Mathematical Association of America
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enKnots and Borromean Rings, Rep-Tiles, and Eight Queens
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<h3>By Martin Gardner</h3>
<p>Catalog Code: MGL-04<br />
Print ISBN: 978-0-52175-871-0<br />
<!---Electronic ISBN:<br />---> 240 pp., Paperbound, 2014<br />
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Series: The New Martin Gardner Mathematical Library</p>
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<p><em>Martin Gardner's fifteen volumes about Mathematical Games are The Canon – timeless classics that are always worth reading and rereading</em>. —Don Knuth</p>
<p><em>I recommend you approach this book on a Sunday afternoon with paper and pen a few biscuits for brain-power and a good hour to spare for puzzling. It is worth it</em>. —Charlotte Mulcare, +plus Magazine</p>
<p>The hangman’s paradox, cat’s cradle, gambling, peg solitaire, pi and e—all these and more are back in Martin Gardner’s inimitable style, with updates on new developments and discoveries. Read about how knots and molecules are related; take a trip into the fourth dimension; try out new dissections of stars, crosses, and polygons; and challenge yourself with new twists on classic games.</p>
<p>This volume includes updates by Martin Gardner, Peter Renz, Greg Frederickson, and Erica Flapan. New illustrations have been included and replace some of the older illustrations. The references have been updated</p>
<h3>Table of Contents</h3>
<p style="margin-left:20px">Acknowledgements<br />
1. The Paradox of the Unexpected Hanging<br />
2. Knots and Borromean Rings<br />
3. The Transcendental Number <em>e</em><br />
4. Geometric Dissections<br />
5. Scarne on Gambling<br />
6. The Church of the Fourth Dimension<br />
7. Eight Problems<br />
8. A Matchbox Game-Learning Machine<br />
9. Spirals<br />
10. Rotations and Reflections<br />
11. Peg Solitaire<br />
12. Flatlands<br />
13. Chicago Magic Convention<br />
14. Tests of Divisibility<br />
15. Nine Problems<br />
16. The Eight Queens and Other Chessboard Diversions<br />
17. A Loop of String<br />
18. Curves of Constant Width<br />
19. Rep-Tiles: Replicating Figures on the Plane<br />
20. Thirsty-Six Catch Questions<br />
Index</p>
<!---<h3>(p. 3)</h3>
<p>
</p>--->
<h3>About the Author</h3>
<p>MAA members need no introduction to Martin Gardner. For three-quarters of a century he magically converted mathematics into play.(And, sometimes, playfully converted magic into mathematics.) His <em>Scientific American</em> columns inspired generations of mathematicians. He also made significant contributions to magic, philosophy, debunking pseudoscience, and children’s literature. He produced more than 60 books, including many best sellers, most of which are still in print, and wrote a regular column for the <em>Skeptical Inquirer</em> magazine from 1983 to 2002. His <em>Annotated Alice</em> has sold more than a million copies.</p>
<!---<h3>
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<h3>More Books in the MGL Series</h3>
<p><a href="/publications/books/hexaflexagons-probability-paradoxes-and-the-tower-of-hanoi" title="Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi">Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi</a><br />
<a href="/publications/books/origami-eleusis-and-the-soma-cube" title="Origami, Eleusis, and the Soma Cube">Origami, Eleusis, and the Soma Cube</a><br />
<a href="/publications/books/sphere-packing-lewis-carroll-and-reversi" title="Sphere Packing, Lewis Carroll, and Reversi">Sphere Packing, Lewis Carroll, and Reversi</a><br />
<a href="/publications/books/knots-and-borromean-rings-rep-tiles-and-eight-queens" title="Knots and Borromean Rings, Rep-Tiles, and Eight Queens">Knots and Borromean Rings, Rep-Tiles, and Eight Queens</a></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>Fri, 19 Sep 2014 18:39:05 +0000swebb480555 at http://www.maa.orghttp://www.maa.org/publications/books/knots-and-borromean-rings-rep-tiles-and-eight-queens#commentsMathematics Magazine Contents—June 2014
http://www.maa.org/publications/periodicals/mathematics-magazine/mathematics-magazine-contents-june-2014
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<p>Evangelista Torricelli was a master of areas and volumes. Writing in 1644, he recognized Archimedes's work on these subjects as an integrated whole. We saw Torricelli on these pages in October, 2013, and we will see him again before this year is out.<br />
<br />
This issue has articles by Andrew Leahy on Toricelli, by Scott Chapman on unique (and nonunique) factorization, by Russ Gordon on triangles with trisectible angles, and much more—including Problems, Reviews, and even a crossword puzzle.—<em style="line-height: 1.25em;">Walter Stromquist</em></p>
<p>Vol. 87, No. 3, pp. 162-239.</p>
<h5 style="font-size: 18px;"> </h5>
<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>
<h2 style="font-size: 28px;">ARTICLES</h2>
<h3 style="font-size: 24px;">A Tale of Two Monoids: A Friendly Introduction to Nonunique Factorizations</h3>
<p>Scott C. Chapman</p>
<p>Arithmetic sequences are among the most basic of structures in a discrete mathematics course. We consider here two particular arithmetic sequences: 1, 5, 9, 13, 17, . . . (<strong>H</strong>) and 4, 10, 16, 22, 28, . . .(<strong>M</strong>).</p>
<p>In addition to their additive definitions, these sequences are also multiplicatively closed. We show that both have multiplicative structures much different than that of the regular system of the integers. In particular, both fail the celebrated Fundamental Theorem of Arithmetic. While this is relatively easy to see, we will show that while factoring elements in the set <strong>H</strong> is fairly straightforward, factoring elements in <strong>M</strong> is much more complicated. This gives us a glimpse of how systems that fail the Fundamental Theorem of Arithmetic are studied and analyzed.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.3.163">http://dx.doi.org/10.4169/math.mag.87.3.163</a></p>
<h3 style="font-size: 24px;">Evangelista Torricelli and the “Common Bond of Truth” in Greek Mathematics</h3>
<p>Andrew Leahy</p>
<p>In 1664, Evangelista Torricelli published his Opera Geometrica, one of the most important—yet most unheralded—publications in the history of integral calculus. In the chapter <em>de Dimensione arabolae</em>, Torricelli uses the newfound analytic techniques of Bonaventura Cavalieri to prove, among other things, that all of the major geometrical works of Archimedes—<em>Quadrature of the Parabola</em>,<em> On the Sphere and the Cylinder</em>,<em> On Spirals</em>,<em> and On the Equilibrium of Planes</em>—are joined by a “common bond of truth.” In this article, we show how Torricelli establishes this connection and discuss briefly the impact it had on subsequent mathematicians such as John Wallis.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.3.174">http://dx.doi.org/10.4169/math.mag.87.3.174</a> </p>
<h3 style="font-size: 24px;">Outer Median Triangles</h3>
<p>Árpad Benyi and Branko Ćurgus</p>
<p>We define the notions of outer medians and outer median triangles. We show that outer median triangles enjoy similar properties to that of the median triangle.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.3.185">http://dx.doi.org/10.4169/math.mag.87.3.185</a></p>
<h3 style="font-size: 24px;">Types Theory</h3>
<p>Brendan W. Sullivan</p>
<p>Supplements to this crossword puzzle are available <a href="/publications/periodicals/mathematics-magazine/mathematics-magazine-supplements" title="Supplements to Articles in [em]Mathematics Magazine[/em]">here</a> or <a href="http://www.mathematicsmagazine.org/">here</a>.</p>
<p><span style="line-height: 1.25em;">To purchase the article fro</span>m JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.3.196">http://dx.doi.org/10.4169/math.mag.87.3.196</a> </p>
<h3 style="font-size: 24px;">Integer-Sided Triangles with Trisectible Angles</h3>
<p>Russell A. Gordon</p>
<p>We consider the problem of finding integer-sided triangles for which all three angles in the triangle can be trisected with a compass and unmarked straightedge. Since some angles (such as 60º) cannot be trisected using only these tools, some care is required to find triangles with these properties. By the law of cosines, the cosines of the angles are rational numbers (since the sides of the triangles are integers). In order for the three angles of the triangle to be trisectible, the rational cosine values must meet certain conditions. Using some elementary aspects of the theory of constructible numbers, we obtain several general methods for finding triangles that meet our conditions, then present some examples and explore a few properties of these triangles.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.3.198">http://dx.doi.org/10.4169/math.mag.87.3.198</a></p>
<h3 style="font-size: 24px;">Surprises</h3>
<p>Felix Lazebnik</p>
<p>In this article the author presents twenty-three mathematical statements that he finds surprising. Understanding most of the statements requires very modest mathematical background. The reasons why he finds them surprising are analyzed.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.3.212">http://dx.doi.org/10.4169/math.mag.87.3.212</a></p>
<h2 style="font-size: 28px;">NOTES</h2>
<h3 style="font-size: 24px;">A Solution to the Basel Problem that Uses Euclid’s Inscribed Angle Theorem</h3>
<p>David Brink</p>
<p>We present a short, rigorous solution to the Basel Problem that uses Euclid’s Inscribed Angle Theorem (Proposition 20 in Book III of the <em>Elements</em>) and can be seen as an elaboration of an idea of Leibniz communicated to Johann Bernoulli in 1696.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.3.222">http://dx.doi.org/10.4169/math.mag.87.3.222</a></p>
<h3 style="font-size: 24px;">Characterizing Power Functions by Hypervolumes of Revolution</h3>
<p>Vincent Coll and Maria Qirjollari</p>
<p>A power function is characterized by a certain constant volume ratio associated with the surface of revolution generated by the graph of the function. We generalize this characterization to include hypersurfaces of revolution and find that power functions are similarly identified by the analogous ratio of hypervolumes of revolution. We write this ratio as an explicit function of the exponent of the power function and the dimension of the hypersurface.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.3.225">http://dx.doi.org/10.4169/math.mag.87.3.225</a></p>
<h3 style="font-size: 24px;">A Pretzel for the Mind</h3>
<p>B. W. Corson</p>
<p>A variant of Laisant’s linkage-based trisector is described; its head-to-tail design has fewer parts and no slides.</p>
<p>To purchase from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.3.228">http://dx.doi.org/10.4169/math.mag.87.3.228</a> <span style="line-height: 1.25em;"> </span></p>
<h3 style="font-size: 24px;"><span style="color: rgb(196, 18, 48); font-size: 28px; line-height: 0.95em;">PROBLEMS</span></h3>
<p>Proposals 1946-1950<br />
Quickies 1041 & 1042<br />
Solutions 1921-1925</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.3.230">http://dx.doi.org/10.4169/math.mag.87.3.230</a> </p>
<h3 style="font-size: 24px;"><span style="color: rgb(196, 18, 48); font-size: 28px; line-height: 0.95em;">REVIEWS</span></h3>
<p>Sharing rent; a shady underside of lotteries; beyond Ramanujan</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.3.238">http://dx.doi.org/10.4169/math.mag.87.3.238</a></p>
</div></div></div>Thu, 26 Jun 2014 17:12:36 +0000kmerow433794 at http://www.maa.orghttp://www.maa.org/publications/periodicals/mathematics-magazine/mathematics-magazine-contents-june-2014#commentsMathematicians on Creativity
http://www.maa.org/publications/books/mathematicians-on-creativity
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<h3>Peter Borwein, Peter Liljedahl, and Helen Zhai, Editors</h3>
<p>Catalog Code: MCT<br />
Print ISBN: 978-0-88385-574-4<br />
<!---Electronic ISBN: 978-1-61444-614-9<br />--->216 pp., Paperbound, 2014<br />
List Price: $30.00<br />
MAA Member: $24.00<br />
Series: Spectrum</p>
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<p>This book aims to shine a light on some of the issues of mathematical creativity. It is neither a philosophical treatise nor the presentation of experimental results, but a compilation of reflections from top-caliber working mathematicians. In their own words, they discuss the art and practice of their work. This approach highlights creative components of the field, illustrates the dramatic variation by individual, and hopes to express the vibrancy of creative minds at work. <em>Mathematicians on Creativity</em> is meant for a general audience and is probably best read by browsing.</p>
<h3><!---Table of Contents</h3>
<p style="margin-left:20px">Preface<br />
Sample Course Outline<br />
1. Introduction to Differential Equations<br />
2. First-order Differential Equations<br />
3. Second-order Differential Equations<br />
4. Linear Systems of First-order Differential Equations<br />
5. Geometry of Autonomous Systems<br />
6. Laplace Transforms<br />
A. Answers to Odd-numbered Exercises<br />
B. Derivative and Integral Formulas<br />
C. Cofactor Method for Determinants<br />
D. Cramer’s Rule for Solving Systems of Linear Equations<br />
E. The Wronskian<br />
F. Table of Laplace Transforms<br />
Index<br />
About the Author</p>---><!---<h3>Excerpt: (p. 1)
</h3>
<p>
</p>---></h3>
<h3>About the Editors</h3>
<p><strong>Peter Borwein</strong> is the founding Project Leader and currently an Executive Co-Director of the IRMACS Centre. He is a Burnaby Mountain Chair at Simon Fraser University and has been a professor in the mathematics department since 1993 when he moved from Dalhousie University. He is also an adjunct professor in computing science. His research interests span various aspects of mathematics and computer science, health and criminology modelling and visualization.</p>
<p><strong>Peter Liljedahl</strong> is an associate professor of mathematics education in the Faculty of Education, an associate member in the department of mathematics, and co-director of the David Wheeler Institute for Research in Mathematics Education at Simon Fraser University in Vancouver, Canada. His research interests are creativity, insight, and discovery in mathematics teaching and learning; the role of the affective domain on the teaching and learning of mathematics; the professional growth of mathematics teachers; mathematical problem solving; and numeracy.</p>
