This book is a complete guide to mathematical proof. Through plentiful examples and exercises, the mathematical novice will learn how to prove theorems and explore some fascinating areas of abstract mathematics. This book is ideal preparation for a university course in pure mathematics, and a valuable resource for educators.
This book is a complete guide to mathematical proof. Through plentiful examples and exercises, the mathematical novice will learn how to prove theorems and explore some fascinating areas of abstract mathematics. This book is ideal preparation for a university course in pure mathematics, and a valuable resource for educators.
Ralph W. Oberste-Vorth earned his PhD in mathematics from Cornell University. In 2002, he became the Chairman of the Department of Mathematics at Marshall University. In 2011, he accepted a position as the Chairman of the Department of Mathematics and Computer Science at Indiana State University.
Inhaltsangabe
Some notes on notation To the students For the professors Part I. The Axiomatic Method: 1. Introduction 2. Statements in mathematics 3. Proofs in mathematics Part II. Set Theory: 4. Basic set operations 5. Functions 6. Relations on a set 7. Cardinality Part III. Number Systems: 8. Algebra of number systems 9. The natural numbers 10. The integers 11. The rational numbers 12. The real numbers 13. Cantor's reals 14. The complex numbers Part IV. Time Scales: 15. Time scales 16. The Delta Derivative Part V. Hints: 17. Hints for (and comments on) the exercises Index.
Some notes on notation To the students For the professors Part I. The Axiomatic Method: 1. Introduction 2. Statements in mathematics 3. Proofs in mathematics Part II. Set Theory: 4. Basic set operations 5. Functions 6. Relations on a set 7. Cardinality Part III. Number Systems: 8. Algebra of number systems 9. The natural numbers 10. The integers 11. The rational numbers 12. The real numbers 13. Cantor's reals 14. The complex numbers Part IV. Time Scales: 15. Time scales 16. The Delta Derivative Part V. Hints: 17. Hints for (and comments on) the exercises Index.
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