A Readable Introduction to Real Mathematics
Authors: Rosenthal, Daniel, Rosenthal, David, Rosenthal, Peter
Free Preview 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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 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, wellorganised, 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 wellchosen, basic, conceptual mathematics, suitably accessible after a K12 education, in a detailed, selfconscious way that emphasizes methodology alongside content and crucially leads to an ultimate clear payoff. … Summing Up: Recommended. Lowerdivision undergraduates and twoyear technical program students; general readers.” (D. V. Feldman, Choice, Vol. 52 (6), February, 2015)
 Table of contents (12 chapters)


Introduction to the Natural Numbers
Pages 17

Mathematical Induction
Pages 922

Modular Arithmetic
Pages 2329

The Fundamental Theorem of Arithmetic
Pages 3134

Fermat’s Theorem and Wilson’s Theorem
Pages 3540

Table of contents (12 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 A Readable Introduction to Real Mathematics
 Authors

 Daniel Rosenthal
 David Rosenthal
 Peter Rosenthal
 Series Title
 Undergraduate Texts in Mathematics
 Copyright
 2014
 Publisher
 Springer International Publishing
 Copyright Holder
 Springer International Publishing Switzerland
 eBook ISBN
 9783319056548
 DOI
 10.1007/9783319056548
 Series ISSN
 01726056
 Edition Number
 1
 Number of Pages
 XII, 161
 Number of Illustrations
 50 b/w illustrations
 Topics