Mathematical Association of America
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enProofs Without Words III: Further Exercises in Visual Thinking
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<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><h1>Proofs Without Words III: Further Exercises in Visual Thinking</h1>
<h2>Roger B. Nelsen</h2>
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<p>Proofs without words (PWWs) are figures or diagrams that help the reader see why a particular mathematical statement is true, and how one might begin to formally prove it true. PWWs are not new, many date back to classical Greece, ancient China, and medieval Europe and the Middle East. PWWs have been regular features of the MAA journals <em>Mathematics Magazine</em> and the <em>College Mathematics Journal</em> for many years, and the MAA published the collections of PWWs <em>Proofs Without Words: Exercises in Visual Thinking</em> in 1993 and <em>Proofs Without Words II: More Exercises in Visual Thinking</em> in 2000. This book is the third such collection of PWWs.</p>
<p>The proofs in the book are divided by topic into five chapters: Geometry & Algebra; Trigonometry, Calculus & Analytic Geometry; Inequalities; Integers & Integer Sums; and Infinite Series & Other Topics. The proofs in the book are intended primarily for the enjoyment of the reader, however, teachers will want to use them with students at many levels: high school courses from algebra through precalculus and calculus; college level courses in number theory, combinatorics, and discrete mathematics; and pre-service and in-service courses for teachers.</p>
<p>Electronic ISBN: 9781614441212</p>
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</div><div class="field field-name-field-ber-category field-type-taxonomy-term-reference field-label-above"><div class="field-label">Publication Category: </div><div class="field-items"><div class="field-item even">Featured</div></div></div><div class="field field-name-field-book-series field-type-taxonomy-term-reference field-label-above"><div class="field-label">Book Series: </div><div class="field-items"><div class="field-item even"><a href="/book-series/classroom-resource-materials">Classroom Resource Materials</a></div></div></div><div class="field field-name-field-ebook-category field-type-taxonomy-term-reference field-label-above"><div class="field-label">Category: </div><div class="field-items"><div class="field-item even"><a href="/ebook-category/algebraabstract-algebra">Algebra/Abstract Algebra</a></div><div class="field-item odd"><a href="/ebook-category/calculus">Calculus</a></div><div class="field-item even"><a href="/ebook-category/geometry">Geometry</a></div><div class="field-item odd"><a href="/ebook-category/popular-exposition">Popular Exposition</a></div></div></div>Wed, 10 Feb 2016 22:24:48 +0000bruedi733553 at http://www.maa.orghttp://www.maa.org/press/ebooks/proofs-without-words-iii-further-exercises-in-visual-thinking#commentsThe Riemann Hypothesis
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<h3>Roland van der Veen and Jan van de Craats</h3>
<p>Catalog Code: NML-46<br />
Print ISBN: 978-0-88385-650-5<br />
Electronic ISBN: 978-0-88385-989-6<br />
154 pp., Paperbound, 2016<br />
List Price: $45.00<br />
Member Price: $33.750<br />
Series: Anneli Lax New Mathematical Library</p>
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<p>This book introduces interested readers to one of the most famous and difficult open problems in mathematics: the Riemann hypothesis. Finding a proof will not only make you famous, but also earns you a one million dollar prize. The book originated from an online internet course at the University of Amsterdam for mathematically talented secondary school students. Its aim was to bring them into contact with challenging university level mathematics and show them why the Riemann Hypothesis is such an important problem in mathematics. After taking this course, many participants decided to study in mathematics at university.</p>
<h3>Table of Contents</h3>
<p style="margin-left:20px">1. Prime Numbers<br />
1.1 Primes as elementary building blocks<br />
1.2 Counting Primes<br />
1.3 Using the logarithm to count powers<br />
1.4 Approximations for \(\pi(x)\)<br />
1.5 The prime number theorem<br />
1.6 Counting prime powers logarithmically<br />
1.7 The Riemann hypothesis—a look ahead<br />
1.8 Additional exercises<br />
2. The zeta function<br />
2.1 Infinite sums<br />
2.2 Series for well-known functions<br />
2.3 Computation of <span style="font-size: 13.6136px; line-height: 17.017px;">\(\zeta(2)\)</span><br />
2.4 Euler’s product formula<br />
2.5 Looking back and a glimpse of what is to come<br />
2.6 Additional exercises<br />
3. The Riemann hypothesis<br />
3.1 Euler’s discovery of the product formula<br />
3.2 Extending the domain of the zeta function<br />
