Ebook Number Theory: A Historical ApproachBy John J. Watkins

Ebook Number Theory: A Historical ApproachBy John J. Watkins

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Number Theory: A Historical ApproachBy John J. Watkins

Ebook Number Theory: A Historical ApproachBy John J. Watkins

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The natural numbers have been studied for thousands of years, yet most undergraduate textbooks present number theory as a long list of theorems with little mention of how these results were discovered or why they are important. This book emphasizes the historical development of number theory, describing methods, theorems, and proofs in the contexts in which they originated, and providing an accessible introduction to one of the most fascinating subjects in mathematics.

Written in an informal style by an award-winning teacher, Number Theory covers prime numbers, Fibonacci numbers, and a host of other essential topics in number theory, while also telling the stories of the great mathematicians behind these developments, including Euclid, Carl Friedrich Gauss, and Sophie Germain. This one-of-a-kind introductory textbook features an extensive set of problems that enable students to actively reinforce and extend their understanding of the material, as well as fully worked solutions for many of these problems. It also includes helpful hints for when students are unsure of how to get started on a given problem.

• Uses a unique historical approach to teaching number theory


• Features numerous problems, helpful hints, and fully worked solutions


• Discusses fun topics like Pythagorean tuning in music, Sudoku puzzles, and arithmetic progressions of primes


• Includes an introduction to Sage, an easy-to-learn yet powerful open-source mathematics software package


• Ideal for undergraduate mathematics majors as well as non-math majors


• Digital solutions manual (available only to professors)

• Sales Rank: #874014 in Books
• Published on: 2013-12-26
• Original language: English
• Number of items: 1
• Dimensions: 10.10" h x 1.30" w x 7.20" l, 2.60 pounds
• Binding: Hardcover
• 592 pages

Review
"An excellent contribution to the list of elementary number theory textbooks. Number theory, it is true, has as rich a history as any branch of mathematics, and Watkins has done terrific work in integrating the stories of the people behind this subject with the traditional topics of elementary number theory. There is more than enough material here for a one-semester course, and while this is standard for textbooks at this level, the added historical and biographical material--which cover mathematical developments and people well into the 20th century--are well worth the increased weight of the text."--Mark Bollman, MAA Reviews

From the Back Cover

"I know of no other book at this easily accessible level that combines extensive coverage of the mathematics with so many interesting biographical facts and anecdotes."--Thomas W. Cusick, University at Buffalo, State University of New York

"This is a very nice introductory text on number theory. It has a good selection of topics, lots of nice history, and many exercises. There is a lot to like here."--David A. Cox, Amherst College

"Watkins has advanced an outstanding and engaging treatise on the elementary theory of numbers. I expect it to be extremely valuable in inspiring young minds to think deeply about mathematics, and intend to use this text in my own courses on the topic."--Alex Kontorovich, Yale University

About the Author
John J. Watkins is professor emeritus of mathematics at Colorado College. His books include Across the Board: The Mathematics of Chessboard Problems (Princeton), Topics in Commutative Ring Theory (Princeton), Graphs: An Introductory Approach, and Combinatorics: Ancient and Modern.

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Ebook Download Leonardo da Vinci: Flights of the MindBy Charles Nicholl

Ebook Download Leonardo da Vinci: Flights of the MindBy Charles Nicholl

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Leonardo da Vinci: Flights of the MindBy Charles Nicholl

Ebook Download Leonardo da Vinci: Flights of the MindBy Charles Nicholl

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In this engaging and thoroughly researched biography, Charles Nicholl uncovers the man behind the myth of the great Renaissance master. At times a painter, sculptor, inventor, draftsman, and anatomist, Leonardo’s life cannot easily be summarized. And yet, Nicholl skillfully traces the artist’s early days as an illegitimate child in Tuscany; his apprenticeship with Verrocchio in Florence; his service with some of the most powerful Renaissance families; his relationships with Michelangelo and Machiavelli; and his final days at the French royal court. In addition, Nicholl looks beyond the well-known stories of Leonardo’s famous masterpieces, and gives us a glimpse into the artist’s everyday life. We learn of Leonardo’s penchant for jokes, his fascination with flight, his obsessive note making, and even what he ate. Nicholl weaves these details together in a fascinating portrait that goes far towards revealing the enigmatic figure who continues to fascinate present-day readers.

