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Author: Caren L. Diefenderfer
Publisher: American Mathematical Soc.
ISBN: 0883857618
Category : Mathematics
Languages : en
Pages : 529
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Book Description
The Calculus Collection is a useful resource for everyone who teaches calculus, in high school or in a 2- or 4-year college or university. It consists of 123 articles, selected by a panel of six veteran high school teachers, each of which was originally published in Math Horizons, MAA Focus, The American Mathematical Monthly, The College Mathematics Journal, or Mathematics Magazine. The articles focus on engaging students who are meeting the core ideas of calculus for the first time. The Calculus Collection is filled with insights, alternate explanations of difficult ideas, and suggestions for how to take a standard problem and open it up to the rich mathematical explorations available when you encourage students to dig a little deeper. Some of the articles reflect an enthusiasm for bringing calculators and computers into the classroom, while others consciously address themes from the calculus reform movement. But most of the articles are simply interesting and timeless explorations of the mathematics encountered in a first course in calculus.
Author: Caren L. Diefenderfer
Publisher: American Mathematical Soc.
ISBN: 0883857618
Category : Mathematics
Languages : en
Pages : 529
Get Book Here
Book Description
The Calculus Collection is a useful resource for everyone who teaches calculus, in high school or in a 2- or 4-year college or university. It consists of 123 articles, selected by a panel of six veteran high school teachers, each of which was originally published in Math Horizons, MAA Focus, The American Mathematical Monthly, The College Mathematics Journal, or Mathematics Magazine. The articles focus on engaging students who are meeting the core ideas of calculus for the first time. The Calculus Collection is filled with insights, alternate explanations of difficult ideas, and suggestions for how to take a standard problem and open it up to the rich mathematical explorations available when you encourage students to dig a little deeper. Some of the articles reflect an enthusiasm for bringing calculators and computers into the classroom, while others consciously address themes from the calculus reform movement. But most of the articles are simply interesting and timeless explorations of the mathematics encountered in a first course in calculus.
Author: Aaron Sheehan-Dean
Publisher: Harvard University Press
ISBN: 067491631X
Category : History
Languages : en
Pages : 481
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Book Description
Winner of the Jefferson Davis Award Winner of the Johns Family Book Award Winner of the Army Historical Foundation Distinguished Writing Award “A work of deep intellectual seriousness, sweeping and yet also delicately measured, this book promises to resolve longstanding debates about the nature of the Civil War.” —Gregory P. Downs, author of After Appomattox Shiloh, Chancellorsville, Gettysburg—tens of thousands of soldiers died on these iconic Civil War battlefields, and throughout the South civilians suffered terrible cruelty. At least three-quarters of a million lives were lost during the American Civil War. Given its seemingly indiscriminate mass destruction, this conflict is often thought of as the first “total war.” But Aaron Sheehan-Dean argues for another interpretation. The Calculus of Violence demonstrates that this notoriously bloody war could have been much worse. Military forces on both sides sought to contain casualties inflicted on soldiers and civilians. In Congress, in church pews, and in letters home, Americans debated the conditions under which lethal violence was legitimate, and their arguments differentiated carefully among victims—women and men, black and white, enslaved and free. Sometimes, as Sheehan-Dean shows, these well-meaning restraints led to more carnage by implicitly justifying the killing of people who were not protected by the laws of war. As the Civil War raged on, the Union’s confrontations with guerrillas and the Confederacy’s confrontations with black soldiers forced a new reckoning with traditional categories of lawful combatants and raised legal disputes that still hang over military operations around the world today. In examining the agonizing debates about the meaning of a just war in the Civil War era, Sheehan-Dean discards conventional abstractions—total, soft, limited—as too tidy to contain what actually happened on the ground.
