- explain homework assignments
- exams and quizzes
- how to study mathematics
- reading carefully is the key to success
- you must participate to learn ... mathematics is
**NOT**a spectator sport

- a. Truth (with a capital T) is subject dependent.
- God is dead.
- Workers with Marxist attitudes will disrupt a capitalistic society.
- 2 + 2 = 4
- Every even number is the sum of two prime numbers (Goldbach)

- b. Mathematical truth is a formalism.
- .... true statements are those which follow from the axioms by means of logic.
This is what provides mathematics with its greatest strength - truth can be demonstrated, there is no ambiguity about a mathematical truth; and its greatest weakness - mathematics can not prove anything that is not mathematical.

- c. Logic vs. Meta-logic
- Meta-logic is the language and thinking process we use to talk about logic. It is not itself logic, rather it is a stepping outside of the logical system in order to examine that system. We do this in other areas as well, for instance, we learn English grammar in foreign language classes.
- d. A formal logic system
**MIU**System - Hofstadter,__Godel, Escher, Bach: an eternal golden braid__. Basic Books, 1979.__Symbols__: M, I, U

__Propositions__: Strings of these symbols. (may be empty)

__Axioms__: MI

__Grammar__: (Rules of Production) x is any proposition.- If xI then xIU
- If Mx then Mxx
- If xIIIy then xUy
- If xUUy then xy

A

**theorem**is a proposition which can be obtained from the axioms by applying the rules of the grammar.For instance, MUIU is a theorem.

MI --(2) MII --(2) MIIII --(3) MUI --(1) MUIU.

MUIIU is also a theorem.

MI --(above) MUIU --(2) MUIUUIU --(4) MUIIU.

But clearly U is not a theorem.

**Question**: Is MU a theorem?