3.3 A crash course on complex numbers<br />
3.4 Complex functions and powers<br />
3.5 The complex zeta function<br />
3.6 The zeroes of the zeta function<br />
3.7 The hunt for zeta zeroes<br />
3.8 Additional exercises<br />
4. Primes and the Riemann hypothesis<br />
4.1 Riemann’s functional equation<br />
4.2 The zeroes of the zeta function<br />
4.3 The explicit formula for <span style="font-size: 13.6136px; line-height: 17.017px;">\(\psi(x)\)</span><br />
4.4 Pairing up the non-trivial zeroes<br />
4.5 The prime number theorem<br />
4.6 A proof of the prime number theorem<br />
4.7 The music of the primes<br />
4.8 Looking back<br />
4.9 Additional exercises<br />
Appendix A. Why big primes are useful<br />
Appendix B. Computer support<br />
Appendix C. Further reading and internet surfing<br />
Appendix D. Solutions to the exercises<br />
Index</p>
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<h3>About the Author</h3>
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http://www.maa.org/press/books/varieties-of-integration
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<h3>C. Ray Rosentrater</h3>
<p>Catalog Code: DOL-51<br />
Print ISBN: 978-0-88385-359-7<br />
Electronic ISBN: 978-1-61444-217-2<br />
342 pp., Hardbound, 2015<br />
List Price: $58.00<br />
Member Price: $46.50<br />
Series: Dolciani Mathematical Expositions</p>
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<p><em>Varieties of Integration</em> 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. <em>Varieties of Integration</em> 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>
<h3>Table of Contents</h3>
<p style="margin-left:20px">Preface<br />
1. Historical Introduction<br />
2. The Riemann Integral<br />
3. The Darboux integral<br />
4. A Functional zoo<br />
5. Another Approach: Measure Theory<br />
6. The Lebesgue Integral<br />
7. The Gauge Integral<br />
8. Stieltjes-type Integrals and Extensions<br />
9. A Look Back<br />
10. Afterword: <em>L<sub>s</sub></em> Spaces and Fourier Series<br />
Appendices: A Compendium of Definition and Results<br />
Index<br />
About the Author</p>
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<h3>About the Author</h3>
<p>C. Ray Rosentrater is a Professor of Mathematics at Westmont College where he has also served as department chair and Associate Dean for Curriculum. He has been recognized as Westmont’s Teacher of the Year in the Natural and Behavioral Sciences and has received the Faculty Research Award. He earned a PhD in mathematics from Indiana University and an MSc in computer science from the University of Toronto. Awarded a Fulbright Fellowship in 1995, he now serves as Westmont’s Fulbright Program Advisor. He served multiple terms on the ACMS board including terms as Vice President and President. His other publications include papers in operator theory and articles connecting analysis to computer science and linear algebra to statistics. He co-wrote two chapters in <em>Mathematics through the Eyes of Faith</em>.</p>
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<a href="/tags/analysis">Analysis</a> </div>
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http://www.maa.org/press/books/a-gentle-introduction-to-the-american-invitational-mathematics-exam
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<div><img alt="A Gentle Introduction to the American Invitational Mathematics Exam" src="/sites/default/files/images/pubs/books/covers/GIAcover.jpg" style="width: 180px; height: 257px;" title="A Gentle Introduction to the American Invitational Mathematics Exam" /></div>
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<h3>Scott A. Annin</h3>
<p>Catalog Code: GIA<br />
Print ISBN: 978-0-88385-835-6<br />
<!--Electronic ISBN:<br />--> 398 pp., Paperbound, 2015<br />
List Price: $56.00<br />
Member Price: $45.00<br />
Series: MAA Problem Books</p>
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<p>This book is a celebration of mathematical problem solving at the level of the high school American Invitational Mathematics Examination. There is no other book on the market focused on the AIME. It is intended, in part, as a resource for comprehensive study and practice for the AIME competition for students, teachers, and mentors. After all, serious AIME contenders and competitors should seek a lot of practice in order to succeed. However, this book is also intended for anyone who enjoys solving problems as a recreational pursuit. The AIME contains many problems that have the power to foster enthusiasm for mathematics–the problems are fun, engaging, and addictive. The problems found within these pages can be used by teachers who wish to challenge their students, and they can be used to foster a community of lovers of mathematical problem solving!</p>
