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This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

Product Description
This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

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Georg Cantor, the founder of set theory, published his last paper on sets in 1897. In 1900, David Hilbert made Cantor's Continuum Problem and the challenge of well-ordering the real numbers the first problem of his famous lecture at the international congress in Paris. Thus, as the nineteenth century came to a close and the twentieth century began, Cantor's work was finally receiving its due and Hilbert had made one of Cantor's most important conjectures his number one problem. It was time for the second generation of Cantorians to emerge.Foremost among this group were Ernst Zermelo and Felix Hausdorff. Zermelo isolated the Choice Principle, proved that every set could be well-ordered, and axiomatized the concept of set. He became the father of abstract set theory. Hausdorff eschewed foundations and developed set theory as a branch of mathematics worthy of study in its own right, capable of supporting both general topology and measure theory. He is recognized as the era's leading Cantorian.Hausdorff published seven articles in set theory during the period 1901-1909, mostly about ordered sets. This volume contains translations of these papers with accompanying introductory essays. They are highly accessible, historically significant works, important not only for set theory, but also for model theory, analysis and algebra.This book is suitable for graduate students and researchers interested in set theory and the history of mathematics. ... Read more

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Readings for Calculus
MAA Notes

Presents readings on the history of calculus and of mathematics, on the nature of mathematics and its applications, on the learning of calculus, and on the place of calculus and mathematics in society. Can be used as a supplement to any calculus text. ... Read more

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Publisher: London : Williams and NorgatePublication date: 1891Subjects: CalculusFunctionsNotes: This is an OCR reprint. There may be numerous typos or missing text. There are no illustrations or indexes.When you buy the General Books edition of this book you get free trial access to Million-Books.com where you can select from more than a million books for free. You can also preview the book there. ... Read more

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This is a serious--but not solemn--textbook that attempts to make a clear, conceptual understanding of calculus accessible to all liberal arts students. It presents mathematics as growing out of the classical liberal arts to form a natural bridge between the humanities and the sciences, integrating the history and pedagogy of mathematics in a way that may be of interest to prospective teachers as well. Instead of a pre-calculus review, this book offers an historical development of much of the geometry and algebra needed, emphasizing the fundamental need for students to develop a clear style of writing.

Calculus is here largely restricted to the study of algebraic functions, but all the usual aspects of the interplay between functions and derivatives are covered: optimization, instantaneous rates, Newton's method, freely falling bodies, antiderivatives, integrals, areas, volumes, etc. The fundamental theorem is prominently featured and carefully treated. A brief final chapter about the intellectual climate surrounding the development of calculus offers students further insight into the place of mathematics as an element in the history of thought.

With only a modest amount of high school mathematics required as background and algebraic manipulations kept at a simple level (except for optional material giving stronger students brief glimpses of deeper ideas of real analysis) this text is suitable for a one-semester course designed to fulfill general education requirements. ... Read more

Customer Reviews (2)

Unhealthy rigour-hype
This is on the whole a pretty decent book "intended primarily for liberal arts students" (p. vii). There are some occasional intriguing remarks and stimulating exercises here and there that make this book slightly more interesting than the traditional ones for this audience. But that is not saying much, of course.

I shall argue, however, that the book does it readers generally and its intended clientele especially a major disservice by placing undue emphasis on modern so-called rigour. Although the author claims that his "approach is basically historical in nature" (p. ix), he shares the contempt for early calculus so fashionable with his colleagues, propagating such myths as the ridiculous claim that "mathematicians of the Enlightenment were using their instinct more than their intellect" (p. 310).

Another very harmful myth is this: "What does it mean to assert that the area pictured above is 6 square units? ... Is it nonsense to speak of the 'area' inside a curved figure? This question was profoundly considered long ago by Archimedes" (p. 238).

Riemann sums supposedly "lead to a clear understanding of what is meant by the area beneath a curve" (p. 255), but despite being allegedly so "clear" we can't actually do much with this sterile notion. In fact we cannot even prove that areas as given by this "clear" definition even exist: "the proof of the existence theorem is better left to a course in analysis" (p. 264). Similarly, discussions of both parts of the fundamental theorem of calculus end on the same disappointing note that a complete proof is "better deferred to a course in analysis" (p. 243, 267).

