A Readable Introduction to Real Mathematics. 2nd ed. 2018

種類:

電子ブック

責任表示:

by Daniel Rosenthal, David Rosenthal, Peter Rosenthal

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2018

著者名:

• Rosenthal, Daniel.
• Rosenthal, David.
• Rosenthal, Peter.
• SpringerLink (Online service)

シリーズ名:

Undergraduate Texts in Mathematics ;

ISBN:

9783030006327 [3030006328]    

注記:

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.
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 teach mathematical thinking while conveying the beauty and elegance of mathematics. The book contains a large number of exercises of varying difficulty, some of which are designed to help reinforce basic concepts and others of which will challenge virtually all readers. The sole prerequisite for reading this text is high school algebra. 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 * constructibility (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass)* infinite series * higher dimensional spaces. This textbook is suitable for a wide variety of cou

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