<p>There are more than 250 fully-solved problems in the book, containing examples from AIME competitions of the 1980’s, 1990’s, 2000’s, and 2010’s. In some cases, multiple solutions are presented to highlight variable approaches. To help problem-solvers with the exercises, the author provides two levels of hints to each exercise in the book, one to help stuck starters get an idea how to begin, and another to provide more guidance in navigating an approach to the solution.</p>
<p>Topics include algebra, combinatorics, probability, number theory, sequences and series, logarithms, trigonometry, complex numbers, polynomials, and geometry. Many AIME problems involve using several of these mathematical disciplines simultaneously. To make the book indeed “gentle,” the author has prepared well-motivated, detailed, clear solutions to all examples and exercises in the book. He has not always opted for the shortest solution, but rather, he has presented solutions that a typical student might say “I could have come up with that!” The book avoids excessive reliance on heavy machinery, deep theorems, or undue abstraction.</p>
<h3>Table of Contents</h3>
<p style="margin-left:20px">Preface<br />
List of Abbreviations and Symbols<br />
1. Algebraic Equations<br />
2. Combinatorics<br />
3. Probability<br />
4. Number Theory<br />
5. Sequences and Series<br />
6. Logarithmic and Trigonometric Functions<br />
7. Complex Numbers and Polynomials<br />
8. Plane Geometry<br />
9. Spatial Geometry<br />
10. Hints for the Exercises<br />
11. Solutions to Exercise Sets<br />
Answers to All Exercises<br />
About the Author<br />
Index</p>
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<h3>About the Author</h3>
<p>Scott A. Annin received his B.S. in mathematics and physics from the University of Nebraska in 1995. He earned his Ph.D. in mathematics from the University of California at Berkeley in 2002, specializing in noncommutative algebra. He has been a professor at California State University in Fullerton ever since. Annin has received several teaching awards at Fullerton, including university-wide honors in 2008 and 2015. In 2009, he received the Mathematical Association of America’s Henry L. Alder Award for Outstanding Teaching by a Beginning Faculty Member in Mathematics. In addition to being a former AIME contestant himself (while a student at Lincoln East High School in Lincoln, Nebraska), Annin had led workshops for many AIME contestants. He has also increased awareness of the AMC program among high school teachers at both the state and national levels at math education and MAA meetings. Annin has also co-authored the widely used undergraduate mathematics text <em>Differential Equations and Linear Algebra</em> with Stephen Goode.</p>
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<h3>Roger B. Nelsen</h3>
<p>Catalog Code: CAMC<br />
Print ISBN: 978-0-88385-788-5<br />
Electronic ISBN: 978-1-61444-120-5<br />
186 pp., Hardbound, 2015<br />
List Price: $50.00<br />
Member Price: $40.00<br />
Series: Classroom Resource Materials</p>
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<p>A thespian or cinematographer might define a <em>cameo</em> as “a brief appearance of a known figure,” while a gemologist or lapidary might define it as “a precious or semiprecious stone.” This book presents fifty short enhancements or supplements (the Cameos) for the first-year calculus course in which a geometric figure briefly appears. Some of the Cameos illustrate mainstream topics such as the derivative, combinatorial formulas used to compute Riemann sums, or the geometry behind many geometric series. Other Cameos present topics accessible to students at the calculus level but not usually encountered in the course, such as the Cauchy-Schwarz inequality, the arithmetic mean-geometric mean inequality, and the Euler-Mascheroni constant.</p>
<p>There are fifty Cameos in the book, grouped into five sections: Part I Limits and Differentiation; Part II Integration; Part III Infinite Series; Part IV Additional Topics, and Part V Appendix: Some Precalculus Topics. Many of the Cameos include exercises, so Solutions to all the Exercises follows Part V. The book concludes with References and an Index.</p>
<p>Many of the Cameos are adapted from articles published in journals of the MAA, such as <a href="/press/periodicals/american-mathematical-monthly" title="The American Mathematical Monthly"><em>The American Mathematical Monthly</em></a>, <a href="/press/periodicals/mathematics-magazine" title="Mathematics Magazine"><em>Mathematics Magazine</em></a>, and <a href="/press/periodicals/college-mathematics-journal/the-college-mathematics-journal" title="The College Mathematics Journal "><em>The College Mathematics Journal</em></a>. Some come from other mathematical journals, and some were created for this book. By gathering the Cameos into a book we hope that they will be more accessible to teachers of calculus, both for use in the classroom and as supplementary explorations for students.</p>
