Mathematical Association of America
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enVarieties of integration
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<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><h2>C. Ray Rosentrater</h2>
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<p><strong>Varieties of Integration</strong> explores the critical contributions by Riemann, Darboux, Lebesgue, Henstock, Kurzweil, and Stieltjes to the theory of integration and provides a glimpse of more recent variations of the integral such as those involving operator-valued measures. By the first year of graduate school, a young mathematician will have encountered at least three separate definitions of the integral. The associated integrals are typically studied in isolation with little attention paid to the relationships between them or to the historical issues that motivated their definitions. <strong>Varieties of Integration</strong> redresses this situation by introducing the Riemann, Darboux, Lebesgue, and gauge integrals in a single volume using a common set of examples. This approach allows the reader to see how the definitions influence proof techniques and computational strategies. Then the properties of the integrals are compared in three major areas: the class of integrable functions, the convergence properties of the integral, and the best form of the fundamental theorems of calculus.</p>
<p>342 pp., 2015</p>
<p>Electronic ISBN 9781614442172</p>
<p>Print ISBN 9780883853597</p>
<p><a href="/sites/default/files/pdf/ebooks/pdf/DOL51_Preface.pdf">Preface</a></p>
<p><a href="/sites/default/files/pdf/ebooks/pdf/DOL51_TOC.pdf">Table of Contents</a></p>
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</div><div class="field field-name-field-ber-category field-type-taxonomy-term-reference field-label-above"><div class="field-label">Publication Category: </div><div class="field-items"><div class="field-item even">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/dolciani">Dolciani</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/analysis">Analysis</a></div></div></div>Mon, 05 Oct 2015 17:08:20 +0000bruedi670847 at http://www.maa.orghttp://www.maa.org/press/ebooks/varieties-of-integration#commentsHalf a Century of Pythagoras Magazine
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<h3>Alex van den Brandhof, Jan Guichelaar, and Arnout Jaspers, Editors</h3>
<p>Catalog Code: HCPM<br />
Print ISBN: 978-0-88385-587-4<br />
Electronic ISBN: 978-1-61444-524-1<br />
302 pp., Paperbound, 2015<br />
List Price: $45.00<br />
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<p><em>Half a Century of Pythagoras Magazine</em> is a selection of the best and most inspiring articles from this Dutch magazine for recreational mathematics. Founded in 1961 and still thriving today, <em>Pythagoras</em> has given generations of high school students in the Netherlands a perspective on the many branches of mathematics that are not taught in schools.</p>
<p>The book contains a mix of easy, yet original puzzles, more challenging–and at least as original–problems, as well as playful introductions to a plethora of subjects in algebra, geometry, topology, number theory and more. Concepts like the sudoku and the magic square are given a whole new dimension. One of the first editors was a personal friend of world famous Dutch graphic artist Maurits Escher, whose 'impossible objects' have been a recurring subject over the years. Articles about his work are part of a special section on 'Mathematics and Art'.</p>
<p>While many books on recreational mathematics rely heavily on 'folklore', a reservoir of ancient riddles and games that are being recycled over and over again, most of the puzzles and problems in <em>Half a Century of Pythagoras Magazine</em> are original, invented for this magazine by <em>Pythagoras'</em> many editors and authors over the years. Some are no more than cute little brainteasers which can be solved in a minute, others touch on profound mathematics and can keep the reader entranced indefinitely.</p>
<p>Smart high school students and anyone else with a sharp and inquisitive mind will find in this book a treasure trove which is rich enough to keep his or her mind engaged for many weeks and months.</p>
<h3>Table of Contents</h3>
<p style="margin-left:20px">Preface<br />
1. Brainteasers<br />
2. Puzzles, Games, and Strategies<br />
3. Mathematics and Art<br />
4. Geometry<br />
5. Numbers<br />
6. Dionigmas<br />
7. Solutions<br />
Bibliography<br />
About the Editors</p>
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<h3>About the Editors</h3>
<p>Alex van den Brandhof (1976) completed his master’s degree in mathematics at VU University Amsterdam. Since 2001 he has been a mathematics teacher, first at a high school in Amsterdam and since 2011 in Basel (Switzerland). He was a member of the board of the Dutch Mathematical Olympiad. Since 2001 he has been coordinating editor of <em>Pythagoras</em> magazine. Furthermore, Alex van den Brandhof is a science journalist, writing about mathematics and computation for various media. He is one of the initiators of biographical dictionary of Dutch mathematicians. He wrote a book for high school students about probability theory and was one of the authors of a book about the seven millennium problems.</p>
