
A Discrete Transition to Advanced Mathematics
Second Edition
- English
- PDF
- Available on iOS & Android
About this book
This textbook bridges the gap between lower-division mathematics courses and advanced mathematical thinking. Featuring clear writing and appealing topics, the book introduces techniques for writing proofs in the context of discrete mathematics. By illuminating the concepts behind techniques, the authors create opportunities for readers to sharpen critical thinking skills and develop mathematical maturity.Beginning with an introduction to sets and logic, the book goes on to establish the basics of proof techniques. From here, chapters explore proofs in the context of number theory, combinatorics, functions and cardinality, and graph theory. A selection of extension topics concludes the book, including continued fractions, infinite arithmetic, and the interplay among Fibonacci numbers, Pascal's triangle, and the golden ratio.A Discrete Transition to Advanced Mathematics is suitable for an introduction to proof course or a course in discrete mathematics. Abundant examples and exercises invite readers to get involved, and the wealth of topics allows for course customization and further reading. This new edition has been expanded and modernized throughout. New features include a chapter on combinatorial geometry, a more in-depth treatment of counting, and over 365 new exercises.
Frequently asked questions
- Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
- Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Information
Table of contents
- Contents
- Preface
- Preface to the Second Edition
- Chapter 1. Sets and Logic
- Chapter 2. Proofs
- Chapter 3. Number Theory
- Chapter 4. Combinatorics
- Chapter 5. Relations
- Chapter 6. Functions and Cardinality
- Chapter 7. Graph Theory
- Chapter 8. Sequences
- Chapter 9. Fibonacci Numbers and Pascal’s Triangle
- Chapter 10. Combinatorial Geometry in the Plane
- Chapter 11. Continued Fractions
- Answers or Hints for Selected Exercises
- Bibliography
- Index