Three bijections between naturals and pairs of naturals.

 

MFCS 15-151

Lecture slides.

sets 1 Set operations.
sets 2 Cartesian products.
functions 1 Functions.
functions 2 In/sur/bi-jections.
Peano Dedekind-Peano axioms.
rectypes Inductive structures.
relations 1 Relations.
relations 2 Special relations.
modular Modular arithmetic.
finite sets Finite sets.
fields Ordered fields.
cardinality Cardinality.
probability Probability.
Extra material. This is only for the curious, it's not required.

pset 4 Mathematica notebook for pset 4.
numbers Constructing the reals.
surreals Conway's surreal numbers.
Collatz Collatz (section 2).
ZF Zermelo-Fraenkel axioms (pages 1/2).

If you are looking for a serious textbook that covers a good amount of material, try
John Truss, Discrete Mathematics for Computer Scientiests, Pearson 2001.