
- 488 pages
- English
- PDF
- Available on iOS & Android
About this book
This book offers an introduction to mathematical proofs and to the fundamentals of modern mathematics. No real prerequisites are needed other than a suitable level of mathematical maturity. The text is divided into two parts, the first of which constitutes the core of a one-semester course covering proofs, predicate calculus, set theory, elementary number theory, relations, and functions, and the second of which applies this material to a more advanced study of selected topics in pure mathematics, applied mathematics, and computer science, specifically cardinality, combinatorics, finite-state automata, and graphs. In both parts, deeper and more interesting material is treated in optional sections, and the text has been kept flexible by allowing many different possible courses or emphases based upon different paths through the volume.
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Table of contents
- Contents
- General Preface
- Preface for Instructors
- Chapter 1 Proof Techniques
- Chapter 2 Predicate Calculus
- Chapter 3 Set Theory
- Chapter 4 Elementary Number Theory
- Chapter 5 Relations
- Chapter 6 Functions
- Chapter 7 Cardinality
- Chapter 8 Elements of Combinatorics
- Chapter 9 Languages and Finite State Automata
- Chapter 10 Graphs
- Suggestions for Further Reading