A Readable Introduction to Real Mathematics

Softcover Nachdruck of the original 1. Auflage 2014
ISBN: 978-3-319-37950-0
Verlag: Springer International Publishing

Buch, Englisch, 161 Seiten, Paperback, Format (B × H): 157 mm x 236 mm, Gewicht: 2759 g

Reihe: Undergraduate Texts in Mathematics

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.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Rosenthal, Daniel

Rosenthal, David

Rosenthal, Peter

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Algebra Elementare Algebra
• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines

Inhaltsverzeichnis

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.

Über Autor(innen)

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.