There are many approaches that one can take with regard to
a course dedicated to teaching
proof writing. Some prefer
to teach the mathematics and the
structure of the proofs
simultaneously.
Others choose to teach the methods of proof and then apply
those methods to various topics. This is the strategy of
this text.
Here we boldly jump into a discussion of logic and
examine some details with the belief that if the details
are not understood well, then the application of those
details will suffer later.
Moreover, it is the understanding of how logic interacts
with mathematics that empowers the student to have the
courage and confidence to tackle greater problems in
courses such as Abstract Algebra or Topology.
How we accomplish this is outlined below.
Contents
1- Logical foundations
- Propositional logic
- Predicates and proofs
2- Main topics
- Set theory
- Mathematical induction
- Number theory
- Relations and functions
3- Coming attractions
4- Appendices