A Readable Introduction to Real Mathematics 1st edition by Daniel Rosenthal, David Rosenthal, Peter Rosenthal – Ebook PDF Instant Download/Delivery: 3319056548, 9783319056548
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Product details:
ISBN 10: 3319056548
ISBN 13: 9783319056548
Author: Daniel Rosenthal, David Rosenthal, Peter Rosenthal
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.
A Readable Introduction to Real Mathematics 1st Table of contents:
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 Secret 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
Backmatter
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Tags: Daniel Rosenthal, David Rosenthal, Peter Rosenthal, A Readable, Real Mathematics