=== more rigorous track (1/24/00)
* numbers, their definitions, sizes of each
- integers
- rationals
- reals
- complex
* sets {a,b,c,...}
- union
- intersection
- mappings (into, onto, 1-1)
* formal logic and various notations
- "there exists x such that ..."
- "for all x ... "
- such that : " { x | x>3 }
- if a then b
- truth tables
- proof by induction
- proof by example
- disproof by counter-example
- proof by assuming oppisite, showing contradiction (called?)
assign for next Monday:
- armstrong, 2.5 : Prove that an isometry is a bijection and
that the set of all isometric plane transformations is a group.)
- armstrong, 2.7 : let x,y be members of group G. Prove that
there exists w,z such that (1) wx=y, zw=y and (2) w,z are unique.
- armstrong, 3.3 : Show that for an integer n, {c|c^n=1} where c is
a complex number forms a group. ("same" as what other group?)