1 Working With Sets
1 Finite Sets
2 Venn Diagrams
3 Counting with Sets etc
4 Subset Builder Notation
5 Product Builder Notation
6 Power Set Notation
7 Cautious or Safe Set Construction
8 Sets of Numbers
9 Sets in Probability and Statistics
10 Set View of Wordy Extensions To Arithmetic
Skill Development Notes
This site area literally sketches what
may done with set skills and concepts. Email the site author for further
help.
Modern pure mathematics from counting to calculus may
be formed and expressed in terms of sets and set theory assumptions and
practices. The modern mathematics course designs of the 1950's
emphasized a introductory form of set theory and notation. Most
elements of mathematics were presented in terms of sets. Those course
designs lingers today in mathematics education as is or diluted. The
dilution was evident when I taught senior high school courses whose
content required set concepts to students whose earlier education did
not cover sets.
The question of when to introduce set skills and
concepts further depends on school systems. Just before employed may be
a good time.
Set concepts [Venn
Diagrams and subset builder notation] may be useful in illustrating and
developing logic mastery for the development of mathematics and to aid
precision in reading and writing outside of mathematics. In counting for
its own sake or the calculation of probabilities, sets and functions may
be employed to track and count items, ways or possibilities. And
probability itself may be precisely expressed and calculated with the aid
of set concepts.
The set development of functions and relations is covered in full and
clarified in the site more algebra area on function. Course
designers need to decide how to much cover in senior high school
mathematics and calculus, and how. Show the coverage be all at once. Or,
should the coverage be woven as needed into the study of further
functions and computation rule required by college programs. In
preparation of students for college pograms in technical fields, fields
that employ calculus, a lean coverage of the set and graphic
representation of function may be sufficient with this representation
being one of many until or if the study of pure mathematics begins.
The verbal description of of generalized commutative and associative
laws for arithmetic may be easily described using sets. The expansion
of product
of sums in terms of sums of products of their terms may also be
described with sets.
|
|