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enExercises in (Mathematical) Style
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<h3>John McCleary</h3>
<p>Catalog Code: NML-48<br />
Print ISBN: <span style="color: rgb(34, 34, 34); font-family: arial, sans-serif; font-size: 12.8px;">978-0-88385-652-9 </span><br />
290 pp., Paperbound, 2017<br />
List Price: $48.00<br />
Member Price: $36.00<br />
Series: Anneli Lax New Mathematical Library</p>
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<p>In <em>Exercises in (Mathematical) Style</em>, the author investigates the world of that familiar set of numbers, the binomial coefficients. While the reader learns some of the properties, relations, and generalizations of the numbers of Pascal's triangle, each story explores a different mode of discourse - from arguing algebraically, combinatorially, geometrically, or by induction, contradiction, or recursion to discovering mathematical facts in poems, music, letters, and various styles of stories. The author follows the example of Raymond Queneau's <em>Exercises in Style</em>, giving the reader 99 stories in various styles. The ubiquitous nature of binomial coefficients leads the tour through combinatorics, number theory, algebra, analysis, and even topology.</p>
<p>The book celebrates the joy of writing and the joy of mathematics, found by engaging the rich properties of this simple set of numbers.</p>
<p><a href="/sites/default/files/pdf/pubs/books/NML-48_Preface.pdf" target="_blank">Preface</a></p>
<p><a href="/sites/default/files/pdf/pubs/books/NML-48_TOC.pdf" target="_blank">Table of Contents</a></p>
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http://www.maa.org/press/ebooks/exercises-in-mathematical-style
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><h2>John McCleary</h2>
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<p>What does <em>style</em> mean in mathematics? Style is both how one does something and how one communicates what was done.</p>
<p>In <strong>Exercises in (Mathematical) Style</strong>, the author investigates the world of that familiar set of numbers, the binomial coefficients. While the reader learns some of the properties, relations, and generalizations of the numbers of Pascal's triangle, each story explores a different mode of discourse — from arguing algebraically, combinatorially, geometrically, or by induction, contradiction, or recursion to discovering mathematical facts in poems, music, letters, and various styles of stories. The author follows the example of Raymond Queneau's <em>Exercises in Style</em>, giving the reader 99 stories in various styles. The ubiquitous nature of binomial coefficients leads the tour through combinatorics, number theory, algebra, analysis, and even topology.</p>
<p>The book celebrates the joy of writing and the joy of mathematics, found by engaging the rich properties of this simple set of numbers.</p>
<p> </p>
<p>Electronic ISBN: 9780883859919</p>
<p>Print ISBN: 9780883856529</p>
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http://www.maa.org/press/ebooks/phi-pi-e-and-i
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><h2>David Perkins</h2>
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<p>Certain constants occupy precise balancing points in the cosmos of number, like habitable planets sprinkled throughout our galaxy at just the right distances from their suns. This book introduces and connects four of these constants (φ, π, <em>e</em> and <em>i</em>), each of which has recently been the individual subject of historical and mathematical expositions. But here we discuss their properties, as a group, at a level appropriate for an audience armed only with the tools of elementary calculus. This material offers an excellent excuse to display the power of calculus to reveal elegant truths that are not often seen in college classes. These truths are described here via the work of such luminaries as Nilakantha, Liu Hui, Hemachandra, Khayyám, Newton, Wallis, and Euler.</p>
<p>The book is written with the goal that an undergraduate student can read the book solo. With this goal in mind, the author provides endnotes throughout, in case the reader is unable to work out some of the missing steps. Those endnotes appear in the last chapter, Extra Help. Each chapter concludes with a series of exercises, all of which introduce new historical figures or content.</p>
<p>Electronic ISBN: 9781614445258</p>
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</div></div></div><div class="field field-name-field-book-series field-type-taxonomy-term-reference field-label-above"><div class="field-label">Book Series: </div><div class="field-items"><div class="field-item even"><a href="/book-series/spectrum">Spectrum</a></div></div></div><div class="field field-name-field-ebook-category field-type-taxonomy-term-reference field-label-above"><div class="field-label">Category: </div><div class="field-items"><div class="field-item even"><a href="/ebook-category/calculus">Calculus</a></div><div class="field-item odd"><a href="/ebook-category/new">New</a></div></div></div>Thu, 13 Apr 2017 18:09:51 +0000bruedi862783 at http://www.maa.orghttp://www.maa.org/press/ebooks/phi-pi-e-and-i#commentsPhi, Pi, e and i
http://www.maa.org/press/books/phi-pi-e-and-i
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<h3>By David Perkins</h3>
<p>Catalog Code: PPE<br />
Print ISBN: 978-0-88385-589-8<br />
Electronic ISBN: 978-1-61444-525-8<br />
190 pp., Paperbound, 2017<br />
List Price: $50.00<br />
Member Price: $37.50<br />
Series: Spectrum</p>
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<p>Certain constants occupy precise balancing points in the cosmos of number, like habitable planets sprinkled throughout our galaxy at just the right distances from their suns. This book introduces and connects four of these constants (φ, π, e and i), each of which has recently been the individual subject of historical and mathematical expositions. But here we discuss their properties, as a group, at a level appropriate for an audience armed only with the tools of elementary calculus. This material offers an excellent excuse to display the power of calculus to reveal elegant truths that are not often seen in college classes. These truths are described here via the work of such luminaries as Nilakantha, Liu Hui, Hemachandra, Khayyám, Newton, Wallis, and Euler.</p>
<p><span style="font-size: 13.6136px;">The book is written with the goal that an undergraduate student can read the book solo. With this goal in mind, the author provides </span>endnotes<span style="font-size: 13.6136px;"> throughout, in case the reader is unable to work out some of the missing steps. Those </span>endnotes<span style="font-size: 13.6136px;"> appear in the last chapter, Extra Help. Each chapter concludes with a series of exercises, all of which introduce new historical figures or content.</span></p>
<h3><a href="/sites/default/files/pdf/pubs/books/PPE_TOC.pdf" target="_blank">Table of Contents</a></h3>
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http://www.maa.org/press/books/near-the-horizon-an-invitation-to-geometric-optics
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<h3>By Henk W. Broer</h3>
<p>Catalog Code: CAM-33<br />
Print ISBN: 978-0-88385-142-5<br />
Electronic ISBN: 978-1-61444-030-7<br />
178 pp., Hardbound, 2017<br />
List Price: $63.00<br />
Member Price: $47.25<br />
Series: Carus Mathematical Monographs</p>
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<p><em>Near the Horizon</em> starts out by considering several optical phenomena that can occur when the sun is near the horizon. One can sometimes see objects that are actually below the horizon. Sometimes there seems to be a dark strip in the middle of the solar disk. These are a result of the way that the atmosphere affects the geometry of light rays. Broer starts his book with the Fermat principle (rays of light take least-time paths) and deduces from it laws for refraction and reflection; by expressing these as conservation laws, he can handle both the case of inhomogeneous layers of air and the case of continuous variation in the refraction index.</p>
<p>A surprising application is the brachistochrone problem, in which the path of fastest descent is determined by studying how a light ray would behave in a "flat earth" atmosphere whose refraction index is determined by the gravitational potential. This leads to a very interesting chapter on the cycloid and its properties.</p>
