Discrete Math: Proof
Proof plays a very important role in discrete mathematics.
Sometimes the goal of a discrete mathematics proof is to show that
a solution exists. At other times the goal is to show that all
possible solutions to a particular problem have been found, or that
the optimal solution has been discovered.
Several of the problems listed below require students to create
and prove a formula for a particular sum.
For background information elsewhere on our site, explore the
High School Discrete
Math area of the Ask Dr. Math archives. To find relevant
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in our Internet Mathematics Library.
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- Steve Maurer
Discrete Math, difficulty level 3. Given the definition of binary trees, students discover the relation between interior vertices and leaves and prove that relation.
Heads or Tails
- Leigh Nataro
Discrete Math, difficulty level 2. Is it possible to have an arrangement of four coins go from HHHH to TTTT based on the rules given for flipping the coins?
How Many Graphs?
- Joseph Rosenstein
Discrete Math, difficulty level 3. How many essentially different graphs are there with six vertices, two of which have degree two, two degree three, and two degree four?
- Stephen Maurer
Discrete Math, difficulty level 3. Students are given clues about intervals on the number line and must determine whether they intersect or not.
A Series of Numbers
- Ethel Breuche
Discrete Math, difficulty level 3. Find the sum of the first n positive odd integers, find a formula, and prove it.
Sum of a Sequence
- Ethel Breuche
Discrete Math, difficulty level 3. Determine the sum of a sequence of numbers in terms of n: 1, (1+2), (1+2+22),(1+2+2^2+2^3)... (1+2+2^2+2^3...2^(n-1) ).