<p>Jan Guichelaar (1945) studied mathematics, physics, and astronomy at the University of Amsterdam and got his master’s degree in theoretical physics in 1971. He got his PhD in 1974 on a thesis on relativistic kinetic gas theory. He worked as teacher and principal of a high school in Amsterdam. Later he taught at the faculty of mathematics and natural sciences of the University of Amsterdam. The last ten years of his career he was principal of a group of high schools in Amsterdam. Since his retirement in 2005 he has worked in the field of history of science and published as author and editor on astronomy and physics. He wrote a biography of the Dutch astronomer Willem de Sitter. Since 2001 he has been an editor of <em>Pythagoras</em> magazine.</p>
<p>Arnout Jaspers (1958) got a master’s degree in physics from Leiden University, and then changed course for a career in science journalism, specializing in mathematics, physics, astronomy and statistics. He was science editor at several newspapers and magazines. From 2006 until 2011, he was editor-in-chief of <em>Pythagoras</em> magazine. In 2012, he published <em>Het Labyrint van Occam</em> (<em>Occam’s Labyrinth</em>), a collection of his best, original math puzzles. He contributed to several other popular scientific books. He is now a freelance science writer, working mainly for public radio and several popular scientific websites.</p>
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</div><div class="field field-name-field-book-series field-type-taxonomy-term-reference field-label-above"><div class="field-label">Book Series: </div><div class="field-items"><div class="field-item even"><a href="/book-series/spectrum">Spectrum</a></div></div></div>Tue, 29 Sep 2015 18:37:31 +0000swebb666507 at http://www.maa.orghttp://www.maa.org/press/books/half-a-century-of-pythagoras-magazine#commentsGeometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry
http://www.maa.org/press/books/geometry-illuminated-an-illustrated-introduction-to-euclidean-and-hyperbolic-plane-geometry
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<h3>Matthew Harvey</h3>
<p>Catalog Code: TLI<br />
Print ISBN: 978-1-93951-211-6<br />
Electronic ISBN: 978-1-61444-618-7<br />
560 pp., Hardbound, 2015<br />
List Price: $70.00<br />
Member Price: $56.00<br />
Series: MAA Textbooks</p>
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<p><em>Geometry Illuminated</em> is an introduction to geometry in the plane, both Euclidean and hyperbolic. It is designed to be used in an undergraduate course on geometry, and as such, its target audience is undergraduate math majors. However, much of it should be readable by anyone who is comfortable with the language of mathematical proof. Throughout, the goal is to develop the material patiently. One of the more appealing aspects of geometry is that it is a very "visual" subject. This book hopes to takes full advantage of that, with an extensive use of illustrations as guides.</p>
<p><em>Geometry Illuminated</em> is divided into four principal parts. Part 1 develops neutral geometry in the style of Hilbert, including a discussion of the construction of measure in that system, ultimately building up to the Saccheri-Legendre Theorem. Part 2 provides a glimpse of classical Euclidean geometry, with an emphasis on concurrence results, such as the nine-point circle. Part 3 studies transformations of the Euclidean plane, beginning with isometries and ending with inversion, with applications and a discussion of area in between. Part 4 is dedicated to the development of the Poincaré disk model, and the study of geometry within that model.</p>
<p>While this material is traditional, <em>Geometry Illuminated</em> does bring together topics that are generally not found in a book at this level. Most notably, it explicitly computes parametric equations for the pseudosphere and its geodesics. It focuses less on the nature of axiomatic systems for geometry, but emphasizes rather the logical development of geometry within such a system. It also includes sections dealing with trilinear and barycentric coordinates, theorems that can be proved using inversion, and Euclidean and hyperbolic tilings.</p>
<h3>Table of Contents</h3>
<p style="margin-left:20px">Preface<br />
0. Axioms and Models<br />
I. Neutral Geometry<br />
1. The Axioms of Incidence and Order<br />
2. Angles and Triangles<br />
3. Congruence Verse I: SAS and ASA<br />
4. Congruence Verse II: AAS<br />
5. Congruence Verse III: SSS<br />
6. Distance, Length, and the Axioms of Continuity<br />
7. Angle Measure<br />
8. Triangles in Neutral Geometry<br />
9. Polygons<br />
10. Quadrilateral Congruence Theorems<br />
II. Euclidean Geometry<br />
11. The Axioms on Parallels<br />
12. Parallel Projection<br />
13. Similarity<br />
14. Circles<br />
15. Circumference<br />
16. Euclidean Constructions<br />
17. Concurrence I<br />
18. Concurrence II<br />
19. Concurrence III<br />
20. Trilinear Coordinates<br />
III. Euclidean Transformations<br />
21. Analytic Geometry<br />
22. Isometries<br />
23. Reflections<br />
24. Translations and Rotations<br />
25. Orientation<br />
26. Glide Reflections<br />
27. Change of Coordinates<br />
28. Dilation<br />
29. Applications of Transformations<br />
30. Area I<br />
31. Area II<br />
32. Barycentric Coordinates<br />
33. Inversion<br />
34. Inversion II<br />
35. Applications of Inversion<br />
IV. Hyperbolic<br />
36. The Search for a Rectangle<br />
37. Non-Euclidean Parallels<br />
38. The Pseudosphere<br />
39. Geodesics on the Pseudosphere<br />
40. The Upper Half Plane<br />
41. The Poincaré disk<br />
42. Hyperbolic Reflections<br />
43. Orientation-Preserving Hyperbolic Isometries<br />
44. The Six Hyperbolic Trigonometric Functions<br />
45. Hyperbolic Trigonometry<br />
46. Hyperbolic Area<br />
47. Tiling<br />
Bibliography<br />
Index</p>
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<h3>About the Author</h3>