<p>The final chapters move from the elementary theory to a more sophisticated version in which the Fermat Principle leads to a Riemannian metric whose geodesics are the paths of light rays. This gives us an optics which is geometric in a new sense, and serves as a nice demonstration of the physical applicability of Riemannian geometry.</p>
<p>The book is written in a very personal and engaging style. Broer is passionate about the subject and its history, and his passion helps carry the reader along. The result is readable and charming.</p>
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</div><div class="field field-name-field-book-series field-type-taxonomy-term-reference field-label-above"><div class="field-label">Book Series: </div><div class="field-items"><div class="field-item even"><a href="/book-series/carus-monographs">Carus Monographs</a></div></div></div>Mon, 27 Mar 2017 18:30:18 +0000eteal861250 at http://www.maa.orghttp://www.maa.org/press/books/near-the-horizon-an-invitation-to-geometric-optics#commentsUsing the Philosophy of Mathematics in Teaching Undergraduate Mathematics
http://www.maa.org/press/ebooks/using-the-philosophy-of-mathematics-in-teaching-undergraduate-mathematics
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><h2>Bonnie Gold, Carl E. Behrens, and Roger A. Simons, Editors</h2>
<p><img align="left" border="1" height="187" hspace="15" src="/sites/default/files/images/ebooks/notes/NTE86.png" width="144" /> <SCRIPT src="http://books.google.com/books/previewlib.js"></SCRIPT> <SCRIPT>GBS_setLanguage('en');</SCRIPT> <SCRIPT>GBS_insertPreviewButtonPopup('ISBN:9780883851968');</SCRIPT></p>
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<h3>Ebook Version FREE to MAA Members</h3>
<p><em>Using the Philosophy of Mathematics in Teaching Undergraduate Mathematics</em> is <strong>free</strong> to MAA members as part of your Member Only eBook Library. You must log in on the MAA website to access the free Member Only eBook Library. Click on the LOGIN button at the top of the page and log in using your user name and password. The Member Library is located in the left-hand column under My Profile.</p>
<hr />
<p><em>Using the Philosophy of Mathematics in Teaching Undergraduate Mathematics</em> is a collection of mostly original essays by mathematicians and philosophers on the topic. It was inspired by Bonnie Gold’s CMJ article “How Your Philosophy of Mathematics Impacts Your Teaching.” That article (reprinted in this volume) argued that one’s personal philosophy of mathematics affects his or her teaching and students, usually implicitly and often unconsciously. It also advocated making that impact explicit by having the teacher explain to their students where they are coming from and what some other options might be.</p>
<p>The majority of essays in this volume are reports from colleagues explaining how they tried to implement this mandate in various courses and what successes and challenges they enjoyed. Like most good Notes volumes, it will repay the thoughtful reader with many ideas that can profitably be carried into the classroom.</p>
<p>Print-on-Demand (POD) books are not returnable because they are printed at your request. Damaged books will, of course, be replaced (customer support information is on your receipt). Please note that all Print-on-Demand books are paperbound.</p>
<p>Electronic ISBN: 9781614443216</p>
<p>Print ISBN: 9780883851968</p>
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</div><div class="field field-name-field-ber-category field-type-taxonomy-term-reference field-label-above"><div class="field-label">Publication Category: </div><div class="field-items"><div class="field-item even">Latest</div></div></div><div class="field field-name-field-book-series field-type-taxonomy-term-reference field-label-above"><div class="field-label">Book Series: </div><div class="field-items"><div class="field-item even"><a href="/book-series/notes">Notes</a></div></div></div><div class="field field-name-field-ebook-category field-type-taxonomy-term-reference field-label-above"><div class="field-label">Category: </div><div class="field-items"><div class="field-item even"><a href="/ebook-category/new">New</a></div><div class="field-item odd"><a href="/ebook-category/resources-for-teachers">Resources for Teachers</a></div></div></div>Thu, 09 Mar 2017 14:36:09 +0000bruedi859480 at http://www.maa.orghttp://www.maa.org/press/ebooks/using-the-philosophy-of-mathematics-in-teaching-undergraduate-mathematics#commentsNear the Horizon: An Invitation to Geometric Optics
http://www.maa.org/press/ebooks/near-the-horizon-an-invitation-to-geometric-optics
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><h2>Henk Broer</h2>
<p><img align="left" border="1" height="187" hspace="15" src="/sites/default/files/images/ebooks/carus/CAM33.png" width="127" /> <SCRIPT src="http://books.google.com/books/previewlib.js"></SCRIPT> <SCRIPT>GBS_setLanguage('en');</SCRIPT> <SCRIPT>GBS_insertPreviewButtonPopup('ISBN:9780883851425');</SCRIPT></p>
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<p><strong>Near the Horizon</strong> starts out by considering several optical phenomena that can occur when the sun is near the horizon. One can sometimes see objects that are actually below the horizon. Sometimes there seems to be a dark strip in the middle of the solar disk. These are a result of the way that the atmosphere affects the geometry of light rays. Broer starts his book with the Fermat principle (rays of light take least-time paths) and deduces from it laws for refraction and reflection; by expressing these as conservation laws, he can handle both the case of inhomogeneous layers of air and the case of continuous variation in the refraction index.</p>
<p>A surprising application is the brachistochrone problem, in which the path of fastest descent is determined by studying how a light ray would behave in a “flat earth” atmosphere whose refraction index is determined by the gravitational potential. This leads to a very interesting chapter on the cycloid and its properties.</p>
<p>The final chapters move from the elementary theory to a more sophisticated version in which the Fermat Principle leads to a Riemannian metric whose geodesics are the paths of light rays. This gives us an optics which is geometric in a new sense, and serves as a nice demonstration of the physical applicability of Riemannian geometry.</p>
<p>The book is written in a very personal and engaging style. Broer is passionate about the subject and its history, and his passion helps carry the reader along. The result is readable and charming.</p>
<p>Electronic ISBN: 9781614440307</p>
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<a href="/tags/geometry">Geometry</a>, </div>
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<a href="/tags/optics">Optics</a> </div>
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</div><div class="field field-name-field-ber-category field-type-taxonomy-term-reference field-label-above"><div class="field-label">Publication Category: </div><div class="field-items"><div class="field-item even">Featured</div></div></div><div class="field field-name-field-book-series field-type-taxonomy-term-reference field-label-above"><div class="field-label">Book Series: </div><div class="field-items"><div class="field-item even"><a href="/book-series/carus-monographs">Carus Monographs</a></div></div></div><div class="field field-name-field-ebook-category field-type-taxonomy-term-reference field-label-above"><div class="field-label">Category: </div><div class="field-items"><div class="field-item even"><a href="/ebook-category/geometry">Geometry</a></div></div></div>Mon, 06 Mar 2017 15:44:25 +0000bruedi859310 at http://www.maa.orghttp://www.maa.org/press/ebooks/near-the-horizon-an-invitation-to-geometric-optics#commentsTeaching Statistics Using Baseball
http://www.maa.org/press/books/teaching-statistics-using-baseball
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<h3>By Jim Albert</h3>
<p>Catalog Code: TSB2<br />
Print ISBN: 978-1-93951-216-1<br />
256 pp., Paperbound, 2017<br />
List Price: $55.00<br />
MAA Member: $41.25<br />
Series: MAA Textbooks</p>
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<p>There is an active effort by people in the baseball community to learn more about baseball performance and strategy by the use of statistics. This book illustrates basic methods of data analysis and probability models by means of baseball statistics collected on players and teams. Students often have difficulty learning statistical concepts since they are explained using examples that are foreign to the students. The idea of the book is to describe statistical thinking in a context (that is, baseball) that will be familiar and interesting to students.</p>
