Mathematical Association of America
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enA Mathematical Space Odyssey: Solid Geometry in the 21st Century
http://www.maa.org/publications/ebooks/a-mathematical-space-odyssey-solid-geometry-in-the-21st-century
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><h2>Claudi Alsina and Roger B. Nelsen</h2>
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<p>Solid geometry is the traditional name for what we call today the geometry of three-dimensional Euclidean space. Courses in solid geometry have largely disappeared from American high schools and colleges. The authors are convinced that a mathematical exploration of three-dimensional geometry merits some attention in today’s curriculum. <strong>A Mathematical Space Odyssey: Solid Geometry in the 21st Century</strong> is devoted to presenting techniques for proving a variety of mathematical results in three-dimensional space, techniques that may improve one’s ability to think visually.</p>
<p>Special attention is given to the classical icons of solid geometry (prisms, pyramids, platonic solids, cones, cylinders, and spheres) and many new and classical results: Cavalieri’s principle, Commandino’s theorem, de Gua’s theorem, Prince Rupert’s cube, the Menger sponge, the Schwarz lantern, Euler’s rotation theorem, the Loomis-Whitney inequality, Pythagorean theorems in three dimensions, etc. The authors devote a chapter to each of the following basic techniques for exploring space and proving theorems: enumeration, representation, dissection, plane sections, intersection, iteration, motion, projection, and folding and unfolding. In addition to many figures illustrating theorems and their proofs, a selection of photographs of three-dimensional works of art and architecture are included. Each chapter includes a selection of Challenges for the reader to explore further properties and applications. <strong>A Mathematical Space Odyssey</strong> concludes with solutions to all the Challenges in the book, references, and a complete index.</p>
<p>Readers should be familiar with high school algebra, plane and analytic geometry, and trigonometry. While brief appearances of calculus do occur, no knowledge of calculus is necessary to enjoy this book.</p>
<p>The authors hope that both secondary school and college and university teachers will use portions of it as an introduction to solid geometry, as a supplement in problem solving sessions, as enrichment material in a course on proofs and mathematical reasoning, or in a mathematics course for liberal arts students.</p>
<p>288 pp., 2015</p>
<p>Electronic ISBN 9781614442165</p>
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<h3>Luis F. Moreno</h3>
<p>Catalog Code: IRA<br />
Print ISBN: 978-1-93951-205-5<br />
Electronic ISBN: 978-1-61444-617-0<br />
680 pp., Hardbound, 2015<br />
List Price: $75.00<br />
Member Price: $60.00<br />
Series: MAA Textbooks</p>
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<p><em>An Invitation to Real Analysis</em> is written both as a stepping stone to higher calculus and analysis courses, and as foundation for deeper reasoning in applied mathematics. This book also provides a broader foundation in real analysis than is typical for future teachers of secondary mathematics. In connection with this, within the chapters, students are pointed to numerous articles from<em> The College Mathematics Journal</em> and <em>The American Mathematical Monthly</em>. These articles are inviting in their level of exposition and their wide-ranging content.</p>
<p>Axioms are presented with an emphasis on the distinguishing characteristics that new ones bring, culminating with the axioms that define the reals. Set theory is another theme found in this book, beginning with what students are familiar with from basic calculus. This theme runs underneath the rigorous development of functions, sequences, and series, and then ends with a chapter on transfinite cardinal numbers and with chapters on basic point-set topology.</p>
<p>Differentiation and integration are developed with the standard level of rigor, but always with the goal of forming a firm foundation for the student who desires to pursue deeper study. A historical theme interweaves throughout the book, with many quotes and accounts of interest to all readers.</p>
<p>Over 600 exercises and dozens of figures help the learning process. Several topics (continued fractions, for example), are included in the appendices as enrichment material. An annotated bibliography is included.</p>
<h3>Table of Contents</h3>
<p style="margin-left:20px">To the Student<br />
To the Instructor<br />
0. Paradoxes?<br />
1. Logical Foundations<br />
2. Proof, and the Natural Numbers<br />
3. The Integers, and the Ordered Field of Rational Numbers<br />
4. Induction and Well-Ordering<br />
5. Sets<br />
6. Functions<br />
7. Inverse Functions<br />
8. Some Subsets of the Real Numbers<br />
9. The Rational Numbers are Denumerable<br />
10. The Uncountability of the Real Numbers<br />
11. The Infinite<br />
12. The Complete, Ordered Field of Real Numbers<br />
13. Further Properties of Real Numbers<br />
14. Cluster Points and Related Concepts<br />
15. The Triangle Inequality<br />
16. Infinite Sequences<br />
17. Limit of Sequences<br />
18. Divergence: The Non-Existence of a Limit<br />