• Amazon Sales Rank: #176821 in Books
• Published on: 2005-11-29
• Released on: 2005-11-29
• Original language: English
• Number of items: 1
• Dimensions: 8.50" h x 1.10" w x 5.40" l, 1.87 pounds
• Binding: Paperback
• 622 pages

From Publishers Weekly Nicholl aims for the man behind the myth in this penetrating, highly detailed biography, which recognizes da Vinci's "mysterious greatness as an artist, scientist and philosopher" but avoids hagiography (and nearly steers clear of the word "genius"). The illegitimate child of a Tuscan peasant girl and a local notary, da Vinci (1452–1519) was apprenticed as a teen to Florence sculptor Andrea del Verrocchio. Nicholl (Somebody Else: Arthur Rimbaud in Africa) conjectures convincingly about Leonardo's early career, though he tends to dwell overlong on technical aspects of Renaissance art production. Leonardo established a Florentine studio in 1477, but it was not until he moved to Milan five years later that he began to produce his iconic works: the painting Virgin of the Rocks, the famous Vitruvian Man drawing. Nicholl chronicles the production of The Last Supper and makes a firm statement about the Mona Lisa's identity. Numerous questions about Leonardo's life remain, unavoidably, unanswered, but Nicholl fills in the gaps with insight into the artist's cultural milieu, offering tidbits about Leonardo's sexuality, the sordid goings-on at the Borgia court and the multifarious fruits of the artist's astonishingly fertile curiosity and imagination. Nicholl's attention to da Vinci's polymathic pursuits, as well as his own translations from the artist's numerous notebooks, are some of this dense but readable volume's most compelling aspects. Illus. Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved.

From Bookmarks Magazine Forget Dan Brown’s fictional Da Vinci Code (**** May/June 2003); here’s the real deal. Award-winning author Nicholl draws on Leonardo’s notebooks to delve deep inside the mind of the beloved Renaissance icon. Celebrating Leonardo’s life and projects with contagious excitement and putting his achievements in the context of the Italian Renaissance as a whole, Nicholl considers Leonardo’s inspirations and influences. If we learn little new about Leonardo’s most famous works or his competition with Michelangelo, we gain valuable insight into the “cool, interior, ungraspable” creative process that raised Leonardo head and shoulders above his peers in most fields. Even with the spate of recent books on this master, Leonardo da Vinci stands out. It “isn’t merely a lovely book; it’s Leonardesque” (New York Times Book Review).

Copyright © 2004 Phillips & Nelson Media, Inc.

From Booklist Award-winning biographer Nicholl takes a marvelously fresh and human approach to the fascinating life of Leonardo. Evincing delight in the vicissitudes of scholarly sleuthing and a love of literature, Nicholl, who has a gift for spotting overlooked gems, offers a unique focus on the language in Leonardo's famous notebooks. He is also unusually eloquent in his recognition of the importance of Leonardo's country boyhood and the resulting visual lexicon and "ecologically compassionate view of nature" (he eventually became a vegetarian) that underlie all of his work, from his finely detailed drawings and paintings to his fascination with flight. Nicholl carefully explicates Leonardo's musicality, habit of inquisitiveness, love of technology, and artistic practices and renowned works. He also happily extracts evidence of Leonardo's affection for various boyfriends, particularly a man whose nickname, Salai, translates as "Little Devil," and argues convincingly that Leonardo enjoyed a liaison with one of his beautiful female models. In sum, Nicholl portrays a far more complex and appealing man than the chilly word genius usually suggests. Donna SeamanCopyright © American Library Association. All rights reserved

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