<p>The second edition of Teaching Statistics follows the same structure as the first edition, where the case studies and exercises have been replaced by modern players and teams, and the new types of baseball data from the PitchFX system and fangraphs.com are incorporated into the text.</p>
<p><a href="http://www.maa.org/sites/default/files/pdf/ebooks/pdf/TSB2_contents.pdf" target="_blank">Table of Contents</a></p>
<p><a href="http://www.maa.org/sites/default/files/pdf/ebooks/pdf/TSB2_preface.pdf" target="_blank">Preface</a></p>
<h3> </h3>
<!---<h3>
Excerpt: Ch. 8 Dauntless Courage (p. 109)</h3>--->
<h3>About the Author</h3>
<p><strong>Jim Albert</strong> received a BS degree in mathematics from Bucknell University in 1975 and a PhD in statistics from Purdue University in 1979. He has taught at Bowling Green State University since 1979 and is currently a Professor of Mathematics and Statistics. His is a Fellow of the American Statistical Association. His research interest is in Bayesian inference and has published over 60 papers in refereed journals. In addition, he works in the areas of statistical education and applications of statistics in sports. He is currently editor of The American Statistician, the “general interest” journal published by The American Statistical Association (ASA). He has been active both in the Section of Bayseian Statistical Science and the Section on Statistics in Sports of the American Statistical Association. He has written four books: <em>Bayesian Computation Using Minitab, Ordinal Data Modeling</em> (with Val Johnson), <em>Workshop Statistics: Discovery with Data</em>, <em>A Bayesian Approach</em> (with Allan Rossman), and <em>Curve Ball: Baseball, Statistics, and the Role of Chance in the Game</em> (with Jay Bennett). The book <em>Curve Ball</em> has been reviewed favorably in many publications, including <em>The Wall Street Journal</em>, <em>The Journal of the American Statistical Association</em>, <em>Physics Today</em>, <em>Technometrics</em>, <em>MAA Reviews</em>,<em> Tech Directions Magazine</em>, <em>Baseball American</em>, <em>Mathematics Magazine</em>, <em>SIAM News</em>, and Science News. <em>Curve Ball</em> was a winner of the 2001 <em>The Sporting </em><em>News</em>-SABR Baseball Research award, and was recently included in the “The Essential Sabermetric Library” in an article by Randy Klipstein in the Newsletter of the Statistical Analysis interest group of SABR (The Society of American Baseball Research).</p>
<h3>MAA Review</h3>
<p>I have been afflicted with a chronic condition that ensures that at least once each year, usually in August or September, I will feel miserable. I am a Cubs fan. This year, the annual attack came a month later than usual, but it was much stronger than in past years. As I was recovering, I was asked to review <em>Teaching Statistics Using Baseball</em>, by Jim Albert. Heeding the old saying that you can prove anything with statistics, I sought to cheer myself up by searching for some sort of vindication for my years spent rooting for the lovable losers from Chicago, beyond the affirming regularity with which I get to say, "Wait 'til next year!"</p>
<p>Well, I'm still looking for the vindication, but this is a delightful book. Albert has been applying his love of baseball to his vocation of teaching statistics for some time now, and this text uses baseball as a framework to introduce and explore statistical topics. He has created a window through which the statistically-minded baseball fan can explore, explain, and debunk conventional wisdom concerning the national pastime. Albert uses this text for an introductory statistics course focused on baseball, but it's far more valuable as a resource for non-trivial applications and projects for any introductory statistics course, and as a gift for that baseball fan in your department. <a href="/node/108594">Continued...</a></p>
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<a href="/tags/applied-statistics">Applied Statistics</a> </div>
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http://www.maa.org/press/ebooks/portal-through-mathematics-journey-to-advanced-thinking
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><h2>Oleg Ivanov</h2>
<p><img align="left" border="1" height="187" hspace="15" src="/sites/default/files/images/ebooks/nml/NML47.png" width="125" /> <SCRIPT src="http://books.google.com/books/previewlib.js"></SCRIPT> <SCRIPT>GBS_setLanguage('en');</SCRIPT> <SCRIPT>GBS_insertPreviewButtonPopup('ISBN:9780883856512');</SCRIPT></p>
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<h4>Translated by Robert G. Burns</h4>
<p><strong>Portal Through Mathematics</strong> will be useful for prospective secondary teachers of mathematics, and may be used (as a supplementary resource) in university courses in algebra, geometry, calculus, and discrete mathematics. It can also be used for professional development for teachers looking for inspiration. However, the intended audience is much broader. Every fan of mathematics will find enjoyment in it.</p>
<p>The problems and topics are fresh and interesting and frequently surprising. One example: the puzzle that asks how much length must added to a belt around the Earth's equator to raise it one foot has probably achieved old chestnut status. Ivanov, after explaining the surprising answer to this question, goes a step further and asks, if you grabbed that too long belt at some point and raised it as high as possible, how high would that be? The answer to that is more surprising than the classic puzzle's answer.</p>
<p>Electronic ISBN: 9780883859902</p>
<p>Print ISBN: 9780883856512</p>
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</div><div class="field field-name-field-ber-category field-type-taxonomy-term-reference field-label-above"><div class="field-label">Publication Category: </div><div class="field-items"><div class="field-item even">Latest</div></div></div><div class="field field-name-field-book-series field-type-taxonomy-term-reference field-label-above"><div class="field-label">Book Series: </div><div class="field-items"><div class="field-item even"><a href="/book-series/anneli-lax-nml">Anneli Lax NML</a></div></div></div><div class="field field-name-field-ebook-category field-type-taxonomy-term-reference field-label-above"><div class="field-label">Category: </div><div class="field-items"><div class="field-item even"><a href="/ebook-category/resources-for-teachers">Resources for Teachers</a></div></div></div>Thu, 09 Feb 2017 17:38:39 +0000bruedi851634 at http://www.maa.orghttp://www.maa.org/press/ebooks/portal-through-mathematics-journey-to-advanced-thinking#commentsTeaching Statistics Using Baseball
http://www.maa.org/press/ebooks/teaching-statistics-using-baseball
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><h2>Jim Albert</h2>
<h5>TEXTBOOK*</h5>
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<p><strong>Teaching Statistics Using Baseball</strong> is a collection of case studies and exercises applying statistical and probabilistic thinking to the game of baseball. Baseball is the most statistical of all sports, since players are identified and evaluated by their hitting and pitching statistics. There is an active effort by people in the baseball community to learn more about baseball performance and strategy by the use of statistics. This book illustrates basic methods of data analysis and probability models by means of baseball statistics collected on players and teams. Students often have difficulty learning statistical ideas since they are explained using examples that are foreign to the students. The idea of the book is to describe statistical thinking in a context (that is, baseball) that will be familiar and interesting to students.</p>
<p>The book is organized using the same structure as most introductory statistics texts. There are chapters on the analysis of a single batch of data, followed by chapters on comparing batches of data and relationships. There are chapters on probability models and inference. The book can be used as the framework for a one-semester introductory statistics class focused on baseball or sports. This type of class has been taught at Bowling Green State University. It may be very suitable for a statistics class for students with sports-related majors, such as sports management or sports medicine. Alternately, the book can be used as a resource for instructors who wish to infuse their present course in probability or statistics with applications from baseball.</p>
<p>The second edition of Teaching Statistics follows the same structure as the first edition, where the case studies and exercises have been replaced by modern players and teams, and the new types of baseball data from the PitchFX system and fangraphs.com are incorporated into the text.</p>