19. Four Great Theorems in Real Analysis<br />
20. Limit Theorems for Sequences<br />
21. Cauchy Sequences and the Cauchy Convergence Criterion<br />
22. The Limit Superior and Limit Inferior of a Sequence<br />
23. Limits of Functions<br />
24. Continuity and Discontinuity<br />
25. The Sequential Criterion for Continuity<br />
26. Theorems about Continuous Functions<br />
27. Uniform Continuity<br />
28. Infinite Series of Constants<br />
29. Series with Positive Terms<br />
30. Further Tests for Series with Positive Terms<br />
31. Series with Negative Terms<br />
32. Rearrangements of Series<br />
33. Products of Series<br />
34. The Numbers $$e$$ and $$γ$$<br />
35. The Functions exp $$x$$ and ln $$x$$<br />
36. The Derivative<br />
37. Theorems for Derivatives<br />
38. Other Derivatives<br />
39. The Mean Value Theorem<br />
40. Taylor’s Theorem<br />
41. Infinite Sequences of Functions<br />
42. Infinite Series of Functions<br />
43. Power Series<br />
44. Operations with Power Series<br />
45. Taylor Series<br />
46. Taylor Series, Part II<br />
47. The Riemann Integral<br />
48. The Riemann Integral, Part II<br />
49. The Fundamental Theorem of Integral Calculus<br />
50. Improper Integrals<br />
51. The Cauchy-Schwarz and Minkowski Inequalities<br />
52. Metric Spaces<br />
53. Functions and Limits in Metric Spaces<br />
54. Some Topology of the Real Number Line<br />
55. The Cantor Ternary Set<br />
Appendix A: Farey Sequences<br />
Appendix B: Proving that $$\sum_{k=0}^{n} < (1 + \frac{1}{n})^{n+1}$$<br />
Appendix C: The Ruler Function is Riemann Integrable<br />
Appendix D: Continued Fractions<br />
Appendix E: L’Hospital’s Rule<br />
Appendix F: Symbols, and the Greek Alphabet<br />
Annotated Bibliography<br />
Solutions to Odd-Numbered Exercises<br />
Index</p>
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</p>
<h3>
About the Authors</h3>
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<h3>
MAA Review</h3>
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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>Tue, 19 May 2015 13:26:55 +0000swebb638061 at http://www.maa.orghttp://www.maa.org/publications/books/an-invitation-to-real-analysis#commentsThe Heart of Calculus: Explorations and Applications
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<h3>Philip M. Anselone and John W. Lee</h3>
<p>Catalog Code: HCEA<br />
Print ISBN: 978-0-88385-787-8<br />
Electronic ISBN: 978-1-61444-118-2<br />
245 pp., Hardbound, 2015<br />
List Price: $60.00<br />
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<p>This book contains enrichment material for courses in first and second year calculus, differential equations, modeling, and introductory real analysis. It targets talented students who seek a deeper understanding of calculus and its applications. The book can be used in honors courses, undergraduate seminars, independent study, capstone courses taking a fresh look at calculus, and summer enrichment programs. The book develops topics from novel and/or unifying perspectives. Hence, it is also a valuable resource for graduate teaching assistants developing their academic and pedagogical skills and for seasoned veterans who appreciate fresh perspectives.</p>
<p>The explorations, problems, and projects in the book impart a deeper understanding of and facility with the mathematical reasoning that lies at the heart of calculus and conveys something of its beauty and depth. A high level of rigor is maintained. However, with few exceptions, proofs depend only on tools from calculus and earlier. Analytical arguments are carefully structured to avoid epsilons and deltas. Geometric and/or physical reasoning motivates challenging analytical discussions. Consequently, the presentation is friendly and accessible to students at various levels of mathematical maturity. Logical reasoning skills at the level of proof in Euclidean geometry suffice for a productive use of the book.</p>
<p>There are 16 chapters in the book, divided about equally between pure and applied mathematics. The first three chapters are on fundamentals of differential calculus and the last three are on the monumental discoveries of Newton and Kepler on celestial motion and gravitation. The intervening chapters present significant topics in pure and applied mathematics chosen for their intrinsic interest, historical influence, and continuing importance. There is great flexibility in the choice of which chapters to cover and the order of coverage because chapters are essentially independent of each other.</p>
<h3>Table of Contents</h3>
<p style="margin-left:20px">Preface<br />
The Foundation on Which Calculus Stands<br />
1. Critical Points and Graphing<br />
2. Inverse Functions<br />
3. Exponential and Logarithmic Functions<br />
4. Linear Approximation and Newton’s Method<br />
5. Taylor Polynomial Approximation<br />
6. Global Extreme Values<br />
7. Angular Velocity and Curvature<br />
8. <em>π</em> and <em>e</em> are Irrational<br />
9. Hanging Cables<br />
10. The Buffon Needle Problem<br />
11. Optimal Location<br />
12. Energy<br />
13. Springs and Pendulums<br />
14. Kepler’s Laws of Planetary Motion<br />
15. Newton’s Law of Universal Gravitation<br />
16. From Newton to Kepler and Beyond<br />
Index</p>
