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Elements of Mathematics John Stillwell

Elements of Mathematics By John Stillwell

Elements of Mathematics by John Stillwell


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Condition - Very Good
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Elements of Mathematics Summary

Elements of Mathematics: From Euclid to Goedel by John Stillwell

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 math beyond its boundaries.

Elements of Mathematics Reviews

[Stillwell] writes clearly and engagingly... [Elements of Mathematics] can appeal to various constituencies at different levels of mathematical sophistication.--Mark Hunacek, MAA Reviews A great exploration of elementary mathematics, its limitations, how infinity complicates things, and how various branches of mathematics fit together.--Antonio Cangiano, Math-Blog Stillwell is ... One of the better current mathematical authors: he writes clearly and engagingly, and makes more of an effort than most to provide historical detail and a sense of how various mathematical ideas tie in with one another... The features we have learned to expect from Stillwell (including, but not limited to, excellent writing) are present in [Elements of Mathematics] as well.--MAA Reviews An accessible read... Stillwell breaks down the basics, providing both historical and practical perspectives from arithmetic to infinity.--Gemma Tarlach, Discover [A] sophisticated treatment of topics usually described as elementary.--John Allen Paulos [Elements of Mathematics] is quite a tour de force, organized by areas of mathematics--arithmetic, computation, algebra, geometry, calculus, and so on--and in each area Stillwell manages to distill down the big ideas and the connections with other areas. He is a master expositor, and the text manages to be engaging and accessible without watering down the mathematics. I definitely learned new things from the book!--Brent Yorgey, Math Less Traveled blog From a lifetime of teaching, Stillwell has distilled some nice examples from the entire gamut of elementary mathematics.--Mathematical Reviews Clippings [A] wonderful book... I think that [Elements of Mathematics] will itself become a modern classic and a reference work for anyone trying to learn basic topics in any of the major fields of mathematics.--Victor Katz, Bulletin of the American Mathematical Society Elements of Mathematicsis a fine ... overview of the field of mathematics... The writing is clear, succinct, organized, and the diagrams [and] illustrations excellent... While some of the discussion is introductory or elementary, it always leads to deeper, more challenging ideas... [T]his will make a fine basic addition to most mathematicians' bookshelves.--Math Tango Stillwell uses his broad and impressive command of mathematics to transport a reader through each topic and to a higher level of understanding and questioning.--Convergence [A] wonderful book ... I think that [Elements of Mathematics] will itself become a modern classic and a reference work for anyone trying to learn basic topics in any of the major fields of mathematics.--Victor Katz, Bulletin of the American Mathematical Society [Elements of Mathematics] is a book that everybody should read. You will be the better for it.--Reuben Hersh, American Mathematical Monthly

About John Stillwell

John Stillwell is professor of mathematics at the University of San Francisco. His many books include Mathematics and Its History and Roads to Infinity.

Table of Contents

*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. xi*1. Elementary Topics, pg. 1*2. Arithmetic, pg. 35*3. Computation, pg. 73*4. Algebra, pg. 106*5. Geometry, pg. 148*6. Calculus, pg. 193*7. Combinatorics, pg. 243*8. Probability, pg. 279*9. Logic, pg. 298*10. Some Advanced Mathematics, pg. 336*Bibliography, pg. 395*Index, pg. 405

Additional information

GOR009489941
9780691178547
0691178542
Elements of Mathematics: From Euclid to Goedel by John Stillwell
Used - Very Good
Paperback
Princeton University Press
20171107
440
null null null null null null null null null null
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
This is a used book - there is no escaping the fact it has been read by someone else and it will show signs of wear and previous use. Overall we expect it to be in very good condition, but if you are not entirely satisfied please get in touch with us

Customer Reviews - Elements of Mathematics