The Fundamental Ideas of Mathematics

Fall 2015

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".
Classwork: practice with unions and intersections of indexed sets.
Classwork on converse, contrapositive, and inverse.
Lincoln comes to Fundamentals class.
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.
Some history of the concept of negative numbers.
A partition of (NxN).
Sizing infinite sets.