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MAA Review</h3>
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<h3>Peter Casazza, Steven G. Krantz and Randi D. Ruden, Editors</h3>
<p>Catalog Code: IMA<br />
Print ISBN: 978-0-88385-585-0<br />
Electronic ISBN: 978-1-61444-521-0<br />
320 pp., Paperbound, 2015<br />
List Price: $50.00<br />
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Series: Spectrum</p>
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<p>Mathematicians have pondered the psychology of the members of our tribe probably since mathematics was invented, but for certain since Hadamard’s <em>The Psychology of Invention in the Mathematical Field</em>. The editors asked two dozen prominent mathematicians (and one spouse thereof) to ruminate on what makes us different. The answers they got are thoughtful, interesting and thought-provoking.</p>
<p>Not all respondents addressed the question directly. Michael Atiyah reflects on the tension between truth and beauty in mathematics. T.W. Körner, Alan Schoenfeld and Hyman Bass chose to write, reflectively and thoughtfully, about teaching and learning. Others, including Ian Stewart and Jane Hawkins, write about the sociology of our community. Many of the contributions range into philosophy of mathematics and the nature of our thought processes. Any mathematician will find much of interest here.</p>
<h3>Table of Contents</h3>
<p style="margin-left:20px">Preface<br />
<strong>Part I: Who Are Mathematicians?</strong><br />
Foreword to Who Are Mathematicians?<br />
1. Mathematicians and Mathematics <em>Michael Aschbacher</em><br />
2. What Are Mathematicians Really Like? Observations of a Spouse <em>Pamela Aschbacher</em><br />
3. Mathematics: Arts and Science <em>Michael Atiyah</em><br />
4. A Mathematician’s Survival Guide <em>Peter G. Casazza</em><br />
5. We Are Different <em>Underwood Dudley</em><br />
6. The Naked Lecturer <em>T.W. Körner</em><br />
7. Through a Glass Darkly <em>Steven G. Krantz</em><br />
8. What’s a Nice Guy Like Me Doing in a Place Like This? <em>Alan H. Schoenfeld</em><br />
9. A Mathematician’s Eye View <em>Ian Stewart</em><br />
10. I am a Mathematician <em>V. S. Varadarajan</em><br />
<strong>Part II: On Becoming a Mathematician</strong><br />
Foreword to On Becoming a Mathematician<br />
11. Mathematics and Teaching <em>Hyman Bass</em><br />
12. Who We Are and How We Got That Way? <em>Jonathan M. Borwein</em><br />
13. Social Class and Mathematical Values in the USA <em>Roger Cooke</em><br />
14. The Badly Taught High School Calculus Lesson and the Mathematical Journey It Led Me To <em>Keith Devlin</em><br />
15. The Psychology of Being a Mathematician <em>Sol Garfunkel</em><br />
16. Dynamics of Mathematical Groups <em>Jane Hawkins</em><br />
17. Mathematics, Art, Civilization <em>Yuri I. Manin</em><br />
18. Questions about Mathematics <em>Harold R. Parks</em><br />
19. A Woman Mathematician’s Journey <em>Mei-Chi Shaw</em><br />
<strong>Part III: Why I Became a Mathematician</strong><br />
Foreword to Why I Became a Mathematician<br />
20. Why I Became a Mathematician: A Personal Account <em>Harold P. Boas</em><br />
21. Why I Became a Mathematician? <em>Aline Bonami</em><br />
22. Why I am a Mathematician <em>John P. D’Angelo</em><br />
23. Why I am a Mathematician <em>Robert E. Greene</em><br />
24. Why I am a Mathematician <em>Jenny Harrison</em><br />
25. Why I Became a Mathematician <em>Rodolfo H. Torres</em></p>
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About the Authors</h3>
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MAA Review</h3>
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<h3>by Michael E. Boardman and Roger B. Nelsen</h3>
<p>Catalog Code: CCA<br />
Print ISBN: 978-1-93951-206-2<br />
Electronic ISBN: 978-1-61444-616-3<br />
388 pp., Hardbound, 2015<br />
List Price: $60.00<br />
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<p><em>College Calculus: A One-Term Course for Students with Previous Calculus Experience</em> is a textbook for students who have successfully experienced an introductory calculus course in high school. <em>College Calculus</em> begins with a brief review of some of the content of the high school calculus course, and proceeds to give students a thorough grounding in the remaining topics in single variable calculus, including integration techniques, applications of the definite integral, separable and linear differential equations, hyperbolic functions, parametric equations and polar coordinates, L’Hôpital’s rule and improper integrals, continuous probability models, and infinite series. Each chapter concludes with several “Explorations,” extended discovery investigations to supplement that chapter’s material.</p>
<p>The text is ideal as the basis of a course focused on the needs of prospective majors in the STEM disciplines (science, technology, engineering, and mathematics). A one-term course based on this text provides students with a solid foundation in single variable calculus and prepares them for the next course in college level mathematics, be it multivariable calculus, linear algebra, a course in discrete mathematics, statistics, etc.</p>
<h3>Table of Contents</h3>
<p style="margin-left:20px">Preface<br />
0. Preparation for College Calculus<br />
1. Volume Integrals and Integration by Parts<br />
