Elements of Mathematics

Elements of Mathematics PDF Author: John Stillwell
Publisher: Princeton University Press
ISBN: 0691178542
Category : Mathematics
Languages : en
Pages : 440

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Book Description
An exciting look at the world of elementary mathematics 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

Elements of Mathematics PDF Author: John Stillwell
Publisher: Princeton University Press
ISBN: 0691178542
Category : Mathematics
Languages : en
Pages : 440

Get Book Here

Book Description
An exciting look at the world of elementary mathematics 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.

Euclid's Elements

Euclid's Elements PDF Author: Euclid
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 544

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Book Description
"The book includes introductions, terminology and biographical notes, bibliography, and an index and glossary" --from book jacket.

Elements of Mathematics

Elements of Mathematics PDF Author: Nicolas Bourbaki
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Analysis of Written Arithmetic, Bk. 1

Analysis of Written Arithmetic, Bk. 1 PDF Author: Stoddard A. Felter
Publisher:
ISBN:
Category : Arithmetic
Languages : en
Pages : 316

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Book Description


Elements of Pure and Applied Mathematics

Elements of Pure and Applied Mathematics PDF Author: Harry Lass
Publisher: Courier Corporation
ISBN: 0486471861
Category : Mathematics
Languages : en
Pages : 514

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Book Description
Completely self-contained, this survey explores the important topics in pure and applied mathematics. Each chapter can be read independently of the others, and all subjects are unified by cross-references to the complete work. Numerous worked-out examples appear throughout the text, and review questions and references conclude each section. 1957 edition.

Key to the Olney's Science of Arithmetic

Key to the Olney's Science of Arithmetic PDF Author: Edward Olney
Publisher:
ISBN:
Category : Arithmetic
Languages : en
Pages : 174

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The Werner Arithmetic, Oral and Written, Book One, Parts I, II and III

The Werner Arithmetic, Oral and Written, Book One, Parts I, II and III PDF Author: Frank H. Hall
Publisher:
ISBN:
Category : Arithmetic
Languages : en
Pages : 264

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Book Description


Elements of Advanced Mathematics, Third Edition

Elements of Advanced Mathematics, Third Edition PDF Author: Steven G. Krantz
Publisher: CRC Press
ISBN: 1439898340
Category : Mathematics
Languages : en
Pages : 368

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Book Description
For many years, this classroom-tested, best-selling text has guided mathematics students to more advanced studies in topology, abstract algebra, and real analysis. Elements of Advanced Mathematics, Third Edition retains the content and character of previous editions while making the material more up-to-date and significant. This third edition adds four new chapters on point-set topology, theoretical computer science, the P/NP problem, and zero-knowledge proofs and RSA encryption. The topology chapter builds on the existing real analysis material. The computer science chapters connect basic set theory and logic with current hot topics in the technology sector. Presenting ideas at the cutting edge of modern cryptography and security analysis, the cryptography chapter shows students how mathematics is used in the real world and gives them the impetus for further exploration. This edition also includes more exercises sets in each chapter, expanded treatment of proofs, and new proof techniques. Continuing to bridge computationally oriented mathematics with more theoretically based mathematics, this text provides a path for students to understand the rigor, axiomatics, set theory, and proofs of mathematics. It gives them the background, tools, and skills needed in more advanced courses.

National Arithmetic, Oral and Written

National Arithmetic, Oral and Written PDF Author: Joseph Ficklin
Publisher:
ISBN:
Category : Arithmetic
Languages : en
Pages : 412

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Report of the Commissioner of Education Made to the Secretary of the Interior for the Year ... with Accompanying Papers

Report of the Commissioner of Education Made to the Secretary of the Interior for the Year ... with Accompanying Papers PDF Author: United States. Bureau of Education
Publisher:
ISBN:
Category : Education
Languages : en
Pages : 1326

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Book Description