<p><strong>Helen Zhai</strong> graduated with a BSc in mathematics and Bed from Simon Fraser University. She has received undergraduate NSERC grants, one of which initiated her collaboration with Peter Borwein and Peter Liljedahl in their work on creativity in mathematics teaching and learning.</p>
<!--- <h3>
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http://www.maa.org/publications/ebooks/game-theory-through-examples
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><h2>Erich Prisner</h2>
<hr />
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<p><strong>Game Theory Through Examples</strong> is a thorough introduction to elementary game theory, covering finite games with complete information.</p>
<p>The core philosophy underlying this volume is that abstract concepts are best learned when encountered first (and repeatedly) in concrete settings. Thus, the essential ideas of game theory are here presented in the context of actual games, real games much more complex and rich than the typical toy examples. All the fundamental ideas are here: Nash equilibria, backward induction, elementary probability, imperfect information, extensive and normal form, mixed and behavioral strategies. The active-learning, example-driven approach makes the text suitable for a course taught through problem solving. Students will be thoroughly engaged by the extensive classroom exercises, compelling homework problems and nearly sixty projects in the text. Also available are approximately eighty Java applets and three dozen Excel spreadsheets in which students can play games and organize information in order to acquire a gut feeling to help in the analysis of the games. Mathematical exploration is a deep form of play, that maxim is embodied in this book.</p>
<p><strong>Game Theory Through Examples</strong> is a lively introduction to this appealing theory. Assuming only high school prerequisites makes the volume especially suitable for a liberal arts or general education spirit-of-mathematics course. It could also serve as the active-learning supplement to a more abstract text in an upper-division game theory course.</p>
<p>This book is only available in an electronic edition. Both the Excel spreadsheets and the applets are accessed through links in the book. You can download the Excel spreadsheets <a href="/sites/default/files/pdf/ebooks/GameTheory_Excel.zip">here</a> if you wish to have them on your hard drive.</p>
<p>A <a href="/sites/default/files/pdf/ebooks/GTE_sample.pdf">sample PDF</a> can be downloaded that contains the front matter, contents, chapters 1 and 2, the bibliography, and the index.</p>
<p>Electronic ISBN: 9781614441151</p>
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http://www.maa.org/publications/books/ordinary-differential-equations-from-calculus-to-dynamical-systems
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<h3>By V.W. Noonburg</h3>
<p>Catalog Code: FCDS<br />
Print ISBN: 978-1-93951-204-8<br />
Electronic ISBN: 978-1-61444-614-9<br />
334 pp., Hardbound, 2014<br />
List Price: $60.00<br />
MAA Member: $48.00<br />
Series: MAA Textbooks</p>
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<p>This book presents a modern treatment of material traditionally covered in the sophomore-level course in ordinary differential equations. While this course is usually required for engineering students the material is attractive to students in any field of applied science, including those in the biological sciences.</p>
<p>The standard analytic methods for solving first and second-order differential equations are covered in the first three chapters. Numerical and graphical methods are considered, side-by-side with the analytic methods, and are then used throughout the text. An early emphasis on the graphical treatment of autonomous first-order equations leads easily into a discussion of bifurcation of solutions with respect to parameters.</p>
<p>The fourth chapter begins the study of linear systems of first-order equations and includes a section containing all of the material on matrix algebra needed in the remainder of the text. Building on the linear analysis, the fifth chapter brings the student to a level where two-dimensional nonlinear systems can be analyzed graphically via the phase plane. The study of bifurcations is extended to systems of equations, using several compelling examples, many of which are drawn from population biology. In this chapter the student is gently introduced to some of the more important results in the theory of dynamical systems. A student project, involving a problem recently appearing in the mathematical literature on dynamical systems, is included at the end of Chapter 5.</p>
<p>A full treatment of the Laplace transform is given in Chapter 6, with several of the examples taken from the biological sciences. An appendix contains completely worked-out solutions to all of the odd-numbered exercises.</p>
<p>The book is aimed at students with a good calculus background that want to learn more about how calculus is used to solve real problems in today's world. It can be used as a text for the introductory differential equations course, and is readable enough to be used even if the class is being "flipped." The book is also accessible as a self-study text for anyone who has completed two terms of calculus, including highly motivated high school students. Graduate students preparing to take courses in dynamical systems theory will also find this text useful.</p>
<h3>Table of Contents</h3>
<p style="margin-left:20px">Preface<br />
Sample Course Outline<br />
1. Introduction to Differential Equations<br />
2. First-order Differential Equations<br />
3. Second-order Differential Equations<br />
4. Linear Systems of First-order Differential Equations<br />
5. Geometry of Autonomous Systems<br />
6. Laplace Transforms<br />
A. Answers to Odd-numbered Exercises<br />
B. Derivative and Integral Formulas<br />
C. Cofactor Method for Determinants<br />
D. Cramer’s Rule for Solving Systems of Linear Equations<br />
E. The Wronskian<br />
F. Table of Laplace Transforms<br />
Index<br />
About the Author</p>
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<h3>About the Author</h3>
<p><strong>V.W. Noonburg</strong>, better known by her middle name Anne, has enjoyed a somewhat varied professional career. It began with a B.A. in mathematics from Cornell University, followed by a four-year stint as a computer programmer at the knolls Atomic Power Lab near Schenectady, New York. After returning to Cornell and earning a Ph.D. in mathematics, she taught first at Vanderbilt University in Nashville, Tennessee and then at the University of Hartford in West Hartford, Connecticut (from which she has recently retired as professor emerita). During the late 1980s she twice taught as a visiting professor at Cornell, and also earned a Cornell M.S. Eng. degree in computer science.</p>
<p>It was during the first sabbatical at Cornell that she was fortunate to meet John Hubbard and Beverly West as they were working on a mold-breaking book on differential equations (<em>Differential Equations: A Dynamical Systems Approach, Part I</em>, Springer Verlag, 1990). She also had the good fortune to be able to sit in on a course given by John Guckenheimer and Philip Holmes, in which they were using their newly written book on dynamical systems (<em>Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields</em>, Springer-Verlag, 1983). All of this, together with being one of the initial members of the C-ODE-E group founded by Bob Borrelli and Courtney Coleman at Harvey Mudd College, led to a lasting interest in the learning and teaching of ordinary differential equations. This book is the result.</p>
<h3>MAA Review</h3>
<p>All of us have our favorite books in various areas of mathematics, and when it comes to elementary differential equations my favorite was <em>Differential Equations</em> by Blanchard, Devaney, and Hall (hereinafter BDH). There were several things that I particularly liked about the book, which struck me as somewhat less “cookbooky” than the typical sophomore ODE text at this level. I particularly appreciated, for example, the emphasis in BDH on the dynamical system approach, which struck me as a good way to learn the subject, and I also liked the fact that BDH addressed certain little things that other books often gloss over: for example, in the discussion of variables-separable equations, BDH acknowledges that “multiplying” the equation \( dy/dx = f(x)g(y) \) by \(dx\) is something that raises some concerns, and discusses a justification for the process.</p>
<p>I think, however, that the book under review has now edged out BDH as my favorite basic ODE text. As will be shortly noted, the things that I like about BDH are also present here, but this book also remedies what I thought was the one significant problem with using BDH as a text: its price.<span style="font-size: 13px; line-height: 13px;"> </span><a href="/node/413078" target="_blank">Continued...</a></p>
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<a href="/tags/ordinary-differential-equations">Ordinary Differential Equations</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/maa-textbooks">MAA Textbooks</a></div></div></div>Fri, 02 May 2014 18:27:57 +0000swebb396493 at http://www.maa.orghttp://www.maa.org/publications/books/ordinary-differential-equations-from-calculus-to-dynamical-systems#commentsMath Horizons Contents—April 2014
http://www.maa.org/publications/periodicals/math-horizons/math-horizons-contents-april-2014
<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/mh-april2014-cover.JPG" style="margin-right: 5px; margin-left: 5px; float: left; width: 195px; height: 250px;" /></p>
<p>I'm pleased to announce that the April issue of <a href="/publications/periodicals/math-horizons" title="Math Horizons"><em>Math Horizons</em></a> is now online. In the cover story, Julie Barnes, Tom Koehler, and Beth Schaubroeck show how to use multivariable calculus to compute upper-level wind speeds and to predict airline flight times. Andrew Simoson writes about how Bilbo Baggins determined when he and the Company should arrive at the Lonely Mountain. Matt Koetz, Heather A. Lewis, and Mark McKinzie present humorous rewordings of the standard theorems of undergraduate mathematics. And—for those readers wanting more mathematics—eight experts recommend books to read this summer in the long wait between the April and September issues of <em>Math Horizons</em>. I encourage you to read all the fascinating articles on mathematics and the culture of mathematics in this month's issue.—<em>David Richeson, editor</em></p>
<p>Volume 21, Issue 4</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>
<h3 style="font-size: 24px;">Fly with the Wind</h3>
<p>Julie Barnes, Tom Koehler, and Beth Schaubroeck</p>
<p>Use multivariable calculus to calculate wind speed and estimate airline flight times. <span style="line-height: 1.25em;">(</span><a href="/sites/default/files/pdf/horizons/wind_april14.pdf" style="font-size: 12px; line-height: 1.25em;">pdf</a><span style="line-height: 1.25em;">)</span></p>
<p>JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons/21.4.10">http://dx.doi.org/10.4169/mathhorizons/21.4.10</a></p>
<h3 style="font-size: 24px;">Bilbo and the Last Moon of Autumn</h3>
<p>Andrew Simoson</p>
<p>Bilbo uses mathematics to get the hobbits to the Lonely Mountain by Durin’s Day—the last full moon of autumn.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons.21.4.5">http://dx.doi.org/10.4169/mathhorizons.21.4.5</a></p>
<h3 style="font-size: 24px;">Colorful Symmetries</h3>
<p>Brian Bargh, John Chase, and Matthew Wright</p>
<p>Burnside’s lemma is the key to solving one of Google’s colorful <span style="line-height: 1.25em;">puzzles.</span></p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons.21.4.14">http://dx.doi.org/10.4169/mathhorizons.21.4.14</a></p>
<h3 style="font-size: 24px;">Do the Math: TracTricks</h3>
<p>Burkhard Polster</p>
<p>Teach the classical tractrix curve some new tricks.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons.21.4.18">http://dx.doi.org/10.4169/mathhorizons.21.4.18</a></p>
<h3 style="font-size: 24px;">The Bookshelf: Summer Reading List</h3>
<p>Looking for a good book to read when school lets out? Allan Rossman, Jim Wiseman, David Kung, Jim <span style="line-height: 1.25em;">Wilder, Pam Pierce, Marc Chamberland, Tim Chartier, and David Richeson recommend their favorites.</span></p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons.21.4.20">http://dx.doi.org/10.4169/mathhorizons.21.4.20</a></p>
<h3 style="font-size: 24px;">X Goes First: Wild Tales of a Tic-Tac-Toe Grandmaster</h3>
<p>Bryan Clair</p>
<p>A lively dialogue about the not-so-trivial mathematics behind this <span style="line-height: 1.25em;">children’s game.</span></p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons.21.4.23">http://dx.doi.org/10.4169/mathhorizons.21.4.23</a></p>
<h3 style="font-size: 24px;">Bovino-Weierstrass and Other Fractured Theorems</h3>
<p>Matt Koetz, Heather A. Lewis, and Mark McKinzie</p>
<p>Humorous rewordings of the theorems of undergraduate mathematics.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons.21.4.26">http://dx.doi.org/10.4169/mathhorizons.21.4.26</a></p>
<h3 style="font-size: 24px;">The View from Here: Anonymity—A Thing of the Past?</h3>
<p>Elizabeth DeCarlo describes her work in a computational linguistics <span style="line-height: 1.25em;">lab determining the authorship of disputed works.</span></p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons.21.4.28">http://dx.doi.org/10.4169/mathhorizons.21.4.28</a></p>
<h2 style="font-size: 28px;">THE PLAYGROUND!</h2>
<p>The <em>Math Horizons</em> problem section, edited by Gary Gordon</p>
<p>JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons.21.4.30">http://dx.doi.org/10.4169/mathhorizons.21.4.30</a></p>
<h3 style="font-size: 24px;">AFTERMATH: Every Math Major Should Take a Public-Speaking Course</h3>
<p>Rachel Levy argues that all mathematics majors should learn the art <span style="line-height: 1.25em;">of public speaking.</span></p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons.21.4.34">http://dx.doi.org/10.4169/mathhorizons.21.4.34</a></p>