<h3>Table of Contents</h3>
<p style="margin-left:20px">Preface<br />
Part I: Limits and Differentiation<br />
1. The limit of <em>(sin t)/t</em><br />
2. Approximating <em>π</em> with the limit of <em>(sin t)/t</em><br />
3. Visualizing the derivative<br />
4. The product rule<br />
5. The quotient rule<br />
6. The chain rule<br />
7. The derivative of the sine<br />
8. The derivative of the arctangent<br />
9. The derivative of the arcsine<br />
10. Means and the mean value theorem<br />
11. Tangent line inequalities<br />
12. A geometric illustration of the limit for<em> e</em><br />
13. Which is larger, <em>e<sup>π</sup></em> or<em> π<sup>e</sup></em>? <em>a<sup>b</sup></em> or <em>b<sup>a</sup></em>?<br />
14. Derivatives of area and volume<br />
15. Means and optimization<br />
Part II: Integration<br />
16. Combinatorial identities for Riemann sums<br />
17. Summation by parts<br />
18. Integration by parts<br />
19. The world’s sneakiest substitution<br />
20. Symmetry and integration<br />
21. Napier’s inequality and the limit for <em>e</em><br />
22. The <em>n</em>th root of <em>n</em>? and another limit for <em>e</em><br />
23. Does shell volume equal disk volume?<br />
24. Solids of revolution and the Cauchy-Schwarz inequality<br />
25. The midpoint rule is better than the trapezoidal rule<br />
26. Can the midpoint rule be improved?<br />
27. Why is Simpson’s rule exact for cubics?<br />
28. Approximating <em>π</em> with integration<br />
29. The Hermite-Hadamard inequality<br />
30. Polar area and Cartesian area<br />
31. Polar area as a source of antiderivatives<br />
32. The prismoidal formula<br />
Part III Infinite Series<br />
33. The geometry of geometric series<br />
34. Geometric differentiation of geometric series<br />
35. Illustrating a telescoping series<br />
36. Illustrating applications of the monotone sequence theorem<br />
37. The harmonic series and the Euler-Mascheroni constant<br />
38. The alternating harmonic series<br />
39. The alternating series test<br />
40. Approximating<em> π</em> with Maclaurin series<br />
Part IV Additional Topics<br />
41. The hyperbolic functions I: Definintions<br />
42. The hyperbolic functions II: Are they circular?<br />
43. The conic sections<br />
44. The conic sections revisited<br />
45. The AM-GM inequality for <em>π</em> positive numbers<br />
Part V: Appendix: Some Precalculus Topics<br />
46. Are all parabolas similar?<br />
47. Basic trigonometric identities<br />
48. The addition formulas for the sine and cosine<br />
49. The double angle formulas<br />
50. Completing the square<br />
Solutions to the Exercises<br />
References<br />
Index<br />
About the Author</p>
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<h3>About the Author</h3>
<p>Roger B. Nelsen was born in Chicago, Illinois. He received his B.A. in mathematics from DePauw University in 1964 and his Ph.D. in mathematics from Duke 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 <em><a href="/publications/books/proofs-without-words" title="Proofs Without Words: Exercises in Visual Thinking">Proofs Without Words</a></em>, MAA 1993; <em>An Introduction to Copulas</em>, Springer, 1999 (2nd ed. 2006); <em><a href="/publications/books/proofs-without-words-ii" title="Proofs Without Words II: More Exercises in Visual Thinking">Proofs Without Words II</a></em>, MAA, 2000; <em><a href="/press/ebooks/math-made-visual" title="Math Made Visual">Math Made Visual</a></em> (with Claudi Alsina), MAA, 2010; <em><a href="/publications/books/the-calculus-collection" title="The Calculus Collection: A Resource for AP* and Beyond">The Calculus Collection</a></em> (with Caren Diefenderfer), MAA, 2010; <em><a href="/press/books/icons-of-mathematics-an-exploration-of-twenty-key-images" title="Icons of Mathematics: An Exploration of Twenty Key Images">Icons of Mathematics</a></em> (with Claudi Alsina), MAA, 2011; <em><a href="/press/books/college-calculus-a-one-term-course-for-students-with-previous-calculus-experience" title="College Calculus: A One-Term Course for Students with Previous Calculus Experience">College Calculus</a></em> (with Michael Boardman), MAA, 2015; and <em><a href="/press/books/a-mathematical-space-odyssey-solid-geometry-in-the-21st-century" title="A Mathematical Space Odyssey: Solid Geometry in the 21st Century">A Mathematical Space Odyssey</a></em> (with Claudi Alsina), MAA, 2015.</p>
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<a href="/tags/calculus">Calculus</a>, </div>
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<a href="/tags/teaching-mathematics">Teaching Mathematics</a>, </div>
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<a href="/tags/visualization">Visualization</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/classroom-resource-materials">Classroom Resource Materials</a></div></div></div>Wed, 18 Nov 2015 19:30:30 +0000swebb685926 at http://www.maa.orghttp://www.maa.org/press/books/cameos-for-calculus-visualization-in-the-first-year-course#commentsArithmetical Wonderland
