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enThe Circle: A Mathematical Exploration Beyond the Line
http://www.maa.org/press/maa-reviews/the-circle-a-mathematical-exploration-beyond-the-line
<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/CirclePosamentier.jpg" width="96" 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">08/22/2016</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>It’s a reasonably safe bet that anybody with an interest in mathematics education, or mathematics textbooks (particularly those that involve geometry) will have heard of Alfred Posamentier. For many years, he has been a well-known figure in the education community, and has also been a very prolific author and co-author, with (according to the book’s bibliographic blurb) over sixty books published in the areas of mathematics and mathematics education.</p></div></div></div>Fri, 27 May 2016 18:28:41 +0000fqgouvea751828 at http://www.maa.orghttp://www.maa.org/press/maa-reviews/the-circle-a-mathematical-exploration-beyond-the-line#commentsNumbers: Histories, Mysteries, Theories
http://www.maa.org/press/maa-reviews/numbers-histories-mysteries-theories
<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/NumbersBeutelspacher.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">08/22/2016</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 short book is an attempt to answer an obvious, yet very deep and important question. “What exactly is a number?” Intuitively, this is a question that humans and some animals can give a partial answer to. A number is a mechanism used for counting. However, that answer is extremely limited in effectiveness. For as societies became more advanced with dramatic increases in the size and complexity of commerce, other uses and types of numbers were developed. For example, negative numbers are an essential feature of accounting. </p></div></div></div>Sat, 13 Aug 2016 15:38:02 +0000fqgouvea760406 at http://www.maa.orghttp://www.maa.org/press/maa-reviews/numbers-histories-mysteries-theories#commentsScientific Models: Red Atoms, White Lies and Black Boxes in a Yellow Book
http://www.maa.org/press/maa-reviews/scientific-models-red-atoms-white-lies-and-black-boxes-in-a-yellow-book
<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/Scimodels.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">08/22/2016</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 covers the efficacy of models in a reasonable way. There is no better description of models than the famous statement of George E. P. Box, “All models are wrong, some are useful.” Box also stated expansions and modifications of this principle, but the basic idea is that no model precisely describes the relevant phenomena. Yet models are critical to our understanding because within generally known parameters they can be used to mimic natural processes.</p></div></div></div>Sat, 13 Aug 2016 15:44:18 +0000fqgouvea760407 at http://www.maa.orghttp://www.maa.org/press/maa-reviews/scientific-models-red-atoms-white-lies-and-black-boxes-in-a-yellow-book#commentsStatistics for Mathematicians: A Rigorous First Course
http://www.maa.org/press/maa-reviews/statistics-for-mathematicians-a-rigorous-first-course
<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/StatsMathPanaretos.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">08/24/2016</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>Statistical reasoning and analysis is applicable wherever there is data, and today this seems to be everywhere. Despite the importance of the field, it seems that statistics often does not have the same initial appeal to many students attracted to mathematics as do, say, number theory, combinatorics or dynamical systems. This is interesting, since at the level of current research, probability and statistics do seem to have deep relations with each of the fields of number theory, combinatorics and dynamical systems.</p></div></div></div>Fri, 17 Jun 2016 18:36:58 +0000fqgouvea754344 at http://www.maa.orghttp://www.maa.org/press/maa-reviews/statistics-for-mathematicians-a-rigorous-first-course#commentsStochastic Calculus and Applications
http://www.maa.org/press/maa-reviews/stochastic-calculus-and-applications
<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/StochCalcAppsCohen.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">08/19/2016</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>Stochastic calculus is such a broad subject that it is hard to describe. One of the basic objects of study is the stochastic differential equation (SDE), which in its simplest form can be written as \[dX_t=b(X_t)\,dt+\sigma(X_t)\,dB_t\] where \(B_t\) is a one-dimensional Brownian motion. We think of this as the differential equation \(dX_t/dt =b(X_t)\) perturbed by noise (which may or may not be small). These processes arise as large population limits in population genetics and epidemiology, but their most famous use is in mathematical finance to model stock prices.</p></div></div></div>Tue, 08 Dec 2015 16:03:31 +0000fqgouvea698136 at http://www.maa.orghttp://www.maa.org/press/maa-reviews/stochastic-calculus-and-applications#commentsCalculus of Variations: With Applications to Physics and Engineering