<p>Matthew Harvey is an Associate Professor of Mathematics at the University of Virginia’s College at Wise, where he has taught since 2006. Harvey graduated from the University of Virginia in 1995 with a B.A. in Mathematics, and from John Hopkins University in 2002 with a Ph.D in Mathematics.</p>
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</div><div class="field field-name-field-book-series field-type-taxonomy-term-reference field-label-above"><div class="field-label">Book Series: </div><div class="field-items"><div class="field-item even"><a href="/book-series/maa-textbooks">MAA Textbooks</a></div></div></div>Tue, 29 Sep 2015 13:28:13 +0000swebb666409 at http://www.maa.orghttp://www.maa.org/press/books/geometry-illuminated-an-illustrated-introduction-to-euclidean-and-hyperbolic-plane-geometry#commentsThe Lebesgue Integral for Undergraduates
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<h3>William Johnston</h3>
<p>Catalog Code: TLI<br />
Print ISBN: 978-1-93951-207-9<br />
Electronic ISBN: 978-1-61444-620-0<br />
296 pp., Hardbound, 2015<br />
List Price: $60.00<br />
Member Price: $48.00<br />
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<p><em>The Lebesgue Integral for Undergraduates</em> presents the Lebesgue integral at an accessible undergraduate level with surprisingly minimal prerequisites. Anyone who has mastered single-variable calculus concepts of limits, derivatives, and series can learn the material. The key to this success is the text’s use of a method labeled the “Daniell-Riesz approach.” The treatment is self-contained, and so the associated course, often offered as Real Analysis II, no longer needs Real Analysis I as a prerequisite. Additional curricular options then exist. Academic institutions can now offer a course on the integral (and function spaces) along with Complex Analysis and Real Analysis I, where completion of any one course enhances the other two. Students can enroll immediately after Calculus II, after a first course in mathematical proofs, or as a required course in function theory. Along with Vector Calculus and Probability Theory, this set of courses now provides a comprehensive undergraduate investigation into functions.</p>
<p>The benefits are powerful. The reader now has a gateway into the modern mathematics of functions. At a very early stage, undergraduates now have the required background for collaborative research in function theory. Large numbers of students now have significantly improved access to journal articles in analysis. The book’s topics include: the definition and properties of the Lebesgue integral; Banach and Hilbert spaces; integration with respect to Borel measures, along with their associated \(L^2(\mu)\) spaces; bounded linear operators; and the spectral theorem. The text also describes several applications of the theory, such as Fourier series, quantum mechanics, and probability.</p>
<h3>Table of Contents</h3>
<p style="margin-left:20px">Preface Introduction</p>
<p style="margin-left:20px">1. Lebesgue Integrable Functions 1.1 Two Infinities: Countable and Uncountable<br />
1.2 A Taste of Measure Theory<br />
1.3 Lebesgue’s Integral for Step Functions<br />
1.4 Limits<br />
1.5 The Lebesgue Integral and \(L^1\)<br />
Notes for Chapter 1</p>
<p style="margin-left:20px">2. Lebesgue’s Integral Compared to Riemann’s<br />
2.1 The Riemann Integral<br />
2.2 Properties of the Lebesgue Integral<br />
2.3 Dominated Convergence and Further Properties of the Integral<br />
2.4 Application: Fourier Series<br />
Notes for Chapter 2</p>
<p style="margin-left:20px">3. Function Spaces<br />
3.1 The Spaces \(L^p\)<br />
3.2 The Hilbert Space Properties of \(L^2\) and \(\ell^2\)<br />
3.3 Orthonormal Basis for a Hilbert Space<br />
3.4 Application: Quantum Mechanics<br />
Notes from Chapter 3</p>
<p style="margin-left:20px">4. Measure Theory<br />
4.1 Lebesgue Measure<br />
4.2 Lebesgue Integrals with Respect to Other Measures<br />
4.3 The Hilbert Space \(L^2(\mu)\)<br />
4.4 Application: Probability<br />
Notes from Chapter 4</p>
<p style="margin-left:20px">5. Hilbert Space Operators<br />
5.1 Bounded Linear Operations \(L^2\)<br />
5.2 Bounded Linear Operations on General Hilbert Spaces<br />
5.3 The Unilateral Shift Operator<br />
5.4 Application: A Spectral Theorem Example<br />
Notes from Chapter 5</p>
<p style="margin-left:20px">Solutions to Selected Problems<br />
Bibliography<br />
Index</p>
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http://www.maa.org/press/ebooks/arithmetical-wonderland
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><h2>Andrew C. F. Liu</h2>
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<p><strong>Arithmetical Wonderland</strong> is intended as an unorthodox mathematics textbook for students in elementary education, in a contents course offered by a mathematics department. The scope is deliberately restricted to cover only arithmetic, even though geometric elements are introduced whenever warranted. For example, we showcase what the Euclidean Algorithm for finding the greatest common divisors of two numbers has to do with Euclid.</p>
<p>Many students find mathematics somewhat daunting. It is our belief that much of that is caused not by the subject itself, but by the language of mathematics. In this book, much of the discussion is in dialogues between Alice, of Wonderland fame, and the twins Tweedledum and Tweedledee who hailed from <em>Through the Looking Glass</em>. The boys are learning High Arithmetic or Elementary Number Theory from Alice, and the reader is carried along in this academic exploration. Thus many formal proofs are converted to soothing everyday language.</p>