<p>* As a textbook, <strong>Teaching Statistics Using Baseball</strong> does have DRM. Our DRM protected PDFs can be downloaded to three computers. iOS tablets can open secure PDFs using the AWReader app (available in the App Store and the Play Store). The iOS app uses the native iPad PDF reader so it is a very basic reader, no frills. Linux is not supported at this time for our secure PDFs.</p>
<p>280 pages</p>
<p><a href="/sites/default/files/pdf/ebooks/pdf/TSB2_contents.pdf">Contents</a></p>
<p><a href="/sites/default/files/pdf/ebooks/pdf/TSB2_preface.pdf">Preface</a></p>
<p>Electronic ISBN: 9781614446224</p>
<p>Paperback ISBN: 9781939512161</p>
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<a href="/tags/statistical-inference">Statistical Inference</a>, </div>
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<a href="/tags/statistical-models">Statistical Models</a>, </div>
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<a href="/tags/statistics">Statistics</a> </div>
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http://www.maa.org/press/books/portal-through-mathematics-journey-to-advanced-thinking
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<h3>Oleg Ivanov<br />
Translated by Robert G. Burns</h3>
<p>Catalog Code: NML-47<br />
Print ISBN: <span style="color: rgb(34, 34, 34); font-family: arial, sans-serif; font-size: 12.8px;">978-0-88385-651-2</span><br />
318 pp., Paperbound, 2017<br />
List Price: $55.00<br />
Member Price: $41.25<br />
Series: Anneli Lax New Mathematical Library</p>
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<p>A <em>Portal Through Mathematics</em> is a collection of puzzles and problems mostly on topics relating to secondary mathematics. The problems and topics are fresh and interesting and frequently surprising. One example: the puzzle that asks how much length must be added to a belt around the Earth's equator to raise it one foot has probably achieved old chestnut status. Ivanov, after explaining the surprising answer to this question, goes a step further and asks, if you grabbed that too long belt at some point and raised it as high as possible, how high would that be? The answer to that is more surprising than the classic puzzle's answer.</p>
<p>The book is organized into 29 themes, each a topic from algebra, geometry or calculus and each launched from an opening puzzle or problem. There are excursions into number theory, solid geometry, physics and combinatorics. Always there is an emphasis on surprise and delight. And every theme begins at a level approachable with minimal background requirements. With well over 250 puzzles and problems, there is something here sure to appeal to everyone.</p>
<p>A <em>Portal Through Mathematics</em> will be useful for prospective secondary teachers of mathematics and may be used (as a supplementary resource) in university courses in algebra, geometry, calculus, and discrete mathematics. It can also be used for professional development for teachers looking for inspiration. However, the intended audience is much broader. Every fan of mathematics will find enjoyment in it.</p>
<p><a href="/sites/default/files/pdf/pubs/books/NML47_Preface.pdf" target="_blank">Preface</a></p>
<p><a href="/sites/default/files/pdf/pubs/books/NML47_Table_of_contents.pdf" target="_blank">Table of Contents</a></p>
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<a href="/tags/high-school-mathematics">High School Mathematics</a>, </div>
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<a href="/tags/mathematics-for-teachers">Mathematics for Teachers</a>, </div>
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</div><div class="field field-name-field-book-series field-type-taxonomy-term-reference field-label-above"><div class="field-label">Book Series: </div><div class="field-items"><div class="field-item even"><a href="/book-series/anneli-lax-nml">Anneli Lax NML</a></div></div></div>Fri, 13 Jan 2017 19:26:46 +0000eteal835690 at http://www.maa.orghttp://www.maa.org/press/books/portal-through-mathematics-journey-to-advanced-thinking#commentsIntroduction to the Mathematics of Computer Graphics
http://www.maa.org/press/ebooks/introduction-to-the-mathematics-of-computer-graphics
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><h2>Nathan Carter</h2>
<h5>TEXTBOOK*</h5>
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<p><img align="left" border="1" height="187" hspace="15" src="/sites/default/files/images/ebooks/crm/IMCG.png" width="131" /> <SCRIPT src="http://books.google.com/books/previewlib.js"></SCRIPT> <SCRIPT>GBS_setLanguage('en');</SCRIPT> <SCRIPT>GBS_insertPreviewButtonPopup('ISBN:9781614441229');</SCRIPT></p>
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<p>This text, by an award-winning MAA author, was designed to accompany his first-year seminar in the mathematics of computer graphics. Readers learn the mathematics behind the computational aspects of space, shape, transformation, color, rendering, animation, and modeling. The software required is freely available on the Internet for Mac, Windows, and Linux.</p>
<p>The text answers questions such as these: How do artists build up realistic shapes from geometric primitives? What computations is my computer doing when it generates a realistic image of my 3D scene? What mathematical tools can I use to animate an object through space? Why do movies always look more realistic than video games?</p>
<p>Containing the mathematics and computing needed for making their own 3D computer-generated images and animations, the text, and the course it supports, culminates in a project in which students create a short animated movie using free software. Algebra and trigonometry are prerequisites; calculus is not, though it helps. Programming is not required. Includes optional advanced exercises for students with strong backgrounds in math or computer science. Instructors interested in exposing their liberal arts students to the beautiful mathematics behind computer graphics will find a rich resource in this text.</p>
<p>* As a textbook, <em>Introduction to the Mathematics of Computer Graphics</em> does have DRM. Our DRM protected PDFs can be downloaded to three computers. iOS tablets can open secure PDFs using the AWReader app (available in the App Store). The iOS app uses the native iPad PDF reader so it is a very basic reader, no frills. Linux is not supported at this time for our secure PDFs.</p>
<p><a href="/sites/default/files/pdf/ebooks/pdf/Contents_IMCG.pdf">Contents</a></p>
<p><a href="/sites/default/files/pdf/ebooks/pdf/Overview_IMCG.pdf">Overview</a></p>
<p>480 pages</p>
<p>Electronic ISBN: 9781614441229</p>
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<h3>By Mark Gockenbach</h3>
<p>Catalog Code: CAM-32<br />
Print ISBN: 978-0-88385-141-8<br />
Electronic ISBN: 978-1-61444-029-1<br />
336 pp., Hardbound, 2016<br />
List Price: $60.00<br />
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Series: Carus Mathematical Monographs</p>
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<p>Inverse problems occur frequently in science and technology, whenever we need to infer causes from effects that we can measure. Mathematically, they are difficult problems because they are unstable: small bits of noise in the measurement can completely throw off the solution. Nevertheless, there are methods for finding good approximate solutions.</p>
<p><em>Linear Inverse Problems and Tikhonov Regularization</em> examines one such method: Tikhonov regularization for linear inverse problems defined on Hilbert spaces. This is a clear example of the power of applying deep mathematical theory to solve practical problems.</p>
<p>Beginning with a basic analysis of Tikhonov regularization, this book introduces the singular value expansion for compact operators, and uses it to explain why and how the method works. Tikhonov regularization with seminorms is also analyzed, which requires introducing densely defined unbounded operators and their basic properties. Some of the relevant background is included in appendices, making the book accessible to a wide range of readers.</p>
<p><a href="/sites/default/files/pdf/pubs/books/CAM-32_TOC.pdf" target="_blank">Table of Contents</a></p>
<h3>Excerpt: Chapter 2: Well-posed, ill-posed, and inverse problems (p. 15)</h3>
<p>The purpose of this chapter is to explain the properties that a problem must have to be considered an inverse problem, and to study them in some detail. We are going to restrict ourselves to linear inverse problems defined on Hilbert spaces. Throughout this book, <em>X</em> and <em>Y</em> will denote Hilbert spaces and <em>T</em> : <em>X</em> → <em>Y</em> will denote a continuous linear operator. We wish to study the equation </p>
