Cumulative List of Corrections: [pdf]

Selected Solutions to Problems (complete list): [pdf]

(By chapter): Chapter 1 [pdf] Chapter 5 [pdf] Chapter 9 [pdf]

Chapter 2 [pdf] Chapter 6 [pdf] Chapter 10 [pdf]

Chapter 3 [pdf] Chapter 7 [pdf] Chapter 11 [pdf]

Chapter 4 [pdf] Chapter 8 [pdf] Chapter 12 [pdf]








Available for purchase from Springer and Amazon.

Daniel Rosenthal, David Rosenthal, Peter Rosenthal


A Readable Introduction to Real Mathematics

Springer Series: Undergraduate Texts in Mathematics
  • 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

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.