<p>Nevertheless, the book has considerable depth. It examines many arcane corners of the subject, and raises rather unorthodox questions. For instance, Alice tells the twins that six divided by three is two only because of an implicit assumption that division is supposed to be fair, whereas fairness does not come into addition, subtraction or multiplication. Some topics often not covered are introduced rather early, such as the concepts of divisibility and congruence.</p>
<p>Great care is exercised in limiting the number of results labeled Theorems. This focuses the attention of the students on what is really important. Notation is introduced sparingly and with great care. It should be mentioned that one of the highlights of the book is the new notations for greatest common divisor and least (positive) common multiple. We leave it to the reader to look this up.</p>
<p><a href="/sites/default/files/pdf/ebooks/pdf/ARW_Intro.pdf">Introduction</a></p>
<p><a href="/sites/default/files/pdf/ebooks/pdf/ARW_TOC.pdf">Contents</a></p>
<p>Electronic ISBN: 9781614441199</p>
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<h3>Thomas Q. Sibley</h3>
<p>Catalog Code: TGSG<br />
Print ISBN: 978-1-93951-208-6<br />
Electronic ISBN: 978-1-61444-619-4<br />
586 pp., Hardbound, 2015<br />
List Price: $70.00<br />
Member Price: $56.00<br />
Series: MAA Textbooks</p>
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<p><em>Thinking Geometrically: A Survey of Geometries</em> is a well written and comprehensive survey of college geometry that would serve a wide variety of courses for both mathematics majors and mathematics education majors. Great care and attention is spent on developing visual insights and geometric intuition while stressing the logical structure, historical development, and deep interconnectedness of the ideas.</p>
<p>Students with less mathematical preparation than upper-division mathematics majors can successfully study the topics needed for the preparation of high school teachers. There is a multitude of exercises and projects in those chapters developing all aspects of geometric thinking for these students as well as for more advanced students. These chapters include Euclidean Geometry, Axiomatic Systems and Models, Analytic Geometry, Transformational Geometry, and Symmetry. Topics in the other chapters, including Non-Euclidean Geometry, Projective Geometry, Finite Geometry, Differential Geometry, and Discrete Geometry, provide a broader view of geometry. The different chapters are as independent as possible, while the text still manages to highlight the many connections between topics.</p>
<p>The text is self-contained, including appendices with the material in Euclid’s first book and a high school axiomatic system as well as Hilbert’s axioms. Appendices give brief summaries of the parts of linear algebra and multivariable calculus needed for certain chapters. While some chapters use the language of groups, no prior experience with abstract algebra is presumed. The text will support an approach emphasizing dynamical geometry software without being tied to any particular software.</p>
<h3>Table of Contents</h3>
<p style="margin-left:20px">1. Euclidean Geometry<br />
2. Axiomatic Systems<br />
3. Analytic Geometry<br />
4. Non-Euclidean Geometries<br />
5. Transformational Geometry<br />
6. Symmetry<br />
7. Projective Geometry<br />
8. Finite Geometries<br />
9. Differential Geometry<br />
10. Discrete Geometry<br />
11. Epilogue<br />
A. Definitions, Postulates, Common Notions, and Propositions from Book I of Euclid’s <em>Elements</em><br />
B. SMSG Axioms for Euclidean Geometry<br />
C. Hilbert’s Axioms for Euclidean Plane Geometry<br />
D. Linear Algebra Summary<br />
E. Multivariable Calculus Summary<br />
F. Elements of Proofs<br />
Answers to Selected Exercises<br />
Acknowledgements<br />
Index <!--</p>
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<p>
</p>
<h3>About the Author</h3>
<p></p>
<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>Fri, 21 Aug 2015 18:14:32 +0000swebb655226 at http://www.maa.orghttp://www.maa.org/press/books/thinking-geometrically-a-survey-of-geometries#commentsA Mathematical Space Odyssey: Solid Geometry in the 21st Century
http://www.maa.org/press/books/a-mathematical-space-odyssey-solid-geometry-in-the-21st-century
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<h3>Claudi Alsina and Roger B. Nelsen</h3>
<p>Catalog Code: DOL-50<br />
Print ISBN: 978-0-88385-358-0<br />
Electronic ISBN: 978-1-61444-216-5<br />
288 pp., Hardbound, 2015<br />
List Price: $55.00<br />
Member Price: $44.00<br />
Series: Dolciani Mathematical Expositions</p>
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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. <em>A Mathematical Space Odyssey: Solid Geometry in the 21st Century</em> 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. It 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>
<h3>Table of Contents</h3>
<p style="margin-left:20px">Preface<br />
1. Introduction<br />
2. Enumeration<br />
3. Representation<br />
4. Dissection<br />
5. Plane sections<br />
6. Intersection<br />
7. Iteration<br />
8. Motion<br />
9. Projection<br />
10. Folding and Unfolding<br />
Solutions to the Challenges<br />
References<br />
Index<br />
About the Authors</p>
<h3>About the Authors</h3>
