Undergraduate Texts in Mathematics

A Readable Introduction to Real Mathematics

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

  • 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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Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-05654-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $49.99
price for USA
  • ISBN 978-3-319-05653-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $49.99
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: November 4, 2016
  • ISBN 978-3-319-37950-0
  • Free shipping for individuals worldwide
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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 engage the reader and to teach a real understanding of mathematical thinking while conveying the beauty and elegance of mathematics. The text focuses on teaching the understanding of mathematical proofs. The material covered has applications both to mathematics and to other subjects. The book contains a large number of exercises of varying difficulty, designed to help reinforce basic concepts and to motivate and challenge the reader. The sole prerequisite for understanding the text is basic high school algebra; some trigonometry is needed for Chapters 9 and 12. 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 - constructability (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass). This textbook is suitable for a wide variety of courses and for a broad range of students in the fields of education, liberal arts, physical sciences and mathematics. Students at the senior high school level who like mathematics will also be able to further their understanding of mathematical thinking by reading this book.

About the authors

Daniel Rosenthal is a mathematics student at 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.

Reviews

“It is carefully written in a precise but readable and engaging style and is tightly organised into eight short ‘core’ chapters and four longer standalone ‘extension’ chapters. … 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)

“Daniel Rosenthal and Peter Rosenthal (both, Univ. of Toronto) and David Rosenthal (St. John's Univ.) present 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)


Table of contents (12 chapters)

  • Introduction to the Natural Numbers

    Rosenthal, Daniel (et al.)

    Pages 1-7

  • Mathematical Induction

    Rosenthal, Daniel (et al.)

    Pages 9-22

  • Modular Arithmetic

    Rosenthal, Daniel (et al.)

    Pages 23-29

  • The Fundamental Theorem of Arithmetic

    Rosenthal, Daniel (et al.)

    Pages 31-34

  • Fermat’s Theorem and Wilson’s Theorem

    Rosenthal, Daniel (et al.)

    Pages 35-40

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-05654-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $49.99
price for USA
  • ISBN 978-3-319-05653-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $49.99
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: November 4, 2016
  • ISBN 978-3-319-37950-0
  • Free shipping for individuals worldwide
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
A Readable Introduction to Real Mathematics
Authors
Series Title
Undergraduate Texts in Mathematics
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-05654-8
DOI
10.1007/978-3-319-05654-8
Hardcover ISBN
978-3-319-05653-1
Softcover ISBN
978-3-319-37950-0
Series ISSN
0172-6056
Edition Number
1
Number of Pages
XII, 161
Number of Illustrations and Tables
50 b/w illustrations
Topics