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Paradoxes And Sophisms In Calculus
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Book Synopsis Paradoxes and Sophisms in Calculus by : Sergiy Klymchuk
Download or read book Paradoxes and Sophisms in Calculus written by Sergiy Klymchuk and published by American Mathematical Soc.. This book was released on 2013-12-31 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paradoxes and Sophisms in Calculus offers a delightful supplementary resource to enhance the study of single variable calculus. By the word paradox the [Author];s mean a surprising, unexpected, counter-intuitive statement that looks invalid, but in fact is true. The word sophism describes intentionally invalid reasoning that looks formally correct, but in fact contains a subtle mistake or flaw. In other words, a sophism is a false proof of an incorrect statement. A collection of over fifty paradoxes and sophisms showcases the subtleties of this subject and leads students to contemplate the underlying concepts. A number of the examples treat historically significant issues that arose in the development of calculus, while others more naturally challenge readers to understand common misconceptions. Sophisms and paradoxes from the areas of functions, limits, derivatives, integrals, sequences, and series are explored.
Book Synopsis Cameos for Calculus by : Roger B. Nelsen
Download or read book Cameos for Calculus written by Roger B. Nelsen and published by American Mathematical Soc.. This book was released on 2015-12-31 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thespian or cinematographer might define a cameo 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. 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. Many of the cameos are adapted from articles published in journals of the MAA, such as The American Mathematical Monthly, Mathematics Magazine, and The College Mathematics Journal. Some come from other mathematical journals, and some were created for this book. By gathering the cameos into a book the [Author]; hopes that they will be more accessible to teachers of calculus, both for use in the classroom and as supplementary explorations for students.
Book Synopsis The Heart of Calculus by : Philip M. Anselone
Download or read book The Heart of Calculus written by Philip M. Anselone and published by American Mathematical Soc.. This book was released on 2015-12-31 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. 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.
Book Synopsis Introduction to the Mathematics of Computer Graphics by : Nathan Carter
Download or read book Introduction to the Mathematics of Computer Graphics written by Nathan Carter and published by American Mathematical Soc.. This book was released on 2016-12-31 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text, by an award-winning [Author];, was designed to accompany his first-year seminar in the mathematics of computer graphics. Readers learn the mathematics behind the computational aspects of space, shape, transformation, color, rendering, animation, and modeling. The software required is freely available on the Internet for Mac, Windows, and Linux. The text answers questions such as these: How do artists build up realistic shapes from geometric primitives? What computations is my computer doing when it generates a realistic image of my 3D scene? What mathematical tools can I use to animate an object through space? Why do movies always look more realistic than video games? Containing the mathematics and computing needed for making their own 3D computer-generated images and animations, the text, and the course it supports, culminates in a project in which students create a short animated movie using free software. Algebra and trigonometry are prerequisites; calculus is not, though it helps. Programming is not required. Includes optional advanced exercises for students with strong backgrounds in math or computer science. Instructors interested in exposing their liberal arts students to the beautiful mathematics behind computer graphics will find a rich resource in this text.
Book Synopsis 101 Careers in Mathematics by : Andrew Sterrett
Download or read book 101 Careers in Mathematics written by Andrew Sterrett and published by American Mathematical Soc.. This book was released on 2014-12-31 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third edition of the immensely popular 101 Careers in Mathematics contains updates on the career paths of individuals profiled in the first and second editions, along with many new profiles. No career counselor should be without this valuable resource. The [Author];s of the essays in this volume describe a wide variety of careers for which a background in the mathematical sciences is useful. Each of the jobs presented shows real people in real jobs. Their individual histories demonstrate how the study of mathematics was useful in landing well-paying jobs in predictable places such as IBM, AT & T, and American Airlines, and in surprising places such as FedEx Corporation, L.L. Bean, and Perdue Farms, Inc. You will also learn about job opportunities in the Federal Government as well as exciting careers in the arts, sculpture, music, and television. There are really no limits to what you can do if you are well prepared in mathematics. The degrees earned by the [Author];s profiled here range from bachelor's to master's to PhD in approximately equal numbers. Most of the writers use the mathematical sciences on a daily basis in their work. Others rely on the general problem-solving skills acquired in mathematics as they deal with complex issues.
Book Synopsis Writing Projects for Mathematics Courses by : Annalisa Crannell
Download or read book Writing Projects for Mathematics Courses written by Annalisa Crannell and published by American Mathematical Soc.. This book was released on 2004-12-31 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Writing Projects for Mathematics Courses is a collection of writing projects suitable for a wide range of undergraduate mathematics courses, from a survey of mathematics to differential equations. The projects vary in their level of difficulty and in the mathematics that they require but are similar in the mode of presentation and use of applications. Students see these problems as real in a way that textbook problems are not, even though many of the characters involved (e.g. dime-store detectives and CEOs) are obviously fictional. The stories are sometimes fanciful and sometimes grounded in standard scientific applications, but the mere existence of the story draws the students in and makes the problem relevant.
