How, when, and why of mathematics
Logically speaking
Introducing the contrapositive and converse
Set notation and quantifiers
Proof techniques
Sets
Operations on sets
More on operations on sets
Power set and the Cartesian product
Relations
Partitions
Order in the reals
Functions, domain, and range
Functions, one-to-one, and onto
Inverses
Images and inverse images
Mathematical induction
Sequences
Convergence of sequences of real numbers
Equivalent sets
Finite sets and an infinite set
Countable and uncountable sets.

Metric spaces
Getting to know open and closed sets
Modular arithmetic
Fermat's little theorem
Projects.