2. Arc Length, Trigonometric Substitution, and Surface Area<br />
3. Differential Equations<br />
4. Logistic Model, Partial Fractions, Least Squares<br />
5. Physical Applications of Integration<br />
6. The Hyperbolic Functions<br />
7. Numerical Integration<br />
8. Parametric Equations and Polar Coordinates<br />
9. Improper Integrals, L’Hôpital’s Rule, and Probability<br />
10. Infinite Series (Part I)<br />
11. Infinite Series (Part II)<br />
Appendix A. A Description of the AP Calculus AB Course<br />
Appendix B. Useful Formulas from Geometry and Trigonometry<br />
Appendix C. Supplemental Topics in Single Variable Calculus<br />
Appendix D. Supplemental Explorations<br />
Appendix E. Answers to Odd-Numbered Exercises<br />
Index</p>
<!---<h3>(p. 3)</h3>
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</p>--->
<h3>About the Authors</h3>
<p><strong>Michael Boardman</strong> and <strong>Roger Nelsen</strong> both have long affiliations with the AP Calculus program. Nelsen has participated in the annual summer AP readings for 25 years, most of these in AP Calculus (with a stint in AP Statistics). For much of that time, Nelsen served as a Table Leader, and more recently as a member of a question team, responsible for working out the details of scoring a particular free-response question. Nelsen is the author or co-author of eight books including <em><a href="/publications/books/proofs-without-words" title="Proofs Without Words: Exercises in Visual Thinking">Proof Without Words I</a>,<a href="/publications/books/proofs-without-words-ii" title="Proofs Without Words II: More Exercises in Visual Thinking"> Proofs Without Words II</a>, Math Made Visual, <a href="/publications/books/the-calculus-collection" title="The Calculus Collection: A Resource for AP* and Beyond">The Calculus Collection</a>, <a href="/publications/books/charming-proofs-a-journey-into-elegant-mathematics" title="Charming Proofs: A Journey into Elegant Mathematics">Charming Proofs</a></em>, and <a href="/publications/books/icons-of-mathematics-an-exploration-of-twenty-key-images" title="Icons of Mathematics: An Exploration of Twenty Key Images"><em>Icons of Mathematics</em></a>. Boardman’s affiliation with AP Calculus began with the 1994 reading. He was the moderator of the AP Calculus listserv for 10 years, and served four years as Chief Reader for AP Calculus. In this role, he was in charge of all aspects of the scoring of approximately 300,000 exams per year including selecting and supervising 800 readers, finalizing scoring rubrics, overseeing the logistics of the summer reading, and working with College Board personnel to set final cut scores. Boardman also served on the Development Committee for AP Calculus (2007-2011) whose members are responsible for updating the course syllabus, writing the exams, and providing outreach to high school teachers and college faculty. Boardman is currently involved in professional development of AP Calculus teachers, instructing summer and school-year workshops. Boardman serves on several MAA committees including the <a href="/programs/faculty-and-departments/curriculum-department-guidelines-recommendations/cupm" title="Committee on the Undergraduate Program in Mathematics">Committee on the Undergraduate Program in Mathematics</a>.</p>
<!---<h3>
MAA Review</h3>
<p>Continued...</p>---></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>Tue, 03 Mar 2015 14:54:54 +0000swebb618754 at http://www.maa.orghttp://www.maa.org/publications/books/college-calculus-a-one-term-course-for-students-with-previous-calculus-experience#commentsCalculus for the Life Sciences: A Modeling Approach
http://www.maa.org/publications/ebooks/calculus-for-the-life-sciences-a-modeling-approach
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><h2>James L. Cornette and Ralph A. Ackerman</h2>
<h5>TEXTBOOK*</h5>
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<p>Freshman and sophomore life sciences students respond well to the modeling approach to calculus, difference equations, and differential equations presented in this book. Examples of population dynamics, pharmacokinetics, and biologically relevant physical processes are introduced in Chapter 1, and these and other life sciences topics are developed throughout the text.</p>
<p>The ultimate goal of calculus for many life sciences students primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral is crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance.</p>
<p>Students should have studied algebra, geometry and trigonometry, but may be life sciences students because they have not enjoyed their previous mathematics courses. This text can help them understand the relevance and importance of mathematics to their world. It is not a simplistic approach, however, and indeed is written with the belief that the mathematical depth of a course in calculus for the life sciences should be comparable to that of the traditional course for physics and engineering students.</p>
<p>* As a textbook, <em>Calculus for the Life Sciences</em> does have DRM. Our DRM protected PDFs can be downloaded to three computers. iOS (iPad & iPhone) and Android devices can open secure PDFs using the AWReader app (available in the App Store and the Play Store). The iOS app uses the native iPad PDF reader so it is a very basic reader, no frills. Linux is not supported at this time for our secure PDFs.</p>