Book Synopsis Mathematical and Algorithmic Puzzles by : Pramod Ganapathi
Download or read book Mathematical and Algorithmic Puzzles written by Pramod Ganapathi and published by . This book was released on 2024-05-29 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents serious mathematical and algorithmic puzzles that are mostly counterintuitive. The presented puzzles are simultaneously entertaining, challenging, intriguing, and haunting. This book introduces its readers to counterintuitive mathematical ideas and revolutionary algorithmic insights from a wide variety of topics. The presented solutions that are discovered by many mathematicians and computer scientists are highly counterintuitive and show supreme mathematical beauty. These counterintuitive solutions are intriguing to the degree that they shatter our preconceived notions, shake our long-held belief systems, debunk our fundamental intuitions, and finally rob us of sleep and haunt us for a lifetime. Multiple ways of attacking the same puzzle are presented which teach the application of elegant problem-solving strategies.
Book Synopsis Essays on Mathematical Reasoning by : Jerzy Pogonowski
Download or read book Essays on Mathematical Reasoning written by Jerzy Pogonowski and published by LIT Verlag Münster. This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains four essays which may attract the attention of those readers, who are interested in mathematical cognition The main issues and questions addressed include: How do we achieve understanding of mathematical notions and ideas? What benefits can be obtained from mistakes of great mathematicians? Which mathematical objects are standard and which are pathological? Is it possible characterize the intended models of mathematical theories in a unique way?
Book Synopsis Arithmetical Wonderland by : Andy Liu
Download or read book Arithmetical Wonderland written by Andy Liu and published by American Mathematical Soc.. This book was released on 2015-12-31 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arithmetical Wonderland 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. 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 Through the Looking Glass. 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. 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.
Book Synopsis Game Theory through Examples by : Erich Prisner
Download or read book Game Theory through Examples written by Erich Prisner and published by American Mathematical Soc.. This book was released on 2014-12-31 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Game Theory through Examples is a thorough introduction to elementary game theory, covering finite games with complete information. The core philosophy underlying this volume is that abstract concepts are best learned when encountered first (and repeatedly) in concrete settings. Thus, the essential ideas of game theory are here presented in the context of actual games, real games much more complex and rich than the typical toy examples. All the fundamental ideas are here: Nash equilibria, backward induction, elementary probability, imperfect information, extensive and normal form, mixed and behavioral strategies. The active-learning, example-driven approach makes the text suitable for a course taught through problem solving. Students will be thoroughly engaged by the extensive classroom exercises, compelling homework problems, and nearly sixty projects in the text. Also available are approximately eighty Java applets and three dozen Excel spreadsheets in which students can play games and organize information in order to acquire a gut feeling to help in the analysis of the games. Mathematical exploration is a deep form of play; that maxim is embodied in this book. Game Theory through Examples is a lively introduction to this appealing theory. Assuming only high school prerequisites makes the volume especially suitable for a liberal arts or general education spirit-of-mathematics course. It could also serve as the active-learning supplement to a more abstract text in an upper-division game theory course.
Book Synopsis Exploring Advanced Euclidean Geometry with GeoGebra by : Gerard A. Venema
Download or read book Exploring Advanced Euclidean Geometry with GeoGebra written by Gerard A. Venema and published by American Mathematical Soc.. This book was released on 2013-12-31 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an inquiry-based introduction to advanced Euclidean geometry. It utilizes dynamic geometry software, specifically GeoGebra, to explore the statements and proofs of many of the most interesting theorems in the subject. Topics covered include triangle centers, inscribed, circumscribed, and escribed circles, medial and orthic triangles, the nine-point circle, duality, and the theorems of Ceva and Menelaus, as well as numerous applications of those theorems. The final chapter explores constructions in the Poincare disk model for hyperbolic geometry. The book can be used either as a computer laboratory manual to supplement an undergraduate course in geometry or as a stand-alone introduction to advanced topics in Euclidean geometry. The text consists almost entirely of exercises (with hints) that guide students as they discover the geometric relationships for themselves. First the ideas are explored at the computer and then those ideas are assembled into a proof of the result under investigation. The goals are for the reader to experience the joy of discovering geometric relationships, to develop a deeper understanding of geometry, and to encourage an appreciation for the beauty of Euclidean geometry.
Book Synopsis Ordinary Differential Equations by : David A. Sanchez
Download or read book Ordinary Differential Equations written by David A. Sanchez and published by American Mathematical Soc.. This book was released on 2002-12-31 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the instructor or student confronting an introductory course in ordinary differential equations there is a need for a brief guide to the key concepts in the subject. Important topics like stability, resonance, existence of periodic solutions, and the essential role of continuation of solutions are often engulfed in a sea of exercises in integration, linear algebra theory, computer programming and an overdose of series expansions. This book is intended as that guide. It is more conceptual than definitive and more light-hearted than pedagogic. It covers key topics and theoretical underpinnings that are necessary for the study of rich topics like nonlinear equations or stability theory. The [Author]; has included a great many illuminating examples and discussions that uncover the conceptual heart of the matter.