<p class="rtecenter"><em><span style="font-size: 13.6136px; line-height: 1.25em;">T x = y</span></em><span style="font-size: 13.6136px; line-height: 1.25em;">,<em><span style="font-size: 13.6136px; line-height: 1.25em;"> </span></em>(2.1)</span></p>
<p><span style="font-size: 13.6136px; line-height: 1.25em;">where<em> y</em> ∈ <em>Y</em> is given and<em> x</em> ∈ <em>X</em> is to be determined. It may be straightforward or difficult to solve accurately, depending on the properties of T. In this chapter, we describe the conditions that make (2.1) <em>well-posed</em>, <em>ill-posed</em>, or an <em>inverse problem</em>. An inverse problem is a special kind of ill-posed problem that is particularly difficult to solve, and such problems are the subject of this book.</span></p>
<h3>About the Author</h3>
<p><strong>Mark Gockenbach</strong> received his PhD in Computational and Applied Mathematics from Rice University in 1994. He has held faculty positions at Indiana University (teaching in the ITM/MUCIA-Indiana University cooperative program in Malaysia for two years), the University of Michigan, and Rice University. He is now Professor and Chair of the Department of Mathematical Sciences at Michigan Technological University. Professor Gockenbach has won several awards for teaching, and he currently serves as a volunteer lecturer in the International Mathematical Union’s Volunteer Lecturer Program (VLP). As a VLP lecturer, he has taught master’s degree courses in Phnom Penh, Cambodia.</p>
<p>Professor Gockenbach’s research interests are primarily in inverse problems in partial differential equations. His previous books are <em>Partial Differential Equations: Analytical and Numerical Methods</em> (first edition 2002, second edition 2010) and <em>Understanding and Implementing the Finite Element Method</em> (2006), both published by the Society for Industrial and Applied Mathematics, and Finite-Dimensional Linear Algebra (2010), published by CRC Press.</p>
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<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><h1>Resources and Pedagogical Techniques for Enhancing the Teaching of Proof-Writing Across the Curriculum</h1>
<h2>Rachel Schwell, Aliza Steurer and Jennifer F. Vasquez, Editors</h2>
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<p><em>Beyond Lecture: Resources and Pedagogical Techniques for Enhancing the Teaching of Proof-Writing Across the Curriculum</em> is <strong>free</strong> to MAA members as part of your Member Only ebook Library. You must log in on the MAA website to access the free Member Only ebook Library. Click on the LOGIN button at the top of the page and log in using your user name and password. The Member Library is located in the left-hand column under My Profile.</p>
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<p>The challenges students can face in the transition from computational mathematics to proof-writing lead many instructors to seek pedagogical techniques that extend beyond standard lecture. This Notes volume unites a wide variety of such techniques, along with resources to aid in incorporating them. Written with the busy instructor in mind, the articles present practical methods in a "nuts-and-bolts" fashion, for easy access to the details of each technique. Courses throughout the entire undergraduate mathematics curriculum are represented: this includes a variety of proof-based courses and also non-traditional ones such as calculus and mathematics for liberal arts</p>
<p><strong>Beyond Lecture</strong> should appeal to both novice and seasoned instructors, while also hopefully providing a springboard for experimentation in readers' own classrooms.</p>
<p>Print-on-Demand (POD) books are not returnable because they are printed at your request. Damaged books will, of course, be replaced (customer support information is on your receipt). Please note that all Print-on-Demand books are paperbound.</p>
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</div></div></div><div class="field field-name-field-ber-category field-type-taxonomy-term-reference field-label-above"><div class="field-label">Publication Category: </div><div class="field-items"><div class="field-item even">Featured</div></div></div><div class="field field-name-field-book-series field-type-taxonomy-term-reference field-label-above"><div class="field-label">Book Series: </div><div class="field-items"><div class="field-item even"><a href="/book-series/notes">Notes</a></div></div></div><div class="field field-name-field-ebook-category field-type-taxonomy-term-reference field-label-above"><div class="field-label">Category: </div><div class="field-items"><div class="field-item even"><a href="/ebook-category/resources-for-teachers">Resources for Teachers</a></div><div class="field-item odd"><a href="/ebook-category/transition-course">Transition Course</a></div></div></div>Wed, 17 Aug 2016 02:57:06 +0000bruedi760688 at http://www.maa.orghttp://www.maa.org/press/ebooks/beyond-lecture#commentsLinear Inverse Problems and Tikhonov Regularization
http://www.maa.org/press/ebooks/linear-inverse-problems-and-tikhonov-regularization
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><h2>Mark S. Gockenbach</h2>
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<p><a name="_GoBack"></a>Inverse problems occur frequently in science and technology, whenever we need to infer causes from effects that we can measure. Mathematically, they are difficult problems because they are unstable: small bits of noise in the measurement can completely throw off the solution. Nevertheless, there are methods for finding good approximate solutions.</p>
<p><em>Linear Inverse Problems and Tikhonov Regularization</em> examines one such method: Tikhonov regularization for linear inverse problems defined on Hilbert spaces. This is a clear example of the power of applying deep mathematical theory to solve practical problems.</p>
<p>Beginning with a basic analysis of Tikhonov regularization, this book introduces the singular value expansion for compact operators, and uses it to explain why and how the method works. Tikhonov regularization with seminorms is also analyzed, which requires introducing densely defined unbounded operators and their basic properties. Some of the relevant background is included in appendices, making the book accessible to a wide range of readers.</p>
<p>Electronic ISBN: 9781614440291</p>
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http://www.maa.org/press/periodicals/mathematics-magazine/mathematics-magazine-june-2016
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<div>The June issue is here with articles on varied topics, perfect for summer reading. Roger Nelsen investigates multi-polygonal numbers. Bijections, permutations, and cycles are used by Pozdnyakov and Steele to analyze changing seats on a bus. Gary Brookfield tests your intuition on cyclotomic polynomials.</div>
<div> </div>
<div>Other articles examine the binomial recurrence, the Symmedian point, a classic calculus problem involving a Diophantine equation, Morrie’s law, and a relationship between GCDs and LCMs. This issue marks the return of both the art interview (of Robert Fathauer) and the crossword puzzle (on MathFest). Reviews and Problems round out the issue. Happy reading.</div>
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<p>—<em>Michael A. Jones, Editor</em></p>
<h5 style="font-size: 18px;">JOURNAL SUBSCRIBERS AND MAA MEMBERS:</h5>
<p>To read the full articles, please log in to the member portal by clicking on 'Login' in the upper right corner. Once logged in, click on 'My Profile' in the upper right corner.</p>
<p>Vol. 89, No. 3, pp 157 – 232</p>
<h2>Articles</h2>
<h3>Multi-Polygonal Numbers</h3>
<p>Robert B. Nelsen</p>
<p>We study some sequences of multi-polygonal numbers, specifically the square triangular, oblong triangular, pentagonal triangular, and pentagonal square numbers. To do so, we state and prove theorems that relate the factors of a given triangular number to a pair of larger triangular numbers with a triangular sum, and relate a triangular number that is three times another triangular number (or three times a square) to a larger pair of triangular numbers with the same property.</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.3.159" target="_blank">10.4169/math.mag.89.3.159</a></p>
<h3>Proof Without Words: Every Cobalancer Is a Balancing Number</h3>
<p>G. K. Panda and Ravi Kumar Davala</p>
<p>A visual proof that every cobalancer is a balancing number.</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.3.165" target="_blank">10.4169/math.mag.89.3.165</a></p>
