Math 450 Presents "The Pioneering Role of the Sierpinski Gasket"

We will be looking at different aspects of the Sierpinski Gasket and how it relates to the different generations of the Ulam-Warburton Automation and the Hex-Ulum-Warburton Automation as shown in the September 2015 edition of Math Horizons.

Math 450 Presents

The Pioneering Role of the Sierpinski Gasket

by Zach Brown

Tuesday, November 24, 2015

1:40 p.m.

Patterson 301

Come join us! All are Welcome.

Math 450 Presents "The Mathematics Behind Spot It!"

In the game, Spot It!, each of the 55 cards have eight pictures and any two cards have exactly one picture in common. It may be easy to spot the similarity between two given cards, but how easily is this game created? In the April 2015 edition of Math Horizons, Burkard Polster wrote "The Intersection Game" to address that question. This talk will present how to build Spot It! decks and vaiations using point-line geometry, projective planes, t- (v,k,λ) designs.

 

 

Math 450 Presents

The Mathematics Behind Spot It!

by Grace McCourt

Tuesday, November 17, 2015

1:40 p.m.

Patterson 301

 

Come join us! All are Welcome.

Math 450 Presents "The Logistic Equation"

The logistic differential equation, dP/dt = rP(1 – P), was first proposed in a slightly different form by Pierre-Francois Verhulst in 1838 to model population growth. Since then, it has found a wide array of applications – from modeling growth in economics to use as an activation function in artificial neural networks. Analytical solutions may easily be obtained for this equation, aiding in its popularity.

In an early paper dating from 1920, Raymond Pearl and Lowell Reed attempt to fit a number of potential population models to population data obtained by the United States census. I propose a more general equation, dP/dt = rP(L(t) – P), where the function L(t) is the limit of the population varying with time. After finding a general, open form solution to this equation, I propose several models for L(t), and attempt to solve the equation both analytically and numerically.

Pearl, R., & Reed, L. (1920). On the Rate of Growth of the Population of the United States Since 1790 and it's Mathematical Representation. Proceedings of the National Academy of Sciences, 6(6). Retrieved October 27, 2015, from http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1084522/

Math 450 Presents

"The Logistic Equation"

by: Paul Pernici

Tuesday, November 10, 2015

1:40 p.m.

in Patterson 301

Come join us! All are Welcome.

2015 ACM-ICPC Annual Competition

Dr. Iyad Ajwa and two teams of undergraduate computer science students traveled to Youngstown, Ohio on October 30-31, 2015 to participate in the 2016 ACM-ICPC East Central North America Regional Programming Contest that was held at Youngstown State University. The contest draws teams from institutions across Ohio, Indiana, Michigan, Western Pennsylvania, and Eastern Ontario in Canada. 

Paul Pernici, Rupesh Maharjan and Alex Gregory

Ashland University was represented by two teams: AU Purple (Alex Gregory, Rupesh Maharjan, Paul Pernici) and AU Gold (Raymond Acevedo and Erich Berger. The third student on the team was Benjamin Bushong, but he was not able to attend). The competition was for five hours and consisted of nine very challenging problems. Team AU Purple solved one problem.

Erich Berger and Raymond Acevedo

Congratulations to Team AU Purple and thank you to all five students who participated in this highly competitive contest!

Math 450 Presents "Cups and Downs"

 


How many moves does it take to flip three pennies so that they're all showing the same face? How many moves does it take to flip three cups so they are all upside down when one move inverts two cups at a time?

 

The article Cups and Downs, found in the January 2012 issue of the College Mathematics Journal, looks at the state diagrams for each of these "magic tricks" to determine the maximum number of moves needed to solve each problem. using matrices, the cups problem is extended to see how many moves are required to invert n number of cups if each move inverts exactly m cups at a time. Although the solution seems simple, it turns out to be surprisingly complicated.

 

Stewart, Ian. "Cups and Downs." The College Mathematics Journal January 2012: 15-19. Print.

Math 450 Presents

"Cups and Downs"

by: Emily Marconi

Tuesday, November 3, 2015

1:40 p.m.

in Patterson 301

 

Come join us! All are Welcome.

 
 
 
 

 

 

 

Math 450 Presents "Fractals and Mysterious Triangles"

Cards of three colors are dealt in a row of size n. The cards are then continually dealt into rows above each other of size n-1, n-2, n-3, … until the row of size 1 is reached. The cards must be placed following 2 rules. One, if two cards, adjacent cards, from the previous row share the same color, the card above them must be that color as well. Two, if two adjacent cards are different colors, the card above them must be of the third color. These cards form a “mysterious triangle.” We want to know how we could predict the color of the apex card of the triangle without dealing out all the cards. Using Sierpinski Triangles, mod 3 arithmetic, and fractals, we will figure out exactly that.

Jones, M. A., Mitchell, L., Shelton, B. “Fractals and Mysterious Triangles.” Math Horizons.

      September 2015. pp 22-25.

 

Math 450 Presents

"Fractals and Mysterious Triangles"

by: Shelbey Linder

Tuesday, October 20, 2015, 1:40 p.m.

in Patterson 301

 

Come join us! All are welcome.



Math 450 Seminar Presents "Mathematics for Gamers!"

The problem discussed in this article begins with the introduction of zombies in the video game Call of Duty: Black Ops. However, the solution to this problem is a mathematical problem that needs a solution as well. There are four dials placed among four levels of a building, and the solution of this problem requires a certain algorithm of turning the dials to read in order 2, 7, 4, and 6.

In Math Horizons, February 2014 edition, Heidi Hulsizer tackles the problem presented to her in one of the video games she plays regularly. After careful consideration she discovered two ways to mathematically solve this Easter egg. The first way is with an algebraic approach, while the second deals with a matrix approach.  Who knew video games involved so much thinking!

Math 450 Presents

"Mathematics for Gamers!"

by: Jacob Ackerman

Tuesday, October 13, 2015, 1:40 p.m.

in Patterson 301

Come join us! All are welcome.