Mathematical Thinking - John D'Angelo

. .

Résumé :
Mathematical Thinking, 2nd Edition is designed to prepare students with the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics (skills vital for success throughout the upperclass mathematics curriculum). It offers both discrete and continuous mathematics, allowing instructors to emphasize one or to present the fundamentals of both. It begins by discussing mathematical language and proof techniques, applies them to easily understood questions in elementary number theory and counting, and then develops additional techniques of proof via important topics in discrete and continuous mathematics. The exercises are acclaimed for their exceptional quality.This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price....

Sommaire:

• I. ELEMENTARY CONCEPTS.
• 1. Numbers, Sets and Functions.
• 2. Language and Proofs.
• 3. Induction.
• 4. Bijections and Cardinality.
• II. PROPERTIES OF NUMBERS.
• 5. Combinatorial Reasoning.
• 6. Divisibility.
• 7. Modular Arithmetic.
• 8. The Rational Numbers.
• III. DISCRETE MATHEMATICS.
• 9. Probability.
• 10. Two Principles of Counting.
• 11. Graph Theory.
• 12. Recurrence Relations.
• IV. CONTINUOUS MATHEMATICS.
• 13. The Real Numbers.
• 14. Sequences and Series.
• 15. Continuous Functions.
• 16. Differentiation.
• 17. Integration.
• 18. The Complex Numbers.