# Part IA - Analysis I

## Lectured by W. T. Gowers, Lent 2015

These notes are not endorsed by the lecturers, and I have modified them (often significantly) after lectures. They are nowhere near accurate representations of what was actually lectured, and in particular, all errors are almost surely mine.

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# Contents

- V Full version
- 0 Introduction
- 1 The real number system
- 2 Convergence of sequences
- 2.1 Definitions
- 2.2 Sums, products and quotients
- 2.3 Monotone-sequences property
- 2.4 Cauchy sequences
- 2.5 Limit supremum and infimum
- 3 Convergence of infinite sums
- 4 Continuous functions
- 5 Differentiability
- 6 Complex power series
- 6.1 Exponential and trigonometric functions
- 6.2 Differentiating power series
- 6.3 Hyperbolic trigonometric functions
- 7 The Riemann Integral