<p><strong>Claudi Alsina</strong> was born 30 January 1952 in Barcelona, Spain. He received his BA and PhD in mathematics from the University of Barcelona. His post-doctoral studies were at the University of Massachusetts, Amherst. Claudi, Professor of Mathematics at the Technical University of Catalonia, has developed a wide range of international activities, research papers, publications and hundreds of lectures on mathematics and mathematics education. His latest books include <em>Associative Functions: Triangular Norms and Copulas</em> with M. J. Frank and B. Schweizer, WSP, 2006; <a href="http://www.maa.org/press/ebooks/math-made-visual"><em>Math Made Visual</em></a> (with Roger Nelsen) MAA, 2006; <em>Vitaminas Mathemáticas and El Club de la Hipotenusa</em>, Ariel, 2008, <em>Geometria para Turistas</em>, Ariel, 2009; <a href="http://www.maa.org/press/books/when-less-is-more-visualizing-basic-inequalities"><em>When Less is More</em></a> (with Roger Nelsen) MAA, 2009; <em>Asesinatos Matematicos</em>, Ariel, 2010; <a href="http://www.maa.org/press/books/charming-proofs-a-journey-into-elegant-mathematics"><em>Charming Proofs</em></a> (with Roger Nelsen) MAA, 2010; and<em> <a href="http://www.maa.org/press/books/icons-of-mathematics-an-exploration-of-twenty-key-images">Icons of Mathematics</a></em> (with Roger Nelsen) MAA, 2011.</p>
<p><strong>Roger B. Nelsen</strong> was born in Chicago, Illinois. He received his BA in mathematics from DePauw University in 1969. Roger was elected to Phi Beta Kappa and Sigma Xi, and tAught mathematics and statistics at Lewis & Clark College for forty years before his retirement in 2009. His previous books include <a href="http://www.maa.org/publications/books/proofs-without-words"><em>Proof Without Words</em></a>, MAA, 1993; <em>An Introduction to Copulas</em>, Springer, 1999 (2nd ed. 2006); <a href="http://www.maa.org/publications/books/proofs-without-words-ii"><em>Proofs Without Words II</em></a>, MAA, 2000; <a href="http://www.maa.org/press/ebooks/math-made-visual"><em>Math Made Visual</em></a> (with Claudi Alsina), MAA, 2006;<a href="http://www.maa.org/press/books/when-less-is-more-visualizing-basic-inequalities"> <em>When Less is More</em></a> (with Claudi Alsina), MAA, 2009; <a href="http://www.maa.org/press/books/charming-proofs-a-journey-into-elegant-mathematics"><em>Charming Proofs</em></a> (with Claudi Alsina), MAA 2010; <a href="http://www.maa.org/publications/books/the-calculus-collection"><em>The Calculus Collection</em> </a>(with Caren Diefenderfer), MAA, 2010; <a href="http://www.maa.org/press/books/icons-of-mathematics-an-exploration-of-twenty-key-images"><em>Icons of Mathematics</em></a> (with Claudi Alsina), MAA, 2011; and<em> <a href="http://www.maa.org/press/books/college-calculus-a-one-term-course-for-students-with-previous-calculus-experience">College Calculus</a></em> (with Michael Boardman), MAA, 2015.</p>
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<h3>Stephen F. Kennedy, Editor<br />
Donald J. Albers, Gerald L. Alexanderson, Della Dumbaugh, Frank A. Farris, Deanna B. Haunsperger, and Paul Zorn; Associate Editors</h3>
<p>Catalog Code: CAM<br />
Print ISBN: 978-0-88385-588-1<br />
Electronic ISBN: 978-1-61444-522-7<br />
420 pp., Hardbound, 2015<br />
List Price: $60.00<br />
Member Price: $48.00</p>
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<p>The MAA was founded in 1915 to serve as a home for <a href="/press/periodicals/american-mathematical-monthly" title="The American Mathematical Monthly"><em>The American Mathematical Monthly</em></a>. The mission of the Association-to advance mathematics, especially at the collegiate level-has, however, always been larger than merely publishing world-class mathematical exposition. MAA members have explored more than just mathematics; we have, as this volume tries to make evident, investigated mathematical connections to pedagogy, history, the arts, technology, literature, every field of intellectual endeavor. Essays, all commissioned for this volume, include exposition by Bob Devaney, Robin Wilson, and Frank Morgan; history from Karen Parshall, Della Dumbaugh, and Bill Dunham; pedagogical discussion from Paul Zorn, Joe Gallian, and Michael Starbird, and cultural commentary from Bonnie Gold, Jon Borwein, and Steve Abbott.</p>
<p>This volume contains 35 essays by all-star writers and expositors writing to celebrate an extraordinary century for mathematics-more mathematics has been created and published since 1915 than in all of previous recorded history. We've solved age-old mysteries, created entire new fields of study, and changed our conception of what mathematics is. Many of those stories are told in this volume as the contributors paint a portrait of the broad cultural sweep of mathematics during the MAA's first century. Mathematics is the most thrilling, the most human, area of intellectual inquiry; you will find in this volume compelling proof of that claim.</p>
<h3>Table of Contents</h3>
<p style="margin-left:20px">Preface<br />
<strong>Part I Mathematical Developments</strong><br />
The Hyperbolic Revolution: From Topology to Geometry, and Back <em>Francis Bonahon</em><br />
A Century of Complex Dynamics <em>Daniel Alexander and Robert L. Devaney</em><br />
Map-Coloring Problems <em>Robin Wilson</em><br />
Six Milestones in Geometry <em>Frank Morgan</em><br />
Defying God: the Stanley-Wilf Conjecture, Stanley-Wilf Limits, and a Two-Generation Explosion of Combinatorics <em>Eric S. Egge</em><br />
What Is the Best Approach to Counting Primes? <em>Andrew Granville</em><br />
A Century of Elliptic Curves <em>Joseph H. Silverman</em><br />
<strong>Part II Historical Developments</strong><br />
The Mathematical Association of America: Its First 100 Years <em>David E. Zitarelli</em><br />
The Stratification of the American Mathematical Community: The Mathematical Association of America and the American Mathematical Society, 1915–1925 <em>Karen Hunger Parshall</em><br />
Time and Place: Sustaining the American Mathematical Community <em>Della Dumbaugh</em><br />
Abstract (Modern) Algebra in America 1870–1950: A Brief Account <em>Israel Kleiner</em><br />
