The Heart of Calculus

The Heart of Calculus
Author: Philip M. Anselone
Publisher: American Mathematical Soc.
Total Pages: 248
Release: 2015-12-31
Genre: Mathematics
ISBN: 0883857871

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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.

The Heart of Calculus

The Heart of Calculus
Author: Philip M. Anselone
Publisher: American Mathematical Soc.
Total Pages: 228
Release: 2015-12-31
Genre: Mathematics
ISBN: 1614441189

Download The Heart of Calculus Book in PDF, Epub and Kindle

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.

The Heart of Mathematics

The Heart of Mathematics
Author: Edward B. Burger
Publisher: Springer Science & Business Media
Total Pages: 798
Release: 2004-08-18
Genre: Mathematics
ISBN: 9781931914413

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Hallmark features include: * A focus on the important ideas of mathematics that students will retain long after their formal studies are complete. * An engaging and humorous style, written to be read and enjoyed. * Ten Life Lessons that readers will apply beyond their study of mathematics. * Use of a variety of visualization techniques that direct students to model their thinking and to actively explore the world around them. New to this Edition: * A new chapter, Deciding Wisely: Applications of Rigorous Thought, provides a thought-provoking capstone. * Expanded and improved statistics and probability content in Chapter 7, Taming Uncertainty. * Enhanced Mindscapes at the end of each section which ask the reader to review, apply and think deeply about the ideas presented in the chapter. * Radically superior ancillary package.

Love and Math

Love and Math
Author: Edward Frenkel
Publisher: Basic Books
Total Pages: 314
Release: 2013-10-01
Genre: Mathematics
ISBN: 0465069959

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An awesome, globe-spanning, and New York Times bestselling journey through the beauty and power of mathematics What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren't even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry. In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we've never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space. Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man's journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century's leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat's last theorem, that had seemed intractable before. At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

The Calculus of Friendship

The Calculus of Friendship
Author: Steven Strogatz
Publisher: Princeton University Press
Total Pages: 181
Release: 2011-03-07
Genre: Mathematics
ISBN: 1400830885

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The Calculus of Friendship is the story of an extraordinary connection between a teacher and a student, as chronicled through more than thirty years of letters between them. What makes their relationship unique is that it is based almost entirely on a shared love of calculus. For them, calculus is more than a branch of mathematics; it is a game they love playing together, a constant when all else is in flux. The teacher goes from the prime of his career to retirement, competes in whitewater kayaking at the international level, and loses a son. The student matures from high school math whiz to Ivy League professor, suffers the sudden death of a parent, and blunders into a marriage destined to fail. Yet through it all they take refuge in the haven of calculus--until a day comes when calculus is no longer enough. Like calculus itself, The Calculus of Friendship is an exploration of change. It's about the transformation that takes place in a student's heart, as he and his teacher reverse roles, as they age, as they are buffeted by life itself. Written by a renowned teacher and communicator of mathematics, The Calculus of Friendship is warm, intimate, and deeply moving. The most inspiring ideas of calculus, differential equations, and chaos theory are explained through metaphors, images, and anecdotes in a way that all readers will find beautiful, and even poignant. Math enthusiasts, from high school students to professionals, will delight in the offbeat problems and lucid explanations in the letters. For anyone whose life has been changed by a mentor, The Calculus of Friendship will be an unforgettable journey.

The Humongous Book of Calculus Problems

The Humongous Book of Calculus Problems
Author: W. Michael Kelley
Publisher: Penguin
Total Pages: 578
Release: 2013-11-07
Genre: Mathematics
ISBN: 1615646973

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Now students have nothing to fear! Math textbooks can be as baffling as the subject they're teaching. Not anymore. The best-selling author of The Complete Idiot's Guide® to Calculus has taken what appears to be a typical calculus workbook, chock full of solved calculus problems, and made legible notes in the margins, adding missing steps and simplifying solutions. Finally, everything is made perfectly clear. Students will be prepared to solve those obscure problems that were never discussed in class but always seem to find their way onto exams. --Includes 1,000 problems with comprehensive solutions --Annotated notes throughout the text clarify what's being asked in each problem and fill in missing steps --Kelley is a former award-winning calculus teacher

The Hidden Reality

The Hidden Reality
Author: Brian Greene
Publisher: Penguin UK
Total Pages: 502
Release: 2012
Genre: Science
ISBN: 0141029811

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There was a time when 'universe' meant all there is. Everything. Yet, as Brian Greene's extraordinary book shows, ours may be just one universe among many, like endless reflections in a mirror. He takes us on a captivating exploration of parallel worlds - from a multiverse where an infinite number of your doppelg ngers are reading this sentence, to vast oceans of bubble universes and even multiverses made of mathematics - showing just how much of reality's true nature may be hidden within them.

Calculus I by Heart

Calculus I by Heart
Author: J. Austin French
Publisher:
Total Pages:
Release: 2004-03-01
Genre: Calculus
ISBN: 9780974800387

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The Heart of Mathematics

The Heart of Mathematics
Author: Edward B. Burger
Publisher: John Wiley & Sons
Total Pages: 948
Release: 2009-08-01
Genre: Mathematics
ISBN: 9780470586594

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The Heart of Mathematics: An invitation to effective thinking --now in its second edition--succeeds at reaching non-math, non-science-oriented readers and encourages them to discover the mathematics inherent in the world around them. Infused throughout with the authors' humor and enthusiasm, The Heart of Mathematics introduces readers to the most important and interesting ideas in mathematics while inspiring them to actively engage in mathematical thinking.