http://www.maa.org/press/maa-reviews/calculus-of-variations-with-applications-to-physics-and-engineering
<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/CalcVariationsWeinstock.jpg" width="89" 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">08/23/2016</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 an introduction to the calculus of variations that concentrates very heavily on its applications, and only outlines the general theory. It makes heavy use of eigenfunctions and does have a good discussion of those. The present volume is a Dover 1974 corrected reprint of the 1952 McGraw-Hill edition.</p></div></div></div>Tue, 29 Jan 2013 19:35:49 +0000newton_admin106380 at http://www.maa.orghttp://www.maa.org/press/maa-reviews/calculus-of-variations-with-applications-to-physics-and-engineering#commentsSymplectic Lie Groups
http://www.maa.org/press/maa-reviews/symplectic-lie-groups
<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/SymplecticLieGroups.jpg" width="100" height="134" 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">08/22/2016</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>A <em>symplectic Lie group</em> is a symplectic manifold that is also a Lie group whose symplectic form is left-invariant. Symplectic Lie groups appear naturally when one considers symplectic manifolds \(M\) that admit a transitive Lie group \(G\) of symplectic automorphisms, and in this case the manifold is a homogeneous symplectic manifold \(M=G/H\). Thus, a symplectic Lie group \(G\) is a symplectic homogeneous manifold \(G/H\) with trivial stabilizer \(H\).</p></div></div></div>Tue, 07 Jun 2016 18:03:32 +0000fqgouvea753363 at http://www.maa.orghttp://www.maa.org/press/maa-reviews/symplectic-lie-groups#commentsPoisson Point Processes and Their Application to Markov Processes
http://www.maa.org/press/maa-reviews/poisson-point-processes-and-their-application-to-markov-processes
<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/PoissonPoint.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">08/22/2016</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>Itô received his Ph.D. in 1945. In the next five years he wrote several papers laying the groundwork for stochastic integration and the associated stochastic calculus, including the formula that bears his name. Throughout his career, Itô made a number of important contributions to stochastic analysis in finite and infinite dimensional spaces. The work under review is not one of them.</p></div></div></div>Fri, 12 Feb 2016 18:03:28 +0000fqgouvea734063 at http://www.maa.orghttp://www.maa.org/press/maa-reviews/poisson-point-processes-and-their-application-to-markov-processes#commentsNiels Bohr, 1913 - 2013
http://www.maa.org/press/maa-reviews/niels-bohr-1913-2013
<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/NielsBohr.jpg" width="96" 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">08/10/2016</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 book under review is the product of a Paris seminar devoted to the celebration of the hundredth anniversary of the publication in 1913 of Niels Bohr’s three seminal papers on what is known nowadays as the <em>Bohr model</em> of the hydrogen atom. It collects several essays presented in this seminar that are quite accessible to a broad section of readers, either mathematicians, physicists or philosophers.</p></div></div></div>Fri, 29 Apr 2016 13:30:58 +0000fqgouvea747780 at http://www.maa.orghttp://www.maa.org/press/maa-reviews/niels-bohr-1913-2013#commentsThe R Student Companion
http://www.maa.org/press/maa-reviews/the-r-student-companion
<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/RStudentCompanion.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">08/10/2016</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>Beginning in the 1980s, commercially developed calculators with graphing and programmable capabilities have been available to students and others for aid in solving various mathematical problems. In parallel, many mathematics software packages were developed for use by both students and professionals in mathematics, science and related fields.</p></div></div></div>Mon, 06 Jun 2016 13:27:37 +0000fqgouvea753161 at http://www.maa.orghttp://www.maa.org/press/maa-reviews/the-r-student-companion#comments