<strong>Part III Pedagogical Developments</strong><br />
The History of the Undergraduate Program in Mathematics in the United States <em>Alan Tucker</em><br />
Inquiry-Based Learning Through the Life of the MAA <em>Michael Starbird</em><br />
A Passport to Pleasure <em>Bob Kaplan and Ellen Kaplan</em><br />
Strength in Numbers: Broadening the View of the Mathematics Major <em>Rhonda Hughes</em><br />
A History of Undergraduate Research in Mathematics <em>Joseph A. Gallian</em><br />
The Calculus Reform Movement: A Personal Account <em>Paul Zorn</em><br />
Introducing <em>e<sup>x</sup></em> <em>Gilbert Strang</em><br />
<strong>Part IV Computational Developments</strong><br />
Computational Experiences in the Pre-Electronic Days <em>Philip J. Davis</em><br />
A Century of Visualization: One Geometer’s View <em>Thomas F. Banchoff</em><br />
The Future of Mathematics: 1965 to 2065 <em>Jonathan M. Borwein</em><br />
<strong>Part V Culture and Communities</strong><br />
Philosophy of Mathematics: What Has Happened Since Gödel’s Results? <em>Bonnie Gold</em><br />
Twelve Classics People who Love Mathematics Should Know; or, “What do you mean, you haven’t read E. T. Bell?” <em>Gerald L. Alexanderson</em><br />
The Dramatics Life of Mathematics: A Centennial History of the Intersection of Mathematics and Theater in a Prologue, Three Acts, and an Epilogue <em>Stephen D. Abbott</em><br />
2007: The Year of Euler <em>William Dunham</em><br />
The Putnam Competition: Origin, Lore, Structure <em>Leonard F. Klosinski</em><br />
Getting Involved with the MAA: A Path Less Traveled <em>Ezra “Bud” Brown</em><br />
Henry L. Alder <em>Donald J. Albers and Gerald L. Alexanderson</em><br />
Lida K. Barrett <em>Kenneth A. Ross</em><br />
Ralph P. Boas <em>Daniel Zelinsky</em><br />
Leonard Gillman—Reminiscences <em>Martha J. Siegel</em><br />
Paul Halmos: No Apologies <em>John Ewing</em><br />
Ivan Niven <em>Kenneth A. Ross</em><br />
George Pólya and the MAA <em>Gerald L. Alexanderson</em></p>
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About the Author</h3>
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MAA Review</h3>
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</div>Fri, 14 Aug 2015 14:43:46 +0000swebb653699 at http://www.maa.orghttp://www.maa.org/press/books/a-century-of-advancing-mathematics#commentsTrigonometry: A Clever Study Guide
http://www.maa.org/press/books/trigonometry-a-clever-study-guide
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<h3>James Tanton</h3>
<p>Catalog Code: CLP-1<br />
Print ISBN: 978-0-88385-836-3<br />
Electronic ISBN: 978-1-61444-406-0<br />
232 pp., Paperbound, 2015<br />
List Price: $19.95<br />
Series: Problem Book Series</p>
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<p>This guide covers the story of trigonometry. It is a swift overview, but it is complete in the context of the content discussed in beginning and advanced high-school courses. The purpose of these notes is to supplement and put into perspective the material of any course on the subject you may have taken or are currently taking. (These notes will be tough going for those encountering trigonometry for the very first time!)</p>
<h3>Table of Contents</h3>
<p style="margin-left:20px">About these Study Guides<br />
This Guide and Mathematics Competitions<br />
<span style="padding-left:20px">On Competition Names</span><br />
<span style="padding-left:20px">On Competition Success</span><br />
This Guide and the Craft of Solving Problems<br />
This Guide and Mathematics Content: Trigonometry<br />
For Educators: This Guide and the Common Core State Standards<br />
<strong>Part 1: Trigonometry</strong><br />
1. The Backbone Theorem: The Pythagorean Theorem<br />
2. Some Surprisingly Helpful Background History<br />
3. The Basics of “Circle-ometry”<br />
4. Radian Measure<br />
5. The Graphs of Sine and Cosine in Degrees<br />
6. The Graphs of Sine and Cosine in Radians<br />
7. Basic Trigonometric Identities<br />
8. Sine and Cosine for Circles of Different Radii<br />
9. A Paradigm Shift<br />
10. The Basics of Trigonometry<br />
11. The Tangent, Cotangent, Secant, and Cosecant Graphs<br />
12. Inverse Trigonometric Functions<br />
13. Addition and Subtraction Formulas; Double and Half Angle Formulas<br />
14. The Law of Cosines<br />
15. The Area of a Triangle<br />
16. The Law of Sines<br />
17. Heron’s Formula for the Area of a Triangle<br />
18. Fitting Trigonometric Functions to Periodic Data<br />
19. (EXTRA) Polar Coordinates<br />
20. (EXTRA) Polar Graphs<br />
<strong>Part II: Solutions</strong><br />
Solutions<br />
Appendix: Ten Problem-Solving Strategies</p>
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</p>--->
<h3>About the Author</h3>
<p><strong>James Tanton</strong> (PhD, Princeton 1994, mathematics) is an education consultant and an ambassador for the Mathematical Association of America in Washington, D.C. He has taught mathematics both at university and high-school institutions. In 2004 James founded and directed the St. Mark’s Institute of Mathematics, conducting mathematics outreach for students of all ages and designing and teaching graduate courses in mathematics for educators. James is also the author of the MAA books <a href="http://www.maa.org/press/books/solve-this-math-activities-for-students-and-clubs"><em>Solve This!</em></a> and <a href="http://www.maa.org/press/books/mathematics-galore-the-first-five-years-of-the-st-marks-institute-of-mathematics"><em>Mathematics Galore!</em></a> and is writing and doing video work on problem-solving for the MAA’s <a href="http://www.maa.org/math-competitions/teachers/curriculum-inspirations">Curriculum Inspirations</a> project.</p>
