We'll start with a brief introduction to the language and
grammar of mathematics. A good, basic English course makes much of this
unnecessary. However the standards for language education, just as for
mathematics education, vary widely. I find that it doesn't hurt to
revisit how we present mathematical ideas.
Introduction to the
language and grammar of mathematics.
definitions
mathematical statements
statements of results to be proved
logical relations --- truth tables
proofs and metthods of proof
notation
Basic Objects
sets, functions
counting, the Peano Axioms and Mathematical Induction
natural numbers, integers and rational numbers
the "holes" in the rational numbers
an intuitive introduction to limits
decimals and real numbers
equivalence relations
arithmetic and ordering in the rationals and reals
Approximation, limits and
continuity
distance as a unifying concept
AND MORE
See the Homework Page for further topics