</div></div></div>Wed, 02 Apr 2014 14:30:54 +0000kmerow373009 at http://www.maa.orghttp://www.maa.org/publications/periodicals/math-horizons/math-horizons-contents-april-2014#commentsTextbooks, Testing, Training: How We Discourage Thinking
http://www.maa.org/publications/ebooks/textbooks-testing-training-how-we-discourage-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>Stephen S. Willoughby</h2>
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<p><em>Willoughby's essay is a gem. It should be in the hands of every young teacher. I wish that I had read it many years ago. I have no doubt that many of his observations and the information he imparts will remain with me for a while. I certainly hope so. A collection of reminiscences from other teachers with their valuable insights and experiences (who could write with such expertise as he does) would make a fine addition to the education literature.</em> — James Tattersall, Providence College</p>
<p>Stephen S. Willoughby has taught mathematics for 59 years and he has seen everything. Some of it has annoyed him, some has inspired him. This little book is something of a valedictory and he shares some parting thoughts as he contemplates the end of his teaching career. Willoughby has strong, cogent and mostly negative opinions about textbooks, standardized testing, and teacher training. These opinions have been forged in the cauldron of the classroom of a deeply caring teacher. They might not please you, but they ought to make you think. They should spark needed debate in our community. Ultimately this is a human tale with rough parallels to Hardy's Apology; replace "Mathematician's" with "Teacher's" perhaps. Every teacher will sympathize with Willoughby's frustrations and empathize with the humanity and compassion that animated his life's work and that beat at the center of this book.</p>
<p>Print on demand (POD) books are not returnable because they are printed at your request. The POD version of this book is saddle stitched. Damaged books will, of course, be replaced (customer support information will be on your receipt).</p>
<p>Electronic edition ISBN: 9781614448037</p>
<p>Paperbound ISBN: 9780883859148</p>
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<a href="/tags/teaching-mathematics">Teaching Mathematics</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/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/new">New</a></div><div class="field-item odd"><a href="/ebook-category/popular-exposition">Popular Exposition</a></div><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/teacher-education">Teacher Education</a></div></div></div>Mon, 10 Mar 2014 21:50:58 +0000bruedi352504 at http://www.maa.orghttp://www.maa.org/publications/ebooks/textbooks-testing-training-how-we-discourage-thinking#comments101 Careers in Mathematics
http://www.maa.org/publications/books/101-careers-in-mathematics
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<div><img alt="101 Careers in Mathematics, 3rd Edition" src="/sites/default/files/images/pubs/books/covers/OCM-3cover.jpg" style="height: 268px; width: 180px; border-width: 1px; border-style: solid;" title="101 Careers in Mathematics, 3rd Edition" /></div>
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<h3>Andrew Sterrett, Editor</h3>
<p>3rd Edition<br />
Catalog Code: OCM-3<br />
Print ISBN: 978-0-88385-786-1<br />
Electronic ISBN: 978-1-61444-116-8<br />
334 pp., Paperbound, 2014<br />
List Price: $35.00<br />
MAA Member: $28.00<br />
Series: Classroom Resource Materials</p>
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<p>This third edition of the immensely popular,<em> 101 Careers in Mathematics</em>, contains updates on the career paths of individuals profiled in the first and second editions, along with many new profiles. No career counselor should be without this valuable resource.</p>
<p>The authors of the essays in this volume describe a wide variety of careers for which a background in the mathematical sciences is useful. Each of the jobs presented shows real people in real jobs. Their individual histories demonstrate how the study of mathematics was useful in landing well-paying jobs in predictable places such as IBM, AT&T, and American Airlines, and in surprising places such as FedEx Corporation, L.L. Bean, and Perdue Farms, Inc. You will also learn about job opportunities in the Federal Government as well as exciting careers in the arts, sculpture, music, and television. There are really no limits to what you can do if you are well prepared in mathematics.</p>
<p>The degrees earned by the authors profiled here range from bachelor’s to master’s to PhD in approximately equal numbers. Most of the writers use the mathematical sciences on a daily basis in their work. Others rely on the general problem-solving skills acquired in mathematics as they deal with complex issues.</p>
<!---<h3>
Table of Contents</h3>
<p style="margin-left:20px">
Preface<br />
</p>--->
<h3>Excerpt: Amanda Quiring, Project Manager (p.206)</h3>
<p>‘Oh, so you’re both good with numbers!’ I’m an accountant and my twin sister is a math teacher and I can’t tell you how many times I’ve heard that statement. Although the comment considerably understates the nature, diversity and complexity of both accounting and mathematics, there is some truth behind it. The skill set that I developed in my math degree has been extremely useful as I have pursued a career as an accountant.</p>
<p>In my role as a project manager at the International Accounting Standards Board, I spend the majority of my time researching complex accounting issues and writing papers with my related analyses and proposed solutions. Without even realizing it, I find myself applying the same approach to my work as I would to a mathematical proof¬—laying out all of the known relevant information, fitting it together in a logical order, and ending up with an understandable solution to a complex problem.</p>
<p>My mathematical background also has been useful in studying academic research related to accounting. While I have seen some people’s eyes glaze over when they flip through the pages of statistical analyses, I am able to approach the research with confidence and with a passion for understanding the mathematical tests performed as well as the accounting implications. My mathematical background has given me a great foundation should I decide to pursue a PhD in accounting.</p>
<p>I would highly recommend a math degree (or a double-major in math and another field) to anyone who is considering a career that requires problem-solving and logic skills. I came really close to not majoring in math. In fact, my first week of college I was so convinced that I wasn't going to pursue a math degree that I dropped out of Calculus III. However, thanks to the persistence of one of my math professors, I signed up for the course again the next year and the rest is history. Even though it was extremely challenging and I had to take summer classes in order to graduate in four years, it is a decision that I never have regretted.</p>
<h3>MAA Review</h3>
<p>This is a wonderful book, potentially of great value to students and those who advise them. It has some frustrating gaps too, but in a way they also emphasize how useful it is and could be. In brief, this book presents a collection of profiles of people who have (or had) a career that involves some aspect of mathematics. Nearly all the people here have at least one degree in mathematics; the few exceptions have degrees in field like physics, operations research, or a statistics-related area. Short essays at the end of the book discuss the processes of interviewing and finding a job, and what it’s like to work in industry (or, more broadly, outside the academic community).</p>
<p>There are 25 new entries in this new edition that bring the total number of profiles to 146. The “101 Careers” of the title is best regarded as meaning “lots of careers”; even the first edition had more than 101 profiles. Counting careers is also a little funny: they don’t match up one-to-one with people. As many of the profiles demonstrate, many people have more than one career. Indeed it is increasingly uncommon for people to have a single career throughout their lives. <a href="/publications/maa-reviews/101-careers-in-mathematics-1" target="_blank" title="101 Careers in Mathematics">Continued...</a></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/classroom-resource-materials">Classroom Resource Materials</a></div></div></div>Wed, 05 Mar 2014 15:28:51 +0000swebb349084 at http://www.maa.orghttp://www.maa.org/publications/books/101-careers-in-mathematics#commentsCollege Mathematics Journal Contents—March 2014
http://www.maa.org/publications/periodicals/college-mathematics-journal/college-mathematics-journal-contents-march-2014
<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/cmj_march2014.jpg" style="width: 175px; height: 250px; float: left; margin-left: 5px; margin-right: 5px;" /></p>
<p>The March issue of <em>The College Mathematics Journal</em> features an abundance of student authors and several articles on algebraic topics. In that intersection, Arthur Benjamin and Ethan Brown (who was in middle school when they wrote the article) help prepare us for the upcoming Mathematics Awareness Month on "Mathematics, Magic, and Mystery." The cover art resonates with two articles: the quartet Field, Ivison, Reyher, and Warner help you determine the best direction to run from an oncoming truck, while trio Bolt, Meyer, and Visser consider how to run fast without ever breaking a four minute mile (six of those seven authors are students). Keep reading for topics ranging from permutations and matroids to golden triangles and cookies. <span style="line-height: 1.25em;">—</span><em style="line-height: 1.25em;">Brian Hopkins</em><span style="line-height: 1.25em;"> </span></p>
<p>Vol. 45, No. 2, pp. 82-159.</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>
<h2 style="font-size: 28px;">
FROM THE EDITOR</h2>
<h3 style="font-size: 24px;">
Anonymity and Youth</h3>
<p>Brian Hopkins</p>
<p>JSTOR: <a href="http://dx.doi.org/10.4169/college.math.j.45.2.082">http://dx.doi.org/10.4169/college.math.j.45.2.082</a></p>
<h2 style="font-size: 28px;">
ARTICLES</h2>
<h3 style="font-size: 24px;">
Power Series for Up-Down Min-Max Permutations</h3>
<p>Fiacha Heneghan and T. Kyle Petersen</p>
<p>Calculus and combinatorics overlap, in that power series can be used to study combinatorially defined sequences. In this paper, we use exponential generating functions to study a curious refinement of the Euler numbers, which count the number of “up-down” permutations of length <em>n</em>.</p>
<p>JSTOR: <a href="http://dx.doi.org/10.4169/college.math.j.45.2.083">http://dx.doi.org/10.4169/college.math.j.45.2.083</a></p>
<h3 style="font-size: 24px;">
Challenging Magic Squares for Magicians</h3>
<p>Arthur T. Benjamin and Ethan J. Brown</p>
<p>We present several effective ways for a magician to create a 4-by-4 magic square where the total and some of the entries are prescribed by the audience.</p>
<p>JSTOR: <a href="http://dx.doi.org/10.4169/college.math.j.45.2.092">http://dx.doi.org/10.4169/college.math.j.45.2.092</a></p>
<h3 style="font-size: 24px;">
The Fastest Way Not to Run a Four-Minute Mile</h3>
<p>Michael Bolt, Anthony Meyer, and Nicholas Visser</p>
<p>In this manuscript we present the mathematics that is needed to answer three counterintuitive problems related to the averaging of functions. The problems are manifestations of the question, “Is the average rate of change on a given interval determined by the average rate of change on subintervals of a fixed length?” We also ask questions in higher dimensions that may have interesting geometric significance.</p>
<p>JSTOR: <a href="http://dx.doi.org/10.4169/college.math.j.45.2.101">http://dx.doi.org/10.4169/college.math.j.45.2.101</a></p>
<h3 style="font-size: 24px;">
Classifying Nilpotent Maps via Partition Diagrams</h3>
<p>Nicholas Loehr</p>
<p>This note uses a visual analysis of partition diagrams to give an elementary, pictorial proof of the classification theorem for nilpotent linear maps. We show that any nilpotent map is represented by a matrix with ones in certain positions on the first super-diagonal and zeroes elsewhere.</p>
<p>JSTOR: <a href="http://dx.doi.org/10.4169/college.math.j.45.2.108">http://dx.doi.org/10.4169/college.math.j.45.2.108</a></p>
<h3 style="font-size: 24px;">
PROOF WITHOUT WORDS: Componendo et Dividendo, a Theorem on Proportions</h3>
<p>Yukio Kobayashi</p>
<p>We provide a geometric proof of a classical result on proportions.</p>
<p>JSTOR: <a href="http://dx.doi.org/10.4169/college.math.j.45.2.120">http://dx.doi.org/10.4169/college.math.j.45.2.120</a></p>
<h3>
Truck Versus Human: Mathematics Under Pressure</h3>
<p>Elizabeth Field, Rachael Ivison, Amanda Reyher, and Steven Warner</p>
<p>If you are ever faced with an oncoming truck, this paper could save your life. We investigate the optimal path that you should take from the middle of the road to the curb in order to avoid being hit by an oncoming truck. Although your instincts may tell you to run directly toward the curb, it turns out that this path, although the shortest, is not generally the safest.</p>
<p>JSTOR: <a href="http://dx.doi.org/10.4169/college.math.j.45.2.116">http://dx.doi.org/10.4169/college.math.j.45.2.116</a></p>
<h3 style="font-size: 24px;">
Proof Without Words: An Infinite Series Using Golden Triangles</h3>
<p>Steven Edwards</p>
<p>We give a visual proof of an infinite series involving the golden ratio.</p>
<p>JSTOR: <a href="http://dx.doi.org/10.4169/college.math.j.45.2.120">http://dx.doi.org/10.4169/college.math.j.45.2.120</a> </p>
<h3 style="font-size: 24px;">
Matroids on Groups?</h3>
<p>Jeremy S. LeCrone and Nancy Ann Neudauer</p>
<p>By carefully defining independence, we create two structures on a finite group that satisfy the matroid axioms. Both of these matroids are transversal and graphic, they are duals of each other, and are fundamental transversal matroids. The matroids capture some of the group structure, but two isomorphic matroids may have come from non-isomorphic groups, so we may not be able to recapture the group from the matroid. Our definitions of independent sets cannot be extended in what seems the natural way based on independence of vectors. Finding a definition of independence that satisfies the matroid axioms may not always be possible, though there are always more possibilities on the horizon.</p>