<p>He serves as a writer or an advisor on a number of curriculum projects and regularly travels across the nation and overseas to work directly with educators. James is absolutely committed to sharing joyful and beautiful mathematical thinking and doing with all. His sites <a href="http://www.jamestanton.com/">www.jamestanton.com</a> and <a href="http://gdaymath.com/">www.gdaymath.com</a> explain more.</p>
<h3><!---MAA Review</h3>
<p>Continued...</p>---></h3>
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<a href="/tags/pre-calculus">Pre-Calculus</a>, </div>
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<a href="/tags/problem-solving">Problem Solving</a>, </div>
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<a href="/tags/trigonometry">Trigonometry</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/problem-books">Problem Books</a></div></div></div>Tue, 11 Aug 2015 14:39:26 +0000swebb652373 at http://www.maa.orghttp://www.maa.org/press/books/trigonometry-a-clever-study-guide#commentsAn Invitation to Real Analysis
http://www.maa.org/press/books/an-invitation-to-real-analysis
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<div id="rightcolumn">
<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>
<p></p>
<h3>
MAA Review</h3>
<p>Continued...</p>---></div>
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<div class="field-label">Tags: </div>
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<a href="/tags/real-analysis">Real Analysis</a> </div>
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</div><div class="field field-name-field-book-series field-type-taxonomy-term-reference field-label-above"><div class="field-label">Book Series: </div><div class="field-items"><div class="field-item even"><a href="/book-series/maa-textbooks">MAA Textbooks</a></div></div></div>Tue, 19 May 2015 13:26:55 +0000swebb638061 at http://www.maa.orghttp://www.maa.org/press/books/an-invitation-to-real-analysis#commentsThe Heart of Calculus: Explorations and Applications
http://www.maa.org/press/books/the-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 />
Member Price: $48.00<br />
Series: Classroom Resource Materials</p>
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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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</p>
<h3>
About the Authors</h3>
<p></p>
<h3>
MAA Review</h3>
<p>Continued...</p>---></div>
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<a href="/tags/calculus">Calculus</a> </div>
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http://www.maa.org/press/books/i-mathematician
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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 />
Member Price: $40.00<br />
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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</p>
<h3>
About the Authors</h3>
<p></p>
<h3>
MAA Review</h3>
<p>Continued...</p>---></div>
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<a href="/tags/mathematics-and-culture">Mathematics and Culture</a>, </div>
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<a href="/tags/mathematics-for-the-general-reader">Mathematics for the General Reader</a>, </div>
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<a href="/tags/philosophy-of-mathematics">Philosophy 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>Tue, 10 Mar 2015 18:20:48 +0000swebb620835 at http://www.maa.orghttp://www.maa.org/press/books/i-mathematician#commentsCollege Calculus: A One-Term Course for Students with Previous Calculus Experience
http://www.maa.org/press/books/college-calculus-a-one-term-course-for-students-with-previous-calculus-experience
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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 />
Member Price: $48.00<br />
Series: MAA Textbooks</p>
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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="/press/books/charming-proofs-a-journey-into-elegant-mathematics" title="Charming Proofs: A Journey into Elegant Mathematics">Charming Proofs</a></em>, and <a href="/press/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>
</div></div></div><div class="field field-name-field-ber-topics field-type-taxonomy-term-reference field-label-inline clearfix clearfix">
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<a href="/tags/calculus">Calculus</a>, </div>
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</div><div class="field field-name-field-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/press/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/press/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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<a href="/tags/applied-mathematics">Applied Mathematics</a>, </div>
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<a href="/tags/mathematical-biology">Mathematical Biology</a> </div>
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</div><div class="field field-name-field-ber-category field-type-taxonomy-term-reference field-label-above"><div class="field-label">Publication Category: </div><div class="field-items"><div class="field-item even">Featured</div></div></div><div class="field field-name-field-book-series field-type-taxonomy-term-reference field-label-above"><div class="field-label">Book Series: </div><div class="field-items"><div class="field-item even"><a href="/book-series/maa-textbooks">MAA Textbooks</a></div></div></div><div class="field field-name-field-ebook-category field-type-taxonomy-term-reference field-label-above"><div class="field-label">Category: </div><div class="field-items"><div class="field-item even"><a href="/ebook-category/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/press/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="/press/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="/press/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/applied-mathematics">Applied Mathematics</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/press/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 />