<p><a href="/sites/default/files/pdf/ebooks/pdf/CLS_TOC.pdf">Table of Contents</a></p>
<p><a href="/sites/default/files/pdf/ebooks/pdf/CLS_about.pdf">About Calculus for the Life Sciences</a></p>
<p>732 pages</p>
<p>Electronic ISBN: 9781614446156</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">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/applied-mathematics">Applied Mathematics</a></div><div class="field-item odd"><a href="/ebook-category/calculus">Calculus</a></div></div></div>Tue, 20 Jan 2015 20:49:19 +0000bruedi607754 at http://www.maa.orghttp://www.maa.org/publications/ebooks/calculus-for-the-life-sciences-a-modeling-approach#commentsWhen Life is Linear: From Computer Graphics to Bracketology
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<h3>by Tim Chartier</h3>
<p>Catalog Code: NML-45<br />
Print ISBN: 978-0-88385-649-9<br />
Electronic ISBN: 978-0-88385-988-9<br />
140 pp., Paperbound, 2015<br />
List Price: $50.00<br />
Member Price: $40.00<br />
Series: Anneli Lax New Mathematical Library</p>
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<p><em>Tim Chartier has written the perfect supplement to a linear algebra course. Every major topic is driven by applications, such as computer graphics, cryptography, webpage ranking, sports ranking and data mining. Anyone reading this book will have a clear understanding of the power and scope of linear algebra.</em> — Arthur Benjamin, Harvey Mudd College</p>
<p><em>I’m often asked which areas of mathematics should students study. I always say linear algebra. However, typical linear algebra texts I've seen either have very few applications, or the applications are contrived and not very relevant to students. Chartier's text is a refreshing change as it is driven by real-world applications that are inspiring and familiar to his audience. From Google searches and image processing, to sports rankings and (my favorite) computer graphics.</em> — Tony DeRose, Pixar Animation Studios</p>
<p>From simulating complex phenomenon on supercomputers to storing the coordinates needed in modern 3D printing, data is a huge and growing part of our world. A major tool to manipulate and study this data is linear algebra. This book introduces concepts of matrix algebra with an emphasis on application, particularly in the fields of computer graphics and data mining. Readers will learn to make an image transparent, compress an image and rotate a 3D wireframe model. In data mining, readers will use linear algebra to read zip codes on envelopes and encrypt sensitive information. The books details methods behind web search, utilized by such companies as Google, and algorithms for sports ranking which have been applied to creating brackets for March Madness and predict outcomes in FIFA World Cup soccer. The book can serve as its own resource or to supplement a course on linear algebra.</p>
<h3>Table of Contents</h3>
<p style="margin-left:20px">Preface<br />
Acknowledgements</p>
<p style="margin-left:20px">1. X Marks the Spot</p>
<p style="margin-left:20px">2. Entering the Matrix<br />
2.1 Sub Swapping<br />
2.2 Spying on the Matrix<br />
2.3 Math in the Matrix</p>
<p style="margin-left:20px">3. Sum Matrices<br />
3.1 Adding to Things<br />
3.2 Getting Inverted<br />
3.3 Blending Space<br />
3.4 Linearly Invisible<br />
3.5 Leaving Through a Portal</p>
<p style="margin-left:20px">4. Fitting the Norm<br />
4.1 Recommended Movie<br />
4.2 Handwriting at a Distance</p>
<p style="margin-left:20px">5. Go Forth and Multiply<br />
5.1 Scaly by Product<br />
5.2 Computing Similar Taste<br />
5.3 Scaling to Higher Dimensions<br />
5.4 Escher in the Matrix<br />
5.5 Lamborghini Spinout<br />
5.6 Line Detector</p>
<p style="margin-left:20px">6. It's Elementary, My Dear Watson<br />
6.1 Visual Operation<br />
6.2 Being Cryptic</p>
<p style="margin-left:20px">7. Math to the Max<br />
7.1 Dash of Math<br />
7.2 Linear Path to College<br />
7.3 Going Cocoa for Math</p>
<p style="margin-left:20px">8. Stretch and Shrink<br />
8.1 Getting Some Definition<br />
8.2 Getting Graphic<br />
8.3 Finding Groupies<br />
8.4 Seeing the Principal</p>
<p style="margin-left:20px">9. Zombie Math—Decomposing<br />
9.1 A Singularly Valuable Matrix Decomposition<br />
9.2 Feeling Compressed<br />
9.3 In a Blur<br />
9.4 Losing Some Memory</p>
<p style="margin-left:20px">10. What Are the Chances?<br />
10.1 Down the Chute<br />
10.2 Google's Rankings of Web Pages<br />
10.3 Enjoying the Chaos</p>
<p style="margin-left:20px">11. Mining for Meaning<br />
11.1 Slice and Dice<br />
11.2 Movie with not Much Dimension<br />
11.3 Presidential Library of Eigenfaces<br />
11.4 Recommendation—Seeing Stars</p>
<p style="margin-left:20px">12. Who's Number 1?<br />
12.1 Getting Massey<br />
12.2 Colley Method<br />
12.3 Rating Madness<br />
12.4 March MATHness<br />
12.5 Adding Weight to the Madness<br />
12.6 World Cup Rankings\</p>
<p style="margin-left:20px">13. End of the Line</p>
<p style="margin-left:20px">Bibliography<br />
Index</p>
<!---<h3>(p. 3)</h3>
<p>
</p>--->
<h3>About the Author</h3>