<p>JSTOR: <a href="http://dx.doi.org/10.4169/college.math.j.45.2.121">http://dx.doi.org/10.4169/college.math.j.45.2.121</a></p>
<h3>
Cookie Monster Devours Naccis</h3>
<p>Leigh Marie Braswell and Tanya Khovanova</p>
<p>The Cookie Monster wants to empty a set of jars filled with various numbers of cookies. On each of his moves, he may choose any subset of jars and take the same number of cookies from each of those jars. The minimal number of moves to accomplish this depends on the initial distribution of cookies in the jars. We discuss bounds of these Cookie Monster numbers and explicitly find them for jars containing numbers of cookies in the Fibonacci, Tribonacci, and other nacci sequences.</p>
<p>JSTOR: <a href="http://dx.doi.org/10.4169/college.math.j.45.2.129">http://dx.doi.org/10.4169/college.math.j.45.2.129</a></p>
<h3 style="font-size: 24px;">
Proof Without Words: The Difference of Consecutive Integer Cubes Is Congruent to 1 Modulo 6</h3>
<p>Claudi Alsina, Roger Nelsen, and Hasan Unal</p>
<p>We prove wordlessly that the difference of consecutive integer cubes is congruent to 1 modulo 6.</p>
<p>JSTOR: <a href="http://dx.doi.org/10.4169/college.math.j.45.2.135">http://dx.doi.org/10.4169/college.math.j.45.2.135</a></p>
<h3 style="font-size: 24px;">
A Single Family of Semigroups with Every Positive Rational Commuting Probability</h3>
<p>Michelle Soule</p>
<p>A semigroup is a set with an associative binary operation (which may not contain an identity element). The <em>commuting probability </em>of a semigroup is the probability that two elements chosen at random commute with each other. In this paper, we construct a single family of semigroups which achieves each positive rational in the interval (0, 1] as a commuting probability.</p>
<p>JSTOR: <a href="http://dx.doi.org/10.4169/college.math.j.45.2.136">http://dx.doi.org/10.4169/college.math.j.45.2.136</a></p>
<h3 style="font-size: 24px;">
<span style="color: rgb(196, 18, 48); font-size: 28px; line-height: 0.95em;">CLASSROOM CAPSULES</span></h3>
<h3>
On the Differentiation Formulae for Sine, Tangent, and Inverse Tangent</h3>
<p>Daniel McQuillan and Rob Poodiack</p>
<p>We prove the derivative formula for sine via a geometric argument and the symmetric derivative, and then use similar techniques for tangent and inverse tangent.</p>
<p>JSTOR: <a href="http://dx.doi.org/10.4169/college.math.j.45.2.140">http://dx.doi.org/10.4169/college.math.j.45.2.140</a></p>
<h3 style="font-size: 24px;">
A Proof for a Quadratic Function without Using Calculus</h3>
<p>Connie Xu</p>
<p>We strengthen a result on tangent lines of parabolas, originally proved with Taylor series, without making use of calculus.</p>
<p>JSTOR: <a href="http://dx.doi.org/10.4169/college.math.j.45.2.143">http://dx.doi.org/10.4169/college.math.j.45.2.143</a></p>
<h2 style="font-size: 28px;">
PROBLEMS AND SOLUTIONS</h2>
<p>Problems 1021-1025<br />
Solutions 996-1000</p>
<p>JSTOR: <a href="http://dx.doi.org/10.4169/college.math.j.45.2.145">http://dx.doi.org/10.4169/college.math.j.45.2.145</a></p>
<h2 style="font-size: 28px;">
MEDIA HIGHLIGHTS</h2>
<p>JSTOR: <a href="http://dx.doi.org/10.4169/college.math.j.45.2.152">http://dx.doi.org/10.4169/college.math.j.45.2.152</a></p>
</div></div></div>Tue, 18 Feb 2014 17:24:10 +0000kmerow336550 at http://www.maa.orghttp://www.maa.org/publications/periodicals/college-mathematics-journal/college-mathematics-journal-contents-march-2014#commentsAmerican Mathematical Monthly Contents—March 2014
http://www.maa.org/publications/periodicals/american-mathematical-monthly/american-mathematical-monthly-contents-march-2014
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p class="rtecenter" style="font-size: 14px;"><img alt="" src="/sites/default/files/images/pubs/amm_logo2014.jpg" style="width: 400px; height: 70px;" /></p>
<p>March clearly comes in like a lion in this month’s <em>Monthly</em>. We honor Pi Day with a special article by <em>Monthly</em> Associate Editor Jon Borwein and David Bailey: "Pi Day Is Upon Us Again and We Still Do Not Know if Pi Is Normal." This paper is based on an annual lecture that Professor Borwein gives at his home institution in Australia which has gained a “cult” following. We also honor Joan Leitzel, the winner of the 2014 Gung and Hu Award for distinguished service to mathematics.</p>
<p>In our Notes section, don’t miss Bill Johnston’s student-friendly proof that the weighted Hermite polynomials form a basis for $$L^2(\mathbb{R})$$. Mark Kozek reviews <em>Mathematics in Popular Culture: Essays on Appearances in Film, Fiction, 274 Games, Television and Other Media</em> by Jessica Sklar and Elizabeth Sklar. Need something to do over Spring Break? Take our Problem Section along for the ride. Stay tuned for the April edition when Andrew Simoson shows us when to expect the next transit of Venus. <span style="line-height: 1.25em;">—</span><em style="line-height: 1.25em;">Scott Chapman</em></p>
<div>
<p style="font-size: 14px;">Vol. 121, No. 3, pp.187-278.</p>
<h5 style="font-size: 18px;">
JOURNAL SUBSCRIBERS AND MAA MEMBERS:</h5>
<p style="font-size: 14px;">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>
<h3>
Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2014 to Joan Leitzel for Distinguished Service to Mathematics</h3>
<p>Kenneth A. Ross and Ann E. Watkins</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/amer.math.monthly.121.03.187">http://dx.doi.org/10.4169/amer.math.monthly.121.03.187</a></p>
<h2 style="font-size: 28px;">
ARTICLES</h2>
<h3 style="font-size: 24px;">
Pi Day Is Upon Us Again and We Still Do Not Know if Pi Is Normal</h3>
<p>David H. Bailey and Jonathan Borwein</p>
<div>
<p>The digits of $$\pi$$ have intrigued both the public and research mathematicians from the beginning of time. This article briefly reviews the history of this venerable constant, and then describes some recent research on the question of whether $$\pi$$ is normal, or, in other words, whether its digits are statistically random in a specific sense.</p>
</div>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/amer.math.monthly.121.03.191">http://dx.doi.org/10.4169/amer.math.monthly.121.03.191</a> <span style="font-size: 16px; line-height: 18px;">(</span><a href="/sites/default/files/pdf/pubs/BaileyBorweinPiDay.pdf" style="line-height: 18px;"><span class="style5">pdf</span></a><span style="font-size: 16px; line-height: 18px;">)</span></p>
<h3 style="font-size: 24px;">
The Length of Spirographic Curves</h3>
<p>Stephan Berendonk</p>
<p>In this note we will show, by elementary means, that we can express the length of curves drawn with a spirograph in terms of the perimeter of certain ellipses. We will present the proof in the language of Euclidean geometry.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/amer.math.monthly.121.03.207">http://dx.doi.org/10.4169/amer.math.monthly.121.03.207</a></p>
<h3>
Martin Gardner’s Minimum No-3-in-a-Line Problem</h3>
<p>Alec S. Cooper, Oleg Pikhurko, John R. Schmitt, and Gregory S.Warrington</p>
<p>In Martin Gardner’s October 1976 Mathematical Games column in <em>Scientific American</em>, he posed the following problem: “What is the smallest number of [queens] you can put on an [$$n\times n$$ chessboard] such that no [queen] can be added without creating three in a row, a column, or, except in the case when $$n$$ is congruent to 3 modulo 4, in which case one less may suffice.” We use the Combinatorial Nullstellensatz to prove that this number is at least $$n$$. A second, more elementary proof is also offered in the case that $$n$$ is even. </p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/amer.math.monthly.121.03.213">http://dx.doi.org/10.4169/amer.math.monthly.121.03.213</a></p>
<h3 style="font-size: 24px;">
Level Sets on Disks</h3>
<p>Aleksander Maliszewski and Marcin Szyszkowski</p>
<p>We prove that every continuous function from a disk to the real line has a level set containing a connected component of diameter at least $$\sqrt{3}$$<img src="file:///C:/Users/kmerow/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" />. We also show that if the disk is split into two sets—one open and the other closed—then one of them contains a component of diameter at least $$\sqrt{3}$$<img src="file:///C:/Users/kmerow/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" />.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/amer.math.monthly.121.03.222">http://dx.doi.org/10.4169/amer.math.monthly.121.03.222</a></p>
<h3 style="font-size: 24px;">
Series Involving the Zeta Functions and a Family of Generalized Goldbach–Euler Series</h3>
<p>Junesang Choi and Hari M. Srivastava</p>
<p>We first present the corrected expression for a certain widely-recorded generalized Goldbach–Euler series. The corrected forms are then shown to be connected with the problem of closed-form evaluation of series involving the Zeta functions, which happens to be an extensively-investigated subject since the time of Euler as (for example) in the classical three-century old-Goldbach theorem.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/amer.math.monthly.121.03.229">http://dx.doi.org/10.4169/amer.math.monthly.121.03.229</a></p>
<h3 style="font-size: 24px;">
Mathbit: A Polynomial Parent to a Fibonacci–Lucas Relation</h3>
<p>B. Sury</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/amer.math.monthly.121.03.236">http://dx.doi.org/10.4169/amer.math.monthly.121.03.236</a></p>
<h3 style="font-size: 24px;">
A Wallis Product on Clovers</h3>
<p>Trevor Hyde</p>
<p>The $$m$$-clover is the plane curve defined by the polar equation $$r^{m/2}=\cos{\left(\frac{m}{2}\theta\right)}$$. In this article we extend a well-known derivation of the Wallis product to derive a generalized Wallis product for arc lengths of $$m$$-clovers.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/amer.math.monthly.121.03.237">http://dx.doi.org/10.4169/amer.math.monthly.121.03.237</a></p>
<h2 style="font-size: 28px;">
NOTES</h2>
<h3 style="font-size: 24px;">
On Some Power Sums of Sine or Cosine</h3>
<p>Mircea Merca</p>
<p>In this note, using the multisection series method, we establish the formulas for various power sums of sine or cosine functions.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/amer.math.monthly.121.03.244">http://dx.doi.org/10.4169/amer.math.monthly.121.03.244</a></p>
<h3>
The Weighted Hermite Polynomials Form a Basis for $$L^{2}(\mathbb{R})$$</h3>
<p>William Johnston</p>
<p>We present a student-friendly proof that the weighted Hermite polynomials form a complete orthonormal system (a basis) for the collection <img src="file:///C:/Users/kmerow/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" />of $$L^{2}(\mathbb{R})$$ real-valued functions.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/amer.math.monthly.121.03.249">http://dx.doi.org/10.4169/amer.math.monthly.121.03.249</a></p>
<h3 style="font-size: 24px;">
A Proof of Lie’s Product Formula</h3>
<p>Gerd Herzog</p>
<p>For $$d\times d$$ matrices $$A$$, $$B$$ and entire functions $$f$$, $$g$$ with $$f(0) = g(0) = 1$$, we give an elementary proof of the formula</p>
<p>$$\lim_{k\to\infty}(f(A/k)g)(B/k))^{k}=\exp (f'(0)A+g'(0)B)$$</p>
<p><img src="file:///C:/Users/kmerow/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif" /><img src="file:///C:/Users/kmerow/AppData/Local/Temp/msohtmlclip1/01/clip_image006.gif" /><span style="line-height: 1.25em;">For the case $$f = g = \exp$$, this is Lie’s famous product formula for matrices.</span></p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/amer.math.monthly.121.03.254">http://dx.doi.org/10.4169/amer.math.monthly.121.03.254</a></p>
<h3>
Hadamard’s Determinant Inequality</h3>
<p>Kenneth Lange</p>
<p>This note is devoted to a short, but elementary, proof of Hadamard’s determinant inequality.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/amer.math.monthly.121.03.258">http://dx.doi.org/10.4169/amer.math.monthly.121.03.258</a></p>
<h3>
Mathbit: Mean of the Mean of the Mean . . .</h3>
<p>S. Kocak and M. Limoncu</p>
<p><span style="line-height: 17.016998291015625px;">To purchase the article from JST</span>OR: <a href="http://dx.doi.org/10.4169/amer.math.monthly.121.03.259">http://dx.doi.org/10.4169/amer.math.monthly.121.03.259</a></p>
<h3 style="font-size: 24px;">
A Zorn’s Lemma Proof of the Dimension Theorem for Vector Spaces</h3>
<p>Justin Tatch Moore</p>
<p>This note gives a “Zorn’s Lemma” style proof that any two bases in a vector space have the same cardinality.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/amer.math.monthly.121.03.260">http://dx.doi.org/10.4169/amer.math.monthly.121.03.260</a></p>
<h3 style="font-size: 24px;">
A Short Proof of McDougall’s Circle Theorem</h3>
<p>Marc Chamberland and Doron Zeilberger</p>
<p>This note offers a short, elementary proof of a result similar to Ptolemy’s theorem. Specifically, let $$d_{i, j}$$ denote the distance between $$P_{i}$$ and $$P_{j}$$ . Let $$n$$ be a positive integer and $$P_{i}$$ , for $$1\leq i \leq 2n$$, be cyclically ordered points on a circle. If</p>
<p>$$\sum_{i=1}^{n}\frac{1}{R_{2i}}=\sum_{i=1}^{n}\frac{1}{R_{2i-1}}$$ <img src="file:///C:/Users/kmerow/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" /></p>
<p><img src="file:///C:/Users/kmerow/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif" /><span style="line-height: 1.25em;">Then</span></p>
<p>$$\sum_{i=1}^{n}\frac{1}{R_{2i}}=\sum_{i=1}^{n}\frac{1}{R_{2i-1}}$$</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/amer.math.monthly.121.03.263">http://dx.doi.org/10.4169/amer.math.monthly.121.03.263</a></p>
<h2 style="font-size: 28px;">
PROBLEMS AND SOLUTIONS</h2>
<p>Problems 11761-11767<br />
Solutions 11613, 11620, 11623, 11624, 11625</p>
<p>To purchase from JSTOR: <a href="http://dx.doi.org/10.4169/amer.math.monthly.121.03.266">http://dx.doi.org/10.4169/amer.math.monthly.121.03.266</a></p>
<h2 style="font-size: 28px;">
REVIEWS</h2>
<p><em>Mathematics in Popular Culture: Essays on Appearances in Film, Fiction, Games, Television and Other Media</em>. Edited by Jessica K. Sklar and Elizabeth S. Sklar; Foreword by Keith Devlin.</p>
<p>Reviewed by Mark Kozek</p>
<p>To purchase from <span style="line-height: 1.25em;">JS</span>TOR: <a href="http://dx.doi.org/10.4169/amer.math.monthly.121.03.274">http://dx.doi.org/10.4169/amer.math.monthly.121.03.274</a></p>
</div>
<div>
</div>
