Elements of Mathematics : From Euclid to Gödel / John Stillwell.

Format:

Book

Author/Creator:

Stillwell, John, author.

Language:

English

Subjects (All):

Mathematics--Study and teaching (Higher).

Mathematics.

Physical Description:

1 online resource (439 p.)

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

English

Summary:

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.

Contents:

Frontmatter

Contents

Preface

1. Elementary Topics

2. Arithmetic

3. Computation

4. Algebra

5. Geometry

6. Calculus

7. Combinatorics

8. Probability

9. Logic

10. Some Advanced Mathematics

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 23. Mai 2019)

ISBN:

9781400880560

1400880564

OCLC:

946359807