Undergraduate Texts in Mathematics

A Readable Introduction to Real Mathematics

Authors: Rosenthal, Daniel, Rosenthal, David, Rosenthal, Peter

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  • Presents sophisticated ideas in algebra and geometry in an elementary fashion
  • Includes exercises of varying difficulty to help motivate and teach the reader
  • Develops mathematical thinking that will be useful for future mathematics teachers and mathematics majors
  • Solutions to selected exercises are freely available in PDF
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eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-030-00632-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $54.99
price for USA in USD
  • ISBN 978-3-030-00631-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

Designed for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to teach mathematical thinking while conveying the beauty and elegance of mathematics. The book contains a large number of exercises of varying difficulty, some of which are designed to help reinforce basic concepts and others of which will challenge virtually all readers. The sole prerequisite for reading this text is high school algebra. Topics covered include: * mathematical induction * modular arithmetic * the Fundamental Theorem of Arithmetic * Fermat's Little Theorem * RSA encryption * the Euclidean algorithm * rational and irrational numbers * complex numbers * cardinality * Euclidean plane geometry * constructibility (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass)* infinite series * higher dimensional spaces.

This textbook is suitable for a wide variety of courses and for a broad range of students of mathematics and other subjects. Mathematically inclined senior high school students will also be able to read this book.

From the reviews of the first edition:

“It is carefully written in a precise but readable and engaging style… I thoroughly enjoyed reading this recent addition to the Springer Undergraduate Texts in Mathematics series and commend this clear, well-organised, unfussy text to its target audiences.” (Nick Lord, The Mathematical Gazette, Vol. 100 (547), 2016)

 “The book is an introduction to real mathematics and is very readable. … The book is indeed a joy to read, and would be an excellent text for an ‘appreciation of mathematics’ course, among other possibilities.” (G.A. Heuer, Mathematical Reviews, February, 2015)

“Many a benighted book misguidedly addresses the need [to teach mathematical thinking] by framing reasoning, or narrowly, proof, not as pervasive modality but somehow as itself an autonomous mathematical subject. Fortunately, the present book gets it right.... [presenting] well-chosen, basic, conceptual mathematics, suitably accessible after a K-12 education, in a detailed, self-conscious way that emphasizes methodology alongside content and crucially leads to an ultimate clear payoff. … Summing Up:  Recommended. Lower-division undergraduates and two-year technical program students; general readers.” (D.V. Feldman, Choice, Vol. 52 (6), February, 2015)

About the authors

Daniel Rosenthal obtained his mathematics degree from the University of Toronto. 
David Rosenthal is Associate Professor of Mathematics at St. John's University in New York City.
Peter Rosenthal is Professor Emeritus of Mathematics at the University of Toronto.

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Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-030-00632-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $54.99
price for USA in USD
  • ISBN 978-3-030-00631-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
A Readable Introduction to Real Mathematics
Authors
Series Title
Undergraduate Texts in Mathematics
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-00632-7
DOI
10.1007/978-3-030-00632-7
Hardcover ISBN
978-3-030-00631-0
Series ISSN
0172-6056
Edition Number
2
Number of Pages
XVIII, 218
Number of Illustrations
63 b/w illustrations
Topics