Member Price: $28.00<br />
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="/press/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="/press/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/press/books/how-euler-did-even-more#commentsDoing the Scholarship of Teaching and Learning in Mathematics
http://www.maa.org/press/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>
<hr />
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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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</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/press/ebooks/doing-the-scholarship-of-teaching-and-learning-in-mathematics#commentsKnots and Borromean Rings, Rep-Tiles, and Eight Queens
http://www.maa.org/press/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="/press/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="/press/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/press/books/knots-and-borromean-rings-rep-tiles-and-eight-queens#commentsMathematics Magazine Contents—June 2014
http://www.maa.org/press/periodicals/mathematics-magazine/mathematics-magazine-contents-june-2014
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<p>Evangelista Torricelli was a master of areas and volumes. Writing in 1644, he recognized Archimedes's work on these subjects as an integrated whole. We saw Torricelli on these pages in October, 2013, and we will see him again before this year is out.<br />
<br />
This issue has articles by Andrew Leahy on Toricelli, by Scott Chapman on unique (and nonunique) factorization, by Russ Gordon on triangles with trisectible angles, and much more—including Problems, Reviews, and even a crossword puzzle.—<em style="line-height: 1.25em;">Walter Stromquist</em></p>
<p>Vol. 87, No. 3, pp. 162-239.</p>
<h5 style="font-size: 18px;"> </h5>
<h5 style="font-size: 18px;">JOURNAL SUBSCRIBERS AND MAA MEMBERS:</h5>
<p>To read the full articles, please log in to the member portal by clicking on 'Login' in the upper right corner. Once logged in, click on 'My Profile' in the upper right corner.</p>
<h2 style="font-size: 28px;">ARTICLES</h2>
<h3 style="font-size: 24px;">A Tale of Two Monoids: A Friendly Introduction to Nonunique Factorizations</h3>
<p>Scott C. Chapman</p>
<p>Arithmetic sequences are among the most basic of structures in a discrete mathematics course. We consider here two particular arithmetic sequences: 1, 5, 9, 13, 17, . . . (<strong>H</strong>) and 4, 10, 16, 22, 28, . . .(<strong>M</strong>).</p>
<p>In addition to their additive definitions, these sequences are also multiplicatively closed. We show that both have multiplicative structures much different than that of the regular system of the integers. In particular, both fail the celebrated Fundamental Theorem of Arithmetic. While this is relatively easy to see, we will show that while factoring elements in the set <strong>H</strong> is fairly straightforward, factoring elements in <strong>M</strong> is much more complicated. This gives us a glimpse of how systems that fail the Fundamental Theorem of Arithmetic are studied and analyzed.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.3.163">http://dx.doi.org/10.4169/math.mag.87.3.163</a></p>
<h3 style="font-size: 24px;">Evangelista Torricelli and the “Common Bond of Truth” in Greek Mathematics</h3>
<p>Andrew Leahy</p>
<p>In 1664, Evangelista Torricelli published his Opera Geometrica, one of the most important—yet most unheralded—publications in the history of integral calculus. In the chapter <em>de Dimensione arabolae</em>, Torricelli uses the newfound analytic techniques of Bonaventura Cavalieri to prove, among other things, that all of the major geometrical works of Archimedes—<em>Quadrature of the Parabola</em>,<em> On the Sphere and the Cylinder</em>,<em> On Spirals</em>,<em> and On the Equilibrium of Planes</em>—are joined by a “common bond of truth.” In this article, we show how Torricelli establishes this connection and discuss briefly the impact it had on subsequent mathematicians such as John Wallis.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.3.174">http://dx.doi.org/10.4169/math.mag.87.3.174</a> </p>
<h3 style="font-size: 24px;">Outer Median Triangles</h3>
<p>Árpad Benyi and Branko Ćurgus</p>
<p>We define the notions of outer medians and outer median triangles. We show that outer median triangles enjoy similar properties to that of the median triangle.</p>
<p>To purchase the article from JSTOR: <a href="http://dx.doi.org/10.4169/math.mag.87.3.185">http://dx.doi.org/10.4169/math.mag.87.3.185</a></p>
<h3 style="font-size: 24px;">Types Theory</h3>
<p>Brendan W. Sullivan</p>
<p>Supplements to this crossword puzzle are available <a href="/press/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/press/periodicals/mathematics-magazine/mathematics-magazine-contents-june-2014#commentsMathematicians on Creativity
http://www.maa.org/press/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 />
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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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</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/press/books/mathematicians-on-creativity#comments