http://www.maa.org/press/books/arithmetical-wonderland
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<div id="rightcolumn">
<h3>Andy Liu</h3>
<p>Catalog Code: ARW<br />
Print ISBN: 978-0-88385-789-2<br />
Electronic ISBN: 978-1-61444-119-9<br />
240 pp., Hardbound, 2015<br />
List Price: $50.00<br />
Member Price: $40.00<br />
Series: Classroom Resource Materials</p>
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<p><em>Arithmetical Wonderland</em> 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, what the Euclidean Algorithm for finding the greatest common divisors of two numbers has to do with Euclid is showcased.</p>
<p>Many students find mathematics somewhat daunting. It is the author's 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>
<h3>Table of Contents</h3>
<p style="margin-left:20px">Preface to a Preliminary Edition<br />
Introduction<br />
0. Review of Arithmetic<br />
0.1 Counting Numbers<br />
0.2 Integers<br />
0.3 Inequalities<br />
0.4 Extras<br />
1. Divisibility<br />
1.1 Basic Properties of Divisibility<br />
1.2 The Arithmetic of Divisibility<br />
1.3 Divisibility Problems<br />
1.4 Extras<br />
2. Congruence<br />
2.1 The Division Algorithm<br />
2.2 Basic Properties and Arithmetic of Congruence<br />
2.3 Congruence and Divisibility<br />
2.4 Extras<br />
3. Common Divisors and Multiples<br />
3.1 Greatest Common Divisors and the Euclidean Algorithm<br />
3.2 Relatively Prime Numbers<br />
3.3 Least Common Multiples<br />
3. 4 Extras<br />
4. Linear Diophantine Equations<br />
4.1 Bézoutain Algorithm<br />
4.2 Homogeneous and Non-homogeneous Equations<br />
4.3 Linear Diophantine Problems<br />
4.4 Extras<br />
5. Prime Factorizations<br />
5.1 Prime and Composite Numbers<br />
5.2 Fundamental Theorem of Arithmetic<br />
5.3 Applications of the Fundamental Theorem of Arithmetic<br />
5.4 Extras<br />
6. Rational and Irrational Numbers<br />
6.1 Fractions<br />
6.2 Decimals<br />
6.3 Real Numbers<br />
6.4 Extras<br />
7. Numeration Systems<br />
7.1 Arithmetic in Other Bases<br />
7.2 Conversion between Bases<br />
7.3 Applications of Other Bases<br />
7.4 Extras<br />
Appendix: A Legacy of Martin Gardner<br />
Solution to Odd-numbered Exercises<br />
Index<br />
About the Author</p>
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<h3>About the Author</h3>
<p>Andy Liu is a Professor Emeritus of the University of Alberta in Edmonton, Canada. He has a doctorate in mathematics as well as a professional diploma after degree in elementary education. Over his career, he was the person within the Department of Mathematical and Statistical Sciences with primary responsibility for designing and teaching the lone course offered to students in elementary education. He was the deputy leader of the USA team and the leader of the Canadian team in the International Mathematical Olympiad. He also ran a mathematical circle for junior high school students for thirty-two years. He authored ten other books prior to this volume, four of which were published by the Mathematical Association of America. He was a winner of the Deborah and Franklin Teppo-Haimo Award.</p>
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<h3>More MAA Books by Andy Liu</h3>
<p><a href="http://maa-store.hostedbywebstore.com/HUNGARIAN-PROBLEM-BOOK-III-COMPETITIONS/dp/0883856441">Hungarian Problem Book III</a><br />
<a href="http://www.maa.org/press/books/hungarian-problem-book-iv">Hungarian Problem Book IV</a> (with Robert Barrington)<br />
<a href="http://www.maa.org/press/books/the-alberta-high-school-math-competitions-1957-2006-a-canadian-problem-book">The Alberta High School Math Competitions 1957-2006: A Canadian Problem Books</a><br />
<a href="http://www.maa.org/press/books/problems-from-murray-klamkin-the-canadian-collection">Problems from Murray Klamkin: The Canadian Collection</a> (with Bruce Shawyer)</p>
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<a href="/tags/teaching-mathematics">Teaching Mathematics</a> </div>
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http://www.maa.org/press/books/the-g-h-hardy-reader
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<h3>Donald J. Albers, Gerald L. Alexanderson, and William Dunham, Editors</h3>
<p>Catalog Code: THR<br />
Print ISBN: 978-1-10759-464-7<br />
331 pp., Paperbound, 2015<br />
List Price: $49.99<br />
Member Price: $39.99<br />
Series: Spectrum</p>
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<p>G. H. Hardy (1877-1947) ranks among the great mathematicians of the 20th century. He did essential research in number theory and analysis, held professorships at Cambridge and Oxford, wrote classic textbooks, and famously collaborated with J. E. Littlewood and Srinivasa Ramanujan. Hardy was a colorful character with remarkable expository skills. And he was nuts about cricket.</p>
