Contents
Preface xi
Chapter 1. Basic Principles 1
1.1. Mathematical induction 1
1.2. Real numbers 2
1.3. Completeness principles 5
1.4. Numerical sequences 12
1.5. Infinite series 18
1.6. Continuous functions and derivatives 22
1.7. The Riemann integral 27
1.8. Uniform convergence 33
1.9. Historical remarks 39
1.10. Metric spaces 41
1.11. Complex numbers 42
Exercises 46
Chapter 2. Special Sequences 51
2.1. The number e 51
2.2. Irrationality of π 55
2.3. Euler’s constant 56
2.4. Vieta’s product formula 60
2.5. Wallis product formula 61
2.6. Stirling’s formula 63
Exercises 66
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