Author: William Johnston
Publisher: American Mathematical Society
ISBN: 1470465655
Category : Mathematics
Languages : en
Pages : 456
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Book Description
The book introduces complex analysis as a natural extension of the calculus of real-valued functions. The mechanism for doing so is the extension theorem, which states that any real analytic function extends to an analytic function defined in a region of the complex plane. The connection to real functions and calculus is then natural. The introduction to analytic functions feels intuitive and their fundamental properties are covered quickly. As a result, the book allows a surprisingly large coverage of the classical analysis topics of analytic and meromorphic functions, harmonic functions, contour integrals and series representations, conformal maps, and the Dirichlet problem. It also introduces several more advanced notions, including the Riemann hypothesis and operator theory, in a manner accessible to undergraduates. The last chapter describes bounded linear operators on Hilbert and Banach spaces, including the spectral theory of compact operators, in a way that also provides an excellent review of important topics in linear algebra and provides a pathway to undergraduate research topics in analysis. The book allows flexible use in a single semester, full-year, or capstone course in complex analysis. Prerequisites can range from only multivariate calculus to a transition course or to linear algebra or real analysis. There are over one thousand exercises of a variety of types and levels. Every chapter contains an essay describing a part of the history of the subject and at least one connected collection of exercises that together comprise a project-level exploration.
Author: Shahriar Shahriari
Publisher: American Mathematical Soc.
ISBN: 0821837508
Category : Mathematics
Languages : en
Pages : 314
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Book Description
Is there always a prime number between $n$ and $2n$? Where, approximately, is the millionth prime? And just what does calculus have to do with answering either of these questions? It turns out that calculus has a lot to do with both questions, as this book can show you. The theme of the book is approximations. Calculus is a powerful tool because it allows us to approximate complicated functions with simpler ones. Indeed, replacing a function locally with a linear--or higher order--approximation is at the heart of calculus. The real star of the book, though, is the task of approximating the number of primes up to a number $x$. This leads to the famous Prime Number Theorem--and to the answers to the two questions about primes. While emphasizing the role of approximations in calculus, most major topics are addressed, such as derivatives, integrals, the Fundamental Theorem of Calculus, sequences, series, and so on. However, our particular point of view also leads us to many unusual topics: curvature, Pade approximations, public key cryptography, and an analysis of the logistic equation, to name a few. The reader takes an active role in developing the material by solving problems. Most topics are broken down into a series of manageable problems, which guide you to an understanding of the important ideas. There is also ample exposition to fill in background material and to get you thinking appropriately about the concepts. Approximately Calculus is intended for the reader who has already had an introduction to calculus, but wants to engage the concepts and ideas at a deeper level. It is suitable as a text for an honors or alternative second semester calculus course.
Author: Michael Spivak
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 680
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Book Description
Author: Margaret L. Lial
Publisher: Addison-Wesley Longman
ISBN:
Category : Mathematics
Languages : en
Pages : 956
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Book Description
A calculus textbook that covers linear and nonlinear functions, derivatives, graphs, integration, differential equations, probability, sequences, and other related topics, and includes applications as well as reviews problems with answers to half of them.
Author: Robert Fraga
Publisher:
ISBN:
Category : Calculus
Languages : en
Pages : 302
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Book Description
Author: Glenn Ledder
Publisher: MAA
ISBN: 0883851911
Category : Education
Languages : en
Pages : 228
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Book Description
There is a gap between the extensive mathematics background that is beneficial to biologists and the minimal mathematics background biology students acquire in their courses. The result is an undergraduate education in biology with very little quantitative content. New mathematics courses must be devised with the needs of biology students in mind. In this volume, authors from a variety of institutions address some of the problems involved in reforming mathematics curricula for biology students. The problems are sorted into three themes: Models, Processes, and Directions. It is difficult for mathematicians to generate curriculum ideas for the training of biologists so a number of the curriculum models that have been introduced at various institutions comprise the Models section. Processes deals with taking that great course and making sure it is institutionalized in both the biology department (as a requirement) and in the mathematics department (as a course that will live on even if the creator of the course is no longer on the faculty). Directions looks to the future, with each paper laying out a case for pedagogical developments that the authors would like to see.
Author: Amy Shell-Gellasch
Publisher: MAA
ISBN: 0883851822
Category : Education
Languages : en
Pages : 191
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Book Description
In an increasingly electronic society, these exercises are designed to help school and collegiate educators use historical devices of mathematics to balance the digital side of mathematics.
Author: V. P. Orevkov
Publisher: University of Pennsylvania Press
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 252
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Book Description
