This course provides an introduction to analysis, and the goal is two folds.

1. To learn how to read mathematical arguments and how to reproduce them. In other words, learning how to write proofs.

2. To learn important theorems in calculus (and more) in the modern mathematical standard.

The course will start with real numbers, sequences and series. We will then proceed to single variable functions, with emphasis on continuity, derivative and integral. Abstract point set topology will be introduced with continuous functions serving as the primary example and the Picard–Lindelof theorem will be the main application.