Explaining, convincing and proving

Starting with one of the mini-challenges, how many of the other mini-challenges will you invent for yourself?

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

Consider these questions concerning inverting rational functions

Can you make all of these statements about averages true at the same time?

By proving these particular identities, prove the existence of general cases.

Discover how networks can be used to prove Euler's Polyhedron formula.

Three of Santa's elves and their best friends are sitting down to a festive feast. Can you find the probability that each elf sits next to their bestie?

Can the pdfs and cdfs of an exponential distribution intersect?

Given that a, b and c are natural numbers show that if sqrt a+sqrt b is rational then it is a natural number. Extend this to 3 variables.

Show that x = 1 is a solution of the equation x^(3/2) - 8x^(-3/2) = 7 and find all other solutions.