<p><a href="http://academics.davidson.edu/math/chartier/" target="_blank"><strong>Tim Chartier</strong></a> is an Associate Professor in the Departments of Mathematics and Computer Science at Davidson College. In 2014, he was named the inaugural Mathematical Association of America’s Math Ambassador. He is a recipient of the Henry Alder Award for Distinguished Teaching by a Beginning College or University Mathematics Faculty Member from the MAA. Published by Princeton University Press, Tim authored <em>Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing</em> and coauthored <em>Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms</em> with Anne Greenbaum. As a researcher, Tim has worked with both Lawrence Livermore and Los Alamos National Laboratories on the development and analysis of computational methods targeted to increase efficiency and robustness of numerical simulation on the lab’s supercomputers, which are among the fastest in the world. Tim’s research with and beyond the labs was recognized with an Alfred P. Sloan Research Fellowship. He serves on the Editorial Board for <a href="/publications/periodicals/math-horizons" title="Math Horizons"><em>Math Horizons</em></a>. He was the first of the Advisory Council for the Museum of Mathematics, which opened in 2012 and is the first museum of mathematics in the United States. Tim fields mathematical questions for the Sports Science program on ESPN, and has also been a resource for a variety of media inquiries, which include appearances with NPR, the CBS Evening News, USA Today, and The New York Times. He also writes for the Science blog of the Huffington Post.</p>
<h3>MAA Review</h3>
<p>One of the nice things about linear algebra, I’ve always thought, is that there is something in the subject for just about everybody. There’s a lot of beautiful theory, but at the same time those people who like to roll up their sleeves and get their hands dirty with computations, particularly in aid of interesting applications, will find much here to interest them as well.</p>
<p>At Iowa State University, we offer two different introductory undergraduate courses in linear algebra — one is a proof-based course intended for mathematics majors, the other is a more computational course with applications for non-majors. (There is also a more sophisticated joint undergraduate/graduate course in applied linear algebra.) I’ve taught the non-major course a couple of times, and enjoyed it, but have noted that most introductory texts are usually so busy developing the ideas behind linear algebra that they don’t really have time or space in which to really discuss the applications in any depth. Typically an application will just be developed rather briefly, which may result in it appearing somewhat contrived and artificial. The book under review does an excellent job of addressing these concerns, and would make a very useful supplement to a first course in linear algebra. <a href="/publications/maa-reviews/when-life-is-linear-from-computer-graphics-to-bracketology" target="_blank" title="When Life is Linear: From Computer Graphics to Bracketology">Continued...</a></p>
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<a href="/tags/algebra">Algebra</a>, </div>
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<a href="/tags/combinatorics">Combinatorics</a>, </div>
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<a href="/tags/geometry">Geometry</a> </div>
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</div><div class="field field-name-field-book-series field-type-taxonomy-term-reference field-label-above"><div class="field-label">Book Series: </div><div class="field-items"><div class="field-item even"><a href="/book-series/anneli-lax-nml">Anneli Lax NML</a></div></div></div>Tue, 20 Jan 2015 15:28:36 +0000swebb607733 at http://www.maa.orghttp://www.maa.org/publications/books/when-life-is-linear-from-computer-graphics-to-bracketology#commentsHow Euler Did Even More
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<h3>by C. Edward Sandifer</h3>
<p>Catalog Code: HEDM<br />
Print ISBN: 978-0-88385-584-3<br />
<!---Electronic ISBN: <br />---> 240 pp., Paperbound, 2014<br />
List Price: $35.00<br />
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Series: Spectrum</p>
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<p>“Read Euler, read Euler, he is master of us all,” LaPlace exhorted us. And it is true, Euler writes with unerring grace and ease. He is exceptionally clear thinking and clear speaking. It is a joy and a pleasure to follow him. It is especially so with Ed Sandifer as your guide. Sandifer has been studying Euler for decades and is one of the world’s leading experts on his work. This volume is the second collection of Sandifer’s “How Euler Did It” columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler’s clever inventiveness and Sandifer’s wonderful ability to explicate and put it all in context.</p>
<h3>Table of Contents</h3>
<p style="margin-left:20px"><strong>Preface</strong><br />
<strong>Part I: Geometry</strong><br />
1. The Euler Line (January 2009)<br />
2. A Forgotten Fermat Problem (December 2008)<br />
3. A Product of Secants (May 2008)<br />
4. Curves and Paradox (October 2008)<br />
5. Did Euler Prove Cramer’s Rule? (November 2009–A Guest Column by Rob Bradley)<br />
<strong>Part II: Number Theory</strong><br />
6. Factoring $$F_5$$ (March 2007)<br />
7. Rational Trigonometry (March 2008)<br />
8. Sums (and Differences) that are Squares (March 2009)<br />