<p>This book is a feast of G. H. Hardy's writing. There are selections of his mathematical papers, his book reviews, his tributes to departed colleagues. Some articles are serious, and others display his wry sense of humor. To these are added recollections by those who knew Hardy, along with biographical and mathematical pieces written explicitly for this collection.</p>
<p>Those who have read <em>A Mathematician's Apology</em> know that G. H. Hardy could stand alongside the best mathematical expositors of all time. As a consequence, this <em>Reader</em> should be a treat for everyone from the interested amateur to the serious mathematician.</p>
<h3>Table of Contents</h3>
<p style="margin-left:20px">I. Biography<br />
II. Writings by and about G. H. Hardy<br />
III. Mathematics<br />
IV. Tributes<br />
V. Book Reviews<br />
A. Last Word<br />
Sources<br />
Acknowledgements<br />
Index<br />
About the Editors</p>
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<a href="/tags/biography">Biography</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>Fri, 06 Nov 2015 20:06:05 +0000swebb682489 at http://www.maa.orghttp://www.maa.org/press/books/the-g-h-hardy-reader#commentsMath through the Ages: A Gentle History for Teachers and Others
http://www.maa.org/press/books/math-through-the-ages-a-gentle-history-for-teachers-and-others
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<h3>William P. Berlinghoff and Fernando Q. Gouvêa</h3>
<p>Expanded 2nd Edition<br />
Catalog Code: MEX2E<br />
Print ISBN: 978-1-93951-212-3<br />
331 pp., Hardbound, 2015<br />
List Price: $55.00<br />
Member Price: $44.00<br />
Series: MAA Textbooks</p>
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<p>What's new in this edition? We have added new content and also tried to make improvements to the existing material.</p>
<p>There are five new historical sketches, on:</p>
<ol>
<li>The tangent function and how it made its way into trigonometry.</li>
<li>Logarithms, both decimal and natural.</li>
<li>Conic sections: ellipses, parabolas, and hyperbolas.</li>
<li>Irrational numbers.</li>
<li>The derivative.</li>
</ol>
<p>As always, each of these comes with Questions and Projects that try to address both the mathematics and the history, challenging students to go deeper into the topic.</p>
<p>We also worked through the whole book to improve, correct, and update. Research on the history of mathematics continues, and we have learned new things over the last ten years. Historians make mistakes, especially when they are quoting other historians, and we have tried to correct all the ones that we knew about. Many new books have been published over the last dozen years, so the bibliography has been completely updated and the notes on "what to read next" reflect the latest resources. The questions and projects have been examined and, when it seemed appropriate, revised. The <em>Instructor's Guide</em> was thoroughly revised as well.</p>
<h3>Table of Contents</h3>
<p style="margin-left:20px">Preface<br />
History in the Mathematics Classroom<br />
The History of Mathematics in a Large Nutshell<br />
Sketches<br />
What to Read Next<br />
When They Lived<br />
Bibliography<br />
Index<br />
About the Authors</p>
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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 />
Member Price: $36.00<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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<a href="/tags/recreational-mathematics">Recreational 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, 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: GIL<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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<a href="/tags/euclidean-geometry">Euclidean Geometry</a>, </div>
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<a href="/tags/geometry">Geometry</a>, </div>
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<a href="/tags/hyperbolic-geometry">Hyperbolic 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/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
http://www.maa.org/press/books/the-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 />
Series: MAA Textbooks</p>
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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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</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>Mon, 28 Sep 2015 12:42:53 +0000swebb665912 at http://www.maa.orghttp://www.maa.org/press/books/the-lebesgue-integral-for-undergraduates#commentsThinking Geometrically: A Survey of Geometries
http://www.maa.org/press/books/thinking-geometrically-a-survey-of-geometries
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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>
