The Fundamental Ideas of Mathematics



Syllabus.
Day-by-day summary.
Record of assignments.
Solutions distributed in class.
The Greek alphabet.
Some brief tips on writing proofs.
Some longer tips on dealing with proofs.
An introductory example.
A basic fact about union and intersection.
Classwork: practice with unions and intersections of indexed sets.
Classwork on converse, contrapositive, and inverse.
Lincoln comes to Fundamentals class.
Assignment 7 classwork.
More on union and intersection of sets.
A proof of one of the basic properties of sets.
Handout on the Fundamental Theorem of Arithmetic.
Classwork: Using the FTA to count divisors.
Splitting nonconvex polygons.
Some graph theory terminology.
Constructing path "C" (flowchart).
Partitions and equivalence relations.
Classwork: practice with direct and inverse images of sets.
Some history of the concept of negative numbers.
A partition of (NxN).
Sizing infinite sets.