<strong>Part III: Combinatorics</strong><br />
9. St. Petersburg Paradox (July 2007)<br />
10. Life and Death–Part 1 (July 2008)<br />
11. Life and Death–Part 2 (August 2008)<br />
<strong>Part IV: Analysis</strong><br />
12. e, π and i: Why is “Euler” in the Euler Identity (August 2007)<br />
13. Multi-zeta Functions (January 2008)<br />
14. Sums of Powers (June 2009)<br />
15. A Theorem of Newton (April 2008)<br />
16. Estimating π (February 2009)<br />
17. Nearly a Cosine Series (May 2009)<br />
18. A Series of Trigonometric Powers (June 2008)<br />
19. Gamma the Function (September 2007)<br />
20. Gamma the Constant (October 2007)<br />
21. Partial Fractions (June 2007)<br />
22. Inexplicable Functions (November 2007)<br />
23. A False Logarithm Series (December 2007)<br />
24. Introduction to Complex Variables (May 2007)<br />
25. The Moon and the Differential (October 2009–A Guest Column by Rob Bradley)<br />
<strong>Part V: Applied Mathematics</strong><br />
26. Density of Air (July 2009)<br />
27. Bending Light (August 2009)<br />
28. Saws and Modeling (November 2008)<br />
29. PDEs of Fluids (September 2008)<br />
30. Euler and Gravity (December 2009–A Guest Column by Dominic Klyve)<br />
<strong>Part VI: Euleriana</strong><br />
31. Euler and the Hollow Earth: Fact or Fiction? (April 2007)<br />
32. Fallible Euler (February 2008)<br />
33. Euler and the Pirates (April 2009)<br />
34. Euler as a Teacher–Part 1 (January 2010)<br />
35. Euler as a Teacher–Part 2 (February 2010)<br />
<strong>About the Author</strong></p>
<!---<h3>(p. 3)</h3>
<p>
</p>--->
<h3>About the Author</h3>
<p><strong>C. Edward Sandifer</strong> is Professor Emeritus of Mathematics at Western Connecticut State University. He earned his PhD at the Univeristy of Massachusetts under John Fogarty, studying ring theory. He became interested in Euler while attending the Institute for the History of Mathematics and Its Uses in Teaching, IHMT, several summers in Washington DC, under the tutelage of Fred Rickey, Victor Katz, and Ron Calinger. Because of a series of advising mistakes, as an undergraduate Ed studied more foreign languages than he had to, and so now he can read the works of Euler in their original Latin, French, and German. Occasionally he reads Spanish colonial mathematics in its original as well. Ed was the secretary of The Euler Society, and he wrote a monthly online column, “How Euler Did It,” for the MAA—this volume is a collection of some of those columns. He has also written <a href="/publications/books/the-early-mathematics-of-leonhard-euler" target="_blank" title="The Early Mathematics of Leonhard Euler"><em>The Early Mathematics of Leonhard Euler</em></a> and <em>How Euler Did It</em>, both also published by the MAA, and edited, along with Robert E. Bradley, <em>Leonhard Euler: Life, Work, and Legacy</em>. He and his wife Theresa, live in a small town in western Connecticut. Ed used to be an avid runner and he has over 35 Boston Marathons on his shoes.</p>
<h3>MAA Review</h3>
<p>C. Edward Sandifer’s <em>How Euler Did Even More</em> is the second collection of his monthly columns from MAA Online, “How Euler Did It.” The first collection, also titled <em>How Euler Did It</em>, appeared in 2007 as part of the five-volume set published by the MAA in recognition of the tercentenary of Euler’s birth. It contained Sandifer’s columns from November 2003 through February 2007. This second collection contains his columns from March 2007 through February 2010, with the addition of two guest columns by Rob Bradley and one by Dominic Klyve. (Bradley assisted Sandifer with the details of the publication of this collection.)</p>
<p>There are several ways to read this book. First, one may choose simply to open it at random to read Sandifer’s discussion of how Euler attacked and thought about certain problems. <a href="/publications/maa-reviews/how-euler-did-even-more" target="_blank" title="How Euler Did Even More">Continued...</a></p>
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<a href="/tags/history-of-mathematics">History of Mathematics</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/spectrum">Spectrum</a></div></div></div>Mon, 24 Nov 2014 14:29:27 +0000swebb547204 at http://www.maa.orghttp://www.maa.org/publications/books/how-euler-did-even-more#commentsDoing the Scholarship of Teaching and Learning in Mathematics
http://www.maa.org/publications/ebooks/doing-the-scholarship-of-teaching-and-learning-in-mathematics
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><h2>Jacqueline M. Dewar and Curtis D. Bennett, Editors</h2>
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<p>The Scholarship of Teaching and Learning (SoTL) movement encourages faculty to view teaching “problems” as invitations to conduct scholarly investigations. In this growing field of inquiry faculty bring their disciplinary knowledge and teaching experience to bear on questions of teaching and learning. They systematically gather evidence to develop and support their conclusions. The results are to be peer reviewed and made public for others to build on.</p>
<p>This Notes volume is written expressly for collegiate mathematics faculty who want to know more about conducting scholarly investigations into their teaching and their students’ learning. Envisioned and edited by two mathematics faculty, the volume serves as a how-to guide for doing SoTL in mathematics.</p>