<h3>Buses, Bullies, and Bijections</h3>
<p>Vladimir Pozdynakov and J. Michael Steele</p>
<p>The random—or orderly—seating of passengers on a bus is used to motivate several questions about cycles of permutations. These in turn motivates the investigation of bijections between special subsets of permutations. The goal, of course, is to give simple explanations of surprising facts.</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.3.167" target="_blank">10.4169/math.mag.89.3.167</a></p>
<h3>Proof Without Words: Limit of a Recursive Root Mean Square</h3>
<p>Ángel Plaza</p>
<p>Visual proof that the limit of the recursive root mean square sequence defined by a<sub>n + 1</sub><img alt="" src="/sites/default/files/images/Journals/MathMag/89_3_Plaza.gif" style="width: 161px; height: 40px;" /> where a<sub>1</sub> and a<sub>2</sub> are the initial values of the sequence.</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.3.177" target="_blank">10.4169/math.mag.89.3.177</a></p>
<h3>The Coefficients of Cyclotomic Polynomials</h3>
<p>Gary Brookfield</p>
<p>One of the most surprising properties of cyclotomic polynomials is that their coefficients are all 1, -1 or zero—at least that seems to be the case until one notices that the 105th cyclotomic polynomial has a coefficient of -2. This article serves as an introduction to these polynomials with a particular emphasis on their coefficients and proves that the coefficients of the first 104 cyclotomic polynomials are at most one in absolute value.</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.3.179" target="_blank">10.4169/math.mag.89.3.179</a></p>
<h3>Proof Without Words: Limit of a Recursive Arithmetic Mean</h3>
<p>Ángel Plaza</p>
<p>Visual proof that the limit of the recursive arithmetic mean sequence defined by <img alt="" src="/sites/default/files/images/Journals/MathMag/89_3_Plaza1.gif" style="width: 143px; height: 30px;" /> is <img alt="" src="/sites/default/files/images/Journals/MathMag/89_3_Plaza2.gif" style="width: 54px; height: 30px;" />, where a<sub>1</sub> and a<sub>2</sub> are the initial values of the sequence.</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.3.189" target="_blank">10.4169/math.mag.89.3.189</a></p>
<h3>A Curious Result for GCDs and LCMs</h3>
<p>Jathan Austin</p>
<p>We give necessary and sufficient conditions under which the sum of two positive integers equals the difference of their least common multiple and greatest common divisor, and then prove this result.</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.3.190" target="_blank">10.4169/math.mag.89.3.190</a></p>
<h3>Proof Without Words: Sums of Powers of <sup>4</sup>⁄<sub>9</sub></h3>
<p>Tom Edgar</p>
<p>We provide a visual computation of a particular infinite series.</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.3.191" target="_blank">10.4169/math.mag.89.3.191</a></p>
<h3>The Binomial Recurrence</h3>
<p>Michael Z. Spivey</p>
<p>We give a new, direct argument that the solution to the binomial recurrence is the binomial coefficient. Our argument does not assume that the solution is known in advance nor does it rely on anything other than basic properties of two-variable triangular recurrence relations.</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.3.192" target="_blank">10.4169/math.mag.89.3.192</a></p>
<h3>Proof Without Words: Sums of Consecutive Odds and Positive Integer Cubes</h3>
<p>Stanley R. Huddy</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.3.196" target="_blank">10.4169/math.mag.89.3.196</a></p>
<h3>An Algebraic Method to Find the Symmedian Point of a Triangle</h3>
<p>M. Bani-Yaghoub, Noah H. Rhee and Jawad Sadek</p>
<p>A relationship between the symmedian point of a triangle and the least-squares solution of a linear system is presented. The coordinates of the symmedian point are explicitly calculated as a solution to the linear system.</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.3.197" target="_blank">10.4169/math.mag.89.3.197</a></p>
<h3>Building the Biggest Box: Three-factor Polynomials and a Diophantine Equation</h3>
<p>Gregory Convertito and David Cruz-Uribe, OFS</p>
<p>We consider a well known calculus question, and show that the solution of this problem is equivalent to finding integer solutions to a Diophantine equation. We generalize the calculus question, which in turn leads to a more general Diophantine equation. We give solutions to all of these and describe some of the historical background.</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.3.201" target="_blank">10.4169/math.mag.89.3.201</a></p>
<h3>Proof Without Words: Sums of Reciprocals of Binomial Coefficients</h3>
<p>Tom Edgar</p>
<p>We provide a visual computation of the sum of the series obtained by adding the reciprocals of entries from column n from Pascal's triangle.</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.3.212" target="_blank">10.4169/math.mag.89.3.212</a></p>
<h3>A Geometric Proof of a Morrie-Type Formula</h3>
<p>Samuel G. Moreno and Esther M. García-Caballero</p>
<p>We use a regular heptagon to give a geometric proof of a specific instance of a Morrie-type formula.</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.3.214" target="_blank">10.4169/math.mag.89.3.214</a></p>
<h3>Proof Without Words: Viviani for Congruent Cevians</h3>
<p>Grégoire Nicollier</p>
<p>We prove without words that the distances from the sides of a triangle measured parallelly to three congruent cevians sum up to the cevian length. This generalizes Viviani′s theorem about the sum of the distances from the sides of an equilateral triangle.</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.3.216" target="_blank">10.4169/math.mag.89.3.216</a></p>
<h3>Crossword Puzzle: MathFest 2016</h3>
<p>Brendan Sullivan</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.3.218" target="_blank">10.4169/math.mag.89.3.218</a></p>
<h3>Robert Fathauer: Polymath Purveyor</h3>
<p>Amy L. Reimann and David A. Reimann</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.3.220" target="_blank">10.4169/math.mag.89.3.220</a></p>
<h2>Problems and Solutions</h2>
<p>Proposals, 1996-2000</p>
<p>Quickies, 1061-1062</p>
<p>Solutions, 1966-1970</p>
<p>Answers, 1061-1062</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.3.223" target="_blank">10.4169/math.mag.89.3.223</a></p>
<h2>Reviews</h2>
<p>Math circles; ageism in mathematics, mathematics in movies</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.3.231" target="_blank">10.4169/math.mag.89.3.231</a></p>
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</div></div></div>Thu, 28 Jul 2016 15:05:12 +0000eteal757962 at http://www.maa.orghttp://www.maa.org/press/periodicals/mathematics-magazine/mathematics-magazine-june-2016#commentsMathematics Magazine - April 2016
http://www.maa.org/press/periodicals/mathematics-magazine/mathematics-magazine-april-2016
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<div>This issue of the <em>Mathematics Magazine</em> highlights the range of diverse articles we publish. David Nash and Jonathan Needleman ask, and answer, the question: When are finite projective planes magic? Rob Poodiack looks at trigonometry and calculus based on hyperellipses instead of circles and touches on Danish design. Take a look at the symmetry Jeffrey Lawson and Matthew Rave use to analyze geometric phase in dynamical systems, relating the mathematics to Chopin, amusement park rides, and falling cats. </div>
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<div> </div>
<div>Further in the issue, Brian Conrey, James Gabbard, Katie Grant, Andrew Liu, and Kent Morrison query, "How rare are intransitive dice?" They make conjectures about the frequency of certain types of dice behavior and prove asymptotic results for the frequency of "one-step" dice to be intransitive.</div>
</div>
<p>—<em>Michael A. Jones, Editor</em></p>
<h5 style="font-size: 18px;">JOURNAL SUBSCRIBERS AND MAA MEMBERS:</h5>
<p>To read the full articles, please log in to the member portal by clicking on 'Login' in the upper right corner. Once logged in, click on 'My Profile' in the upper right corner.</p>
<p>Vol. 89, No. 2, pp 80 – 155</p>
<h2>Articles</h2>
<h3>When Are Finite Projective Planes Magic?</h3>
<p>David A. Nash and Jonathan Needleman</p>
<p>We study a generalization of magic squares, where the entries come from the natural numbers, to magic finite projective planes, where the entries come from Abelian groups. For each finite projective plane we demonstrate a small group over which the plane can be labeled magically. In the prime order case we classify all groups over which the projective plane can be made magic.</p>
