Readable Introduction to Real Mathematics

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

• Preface to the Second Edition.- Preface for Readers.- Preface for Instructors.- 1. Introduction to the Natural Numbers.- 2. Mathematical Induction.- 3. Modular Arithmetic.- 4. The Fundamental Theorem of Arithmetic.- 5. Fermat's Theorem and Wilson's Theorem.- 6. Sending and Receiving Coded Messages.- 7. The Euclidean Algorithm and Applications.- 8. Rational Numbers and Irrational Numbers.- 9. The Complex Numbers.- 10. Sizes of Infinite Sets.- 11. Fundamentals of Euclidean Plane Geometry.- 12. Constructability.- 13. An Introduction to Infinite Series.- 14. Some Higher Dimensional Spaces.- Index.

“Rosenthals have between them produced a very fine, and very readable, introduction to ‘real’ mathematics.” (Robin Harte, Irish Mathematical Society Bulletin, Issue 83, 2019)“The book was quite an enjoyable read … . It would undoubtedly help students just entering the world of theoretical mathematics, though perhaps after more advanced preparatory material than just high school algebra and trigonometry.” (Meghan De Witt, MAA Reviews, October 6, 2019)Reviews of the first edition:“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)