<h3>Extra Documents</h3>
<p><a href="/sites/default/files/pdf/pubs/books/TGSG_errata.pdf">Errata</a></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>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
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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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<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/dolciani">Dolciani</a></div></div></div>Tue, 18 Aug 2015 13:53:32 +0000swebb654365 at http://www.maa.orghttp://www.maa.org/press/books/a-mathematical-space-odyssey-solid-geometry-in-the-21st-century#commentsA Century of Advancing Mathematics
http://www.maa.org/press/books/a-century-of-advancing-mathematics
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<div><img alt="A Century of Advancing Mathematics" src="/sites/default/files/images/pubs/books/covers/CAMcover.jpg" style="width: 180px; height: 258px;" title="A Century of Advancing Mathematics" /></div>
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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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<div id="leftbook">
<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>
<!---<h3>(p. 3)</h3>
<p>
</p>
<h3>
About the Author</h3>
<p></p>
<h3>
MAA Review</h3>
<p>Continued...</p>---></div>
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<a href="/tags/history-of-mathematics">History of Mathematics</a> </div>
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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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<div><img alt="Trigonometry: A Clever Study Guide" src="/sites/default/files/images/pubs/books/covers/CLP-1cover.jpg" style="width: 180px; height: 277px;" title="Trigonometry: A Clever Study Guide" /></div>
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<div id="rightcolumn">
<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>
</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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<div class="field-label">Tags: </div>
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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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<p><img alt="An Invitation to Real Analysis" src="/sites/default/files/images/pubs/books/covers/IRAcover.jpg" style="width: 200px; height: 285px; border-width: 1px; border-style: solid;" title="An Invitation to Real Analysis" /></p>
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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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<div id="leftbook">
<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>
<!---<h3>(p. 3)</h3>
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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>
</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>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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<div><img alt="The Heart of Calculus: Explorations and Applications" src="/sites/default/files/images/pubs/books/covers/HCEAcover.jpg" style="width: 180px; height: 257px; border-width: 1px; border-style: solid;" title="The Heart of Calculus: Explorations and Applications" /></div>
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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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<div id="leftbook">
<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>
<!---<h3>(p. 3)</h3>
<p>
</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/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>
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About the Authors</h3>
<p></p>
<h3>
MAA Review</h3>
<p>Continued...</p>---></div>
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<a href="/tags/biography">Biography</a>, </div>
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<a href="/tags/communicating-mathematics">Communicating Mathematics</a>, </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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<a href="/tags/psychology-of-mathematics">Psychology 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>
<p><a href="/sites/default/files/doc/pubs/books/CCA_Errata_1st_printing.pdf">Errata</a></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>
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<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>
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<a href="/tags/calculus">Calculus</a>, </div>
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<a href="/tags/textbooks">Textbooks</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#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>
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<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#comments