maa.org/publications/maa-reviews/mathematical-curiosities-a-treasure-trove-of-unexpected-entertainments
<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/MathCuriosities.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">09/23/2014</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 announced goal of this interesting book is to foster a greater appreciation of mathematics among the “uninitiated general readership” through a wide variety of “mathematical curiosities.” The exposition is casual and inviting and the illustrations are of very high quality. That being said, I think the book’s main value is as a source of “curiosities” that teachers (at all levels) can use to spice up a lesson or challenge strong students.</p></div></div></div>Handbook of Probability
http://www.maa.org/publications/maa-reviews/handbook-of-probability
<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/HandbkProbab.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">09/23/2014</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>This reviewer first got interested in the book because of its title. Sure, there are many textbooks on probability, but how will this handbook be different? That question gets answered in the preface of the authors, where we learn that this is a textbook meant for an introductory course on probability!</p></div></div></div>Statistics: A User Friendly Guide
http://www.maa.org/publications/maa-reviews/statistics-a-user-friendly-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/StatsFriendGuide_0.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">09/18/2014</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>Author Gerald Swanson began his career as a chemist, moved onto nuclear analytical chemistry, and later became a behavioral scientist and taught statistics at Bastyr University in Seattle. From his varied background comes a supplemental statistics guide for an introductory statistics course. This overview starts with the very basics, such as levels of measurement, displays such as histogram, and measures of central tendency. These preliminaries assume little to no mathematical skill and extend into the first seven chapters.</p></div></div></div>Developing Essential Understanding of Proof and Proving for Teaching Mathematics in Grades 9–12
http://www.maa.org/publications/maa-reviews/developing-essential-understanding-of-proof-and-proving-for-teaching-mathematics-in-grades-9-12
<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/proofproving.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">09/14/2014</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>Do you enjoy teaching content courses for mathematics education majors? Has your chair just asked you to teach a course for education students on writing proofs? I suspect you might have the same dilemma as mine: finding a course text that is not intimidating and still enables students to reason with definitions, axioms and theorems. I think I have found one that works for my students and recommend that you consider adopting it as your course reading. The book is written by Amy Ellis, Kristen Bieda, and Eric Knuth.</p></div></div></div>Textbooks, 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>Calculus 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>