## The Fundamental Ideas of Mathematics

## Fall 2015

Syllabus.

Day-by-day summary.

Record of assignments.

Solutions distributed in class.

The Greek alphabet.

An introductory example.

Some tips on dealing with proofs.

Why "P => Q" is defined the way it is.

A logic study guide.

Practice with V, &, ==> in quantified statements.

Guidelines for starting some proofs.

Controlling the word "not".

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.

Taylor polynomials and the Binomial Theorem.

Euler paths and Euler circuits.

A little modular arithmetic.

Classwork: compositions/inverses of binary relations.

The subset maps.

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.