Discrete Math in
High Schools
By: Caleb Petrie
What is Discrete Math?
• Focus is on things that are finite or countable
• Opposite idea is continuous
• Subcategories:
Graph Theory , Combinatorics,
Coding Theory, some Number Theory
What is Graph Theory?
•Not your typical graph theory
•Instead, you have a set of vertices
•Edges between those vertices
A Definition
• The degree of a vertex is the number of edges
coinciding with that vertex
Practical Examples
• Let vertices be cities, edges represent a
connecting flight
• Let vertices represent people, edge represents
an acquaintance
Practical Examples
• Shortest Path
Research
• Uniformly (3,r) Regular Graphs
• Pick 3 vertices in a graph, and see how many
neighbors those three vertices have.
• What kind of structure is necessary?
How to Connect to High Schools?
• Introduce students to fundamentals of graph
theory
• Does not require advanced mathematical
background
• Uses some basic tools like permutations,
combinations, and multiplication rule
(Algebra 2 standards--probability)
First Theorem of Graph Theory
• Idea: To have students come up with a
conjecture based on many examples.
• Fill out a chart to notice pattern
• Ask them why they think the pattern makes
sense
4
8
8
16
7
14
Goal
• Have students recognize the pattern
• Can they conjecture that
2 x ( # of edges) = sum of degrees ?
Bridge of Konigsberg
Represented as a Graph
• Area of land --- vertex in the graph
• Bridge --- edge in the graph
Theorem
• In a connected graph, there is a solution if and
only if every vertex has even degree
Ways to Make Interactive
• Draw pictures
• Build their own graphs
Interesting Website
• http://oneweb.utc.edu/~ChristopherMawata/petersen/
Thank You