</div></div></div>Tue, 18 Feb 2014 16:37:03 +0000kmerow336493 at http://www.maa.orghttp://www.maa.org/publications/periodicals/american-mathematical-monthly/american-mathematical-monthly-contents-march-2014#commentsMathematics Magazine Contents—February 2014
http://www.maa.org/publications/periodicals/mathematics-magazine/mathematics-magazine-contents-february-2014
<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-feb14.jpg" style="width: 175px; margin: 5px; float: left; height: 250px;" /></p>
<p>In this issue we have a window into the eighteenth century, as Antonella Cupillari shows us how Maria Gaetana Agnesi graphed rational and algebraic functions in her influential textbook of 1748. We also have a rare hat trick in the Notes section: three new theorems. There is a new way to characterize parabolas that Archimedes would have appreciated, a new way to fill in a rectangle with digits so that each L-shaped triple occurs exactly once, and—illustrated on the cover—a new construction involving a star, a circle, and five concurrent lines. Or, if you prefer, you can start at the back of the issue with the 2013 Putnam solutions. <span style="line-height: 1.25em;">—</span><em style="line-height: 1.25em;">Walter Stromquist</em></p>
<p>Vol. 87, No. 1, pp.2-78.</p>
<h5 style="font-size: 18px;">
</h5>
<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>
<h2 style="font-size: 28px;">
ARTICLES</h2>
<h3 style="font-size: 24px;">
Maria Gaetana Agnesi’s Other Curves (More Than Just the Witch)</h3>
<p>Antonella Cupillari</p>
<p>Maria Gaetana Agnesi’s name is commonly associated with the curve known as “the Witch of Agnesi.” However, the versiera (or versoria), as Agnesi called it, is only one of many curves she introduced in her mathematical compendium, the <em>Instituzioni Analitiche</em> (1748). Some of the other curves are much more interesting and complex than the versiera, and they are grouped in the lengthy section (pp. 351–415) titled “On the construction of Loci of degree higher than second degree.” This article showcases Agnesi’s presentation of some of them, made without using calculus. Instead, her tools of choice were geometry, algebra, and the method of using easier and already-known curves to build more challenging ones.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.1.3">http://dx.doi.org/10.4169/math.mag.87.1.3</a></p>
<h3 style="font-size: 24px;">
Maclaurin’s Inequality and a Generalized Bernoulli Inequality</h3>
<p>Iddo Ben-Ari and Keith Conrad</p>
<p>Maclaurin’s inequality is a natural, but nontrivial, generalization of the arithmetic-geometric mean inequality. We present a new proof that is based on an analogous generalization of Bernoulli’s inequality. Applications of Maclaurin’s inequality to iterative sequences and probability are discussed, along with graph-theoretic versions of the Maclaurin and Bernoulli inequalities.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.1.14.">http://dx.doi.org/10.4169/math.mag.87.1.14</a></p>
<h3 style="font-size: 24px;">
When Can You Factor a Quadratic Form?</h3>
<p>Brian G. Kronenthal and Felix Lazebnik</p>
<p>Consider the problem of determining, without using a computer or calculator, whether a given quadratic form factors into the product of two linear forms. A solution derived by inspection is often highly nontrivial; however, we can take advantage of equivalent conditions. In this article, we prove the equivalence of five such conditions. Furthermore, we discuss vocabulary such as “reducible,” “degenerate,” and “singular” that are used in the literature to describe these conditions, highlighting the inconsistency with which this vocabulary is applied.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.1.25">http://dx.doi.org/10.4169/math.mag.87.1.25</a></p>
<h2 style="font-size: 28px;">
NOTES</h2>
<h3 style="font-size: 24px;">
Defining Exponential and Trigonometric Functions Using Differential Equations</h3>
<p>Harvey Diamond</p>
<p>This note addresses the question of how to rigorously define the functions exp(<em>x</em>), sin(<em>x</em>), and cos(<em>x</em>), and develop their properties directly from that definition. We take a differential equations approach, defining each function as the solution of an initial value problem. Assuming only the basic existence/uniqueness theorem for solutions of linear differential equations, we derive the standard properties and identities associated with these functions. Our target audience is undergraduates with a calculus background.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.1.37">http://dx.doi.org/10.4169/math.mag.87.1.37</a></p>
<h3 style="font-size: 24px;">
Some Logarithmic Approximations for $$\pi$$ and $$e$$</h3>
<p>Poo-Sung Park</p>
<p>We offer the approximations $$\pi\approx\log_{5}157$$ and $$e\approx\log_{8}285$$, which may be useful where other logarithms are involved.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.1.43">http://dx.doi.org/10.4169/math.mag.87.1.43</a></p>
<h3 style="font-size: 24px;">
A 5-Circle Incidence Theorem</h3>
<p>J. Chris Fisher, Larry Hoehn, and Eberhard M. Schröder</p>
<p>We state and prove a surprising incidence theorem that was discovered with the help of a computer graphics program. The theorem involves sixteen points on ten lines and five circles; our proof relies on theorems of Euclid, Menelaus, and Ceva. The result bears a striking resemblance to Miquel’s 5-circle theorem, but as far as we can determine, the relationship of our result to known incidence theorems is superficial.</p>
<p>To purchase from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.1.44">http://dx.doi.org/10.4169/math.mag.87.1.44</a></p>
<h3 style="font-size: 24px;">
A Simple Proof that <em>e<sup>p</sup></em><sup>/<em>q</em></sup> Is Irrational</h3>
<p><span style="line-height: 1.25em;">Thomas Beatty and Timothy W. Jones</span></p>
<p>Using a simple application of the mean value theorem, we show that rational powers of <em>e</em> are irrational.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.1.50">http://dx.doi.org/10.4169/math.mag.87.1.50</a></p>
<h3 style="font-size: 24px;">
A Unique Area Property of the Quadratic Function</h3>
<p>Connie Xu</p>
<p>Suppose that a function $$f$$ defined on the real line is convex or concave with $$f''(x)$$ continuous and nonzero for all $$x$$. Let $$(x_{1}$$, $$f(x_{1}))$$ and $$(x_{2}, f(x_{2}))$$ be two arbitrary points on the graph of $$f$$ with $$x_{1} < x_{2}$$. For $$i = 1, 2$$, let $$L_{i}$$ denote the tangent line to $$f$$ at the point $$(x_{i}, f(x_{i}))$$ and let $$A_{i}$$ be the area of the region $$R_{i}$$ bounded by the graph of $$f$$, the tangent line $$L_{i}$$, and the line $$x =\hat{x}$$, the $$x$$-coordinate of the intersection of $$L_{1}$$ and $$L_{2}$$. It is proved that $$f$$ is a quadratic function if and only if $$A_{1} = A_{2}$$ for every choice of $$x_{1}$$ and $$x_{2}$$.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.1.52">http://dx.doi.org/10.4169/math.mag.87.1.52</a></p>
<h3 style="font-size: 24px;">
de Bruijn Arrays for L-Fillings</h3>
<p><span style="line-height: 1.25em;">Lara Pudwell and Rachel Rockey</span></p>
<p>We use modular arithmetic to construct a de Bruijn L-array, which is a $$k\times k^{2}$$ array consisting of exactly one copy of each L-shaped pattern (a $$2\times2$$ array with the upper right corner removed) with digits chosen from $$\{0,\dots,k-1\}$$.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.1.57">http://dx.doi.org/10.4169/math.mag.87.1.57</a></p>
<h2 style="font-size: 28px;">
PROBLEMS</h2>
<p>Proposals 1936-1940<br />
Quickies 1037 & 1038<br />
Solutions 1911-1915</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.1.61">http://dx.doi.org/10.4169/math.mag.87.1.61</a></p>
<h3>
Escape the Square</h3>
<p>Mark Dalthorp</p>
<p>To purchase from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.1.68">http://dx.doi.org/10.4169/math.mag.87.1.68</a></p>
<h2 style="font-size: 28px;">
REVIEWS</h2>
<p>Algebra: imperative? STEM: crisis? Alive: in 10 years?</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.1.69">http://dx.doi.org/10.4169/math.mag.87.1.69</a></p>
<h2 style="font-size: 28px;">
NEWS AND LETTERS</h2>
<h3>
74th Annual William Lowell Putnam Mathematical Competition</h3>
<p>To purchase from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.1.71">http://dx.doi.org/10.4169/math.mag.87.1.71</a></p>
</div></div></div>Mon, 10 Feb 2014 13:09:12 +0000kmerow327204 at http://www.maa.orghttp://www.maa.org/publications/periodicals/mathematics-magazine/mathematics-magazine-contents-february-2014#commentsMath Horizons Contents—February 2014
http://www.maa.org/publications/periodicals/math-horizons/math-horizons-contents-february-2014
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p style="font-size: 14px;"><img alt="" src="/sites/default/files/images/pubs/mh-feb2014-cover.JPG" style="margin-right: 5px; margin-left: 5px; float: left; width: 195px; height: 249px;" /></p>
<div>
<p style="font-size: 14px;">I am very pleased and honored to be the new editor of <a href="/publications/periodicals/math-horizons" title="Math Horizons"><em>Math Horizons</em></a>. In the February issue, Steven Strogatz talks to Patrick Honner about teaching, writing, and mathematics; Heidi Hulsizer uses linear algebra and modular arithmetic to beat a popular shoot-'em-up video game; James Hamblin and Doug McInvale use data to analyze a controversial decision by the New England Patriots in Super Bowl XLVI; and Erik Tou writes about the mathematics of juggling. I hope you enjoy reading this issue as much as I enjoyed putting it together. —<em>David Richeson, editor</em></p>
</div>
<p style="font-size: 14px;">Volume 21, Issue 3</p>
<h5 style="font-size: 18px;">
JOURNAL SUBSCRIBERS AND MAA MEMBERS:</h5>
<p style="font-size: 14px;">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>
<h3 style="font-size: 24px;">
Do the Math! Juggling with Numbers</h3>
<p>Erik R. Tou</p>
<p>Generate interesting juggling patterns using mathematics.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons.21.3.5">http://dx.doi.org/10.4169/mathhorizons.21.3.5</a></p>
<h3 style="font-size: 24px;">
A Conversation with Steven Strogatz</h3>
<p>Mathematician and author Steven Strogatz talks about writing, teaching, Twitter, and what makes mathematics great in this interview by Patrick Honner. (<a href="/sites/default/files/pdf/horizons/strogatz_feb14.pdf"><span class="style5">pdf</span></a>)</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons.21.3.8">http://dx.doi.org/10.4169/mathhorizons.21.3.8</a></p>
<h3 style="font-size: 24px;">
A ‘Mod’ern Mathematical Adventure in <em>Call of Duty: Black Ops</em></h3>
<p>Heidi Hulsizer</p>
<p>A shoot-’em-up video game contains an Easter egg that can be solved using linear algebra and modular arithmetic.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons.21.3.12">http://dx.doi.org/10.4169/mathhorizons.21.3.12</a></p>
<h3 style="font-size: 24px;">
The View from Here: Who's That Teaching My Class?</h3>
<p>Josh Pabian</p>
<p>This student initially struggles with, but is eventually inspired by, his inquiry-based learning class.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons.21.3.16">http://dx.doi.org/10.4169/mathhorizons.21.3.16</a></p>
<h3 style="font-size: 24px;">
Math Experts Split the Check</h3>
<p>Ben Orlin</p>
<p>A mathematician, a physicist, an engineer, a computer scientist, and an economist tackle the tricky mathematical problem of determining how much to tip the waiter.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons.21.3.18">http://dx.doi.org/10.4169/mathhorizons.21.3.18</a></p>
<h3 style="font-size: 24px;">
Polynomial Long Division and Root Power Sums</h3>
<p>Dan Kalman and Stacy Langton</p>
<p>A clever algorithm involving a derivative and polynomial long division generates the sums of the powers of the roots of a polynomial.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons.21.3.20">http://dx.doi.org/10.4169/mathhorizons.21.3.20</a></p>
<h3>
The Bookshelf:<em>The Simpsons and Their Mathematical Secrets</em></h3>
<p>review by Jim Wiseman</p>
<p>Simon Singh writes about the hidden mathematical nuggets in <em>The Simpsons</em>.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons.21.3.24">http://dx.doi.org/10.4169/mathhorizons.21.3.24</a></p>
<h3 style="font-size: 24px;">
The Bookshelf: <i>Math on Trial: How Numbers Get Used and Abused in the Courtroom</i></h3>
<p>review by Darren Glass</p>
<p>Leila Schneps and Coralie Colmez write about the dangers of misusing mathematics and statistics in the courtroom.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons.21.3.25">http://dx.doi.org/10.4169/mathhorizons.21.3.25</a></p>
<h3 style="font-size: 24px;">
Monday-Morning Math Modeling: Could the Patriots Have Won Super Bowl XLVI?</h3>
<p>James Hamblin and Doug McInvale</p>
<p>The New England Patriots let the New York Giants score a touchdown. Was this the right call?</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons.21.3.26">http://dx.doi.org/10.4169/mathhorizons.21.3.26</a></p>
<h2 style="font-size: 28px;">
THE PLAYGROUND!</h2>
<p style="font-size: 14px;">The <em>Math Horizons</em> problem section, edited by Gary Gordon</p>
<p style="font-size: 14px;">JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons.21.3.30">http://dx.doi.org/10.4169/mathhorizons.21.3.30</a></p>
<h3 style="font-size: 24px;">
AFTERMATH: Steven Strogatz on Math Education</h3>
<p>Steven Strogatz discusses the current state of mathematics <span style="line-height: 1.25em;">education in this interview with Patrick Honner.</span></p>
<p style="font-size: 14px;">To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/mathhorizons.21.3.34">http://dx.doi.org/10.4169/mathhorizons.21.3.34</a></p>
</div></div></div>Tue, 04 Feb 2014 20:15:40 +0000kmerow322868 at http://www.maa.orghttp://www.maa.org/publications/periodicals/math-horizons/math-horizons-contents-february-2014#commentsIllustrated Special Relativity Through Its Paradoxes
http://www.maa.org/publications/ebooks/illustrated-special-relativity-through-its-paradoxes
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><h5>
A Fusion of Linear Algebra, Graphics, and Reality</h5>
<p> </p>
<h2>
John dePillis and José Wudka</h2>
<hr />
<p><img src="/sites/default/files/images/ebooks/spectrum/ISR.png" style="border-width: 1px; border-style: solid; margin-left: 15px; margin-right: 15px; float: left; width: 125px; height: 187px;" /> <SCRIPT src="http://books.google.com/books/previewlib.js"></SCRIPT><SCRIPT>GBS_setLanguage('en');</SCRIPT><SCRIPT>GBS_insertPreviewButtonPopup('ISBN:9781614445173');</SCRIPT></p>