The intended readers---liberal arts students, remember---will of course not go on to this course in analysis. This will most likely be the last they see of mathematics. They will be left with the impression that a central issue of the calculus, on which mathematicians have spent thousands of years of "profound" thought, is whether the notion of area of a curved figure is "nonsense." They will also be left with the impression that they ought not think for themselves but should rather "defer" understanding of key theorems to the experts, their own feeble attempts being restricted to mere "instinct" rather than "intellect."

Great Survey of the Calculus
Priestley's work is a gem in that it incorporates the full-orbed liberal arts approach to the calculus. Professor Priestley places the differential and integral calculus in the context of history (the best methodology for teaching any aspect of mathematics). You will also find a good number of brain-expanding exercises and real world applications strategically placed in the text. This book is a "must-have" text for any teacher of mathematics and for a student who desires to understand the calculus in the context of history, science, philosophy, and literature. This is education at its best! ... Read more

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A HISTORY OF MATHEMATICS (1894) ... Read more

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Walter Rudin's memoirs should prove to be a delightful read specifically to mathematicians, but also to historians who are interested in learning about his colorful history and ancestry. Characterized by his personal style of elegance, clarity, and brevity, Rudin presents in the first part of the book his early memories about his family history, his boyhood in Vienna throughout the 1920s and 1930s, and his experiences during World War II.Part II offers samples of his work, in which he relates where problems came from, what their solutions led to, and who else was involved. As those who are familiar with Rudin's writing will recognize, he brings to this book the same care, depth, and originality that is the hallmark of his work.Co-published with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners. ... Read more

Customer Reviews (2)

Portrait of a brilliant, deeply humane man
This is an inspirational and often moving biography of one of the great mathematicians of our century. Hadamard was not only a brilliant mathematician, but a stimulating mentor, a man of wide-ranging knowledge, insatiable curiosity, humility, and most of all, great humanity. When Japaninvaded Manchuria, he proposed that the League of Nations sendpeace-keeping forces there, only to face ridicule from the French press.Hadamard, more than most of us, deeply felt the tragic wastefulness of war.He lost two beloved sons in World War I. Of his son, Etienne, he once said:"what I did in mathematics is nothing compared to what he could do ifhe were alive today." (Half of the brilliant graduates of the EcoleNormale were killed in that war). I finished this book with feelings ofgratitude and regret--gratitude to Hadamard for sharing his remarkablegifts with such generosity, and deep regret that "fate" was sogrievously unfair to him.

Inspirational and moving
This is an inspirational and often moving biography of one of the great mathematicians of our century. Hadamard was not only a brilliant mathematician, but a stimulating mentor, a man of wide-ranging knowledge,insatiable curiosity, humility, and most of all, great humanity. When Japaninvaded Manchuria, he proposed that the League of Nations send peacekeepingforces there, only to face ridicule from the French press. Hadamard, morethan most of us, deeply felt the tragic wastefulness of war. He lost twobeloved sons in World War I. Of his son Etienne, he once said: "what Idid in mathematics is nothing compared with what he could do if he werealive today."(As the book points out, half the brilliant graduates ofthe Ecole Normale were killed in that war). I finished this book withfeelings of gratitude and regret--gratitude to Hadamard for sharing hisremarkable gifts with such generosity, and deep regret that"fate" was so grievously unfair to him. ... Read more

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A collection of 13 articles relating to developments in the history of 18th-century exact science, focusing on the writings of such figures as Jean d'Alembert, Leonhard Euler, and Joseph Louis Lagrange. The volume presents their work on the principles of calculus and the theory of motion, and serves to clarify the conceptual foundation of analysis and mechanics in the century following Newton. A detailed historical and critical study of conceptual change involving fundamental links between pure and applied mathematics is provided. ... Read more

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This book contains essays on Ramanujan and his work , as well as important survey articles in areas influenced by Ramanujan's mathematics. Most of the articles in the book are nontechnical, but even those that are more technical contain substantial sections that will engage the general reader.