<p>To purchase from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.89.2.83" target="_blank">10.4169/math.mag.89.2.83</a></p>
<h3>Squigonometry, Hyperellipses, and Supereggs</h3>
<p>Robert D. Poodiack</p>
<p>A superegg is the solid of revolution for a hyperellipse, an ellipse with squarish corners. The two objects became the basis of a design revolution of sorts in the 1960s, as practiced by the Danish mathematician and poet Piet Hein. We use an analog of trigonometry called squigonometry to produce a set of constants akin to the well-known and customary π and then find formulas using these constants for the area of a hyperellipse and the volume of Hein′s superegg.</p>
<p>To purchase from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.89.2.92" target="_blank">10.4169/math.mag.89.2.92</a></p>
<h3>Proof Without Words: Infinitely Many Almost-Isosceles Pythagorean Triples Exist</h3>
<p>Roger B. Nelsen</p>
<p>Wordlessly, we show that there are infinitely many Pythagorean triples with consecutive integers as legs and infinitely many Pythagorean triples with consecutive triangular numbers as legs.</p>
<p>To purchase from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.89.2.103" target="_blank">10.4169/math.mag.89.2.103</a></p>
<h3>Spacewalks and Amusement Rides: Illustrations of Geometric Phase</h3>
<p>Jeffrey Lawson and Matthew Rave</p>
<p>Geometric phase in a dynamical system can be visualized as the interplay between two periodic functions which go in and out of “synch.” Using illustrations of a boy′s walk in space and a dizzying fun park ride, we demonstrate that in certain simple mechanical systems we can compute geometric phase directly from a symmetry—we don′t even need to solve the system of differential equations. We can also use geometric phase to explain how cats (almost) always land on their feet. We conclude with an interpretation of geometric phase in terms of the geometric notions of connection and curvature.</p>
<p>To purchase from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.89.2.105" target="_blank">10.4169/math.mag.89.2.105</a></p>
<h3>Bounds for the Representations of Integers by Positive Quadratic Forms</h3>
<p>Kenneth S. Williams</p>
<p>Recent ground-breaking work of Conway, Schneeberger, Bhargava, and Hanke shows that to determine whether a given positive quadratic form <em>F </em>with integer coefficients represents every positive integer (and so is universal), it is only necessary to check that <em>F</em> represents all the integers in an explicitly given finite set S of positive integers. The set contains either nine or twenty-nine integers depending on the parity of the coefficients of the cross-product terms in <em>F</em> and is otherwise independent of <em>F</em>. In this article we show that F represents a given positive integer n if and only if<em> F</em>(<em>y</em><sub>1</sub>, … ,<em> y<sub>k</sub></em>) = <em>n </em>for some integers <em>y</em><sub>1</sub>, … , <em>y<sub>k</sub></em> satisfying <img alt="" src="/sites/default/files/images/Journals/kennethwilliams_1.gif" style="width: 200px; height: 19px;" /> where the positive rational numbers <em>c<sub>i</sub></em> are explicitly given and depend only on<em> F</em>. Let m be the largest integer in <em>S</em> (in fact <em>m</em> = 15 or 290). Putting these results together we have <em>F</em> is universal if and only if <img alt="" src="/sites/default/files/images/Journals/kennethwilliams_2.gif" style="width: 500px; height: 25px;" /></p>
<p>To purchase from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.89.2.122" target="_blank">10.4169/math.mag.89.2.122</a></p>
<h3>Proof Without Words: van Schooten’s Theorem</h3>
<p>Raymond Viglione</p>
<p>We provide a simple visual proof of van Schooten′s theorem: given an equilateral triangle <em>ABC</em> with circumcircle, if point <em>P</em> is chosen on minor arc <em>BC</em>, then <em>PA</em> = <em>PB</em> + <em>PC</em>.</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.2.132" target="_blank">10.4169/math.mag.89.2.132</a></p>
<h3>Intransitive Dice</h3>
<p>Brian Conrey, James Gabbard, Katie Grant, Andrew Liu, and Kent E. Morrison</p>
<p>We consider <em>n</em>-sided dice whose face values lie between 1 and <em>n</em> and whose faces sum to <em>n</em>(<em>n</em> + 1)/2. For two dice <em>A</em> and <em>B</em>, define <em>A</em> ≻ <em>B</em> if it is more likely for <em>A</em> to show a higher face than <em>B</em>. Suppose <em>k</em> such dice <em>A</em>1, … , <em>A</em><em>k</em> are randomly selected. We conjecture that the probability of ties goes to 0 as <em>n</em> grows. We conjecture and provide some supporting evidence that—contrary to intuition—each of the <img src="http://www.jstor.org/s3/sequoia-cedar/cid-prod-1/bc4bc29f/a42b/3268/a943/3d92cfabf164/mathmaga.89.issue-2/math.mag.89.2.133/graphics/figure1.gif?token0=kzptAwmQMxr92v%2Bs8d8IGwrcLnL2Mn1bhA9Hgt4061w%3D&Expires=1467823516&AWSAccessKeyId=ASIAIOFLT3ZH6DDM2XMA&x-amz-security-token=FQoDYXdzEKj%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDIZXcjROPgScPXTQUCKcAzRZRwrQ%2Ff1imuohpCK4floebyMVjqQIUB%2FgYbWm285jOLzVHIZAolXYW7zSqybJ%2B7AwGfRfc1fB1Lq6rss6hxP4LGXUAbENk6oRPIQr%2FVOkpJ%2F4uJc3O6XbPqBULxu7UlB4DMpAYabV7sli%2B7wy4CVrth7CI7YmIRllKqmmheLVV1irpDQY%2Faw76UE6rnjjhnHv8PWRt6Afl09%2Bcuia55XCHr3OtgQR0W3rxmCQqzRkWlZ80v7QyYiUC0BvUtExTtpG5cctnXg1wc%2FRvUOsVirmmka0CCmiRvIIyCd9iPr%2BWDCBD7TIlRKt1XwVyqlpMW1FSL39Wwr9%2FIuXXVKZCZQBYZz4SSYLi56pnpOBnBBUgffa%2FTII3WcSkw92dbm1ZmL9FOrokJAUALeApfkYOmDCu%2B1xmm2u%2Bi7sji5nWZKx6l88YZLd8E7yYfqhTG8ZHG1fPqlwLq7whQq2TjVdLqYstEwHIHowxRrogg7Z5fPdzFGas2DZIPADebHArX6O%2BfibgLim4yQXbYtKCaybmJ0jwLRBfBVtbE5qQfMoiL30uwU%3D&Signature=jjJqKbNGayNcmr86iNWvRecOCFk%3D" style="border:0px;line-height:26px;" /> assignments of ≻ or ≺ to each pair is equally likely asymptotically. For a specific example, suppose we randomly select <em>k</em> dice <em>A</em>1, … , <em>A</em><em>k</em> and observe that <em>A</em>1 ≻ <em>A</em>2 ≻ … ≻ <em>A</em><em>k</em>. Then our conjecture asserts that the outcomes <em>A</em><em>k</em> ≻ <em>A</em>1 and <em>A</em>1 ≻ <em>A</em><em>k</em> both have probability approaching 1<em>/</em>2 as <em>n</em> → ∞.</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.2.133" target="_blank">10.4169/math.mag.89.2.133</a></p>
<h3>Mathematical Methods</h3>
<p>Brendan Sullivan</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.2.144" target="_blank">10.4169/math.mag.89.2.144</a></p>
<h2>Problems and Solutions</h2>
<p>Proposals, 1991-1995</p>
<p>Quickies, 1059-1060</p>
<p>Solutions, 1961-1965</p>
<p>Answers, 1059-1060</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.2.147" target="_blank">10.4169/math.mag.89.2.147</a></p>
<h2>Reviews</h2>
<p>Riemann Hypothesis; Hunger Games; modular forms in context; coincidences</p>
<p>To purchase from JSTOR: <a href="http://www.jstor.org/stable/info/10.4169/math.mag.89.2.155" target="_blank">10.4169/math.mag.89.2.155</a></p>
</div></div></div>Wed, 06 Jul 2016 15:51:51 +0000abranscombe756184 at http://www.maa.orghttp://www.maa.org/press/periodicals/mathematics-magazine/mathematics-magazine-april-2016#commentsSoviet Union Mathematical Olympiad: Grades 8, 9, and 10
http://www.maa.org/press/ebooks/soviet-union-mathematical-olympiad-grades-8-9-and-10
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><h2>Andy C. F. Liu</h2>
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<p>The olympiad movement in the former Soviet Union was initially city-based, with what was then Leningrad taking the lead in 1934, followed by Moscow in 1935. In 1961, the national Russian Mathematical Olympiad was founded. In 1967, the contest was renamed the Soviet Union Mathematical Olympiad.</p>
<p>Later, somewhat confusingly, a new Russian Mathematical Olympiad was organized. To make the distinction, we include the first six contests under the umbrella of the Soviet Union Mathematical Olympiad. We also extend the coverage to 1992, when the Soviet Union had dissolved, and the contest should properly be called the Mathematical Olympiad of the Independent States. The contest ceased operation after this one-time affair.</p>
<p>Much of the work is translated, elaborated, and edited from a book by the Russian authors, A. Yegorov and N. Vasiliev, covering the contest up to 1987. For 1988 to 1992, Chinese translations of original material in Russian have been consulted. For some problems, sometimes only answers or hints are given, sometimes nothing at all. In this book, these gaps are filled, and every problem now has a complete solution.</p>
<p>The book is divided into three parts: one for each grade level group of contests. Each part has its own problem classification and problem index chapters. Also included, in appendices, are grade 11 contests and solutions from 1963–1966.</p>