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<p><strong>Illustrated Special Relativity</strong> shows that linear algebra is a natural language for special relativity. It illustrates and resolves several apparent paradoxes of special relativity including the twin paradox and train-and-tunnel paradox. Assuming a minimum of technical prerequisites the authors introduce inertial frames and use them to explain a variety of phenomena: the nature of simultaneity, the proper way to add velocities, and why faster-than-light travel is impossible. Most of these explanations are contained in the resolution of apparent paradoxes, including some lesser-known ones: the pea-shooter paradox, the bug-and-rivet paradox, and the accommodating universe paradox. The explanation of time and length contraction is especially clear and illuminating.</p>
<p>At the outset of his seminal paper on special relativity, Einstein acknowledges the work of James Clerk Maxwell whose four equations unified the theories of electricity, optics, and magnetism. For this reason, the authors develop Maxwell’s equations which lead to a simple calculation for the frame-independent speed of electromagnetic waves in a vacuum. (Maxwell did not realize that light was a special case of electromagnetic waves.) Several chapters are devoted to experiments of Roemer, Fizeau, and de Sitter to measure the speed of light and the Michelson-Morley experiment abolishing the aether.</p>
<p>Throughout the exposition is thorough, but not overly technical, and often illustrated by cartoons. The volume might be suitable for a one-semester general-education introduction to special relativity. It is especially well-suited to self-study by interested laypersons or use as a supplement to a more traditional text.</p>
<p>Electronic ISBN: 9781614445173</p>
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<a href="/tags/relativity-theory">Relativity Theory</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/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/algebraabstract-algebra">Algebra/Abstract Algebra</a></div><div class="field-item odd"><a href="/ebook-category/new">New</a></div><div class="field-item even"><a href="/ebook-category/resources-for-teachers">Resources for Teachers</a></div></div></div>Tue, 26 Nov 2013 17:09:44 +0000bruedi244516 at http://www.maa.orghttp://www.maa.org/publications/ebooks/illustrated-special-relativity-through-its-paradoxes#commentsMore Fallacies, Flaws and Flimflam
http://www.maa.org/publications/books/more-fallacies-flaws-and-flimflam
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<h3>By Edward J. Barbeau</h3>
<p>Catalog Code: MFFL<br />
Print ISBN: 978-0-88385-580-5<br />
Electronic ISBN: 978-1-61444-515-9<br />
188 pp., Paperbound, 2013<br />
List Price: $35.00<br />
MAA Member: $28.00<br />
Series: Spectrum</p>
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<p><a class="buttonFlex" href="http://maa-store.hostedbywebstore.com/FALLACIES-FLAWS-FLIMFLAM-Edward-Barbeau/dp/B00FY3AGQQ">Buy Print Book</a><a class="buttonFlex" href="/node/193605">Buy eBook</a></p>
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<p><em>More Fallacies, Flaws, and Flimflam</em> is the second volume of selections drawn mostly from <a href="/node/2346"><em>The College Mathematics Journal</em> </a>column “Fallacies, Flaws, and Flimflam” from 2000 through 2008. The MAA published the first collection, <a href="/node/193234"><em>Mathematical Flaws, Fallacies, and Flimflam</em></a>, in 2000.</p>
<p>As in the first volume, <em>More Fallacies, Flaws, and Flimflam</em> contains items ranging from howlers (outlandish procedures that nonetheless lead to a correct answer) to deep or subtle errors often made by strong students. Although some are provided for entertainment, others challenge the reader to determine exactly where things go wrong.</p>
<p>Items are sorted by subject matter. Elementary teachers will find chapter 1 of most use, while middle and high schoolteachers will find chapters 1, 2, 3, 7, and 8 applicable to their levels. College instructors can delve for material in every part of the book.</p>
<p>There are frequent references to <em>The College Mathematics Journal</em>; these are denoted by <em>CMJ</em>.</p>
<h3>Table of Contents</h3>
<p style="margin-left:20px">Preface<br />
1. Arithmetic<br />
2. School Algebra<br />
3. Geometry<br />
4. Limits, Sequences and Series<br />
5. Differential Calculus<br />
6. Integral Calculus<br />
7. Combinatorics<br />
8. Probability and Statistics<br />
9. Complex Analysis<br />
10. Linear and Modern Algebra<br />
11. Miscellaneous<br />
Index<br />
About the Author</p>
<h3>Excerpt: 5.8 A standard box problem (p.89)</h3>
<p>Dale R. Buske put on a recent calculus examination the following standard problem:</p>
<p><strong>Problem</strong> A crate open at the top has vertical sides, a square bottom, and a volume of 4 cubic meters. If the crate is to be constructed so as to have minimal surface area, find its dimensions.</p>
<p>One student started with this formula for the surface area of the crate: <em>SA</em> = 4<em>x</em> + 4<em>y</em>, where <em>x</em> was the length of one side of the base and <em>y</em> was the height of the crate. (After all, there are four line segments of length <em>x</em> on the bottom of the crate, four line segments of length <em>y</em> on the sides, and the four line segments on top do not count since the crate has an open top.) The student then correctly went on to use the volume constraint 4 = <em>x</em><sup>2</sup><em>y</em> to find <em>y</em> = 4/<em>x</em><sup>2</sup> and arrive at the formula <em>SA</em> = 4<em>x</em> + 16/<em>x</em><sup>2</sup>. Taking the derivative and applying the condition for a maximum leads to the correct answer: the crate should have a base with dimensions 2 meters by 2 meters and a height of 1 meter.</p>
<h3>About the Author</h3>
<p><strong>Ed Barbeau</strong> graduated from the University of Toronto (BA, MA) and received his doctorate from the University of Newcastle-upon-Tyne, England in 1964. He was a Postdoctoral Fellow at Yale University in 1966-67, and taught at the University of Toronto from 1967 until 2003. He is currently retired.</p>
<p>Barbeau was named Fellow of the Ontario Institute for Studies in Education (1989), and has received the David Hilbert Award (1991) from the World Federation of National Mathematics Competitions and the Adrien Pouliot Award (1995) from the Canadian Mathematical Society. He has published a number of books with the MAA as well as two books, <em>Polynomials</em> and <em>Pell’s Equation</em> with Springer. He has been invited to give talks frequently to groups of teachers, students and the general public, and has presented three radio broadcasts, “Proof and truth in mathematics,” in the Canadian Broadcasting Corporation series, <em>Ideas</em>.</p>
<h3>MAA Review</h3>
<p>Some fifteen years ago, I reviewed <em>Mathematical Fallacies, Flaws and Flimflam</em>, the first book collecting the best of Edward J. Barbeau’s regular column in <a href="/node/2346" target="_blank"><em>The College Mathematics Journal</em></a>. Much of what I said then applies here as well: this is an entertaining book that can also be useful in the classroom.</p>
<p>The typical FFF item gives an example of a mathematical argument that is wrong but tricky. Sometimes the problem is that the argument, while visibly (even extravagantly) incorrect, gives the right answer. Other times, the argument contains a subtle error, or uses a method that is correct for unexpected reasons. <a href="/node/227222" target="_blank">Continued...</a></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>Fri, 25 Oct 2013 16:25:41 +0000swebb216788 at http://www.maa.orghttp://www.maa.org/publications/books/more-fallacies-flaws-and-flimflam#commentsCalculus: Modeling and Application 2nd edition
http://www.maa.org/publications/ebooks/calculus-modeling-and-application-2nd-edition
<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 A. Smith and Lawrence C. Moore</h2>
<hr />
<p><img src="/sites/default/files/images/ebooks/textbooks/boat_online_calc.png" style="border-width: 1px; border-style: solid; margin-left: 15px; margin-right: 15px; float: right; width: 134px; height: 187px;" /></p>
<p><strong>Calculus: Modeling and Application, 2nd Edition,</strong> responds to advances in technology that permit the integration of text and student activities into a unified whole. In this approach, students can use mathematics to structure their understanding of and investigate questions in the world around them, to formulate problems and find solutions, then to communicate their results to others.</p>
<p><span style="color: rgb(34, 34, 34); font-family: arial, sans-serif; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); display: inline !important; float: none;"><strong>Calculus: Modeling and Application</strong> covers two semesters of single-variable calculus. Its features include </span></p>
<ul>
<li><span style="color: rgb(34, 34, 34); font-family: arial, sans-serif; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); display: inline !important; float: none;">use of real-world contexts for motivation, </span></li>
<li><span style="color: rgb(34, 34, 34); font-family: arial, sans-serif; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); display: inline !important; float: none;">guided discovery learning, </span></li>
<li><span style="color: rgb(34, 34, 34); font-family: arial, sans-serif; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); display: inline !important; float: none;">hands-on activities (including built-in applets), </span></li>
<li><span style="color: rgb(34, 34, 34); font-family: arial, sans-serif; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); display: inline !important; float: none;">a problem-solving orientation, </span></li>
<li><span style="color: rgb(34, 34, 34); font-family: arial, sans-serif; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); display: inline !important; float: none;">encouragement of teamwork, </span></li>
<li><span style="color: rgb(34, 34, 34); font-family: arial, sans-serif; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); display: inline !important; float: none;">written responses to questions, </span></li>
<li><span style="color: rgb(34, 34, 34); font-family: arial, sans-serif; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); display: inline !important; float: none;">tools for self-checking of results, </span></li>
<li><span style="color: rgb(34, 34, 34); font-family: arial, sans-serif; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); display: inline !important; float: none;">intelligent use of technology, and </span></li>
<li><span style="color: rgb(34, 34, 34); font-family: arial, sans-serif; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); display: inline !important; float: none;">high expectations of students.</span></li>
</ul>
<p>It is important to note that <strong>this textbook is a website</strong>. It is designed to be accessible on any computer or tablet device in a standards-compliant browser, such as Firefox or Safari.</p>
<p>Mathematical notation is displayed by MathJax. The text uses the free computer algebra system Sage to provide interactivity through remotely-processed interacts. Sage interacts require only calculator-form entry of functions and numbers. You need not have Sage installed on your machine. There are some activities that require a printer, but these are optional.</p>
<p>At the end of each section there are pages labeled Exercises and Problems. The Exercise pages each have a WebWork button that links to MAA's WebWork courses page. Adopters who set up WebWork courses (at MAA or on their local servers) get access to the <strong>Calculus: Modeling and Application</strong> Library (in addition to the national library), and it has problems that are more or less like the Exercises in <strong>Calculus: Modeling and Application</strong>. Instructors can make up homework sets from both the <strong>Calculus: Modeling and Application</strong> and national libraries. The authors plan to continue to add to the <strong>Calculus: Modeling and Application</strong> collection, so it will get stronger over time. All of the Exercises are potentially machine-gradable (suitable for WebWork), whereas the Problems need human responses.</p>
<p>Three sample chapters (chapters 2, 5, and 8) are available at <a href="http://calculuscourse.maa.org/sample">calculuscourse.maa.org/sample</a>.</p>
<p>Access to <strong>Calculus: Modeling and Application </strong>can be purchased at <a href="http://maa.pinnaclecart.com">maa.pinnaclecart.com</a>. Instructors wishing to adopt the text for their course should contact the MAA Service Center (1-800-331-1MAA) about obtaining desk access.</p>
<p>To see how one professor uses this text and other technologies to create a paperless classroom watch this YouTube video: <a href="http://www.youtube.com/watch?v=4m4WKefT1Mg" style="color: rgb(17, 85, 204); font-family: arial, sans-serif; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" target="_blank">http://www.youtube.com/watch?<wbr />v=4m4WKefT1Mg</a></p>
<p><strong>Note to purchasers of the text: </strong>To gain easy access to the book website in the future</p>
<ul>
<li style="color: rgb(34, 34, 34); font-family: arial; font-size: small; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;">Login at<span class="Apple-converted-space"> </span><a href="http://maa.pinnaclecart.com">maa.pinnaclecart.com</a> using the username and password you created when ordering the book.</li>
<li style="color: rgb(34, 34, 34); font-family: arial; font-size: small; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;">Click on My Orders.</li>
<li style="color: rgb(34, 34, 34); font-family: arial; font-size: small; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;">Click on View Order (right side of page).</li>
<li style="color: rgb(34, 34, 34); font-family: arial; font-size: small; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;">The page that comes up will look like a receipt page and it will have a link to the text (Access Calculus ebook). Click on that link.</li>