<p>The four chapters in Part I provide background on this form of scholarship and specific instructions for undertaking a SoTL investigation in mathematics. Part II contains fifteen examples of SoTL projects in mathematics from fourteen different institutions, both public and private, spanning the spectrum of higher educational institutions from community colleges to research universities. These chapters “reveal the process of doing SoTL” by illustrating many of the concepts, issues, methods and procedures discussed in Part I. An Editors’ Commentary opens each contributed chapter to highlight one or more aspects of the process of doing SoTL revealed within. Toward the end of each chapter the contributing authors describe the benefits that accrued to them and their careers from participating in SoTL.</p>
<p>The final chapter in the volume, the Epilogue, represents a synthesis by the editors of the contributing authors’ perceptions of the value of SoTL. This volume has two goals: to assist mathematics faculty interested in undertaking a scholarly study of their teaching practice and to promote a greater understanding of this work and its value to the mathematics community.</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: 9781614443186</p>
<p>Print ISBN: 9780883851937</p>
<p><a href="/sites/default/files/pdf/ebooks/pdf/NTE83_TOC.pdf">Contents</a><br />
<a href="/sites/default/files/pdf/ebooks/pdf/NTE83_Foreword.pdf">Foreword by David Bressoud</a><br />
<a href="/sites/default/files/pdf/ebooks/pdf/NTE83_Preface.pdf">Preface</a></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">Latest</div></div></div><div class="field field-name-field-book-series field-type-taxonomy-term-reference field-label-above"><div class="field-label">Book Series: </div><div class="field-items"><div class="field-item even"><a href="/book-series/notes">Notes</a></div></div></div><div class="field field-name-field-ebook-category field-type-taxonomy-term-reference field-label-above"><div class="field-label">Category: </div><div class="field-items"><div class="field-item even"><a href="/ebook-category/new">New</a></div><div class="field-item odd"><a href="/ebook-category/resources-for-teachers">Resources for Teachers</a></div></div></div>Mon, 03 Nov 2014 21:10:57 +0000bruedi519694 at http://www.maa.orghttp://www.maa.org/publications/ebooks/doing-the-scholarship-of-teaching-and-learning-in-mathematics#commentsKnots and Borromean Rings, Rep-Tiles, and Eight Queens
http://www.maa.org/publications/books/knots-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 />
List Price: $16.99<br />
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>MAA Review</h3>
<p>This is the fourth entry in the first complete collection of Martin Gardner's Mathematical Library, covering the entire twenty-five-year run of his Scientific American columns. Oddly, the cover and spine have no indication of this ordinal or the count of volumes. It is not immediately obvious this is part of a set.</p>
<p>The back cover does cite Don Knuth as saying that this material is “…always worth reading and rereading.” I agree. This edition contains extensively updated material from Gardner, so that the detailed afterwords and extensive bibliographies are often longer than the original columns. <a href="/nide/608840" target="_blank">Continued...</a></p>
<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
<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-june14.jpg" style="width: 175px; margin: 5px; float: left; height: 250px;" /></p>
<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>
MAA Review</h3>
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</p>---></div>
<p> </p>
</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>Mon, 12 May 2014 17:17:01 +0000swebb401103 at http://www.maa.orghttp://www.maa.org/publications/books/mathematicians-on-creativity#commentsGame Theory Through Examples
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 />
<p><img alt="Game Theory Through Examples" src="/sites/default/files/images/ebooks/crm/GTE.png" style="border-style:solid; border-width:1px; float:left; height:187px; margin-left:15px; margin-right:15px; width:132px" /> <strong> </strong></p>
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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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</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/classroom-resource-materials">Classroom Resource Materials</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/game-theory">Game Theory</a></div></div></div>Thu, 08 May 2014 20:58:22 +0000bruedi399371 at http://www.maa.orghttp://www.maa.org/publications/ebooks/game-theory-through-examples#commentsOrdinary Differential Equations: From Calculus to Dynamical Systems
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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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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</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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<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>
</div>
</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#comments