Mathematical thinking: problem-solving and proofs
D'Angelo, John P.
Mathematical thinking: problem-solving and proofs - 2nd - Noida Pearson India Education Services Pvt. Ltd. 2019 - xx, 412 p.
Table of Content
PART I. ELEMENTARY CONCEPTS. Chapter 1. Numbers, Sets and Functions. Chapter 2. Language and Proofs. Chapter 3. Induction. Chapter 4. Bijections and Cardinality. PART II. PROPERTIES OF NUMBERS. Chapter 5. Combinatorial Reasoning. Chapter 6. Divisibility. Chapter 7. Modular Arithmetic. Chapter 8. The Rational Numbers. PART III. DISCRETE MATHEMATICS. Chapter 9. Probability. Chapter 10. Two Principles of Counting. Chapter 11. Graph Theory. Chapter 12. Recurrence Relations. PART IV. CONTINUOUS MATHEMATICS. Chapter 13. The Real Numbers. Chapter 14. Sequences and Series. Chapter 15. Continuous Functions. Chapter 16. Differentiation. Chapter 17. Integration. Chapter 18. The Complex Numbers."
This text is designed to prepare students thoroughly in the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics—skills vital for success throughout the upperclass mathematics curriculum. The text 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 (including induction), 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 stimulating exercises are acclaimed for their exceptional quality.
9789353433093
Mathematics
Problem solving
510 / DAN
Mathematical thinking: problem-solving and proofs - 2nd - Noida Pearson India Education Services Pvt. Ltd. 2019 - xx, 412 p.
Table of Content
PART I. ELEMENTARY CONCEPTS. Chapter 1. Numbers, Sets and Functions. Chapter 2. Language and Proofs. Chapter 3. Induction. Chapter 4. Bijections and Cardinality. PART II. PROPERTIES OF NUMBERS. Chapter 5. Combinatorial Reasoning. Chapter 6. Divisibility. Chapter 7. Modular Arithmetic. Chapter 8. The Rational Numbers. PART III. DISCRETE MATHEMATICS. Chapter 9. Probability. Chapter 10. Two Principles of Counting. Chapter 11. Graph Theory. Chapter 12. Recurrence Relations. PART IV. CONTINUOUS MATHEMATICS. Chapter 13. The Real Numbers. Chapter 14. Sequences and Series. Chapter 15. Continuous Functions. Chapter 16. Differentiation. Chapter 17. Integration. Chapter 18. The Complex Numbers."
This text is designed to prepare students thoroughly in the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics—skills vital for success throughout the upperclass mathematics curriculum. The text 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 (including induction), 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 stimulating exercises are acclaimed for their exceptional quality.
9789353433093
Mathematics
Problem solving
510 / DAN