<li style="color: rgb(34, 34, 34); font-family: arial; font-size: small; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;">The home page of the book website will come up. BOOKMARK this page so that in the future all you have to do is click on the bookmark, the login window will pop up, you log in, and then the page with the link pops up.</li>
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</div></div></div><div class="field field-name-field-ber-topics field-type-taxonomy-term-reference field-label-inline clearfix clearfix">
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<a href="/tags/calculus">Calculus</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/maa-textbooks">MAA Textbooks</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></div>Thu, 29 Aug 2013 14:11:14 +0000bruedi166212 at http://www.maa.orghttp://www.maa.org/publications/ebooks/calculus-modeling-and-application-2nd-edition#commentsDistilling Ideas: An Introduction to Mathematical Thinking
http://www.maa.org/publications/books/distilling-ideas-an-introduction-to-mathematical-thinking
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<img alt="Distilling Ideas: An Introduction to Mathematical Thinking" src="/sites/default/files/images/pubs/books/covers/DIMTcover.jpg" style="height: 270px; width: 180px;" title="Distilling Ideas: An Introduction to Mathematical Thinking" /></div>
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<h3>
By Brian P. Katz and Michael Starbird</h3>
<p>Catalog Code: DIMT<br />
Print ISBN: 978-1-93951-203-1<br />
Electronic ISBN: 978-1-61444-613-2<br />
171 pp., Paperbound, 2013<br />
List Price: $54.00<br />
MAA Member: $45.00<br />
Series: MAA Textbooks</p>
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<p>Mathematics is not a spectator sport: successful students of mathematics grapple with ideas for themselves. <em>Distilling Ideas</em> presents a carefully designed sequence of exercises and theorem statements that challenge students to create proofs and concepts. As students meet these challenges, they discover strategies of proofs and strategies of thinking beyond mathematics. In order words, <em>Distilling Ideas</em> helps its users to develop the skills, attitudes, and habits of mind of a mathematician and to enjoy the process of distilling and exploring ideas.</p>
<p><em>Distilling Ideas</em> is an ideal textbook for a first proof-based course. The text engages the range of students' preferences and aesthetics through a corresponding variety of interesting mathematical content from graphs, groups, and epsilon-delta calculus. Each topic is accessible to users without a background in abstract mathematics because the concepts arise from asking questions about everyday experience. All the common proof structures emerge as natural solutions to authentic needs. <em>Distilling Ideas</em> or any subset of its chapters is an ideal resource either for an organized Inquiry Based Learning course or for individual study.</p>
<p>A student response to <em>Distilling Ideas</em>: "I feel that I have grown more as a mathematician in this class than in all the other classes I've ever taken throughout my academic life."</p>
<h3>
Table of Contents</h3>
<p style="margin-left:20px">1. Introduction<br />
2. Graphs<br />
3. Groups<br />
4. Calculus<br />
5. Conclusion<br />
Annotated Index<br />
List of Symbols<br />
Abouth the Authors</p>
<h3>
Excerpt: Ch. 3.12 The Man Behind the Curtain (p. 85)</h3>
<p>Many people mistakenly believe that mathematics is arbitrary and magical, or at least that there is some secret knowledge that math teachers have but won't share with their students. Mathematics is no more magical that the Great and Powerful Wizard of Oz, who was just behind a curtain. The development of mathematics is directed by a few simple principles and a strong sense of aesthetics. To develop the ideas of group theory we followed a path of guided discovery. Let's look back on the journey and let the guiding strategies emerge from behind the curtain.</p>
<p>Group theory has many applications, ranging from internet credit card security and cracking the Enigma Code to solving the Rubik's Cube and generalizing the quadratic formula. Our introduction to group theory has only exposed us to a tiny portion of the theorems living in the wild.</p>
<p>We started with familiar activities: adding, multiplying, telling time, and putting blocks in a matching hole. The definition of a group emerged by distilling the essential features and commonalities from these specific examples in the process that we call abstraction. These examples generalized to produce cyclic groups, the dihedral groups, and symmetric groups in the process we call exploration. We defined generators, subgroups, products, and homomorphisms to help us discover and describe the wide variety of groups that we caught in our definition-net. We saw patterns that led us to conjectures about the size of subgroups; we justified these insights, producing theorems. We applied those insights to extend our exploration of the concept of groups.</p>
<p>This investigation represents a complete cycle of inquiry, and it especially emphasizes and deepens the skill of definition exploration. We explored a mathematical idea in its own right, hoping to describe the rich mosaic of possibilities that an abstract diefinitiion could capture. In particular, trying to <em>classify</em> all groups was one of the motivations that guided our explorations. Let us reflect on these new tools in our inquiry tool belt...</p>
<p><br />
<a href="/sites/default/files/pdf/pubs/books/DIMT_p117.pdf">Preview: p. 117</a></p>
<h3>
About the Authors</h3>
<p><strong>Brian Katz</strong> is an Assistant Professor of Mathematics at Augustana College in Rock Island, Illinois. He received his BA from Williams College in 2003 with majors in mathematics, music and chemistry and his PhD from The University of Texas at Austin in 2011, concentrating in algebraic geometry. While at UT Austin, Brian received the Frank Gerth III Graduate Excellence Award and the<span style="line-height: 1.25em;"> Frank Gerth III Graduate Teaching Excellence Award from the Department of Mathematics. Brian is a Project NExT Fellow, supported by </span>Harry Lucas, Jr. and <span style="line-height: 1.25em;">the Educational Advancement Foundation.</span></p>
<p>Brian is a member of the Inquiry Based Learning community, which focuses on helping students to ask and explore mathematical questions for themselves. Brian has given many talks about mathematics, teaching, and technology at national conferences and workshops, including as a plenary speaker for the 2012 MAA IBL PREP workshop. In particular, Brian has written and spoken about ways to use student-written wikis to extend the power of IBL beyond the classroom. Brian has helped to organize the R.L. Moore Legacy Conference hosted by the Academy for Inquiry Based Learning, and serves as a mentor for new practitioners within the organization.</p>
<p>Brian is liberally educated and is passionate about engaging in the Liberal Arts. He sees mathematics at the core of this educational perspective: connecting to the deductive reasoning of philosophy, the structure of communication of linguistics, the abstract beauty of the arts, and all forms of critical writing and speaking. Outside of mathematics, Brian has offered an interdisciplinary first-year course called Mind and Meaning, and one of his mathematics courses has been designated as part of the core curriculum at Augustana College as a "Perspective on Human Values and Existence."</p>
<p>As an educator, Brian enjoys helping all students become clearer thinkers and communicators and empowering people to move from consuming to producing knowledge.</p>
<p><strong>Michael Starbird</strong> is Professor of Mathematics and a University Distinguished Teaching Professor at The University of Texas at Austin. He received his BA degree from Ponoma College and his PhD in mathematics from the University of Wisconsin, Madison. He has been on the faculty of the Department of Mathematics of The University of Texas at Austin except for leaves including as a Visiting Member of the Institute for Advanced Study in Princeton, New Jersey, and as a member of the technical staff at the Jet Propulsion Laboratory in Pasadena, California. He served as Associate Dean in the College of Natural Sciences at UT from 1989 to 1997.</p>
<p>Starbird is a member of the Academy of Distinguished Teachers at The University of Texas of Austin and is an inaugural member of The University of Texas System Academy of Distinguished Teachers. He has won many teaching awards, including the 2007 Mathematical Association of America Deborah and Franklin Tepper Haimo National Award for Distinguished College or University Teaching of Mathematics; a Minnie Stevens Piper Professorship, which is awarded each year to 10 professors from any subject at any college or university in the state of Texas; the inaugural award of the Dad's Association Centennial Teaching Fellowship; the Excellence Award from the Eyes of Texas, twice; the President's Associates Teaching Excellence Award; the Jean Holloway Award for Teaching Excellence, which is the oldest teaching award at UT and is presented to one professor each year; the Chad Oliver Plan II Teaching Award, which is student-selected and awarded each year to one professor in the Plan II liberal arts honors program; and the Friar Society Centennial Teaching Fellowship, which is awarded to one professor at UT annually. He is an inaugural year Fellow of the AMS. In 1989, Professor Starbird was the UT Recreational Sports Super Racquets Champion.</p>
<p>Starbird's mathematical research is in the field of topology. He has served as a member-at-large of the Council of the American Mathematical Society and on the national education committees of both the American Mathematical Society and the Mathematical Association of America. He currently serves on the MAA's CUPM Committee and on its Steering Committee for the next CUPM Curriculum Guide. He directs UT's Inquiry Based Learning Project. He has given more than 200 invited lectures at the colleges and universities throughout the country and more than 20 minicourses and workshops to mathematics teachers.</p>
<p>Starbird strives to present higher-level mathematics authentically to students and the general public and to teach thinking strategies that go beyond mathematics as well. With those goals in mind, he wrote, with co-author Edward B. Burger, <em>The Heart of Mathematics: An invitation to effective thinking</em> (now in its 4th edition), which won a 2001 Robert W. Hamilton Book Award. Burger and Starbird have also written a book that brings intriguing mathematical ideas to the public, entitled <em>Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas</em>, published by W.W. Norton, 2005, and translated into eight foreign languages. In 2012, Burger and Starbird published <em>The 5 Elements of Effective Thinking</em>, which describes practical strategies for creating innovation and insight.</p>
<p>Starbird has produced five courses for The Teaching Company in their Great Courses Series: <em>Change and Motion: Calculus Made Clear </em>(1st edition, 2001, and 2nd edition, 2007)<em>; Meaning from Data: Statistics Made Clear, </em>2005<em>; What are the Chances? Probability Made Clear, </em>2007<em>; Mathematics from the Visual World, </em>2009; and, with collaborator Edward Burger, <em>The Joy of Thinking: The Beauty and Power of Classical Mathematical Ideas, </em>2003<em>.</em>These courses bring an authentic understanding of significant ideas in mathematics to many people who are not necessarily mathematically oriented. Starbird loves to see real people find the intrigue and fascination that mathematical thinking can bring.</p>
<p>David Marshall, Edward Odell, and Michael Starbird wrote <em>Number Theory Through Inquiry</em>, which appeared in 2007 in the MAA's Textbook Series. <em>Number Theory Through Inquiry</em> and the new Katz-Starbird book <em>Distilling Ideas: An Introduction to Mathematical Thinking</em> are books in the newly created MAA Textbook Subseries called "Mathematics Through Inquiry." This subseries contains materials that foster an Inquiry Based Learning strategy of instruction that encourages students to discover and develop mathematical ideas on their own.</p>
<!---<h3>
MAA Review</h3>
<p>Continued...</p>---></div>
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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/maa-textbooks">MAA Textbooks</a></div></div></div>Wed, 07 Aug 2013 16:28:09 +0000swebb151866 at http://www.maa.orghttp://www.maa.org/publications/books/distilling-ideas-an-introduction-to-mathematical-thinking#commentsApplications of Mathematics in Economics
http://www.maa.org/publications/ebooks/applications-of-mathematics-in-economics
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Warren Page, Editor</h2>
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<p><strong>Applications of Mathematics in Economics</strong> presents an overview of the (qualitative and graphical) methods and perspectives of economists. Its objectives are not intended to teach economics, but rather to give mathematicians a sense of what mathematics is used at the undergraduate level in various parts of economics, and to provide students with the opportunities to apply their mathematics in relevant economics contexts.</p>
<p>The volume’s applications span a broad range of mathematical topics and levels of sophistication. Each article consists of self-contained, stand-alone, expository sections whose problems illustrate what mathematics is used, and how, in that subdiscipline of economics. The problems are intended to be richer and more informative about economics than the economics exercises in most mathematics texts. Since each section is self-contained, instructors can readily use the economics background and worked-out solutions to tailor (simplify or embellish) a section’s problems to their students’ needs. Overall, the volume’s 47 sections contain more than 100 multipart problems. Thus, instructors have ample material to select for classroom uses, homework assignments, and enrichment activities.</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: 9781614443179</p>
<p>Print ISBN: 9780883851920</p>
<p><a href="/sites/default/files/pdf/ebooks/NTE82_contents.pdf">Contents</a><br />
<a href="/sites/default/files/pdf/ebooks/NTE82_preface.pdf">Preface</a><br />
<a href="/sites/default/files/pdf/ebooks/NTE82_Notes.pdf">Notes on the Sections</a><br />
