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© 2014 Pacific Crest
63
S
trategies
F
uture
U
ses of
S
et
T
heory
in
T
his
B
ook
Note: Mathematicians like to figure out uses for new mathematical knowledge (this thinking is part of
mathematical thinking; how set theory is used in new contexts).
Design feature: a major design feature of the book is to build proficiency in the learner to access,
evaluate, and put meaning to both quantitative information and resources to produce lifelong learning
in quantitative areas.
Activity
Role of Set Theory in the Experience Applications and Use
Evaluating a
Formula
Structures the limitations for the
formula’s input values
Measurements are often only positive
Solving an Equation Solution set: values that make the
equation true
Testing equivalence to make sure
solutions are truly in the solution set
Analyzing a
Function
Classifying functions into a family
based upon their characteristics
Being able to pick the appropriate
function for a given model
Likelihood
Set of possible outcomes
Subset of outcomes desired
Interpreting a Word
Problem
Pulling out the subset of important
information
Filtering out information that isn’t
important
Transforming Data Conditional transformation based on
characteristics of a set
Conditional treatment based upon an
object's characteristics
Drawing a Graph Domain of values, Range of values
Picking an appropriate graphing window
Data Analysis
Integrating more than one data set
together
Logical reduction or integration of data
from multiple sources
Corporate Finance Profit and Loss Statements use
organization of accounts
The logical structure and the linkage of
accounts is how financial systems are
designed
Interpreting a
Mathematical Model
Sets of inputs, variables, and outputs,
as well as their relationships
Systems thinking involves components
which contain sets of variables,
relationships, inputs, and outputs
2.1 Basics of Set Theory