Book Synopsis Beyond the Quadratic Formula by : Ron Irving
Download or read book Beyond the Quadratic Formula written by Ron Irving and published by American Mathematical Soc.. This book was released on 2020-01-29 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quadratic formula for the solution of quadratic equations was discovered independently by scholars in many ancient cultures and is familiar to everyone. Less well known are formulas for solutions of cubic and quartic equations whose discovery was the high point of 16th century mathematics. Their study forms the heart of this book, as part of the broader theme that a polynomial's coefficients can be used to obtain detailed information on its roots. The book is designed for self-study, with many results presented as exercises and some supplemented by outlines for solution. The intended audience includes in-service and prospective secondary mathematics teachers, high school students eager to go beyond the standard curriculum, undergraduates who desire an in-depth look at a topic they may have unwittingly skipped over, and the mathematically curious who wish to do some work to unlock the mysteries of this beautiful subject.
Book Synopsis Discovering Discrete Dynamical Systems by : Aimee Johnson
Download or read book Discovering Discrete Dynamical Systems written by Aimee Johnson and published by American Mathematical Soc.. This book was released on 2017-12-31 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discovering Discrete Dynamical Systems is a mathematics textbook designed for use in a student-led, inquiry-based course for advanced mathematics majors. Fourteen modules each with an opening exploration, a short exposition and related exercises, and a concluding project guide students to self-discovery on topics such as fixed points and their classifications, chaos and fractals, Julia and Mandelbrot sets in the complex plane, and symbolic dynamics. Topics have been carefully chosen as a means for developing student persistence and skill in exploration, conjecture, and generalization while at the same time providing a coherent introduction to the fundamentals of discrete dynamical systems. This book is written for undergraduate students with the prerequisites for a first analysis course, and it can easily be used by any faculty member in a mathematics department, regardless of area of expertise. Each module starts with an exploration in which the students are asked an open-ended question. This allows the students to make discoveries which lead them to formulate the questions that will be addressed in the exposition and exercises of the module. The exposition is brief and has been written with the intent that a student who has taken, or is ready to take, a course in analysis can read the material independently. The exposition concludes with exercises which have been designed to both illustrate and explore in more depth the ideas covered in the exposition. Each module concludes with a project in which students bring the ideas from the module to bear on a more challenging or in-depth problem. A section entitled "To the Instructor" includes suggestions on how to structure a course in order to realize the inquiry-based intent of the book. The book has also been used successfully as the basis for an independent study course and as a supplementary text for an analysis course with traditional content.
Book Synopsis Proofs Without Words III by : Roger B. Nelsen
Download or read book Proofs Without Words III written by Roger B. Nelsen and published by American Mathematical Soc.. This book was released on 2015-12-31 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Mathematics Magazine and The College Mathematics Journal for many years, and the MAA published the collections of PWWs Proofs Without Words: Exercises in Visual Thinking in 1993 and Proofs Without Words II: More Exercises in Visual Thinking in 2000. This book is the third such collection of PWWs.
Book Synopsis Academic Skepticism in Hume and Kant by : Catalina González Quintero
Download or read book Academic Skepticism in Hume and Kant written by Catalina González Quintero and published by Springer Nature. This book was released on 2022-02-25 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an unprecedented study of the influence of the skepticism of the New Platonic Academy on David Hume’s and Immanuel Kant’s critiques of metaphysics. By demonstrating how the skeptical teachings of the Academy affected these authors’ Enlightened attacks on traditional metaphysics, this book deepens and broadens the burgeoning scholarship on the role that the Ancients schools of skepticism played in the configuration of Modern skeptical outlooks. It bolsters the newfound recognition that we must reconsider the conventional view that the revival of Pyrrhonism in the sixteenth and seventeenth centuries gave birth to Modern skepticism by incorporating the influence of Academic skepticism in the analysis. Giving a new impetus to this line of research, the author argues that Academic ideas and methods informed Hume’s and Kant’s critique of metaphysics in substantial and thus far unacknowledged ways. Specifically, she demonstrates the centrality of Academic skepticism to Hume’s epistemology and critique of religion through a detailed analysis of his theory of belief in the Treatise and the first Enquiry as well as of its application in the Dialogues concerning Natural Religion. Likewise, her analysis reveals how Kant’s anti-metaphysical stance, developed in the Transcendental Dialectic of the Critique of Pure Reason, contains many skeptical insights of Academic inspiration, bequeathed to him by Hume.
Book Synopsis Counterexamples in Calculus by : Sergiy Klymchuk
Download or read book Counterexamples in Calculus written by Sergiy Klymchuk and published by American Mathematical Soc.. This book was released on 2010-12-31 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: Counterexamples in Calculus serves as a supplementary resource to enhance the learning experience in single variable calculus courses. This book features carefully constructed incorrect mathematical statements that require students to create counterexamples to disprove them. Methods of producing these incorrect statements vary. At times the converse of a well-known theorem is presented. In other instances crucial conditions are omitted or altered or incorrect definitions are employed. Incorrect statements are grouped topically with sections devoted to: Functions, Limits, Continuity, Differential Calculus and Integral Calculus. This book aims to fill a gap in the literature and provide a resource for using counterexamples as a pedagogical tool in the study of introductory calculus.
