by John Ehrke | Nov 1, 2019 | Problem of the Week
What Does This Thing Do? Determine what the following algorithm does, and then prove that it does what you think it does. {Input: a real number a and a positive integer n.} begin p := 1 q := a i := n while i > 0 do if i is odd then p := p*q {Do the next two steps...
by John Ehrke | Oct 11, 2019 | Problem of the Week
Two Handy Inequalities This problem was suggested by Alexander Karabegov. Prove the following inequalities are true for all positive real numbers x and y, with equality holding if and only if x = y. Hint: (x-y)2 is greater than or equal to 0. Please submit all work to...
by John Ehrke | Oct 9, 2019 | Mu Sigma Events
The Complex Elephant Returns! Join us on Thursday, October 17th from 11:45 – 12:45 in room OSC 240 as Dr. Karabegov gives a colloquium on the manifestation of complex numbers in our real calculus sequence. In a previous talk on complex numbers, Dr. Karabegov...
by John Ehrke | Oct 4, 2019 | Problem of the Week
Will You Win? This problem was suggested by Brian Jacobs. Your friend has a game for you to try. He rolls two n-sided fair dice and you roll one n-sided fair die. You win if the number on your die is between the numbers on his dice, inclusively. For example, if he...
by John Ehrke | Sep 27, 2019 | Problem of the Week
Are There Infinitely Many? Are there infinitely many positive integers n such that n divides (that is, is a factor of) the number 2^(n)+1? Solutions are due by Thursday, Oct 3rd at 5:00 PM. Please submit all solutions to mathpotw@acu.edu. Solution to Are There...