<p>This book is especially suitable for students preparing for national or international mathematical olympiads.</p>
<p>Electronic ISBN: 9781614444084</p>
</div>
<h2> </h2>
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</div><div class="field field-name-field-ber-category field-type-taxonomy-term-reference field-label-above"><div class="field-label">Publication Category: </div><div class="field-items"><div class="field-item even">Latest</div></div></div><div class="field field-name-field-book-series field-type-taxonomy-term-reference field-label-above"><div class="field-label">Book Series: </div><div class="field-items"><div class="field-item even"><a href="/book-series/problem-books">Problem Books</a></div></div></div><div class="field field-name-field-ebook-category field-type-taxonomy-term-reference field-label-above"><div class="field-label">Category: </div><div class="field-items"><div class="field-item even"><a href="/ebook-category/problem-solving">Problem Solving</a></div></div></div>Tue, 10 May 2016 16:21:21 +0000bruedi749527 at http://www.maa.orghttp://www.maa.org/press/ebooks/soviet-union-mathematical-olympiad-grades-8-9-and-10#commentsEuclidean Geometry in Mathematical Olympiads
http://www.maa.org/press/books/euclidean-geometry-in-mathematical-olympiads
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<h3>Evan Chen</h3>
<p>Catalog Code: EGMO<br />
Print ISBN: 978-0-88385-839-4<br />
Electronic ISBN: 978-1-61444-411-4<br />
311 pp., Paperbound, 2016<br />
List Price: $60.00<br />
Member Price: $45.00<br />
Series: MAA Problem Books</p>
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<p>This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage.</p>
<p>Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures.</p>
<p>The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains as selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions.</p>
<p>This book is especially suitable for students preparing for national or international mathematical olympiads, or for teachers looking for a text for an honor class.</p>
<p><a href="/sites/default/files/pdf/pubs/books/EGMO_TOC.pdf" target="_blank">Table of Contents</a></p>
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<h3>Excerpt: Geometry(p. 542)</h3>
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<h3>About the Author</h3>
<p>Evan Chen is a past contest enthusiast hailing from Fremont, CA. In 2014 he was a winner of the USA Mathematical Olympiad, and earned a gold medal at that year’s International Mathematical Olympiad. He is currently an undergraduate studying in Cambridge, Massachusetts, where he serves as problem czar for the Harvard-MIT Math Tournament.</p>
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http://www.maa.org/press/periodicals/mathematics-magazine/mathematics-magazine-contents-december-2015
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><img alt="" src="/sites/default/files/images/pubs/mm_supplements/mathmag_december2015.PNG" style="width: 202px; margin-right: 10px; margin-left: 10px; float: left; height: 287px;" /></p>
<p>This issue offers diverse cross sections of mathematics: cooperative play in the card game Hanabi is related to hat-guessing games; a fair division algorithm is proposed and analyzed; and surprising ratios between volumes and surfaces areas are considered for different solids of revolutions. Cross sections of tori are shown to be related to foci of families of ellipses. There is also the first in a series of interviews with mathematical artists or artistic mathematicians. Amy and David Reimann interview George Hart in George Hart: Troubadour for Geometry. —<em>Walter Stromquist, editor</em></p>
<h5 style="font-size: 18px;">JOURNAL SUBSCRIBERS AND MAA MEMBERS:</h5>
<p>To read the full articles, please log in to the member portal by clicking on 'Login' in the upper right corner. Once logged in, click on 'My Profile' in the upper right corner.</p>
<p>Vol. 88, No. 5, pp 320 – 388</p>
<h2>Letter from Editor</h2>
<h2>Articles</h2>
<h3>How to Make the Perfect Fireworks Display: Two Strategies for <em>Hanabi</em></h3>
<p>Christopher Cox, Jessica de Silva, Philip Deorsey, Franklin H. J. Kenter, Troy Retter and Josh Tobin</p>
<p>The game of Hanabi is a multiplayer cooperative card game that has many similarities to a mathematical “hat guessing game.” In <em>Hanabi</em>, a player does not see the cards in her own hand and must rely on the actions of the other players to determine information about her cards. This article presents two strategies for <em>Hanabi</em>. These strategies use different encoding schemes, based on ideas from network coding, to efficiently relay information. The first strategy allows players to effectively recommend moves for other players, and the second strategy allows players to determine the contents of their hands. Results from computer simulations demonstrate that both strategies perform well. In particular, the second strategy achieves a perfect score more than 75 percent of the time.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.88.5.323" target="_blank">10.4169/math.mag.88.5.323</a></p>
<h3>Proof Without Words: Half Issues in the Equilateral Triangle and Fair Pizza Sharing</h3>
<p>Grégoire Nicollier</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.88.5.337" target="_blank">10.4169/math.mag.88.5.337</a></p>
<h3>How to Divide Things Fairly</h3>
<p>Steven J. Brams, D. Marc Kilgour, and Christian Klamler</p>
<p>We propose an intuitively simple sequential algorithm (SA) for the fair division of indivisible items that are strictly ranked by two or more players. We analyze several properties of the allocations that it yields and discuss SA's application to real-life problems, such as dividing the marital property in a divorce or assigning people to committees or projects.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.88.5.338" target="_blank">10.4169/math.mag.88.5.338</a></p>
<h3>Volume/Surface Area Ratios for Globes, with Applications</h3>
<p>Tom M. Apostol and Mamikon A. Mnatsakanian</p>
<p>We introduce families of solids called globes, having an invariant ratio of volume to surface area. An application determines the lateral surface area of an elliptical wedge in terms of its volume. We also relate surface areas and volumes of corresponding zonal slices of a spheroid and sinoid via the eccentricity of an ellipse.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.88.5.349" target="_blank">10.4169/math.mag.88.5.349</a></p>
<h3>The Parallelogram with Maximum Perimeter for Given Diagonals Is the Rhombus—A Proof Without Words and a Corollary</h3>
<p>Angel Plaza</p>
<p>By the Law of Cosines and the arithmetic mean-root mean square inequality it is proved without words that The Parallelogram with Maximum Perimeter for given Diagonals is the Rhombus. As a corollary it also proved that for two positive numbers, their arithmetic mean is greater or equal than the arithmetic mean of their geometric mean and their root mean square.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.88.5.360" target="_blank">10.4169/math.mag.88.5.360</a></p>
<h3>Crossword Puzzle: Joint Mathematics Meetings 2016</h3>
<p>Brendan W. Sullivan</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.88.5.362" target="_blank">10.4169/math.mag.88.5.362</a></p>
<h3>The Focus Locus Problem and Toric Sections</h3>
<p>Michael Gaul and Fred Kuczmarski</p>
<p>We investigate curves (foci loci) traced by the foci of one-parameter families of ellipses. The elliptical families are shadows cast by a circle. The focal paths turn out to be cross sections of tori.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.88.5.364" target="_blank">10.4169/math.mag.88.5.364</a></p>
<h3>George Hart: Troubadour for Geometry*</h3>
<p>Amy L. Reimann and David A. Reimann</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.88.5.374" target="_blank">10.4169/math.mag.88.5.374</a></p>
<h2>PROBLEMS</h2>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.88.5.377" target="_blank">10.4169/math.mag.88.5.377</a></p>
<h2>REVIEWS</h2>
<h3>Math’s effects on art; burn math class!; the hot hand is hot; system gaps</h3>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.88.5.385" target="_blank">10.4169/math.mag.88.5.385</a></p>
<h2>NEWS AND LETTERS</h2>
<h3>Acknowledgements</h3>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.88.5.387" target="_blank">10.4169/math.mag.88.5.387</a></p>
</div></div></div>Wed, 23 Mar 2016 22:10:39 +0000abranscombe743574 at http://www.maa.orghttp://www.maa.org/press/periodicals/mathematics-magazine/mathematics-magazine-contents-december-2015#comments