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Elements of Mathematics
From Euclid to Gödel
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Check link for latest rating. ( 72 ratings, 7 reviews)
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Elements of Mathematics
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Book Hero Magic created this recommendation. While it's new and still learning, it may not be perfect - your feedback is welcome! IS THIS YOUR NEXT READ?
Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics--but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had t
Book Hero Magic formatted this description to make it easier to read. While it's new and
still learning, it may not be perfect - your
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Description
Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics—but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary."
Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits. From Gaussian integers to propositional logic, Stillwell delves into arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, and logic. He discusses how each area ties into more advanced topics to build mathematics as a whole.
Through a rich collection of basic principles, vivid examples, and interesting problems, Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity. Infinity has been observed throughout mathematical history, but the recent development of "reverse mathematics" confirms that infinity is essential for proving well-known theorems, and helps to determine the nature, contours, and borders of elementary mathematics.
Elements of Mathematics gives readers, from high school students to professional mathematicians, the highlights of elementary mathematics and glimpses of the parts of maths beyond its boundaries.
Book Hero Magic summarised reviews for this book. While it's new and still learning, it may not be perfect - your feedback is welcome! HOW HAS THIS BEEN REVIEWED?
Elements of Mathematics by John Stillwell has been praised for its clear and engaging writing style, making it accessible to readers with varying levels of mathematical understanding. The book presents an exploration of elementary mathematics, touching upon its limitations, the complexities of infinity, and interconnections between different mathematical branches. Reviewers appreciate Stillwell's effort to include historical details and his ability to simplify complex topics while maintaining depth, making it a valuable addition to any mathematician's collection.
Book Details
INFORMATION
ISBN: 9780691178547
Publisher: Princeton University Press
Format: Paperback / softback
Date Published: 07 November 2017
Country: United States
Imprint: Princeton University Press
Illustration: 127 b/w illus.
Audience: Tertiary education, Professional and scholarly
DIMENSIONS
Width: 152.0mm
Height: 235.0mm
Weight: 709g
Pages: 440
About the Author
John Stillwell is professor of mathematics at the University of San Francisco. He is the author of Reverse Mathematics: Proofs from the Inside Out (Princeton).
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Reverse Mathematics
This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have...Hardback$6799Unit price /UnavailableAvailableShips in 4-6 weeks -
Reverse Mathematics
The first book surveying the history and ideas behind reverse mathematics, Reverse Mathematics is a new field that seeks to find the axioms needed to prove given theorems. In Reverse Mathematics, John Stillwell offers a historical and representative view, emphasizing basic analysis and providing a novel approach to logic. By using a minimum of mathematical logic in a well-motivated way,...Paperback$7200Unit price /UnavailableAvailableShips in 2-3 weeks -
The Story of Proof
How the concept of proof has enabled the creation of mathematical knowledge. The Story of Proof investigates the evolution of the concept of proof—one of the most significant and defining features of mathematical thought—through critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically...HardbackSold Out
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