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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/applied-mathematics">Applied Mathematics</a></div><div class="field-item odd"><a href="/ebook-category/business-mathematics">Business Mathematics</a></div><div class="field-item even"><a href="/ebook-category/resources-for-teachers">Resources for Teachers</a></div></div></div>Fri, 05 Jul 2013 21:22:16 +0000bruedi137264 at http://www.maa.orghttp://www.maa.org/publications/ebooks/applications-of-mathematics-in-economics#commentsUndergraduate Mathematics for the Life Sciences
http://www.maa.org/publications/ebooks/undergraduate-mathematics-for-the-life-sciences
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Models, Processes, and Directions</h1>
<h2>
Glenn Ledder, Jenna P. Carpenter, Timothy D. Comar, Editors</h2>
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<p>There is a gap between the extensive mathematics background that is beneficial to biologists and the minimal mathematics background biology students acquire in their courses. The result is an undergraduate education in biology with very little quantitative content. New mathematics courses must be devised with the needs of biology students in mind.</p>
<p>In this volume, authors from a variety of institutions address some of the problems involved in reforming mathematics curricula for biology students. The problems are sorted into three themes: Models, Processes, and Directions. It is difficult for mathematicians to generate curriculum ideas for the training of biologists so a number of the curriculum models that have been introduced at various institutions comprise the Models section. Processes deals with taking that great course and making sure it is institutionalized in both the biology department (as a requirement) and in the mathematics department (as a course that will live on even if the creator of the course is no longer on the faculty). Directions looks to the future, with each paper laying out a case for pedagogical developments that the authors would like to see.</p>
<p>The authors represent a wide variety of academic institutions, from universities to community colleges, and all of the articles begin with information about the institutional context. Many of the articles also include links to resources that can be found on the internet, and some have associated books in print as well. All emphasize features that could be applied to similar projects at other institutions and offer useful advice for the newcomer to mathematics curriculum development for life science students.</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: 9781614443162</p>
<p>Print ISBN: 9780883851913</p>
<p><a href="/sites/default/files/pdf/ebooks/NTE81_contents.pdf">Contents</a><br />
<a href="/sites/default/files/pdf/ebooks/NTE81_forewords.pdf">Forewords</a><br />
<a href="/sites/default/files/pdf/ebooks/NTE81_Preface.pdf">Preface</a><br />
<a href="/sites/default/files/pdf/ebooks/NTE81_Intro.pdf">General Introduction</a></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/applied-mathematics">Applied Mathematics</a></div><div class="field-item odd"><a href="/ebook-category/resources-for-teachers">Resources for Teachers</a></div></div></div>Fri, 05 Jul 2013 21:06:17 +0000bruedi137263 at http://www.maa.orghttp://www.maa.org/publications/ebooks/undergraduate-mathematics-for-the-life-sciences#commentsLearning Modern Algebra: From early Attempts to Prove Fermat's Last Theorem
http://www.maa.org/publications/books/learning-modern-algebra
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<h3>
By Al Cuoco and Joseph J. Rotman</h3>
<p>Catalog Code: LMA<br />
Print ISBN: 978-1-93951-201-7<br />
Electronic ISBN: 978-1-61444-612-5<br />
456 pp., Hardbound, 2013<br />
List Price: $60.00<br />
MAA Member: 48.00<br />
Series: MAA Textbooks</p>
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<p>Learning Modern Algebra<em> aligns with the CBMS Mathematical Education of Teachers–II recommendations, in both content and practice. It emphasizes rings and fields over groups, and it makes explicit connections between the ideas of abstract algebra and the mathematics used by high school teachers. It provides opportunities for prospective and practicing teachers to experience mathematics for themselves, before the formalities are developed, and it is explicit about the mathematical habits of mind that lie beneath the definitions and theorems.</em></p>
<p>This book is designed for prospective and practicing high school mathematics teachers, but it can serve as a text for standard abstract algebra courses as well. The presentation is organized historically: the Babylonians introduced Pythagorean triples to teach the Pythagorean theorem; these were classified by Diophantus, and eventually this led Fermat to conjecture his Last Theorem. The text shows how much of modern algebra arose in attempts to prove this; it also shows how other important themes in algebra arose from questions related to teaching. Indeed, modern algebra is a very useful tool for teachers, with deep connections to the actual content of high school mathematics, as well as to the mathematics teachers use in their profession that doesn't necessarily "end up on the blackboard."</p>
<p>The focus is on number theory, polynomials, and commutative rings. Group theory is introduced near the end of the text to explain why generalizations of the quadratic formula do not exist for polynomials of high degree, allowing the reader to appreciate the more general work of Galois and Abel on roots of polynomials. Results and proofs are motivated with specific examples whenever possible, so that abstractions emerge from concrete experience. Applications range from the theory of repeating decimals to the use of imaginary quadratic fields to construct problems with rational solutions. While such applications are integrated throughout, each chapter also contains a section giving explicit connections between the content of the chapter and high school teaching.</p>
<h3>
Table of Contents</h3>
<p style="margin-left:20px">Preface<br />
Some features of this book<br />
A Note to Students<br />
A Note to Instructors<br />
Notation<br />
1. Early Number Theory<br />
2. Induction<br />
3. Renaissance<br />
4. Modular Arithmetic<br />
5. Abstract Algebra<br />
6. Arithmetic of Polynomials<br />
7. Quotients, Fields, and Classical Problems<br />
8. Cyclotomic Integers<br />
9. Epilog References<br />
Index</p>
<!---<h3>
Excerpt: Ch. 8 Dauntless Courage (p. 109)</h3>--->
<h3>
About the Authors</h3>
<p><strong>Al Cuoco</strong> is Distinguished Scholar and Director of the Center for Mathematics Education at Education Development Center. He is lead author for The CME Project, a four-year NSF-funded high school curriculum, published by Pearson. He also co-directs Focus on Mathematics, a mathematics-science partnership that has established a mathematical community of mathematicians, teachers, and mathematics educators. The partnership evolved from his 25-year collaboration with Glenn Stevens (BU) on Boston University’s PROMYS for Teachers, a professional development program for teachers based on the Ross program (an immersion experience in mathematics). Al taught high school mathematics to a wide range of students in the Woburn, Massachusetts public schools from 1969 until 1993. A student of Ralph Greenberg, Cuoco holds a Ph.D. from Brandeis, with a thesis and research in Iwasawa theory. In addition to this book, MAA published his <em>Mathematical Connections: a Companion for Teachers and Others</em>. But his favorite publication is a 1991 paper in the <em>American Mathematical Monthly</em>, described by his wife as an attempt to explain a number system that no one understands with a picture that no one can see.</p>
<p><strong>Joseph Rotman</strong> was born in Chicago on May 26, 1934. He studied at the University of Chicago, receiving the degrees BA, MA, and Ph.D. there in 1954, 1956, and 1959, respectively; his thesis director was Irving Kaplansky.</p>
<p>Rotman has been on the faculty of the mathematics department of the University of Illinois at Urbana-Champaign since 1959, with the following ranks: Research Associate 1959-1961; Assistant Professor 1961-1963; Associate Professor 1963-1968; Professor 1968-2004; Professor Emeritus 2004-present. He has held the following visiting appointments: Queen Mary College, London, England 1965, 1985; Aarhus University, Denmark, Summer 1970; Hebrew University, Jerusalem, Israel 1070; University of Padua, Italy, 1972; Technion, Israel Institute of Technology and Hebrew University, Jerusalem (Lady Davis Professor), 1977-78; Tel Aviv University, Israel, 1982; Bar Ilan University, Israel, Summer 1982; Annual visiting lecture, South African Mathematical Society, 1985; University of Oxford, England, 1990. Professor Rotman was an editor of <em>Proceedings of American Mathematical Society</em>, 1970, 1971; managing editor, 1972, 1973.</p>
<p>Aside from writing research articles, mostly in algebra, he has written the following textbooks: <em>Group Theory</em> 1965, 1973, 1984, 1995; <em>Homological Algebra</em> 1970, 1979, 2009; <em>Algebraic Topology</em> 1988; <em>Galois Theory</em> 1990, 1998; <em>Journey into Mathematics</em> 1998, 2007; <em>First Course in Abstract Algebr</em>a 1996, 2000, 2006; <em>Advanced Modern Algebra</em> 2002.</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/maa-textbooks">MAA Textbooks</a></div></div></div>Wed, 26 Jun 2013 19:22:21 +0000swebb135679 at http://www.maa.orghttp://www.maa.org/publications/books/learning-modern-algebra#commentsBeyond the Quadratic Formula
http://www.maa.org/publications/books/beyond-the-quadratic-formula
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<h3>
By Ron Irving</h3>
<p>Catalog Code: BQF<br />
Print ISBN: 978-0-88385-783-0<br />
Electronic ISBN: 978-1-61444-112-0<br />
244 pp., Hardbound, 2013<br />
List Price: $55.00<br />
MAA Member: $44.00<br />
Series: Classroom Resource Materials</p>
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<p>The quadratic formula for the solution of quadratic equations was discovered independently by scholars in many ancient cultures and is familiar to everyone. Less well known are formulas for solutions of cubic and quartic equations whose discovery was the high point of 16th century mathematics. Their study forms the heart of this book, as part of the broader theme that a polynomial’s coefficients can be used to obtain detailed information on its roots. A closing chapter offers glimpses into the theory of higher-degree polynomials, concluding with a proof of the fundamental theorem of algebra. The book also includes historical sections designed to reveal key discoveries in the study of polynomial equations as milestones in intellectual history across cultures.</p>
<p>The book is designed for self-study, with many results presented as exercises and some supplemented by outlines for solution. The intended audience includes in-service and prospective secondary mathematics teachers, high school students eager to go beyond the standard curriculum, undergraduates who desire an in-depth look at a topic they may have unwittingly skipped over, and the mathematically curious who wish to do some work to unlock the mysteries of this beautiful subject.</p>
<h3>
Table of Contents</h3>
<p style="margin-left:20px">Preface<br />
1. Polynomials<br />
2. Quadratic Polynomials<br />
3. Cubic Polynomials<br />
4. Complex Numbers<br />
5. Cubic Polynomials, II<br />
6. Quartic Polynomials<br />
7. Higher-Degree Polynomials<br />
References<br />
Index<br />
About the Author</p>
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Excerpt: Ch. 8 Dauntless Courage (p. 109)</h3>--->
<h3>
About the Author</h3>
<p><strong>Ron Irving</strong> is a mathematics professor at the University of Washington in Seattle. He was born in suburban New York City, studied mathematics and philosophy at Harvard, and received his Ph.D. in mathematics at MIT. Following a postdoctoral position at Brandeis and a National Science Foundation postdoctoral fellowship year at the University of Chicago and UC San Diego, Irving came to Seattle. He has been a visiting faculty member at UCSD and Aarhus and a member of the Institute for Advanced Study in Princeton. His research interests have ranged over several areas of algebra, including ring theory and the representation theory of Lie groups and Lie algebras.</p>
<p>When Irving began teaching the department’s senior algebra course for majors planning on secondary teaching careers, he developed an interest in the preparation of pre-service and in-service teachers. His work with this audience led to receipt of the university’s Distinguished Teaching Award and to his book <em>Integers, Polynomials, and Rings</em>.</p>
<p>Irving spent seven years in academic administration, serving as department chair for a year, divisional dean of natural sciences for four, and interim dean of the College of Arts and Sciences for two. During this time, he established the Summer Institute for Mathematics at UW, a six-week residential program that brings talented high school students in the Pacific Northwest to the university to share in the excitement of doing mathematics. He continues to serve as the program’s executive director. He also began the planning for a new undergraduate degree in integrated sciences designed to meet the needs of future secondary science teachers.</p>
<p>Since returning to the department, Irving has taught a variety of algebra courses and written this book. He has been the director of the Integrated Sciences program, completing its planning, approval, and implementation. He serves as the secretary-treasurer of the Astrophysical Research Consortium, which oversees Apache Point Observatory in the Sacramento Mountains of New Mexico, and is president of the board of the Burke Museum of Natural History and Culture.</p>
<p>Irving is a member of the Mathematical Association of America and the American Mathematical Society. As this book goes to press, he is beginning a second stint as department chair.</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/classroom-resource-materials">Classroom Resource Materials</a></div></div></div>Tue, 25 Jun 2013 13:39:01 +0000swebb134942 at http://www.maa.orghttp://www.maa.org/publications/books/beyond-the-quadratic-formula#comments