Part I. Approaching Limits
1. A Whole Lot of Numbers
1.4. Exercises for Chapter 1
2.1. The Rational Numbers
2.4. A First Look at Infinity
2.5. Exercises for Chapter 2
3.3. The Modulus of a Number
3.5. The Theorem of the Means
3.7. Exercises for Chapter 3
4. Where Do You Go To, My Lovely?
4.3. The Algebra of Limits
4.4. Fibonacci Numbers and the Golden Section
4.5. Exercises for Chapter 4
5.1. Bounded Sequences Revisited
5.3. An Old Friend Returns
5.4. Finding Square Roots
5.5. Exercises for Chapter 5
6.3. Convergence of Series
6.8. General Infinite Series
6.9. Conditional Convergence
6.10. Regrouping and Rearrangements
6.11. Real Numbers and Decimal Expansions
6.12. Exercises for Chapter 6
Part II. Exploring Limits
7. Wonderful Numbers - e, π and γ
8.1. Convergence of Infinite Products
8.2. Infinite Products and Prime Numbers
8.3. Diversion - Complex Numbers and the Riemann Hypothesis
9.2. Rational and Irrational Numbers as Continued Fractions
10. How Infinite Can You Get?
11. Constructing the Real Numbers
12. Where to Next in Analysis? The Calculus
12.2. Limits and Continuity
13. Some Brief Remarks About the History of Analysis
Appendix 1. The Binomial Theorem
Appendix 2. The Language of Set Theory
Appendix 3. Proof by Mathematical Induction
Appendix 4. The Algebra of Numbers
Hints and Solutions to Selected Exercise
