(Detailed notes are posted on the e-classroom.)

Number systems

The natural numbers, ℕ

The integers, ℤ

The rationals, ℚ

The reals, ℝ

The complex numbers, ℂ

Sequences

Limits of real sequences

Limit theorems for sequences

Infinite limits

Monotone sequences and completeness

Limits and completeness in ℂ

Limits and completeness for metric spaces

Subsequences, accumulation points, and Bolzano-Weierstrass

Infinite series

Definition and examples

Tests for nonnegative series

Absolute convergence, conditional convergence

Alternating series and estimation

A little topology of ℝ and other metric spaces

Open and closed sets

Compact sets

Limits and continuity of real functions

Limits of functions

One-sided limits

Continuous functions

Continuous functions on compact sets

The Intermediate Value Theorem

Uniform continuity

Monotone functions

Continuity and topology

Elementary functions

Polynomials

Exponentials

Logarithms

Trigonometric functions

Elementary (and non-elementary) functions