The book opens with the only four existing photographs of Ramanujan, presenting historical accounts and information about other people in the photos. This section includes an account of a cryptic family history written by his younger brother, S. Lakshmi Narasimhan. Following are articles on Ramanujan's illness by R. A. Rankin, the British physician D. A. B. Young, and Nobel laureate S. Chandrasekhar. They present a study of his symptoms, a convincing diagnosis of the cause of his death, and a thorough exposition of Ramanujan's life as a patient in English sanitariums and nursing homes.

Following this are biographies of S. Janaki (Mrs. Ramanujan) and S. Narayana Iyer, Chief Accountant of the Madras Port Trust Office, who first communicated Ramanujan's work to the Journal of the Indian Mathematical Society. The last half of the book begins with a section on "Ramanujan's Manuscripts and Notebooks". Included is an important article by G. E. Andrews on Ramanujan's lost notebook.

The final two sections feature both nontechnical articles, such as Jonathan and Peter Borwein's "Ramanujan and pi", and more technical articles by Freeman Dyson, Atle Selberg, Richard Askey, and G. N. Watson.

This volume complements the book Ramanujan: Letters and Commentary, Volume 9, in the AMS series, History of Mathematics. For more on Ramanujan, see these AMS publications, Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, Volume 136.H, and Collected Papers of Srinivasa Ramanujan, Volume 159.H, in the AMS Chelsea Publishing series.

Copublished with the London Mathematical Society. ... Read more

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After completing his famous Foundations of Analysis (See AMS Chelsea Publishing, Volume 79.H for the English Edition and AMS Chelsea Publishing, Volume 141 for the German Edition, Grundlagen der Analysis), Landau turned his attention to this book on calculus. The approach is that of an unrepentant analyst, with an emphasis on functions rather than on geometric or physical applications. The book is another example of Landau's formidable skill as an expositor. It is a masterpiece of rigor and clarity. ... Read more

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The meaning of analysis
This book would more correctly be described as a book on analysis, because of the completeness of its proofs. It assumes you know just arithmetic of natural numbers, integers, rational, real and complex numbers-that is to say, just how to sum, multiply, subtract and divide. Edmund Landau wrote a masterpiece, because nothing is left without proof. You will not find a single step missing. From arithmetic to all the concepts of calculus, like differentiation, integration, infinite series and sequences, this book contains the mathematics that most mathematicians should know presented in a perfect way. It is not easy reading, though. Landau strives to reach the perfect axiomatic presentation, so like Euclid's "Elements" the book is the clear and beautiful presentation of a doctrine. I dare say that no book in analysis approaches Euclid's ideal of presentation better than Landau's, never in the past and never in the future. What you will find in this book is, in its best appearance, truth, that will not change even in a thousand years. ... Read more

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Guicciardini presents a comprehensive survey of both the research and teaching of Newtonian calculus, the calculus of "fluxions", over the period between 1700 and 1810.Although Newton was one of the inventors of calculus, the developments in Britain remained separate from the rest of Europe for over a century.While it is usually maintained that after Newton there was a period of decline in British mathematics, the author's research demonstrates that the methods used by researchers of the period yielded considerable success in laying the foundations and investigating the applications of the calculus.Even when "decline" set in, in mid century, the foundations of the reform were being laid, which were to change the direction and nature of the mathematics community. The book considers the importance of Isaac Newton, Roger Cotes, Brook Taylor, James Stirling, Abraham de Moivre, Colin Maclaurin, Thomas Bayes, John Landen and Edward Waring.This will be a useful book for students and researchers in the history of science, philosophers of science and undergraduates studying the history of mathematics. ... Read more

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"An attempt has been made in these pages to trace the evolution of intellectual thought in the progress of astronomical discovery, and, by recognising the different points of view of the different ages, to give due credit even to the ancients. No one can expect, in a history of astronomy of limited size, to find a treatise on practical or on theoretical astronomy, nor a complete descriptive astronomy, and still less a book on speculative astronomy. Something of each of these is essential, however, for tracing the progress of thought and knowledge which it is the object of this History to describe. " ... Read more

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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.

*AP is a registered trademark of the College Board, which was not involved in the production of this publication