Mat156: Tanya Jaseph

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Mat156: Tanya Jaseph

Set Theory

Methods of Describing Sets

Set Builder Notation

C = { x| x e N where x < 5 }

Set C / is equal to / the set of / all elements x / such that / x is a natural number/ where / x is less then 5

Listing Method

C = { 1, 2, 3, 4 }

Definitions

Elements

Individual objects or members of a set

Cardinal Number

The number of elements in a set

Set: Any collegtion of objects

Universal Set

All elements being considered in a given discussion

Finite Set

The cardinal number is Zero or a natural number

Empty/Null Set

Has nothing in it

O

the line striking through should be diagonal

{ }

Equal Sets

Two sets are equal if, and only if, they contain exactly the same elements

Sets and relations between sets, are a basis to teach children the concept of whole numbers and the concept of "less then" as well as addition, subtraction, and multiplication of whole.

Gearge Cantor created set theory (1871-1884)

Problem Solving

4 Steps to Problem Solving

4.) Looking Back

Find another problem to practice using this method to solve

Understand the results in terms of the original pattern

Could you solve the problem a different way?

Check your results

3.) Carry Out Your Plan

Show all your work

Is there another method to solve the problem

Check each step

Implement a strategy

2.) Devise a Plan

Use direct reasoning

Use indirect reasoning

Break problem down to subgoals

Work backwards

Guess & Check

Write an equation

Make a diagram

Make a table or a list

Compare to an easier problem

Compare to a similar problem

Look for a pattern

1.) Understand the Problem

What information is missing or not needed?

What information does the problem give?

What information is missing or unknown?

What are you trying to do or find?

State the problem in in your own words

Good Mathematical Problem Solving Occurs When...

Students are required to use mathematical ideas to solve the problem.

Students are interested in finding the answer and attempt to do so

Students are presented with a situation that they understand but do not know how to proceed

Definition

Good to Know

A reasonable amount of tension and discomfort improves problem solving performance.

Engaging in a task for which the solution method is not known in advance