## Thursday, December 10, 2015

### Congratulations to the Students that Participated in the 76th William Lowell Putnam Mathematical Competition

On Saturday, December 5, Grace McCourt, Paul Pernici, Emily Marconi, Michael Woods and Charlie Michel participated in the 76th William Putnam Mathematical Competition. They worked on 6 problems from 10 a.m. - 1 p.m. and then 6 more problems from 3 p.m. - 6 p.m. Typically, 50% of the people who enter this competition nationwide (and in Canada) receive 0 points on it. The exam seemed particularly difficult this year, though it seems a few of the AU students made some progress on a couple of the problems. We are expecting that there may have been some nonzero scores again this year. We hope to follow with some additional news on this at a later date. Keep posted and congratulations to the students that participated.

## Thursday, December 3, 2015

### Math 450 Presents "Designing a Table Both Swinging and Stable"

In an article from the
September 2008 edition of

*The College of Mathematics Journal,*Greg N. Frederickson analyzes Howard Eves’ physical approach to designing a table both swinging and stable. The physical construction of this table was based off of Henry E. Dudeney/Charles W. McElroy’s geometric dissection discovery in 1902. The idea behind this discovery was to transform an equilateral triangle to a square using hinged dissection.
Frederickson takes us through the history and thought
process behind this idea as well as the difficulties faced by these men as they
constructed this design. He also takes into account the improvements that
needed to be made and those that have been made to the overall design. Who knew
the construction of only one table could yield two entirely different shapes?
By the end of this presentation you’ll be tempted to build this geometrically
savvy table yourself!

Frederickson, Greg N.,
“Designing a Table Both Swinging and Stable.”

*The College Mathematics Journal*39.4 (2008):**Math 450 Presents**

**Designing a Table Both Swinging and Stable**

**by Ashley Herman**

**Tuesday, December 8, 2015**

**1:40 p.m.**

**Patterson 301**

**Come join us! All are welcome.**

## Monday, November 23, 2015

### Math 450 Presents "Deriving the Fair Price"

Deriving the Fair Price: Examining the Binomial Pricing Model and the Black-Scholes Formula

Actuaries: "Part super-hero. Part fortune-teller. Part trusted advisor" (www.beanactuary.org/what). However, in order to achieve this part super-hero status, actuarial students must first pass exams published by the Society of Actuaries. Ashland University provides classes for the first two out of nine professional exams, but during my talk, I will explore some topics covered on the syllabus for the third exam, Models of Financial Economics. After reviewing some background information on financial and derivative markets, I will explain the importance of a fair option premium. Then, using the Binomial Pricing Model and the Black-Sholes formula, we will examine these different techniques used in creating and evaluating the market price for Put and Call options with stocks listed on the New York Stock Exchange as the underlying asset.

Primary Sources: McDonald, Robert L.

*Derivatives Markets,*Third Edition, Chapter 10 (sections 10.1 - 10.4) and Chapter 12 (section 12.1)**Math 450 Presents**

**Deriving the Fair Price**

**by Katie Hurley**

**Tuesday, December 1, 2015**

**1:40 p.m.**

**Patterson 301**

**Come join us! All are Welcome.**

### Crocheting Hyperbolic Planes

## Thursday, November 19, 2015

### 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.**

## Friday, November 13, 2015

### 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.**

## Friday, November 6, 2015

### Math 450 Presents "The Logistic Equation"

The logistic differential equation, dP/d

*t*=*r*P(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/d

*t*=*r*P(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.**

## Tuesday, November 3, 2015

### 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 |

## Friday, October 30, 2015

### 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.**

## Friday, October 16, 2015

### 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.**

## Wednesday, October 7, 2015

### 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.**

## Thursday, October 1, 2015

### Math 450 Seminar Presents "The Multiplication Game!"

The game is simple, the dealer hands you a random number that you cannot see, and you then enter your own integer. If the first digit of the product is between 4 and 9 you win! If the first digit of the product is 1, 2, or 3 the dealer wins. The odds seem tempting, would you take them?

In an article from the April 2010 edition of Mathematics Magazine, Kent E. Morrison analyzes this game and discovers what the odds are and how we need to apply game theory to the problem in order to completely solve the total expected outcome of this game. Although this may seem like a very straight forward problem, we will learn that a lot goes into solving this simple multiplication game.

**Math 450 Seminar Presents**

**"The Multiplication Game"**

**by: Alexander Lillich**

**Tuesday, October 6, 2015, 1:40 p.m.**

**in Patterson 301**

**Come join us! All are welcome.**

## Wednesday, September 23, 2015

### PSG Solution Published in School Science and Mathematics, April 2015

The Problem Solving Group (PSG) at Ashland University's Math and Computer Science Department, submitted 4 problems last year. They received acknowledgement for 3 correct solutions and their solution to Problem 5332 from School Science and Mathematics website (April 2015) was selected to be published.

**Congratulations, PSG!****Come and be a part of the Problem Solving Group (PSG) group.**## Tuesday, September 22, 2015

### Math 450 Seminar Presents "Primitive Triangles and Pick's Theorem"

### How long would it take you to calculate the area of this polygon?

### Hopefully not too long.

### But what about this one?

Pick’s Theorem offers an elegant formula that
allows us to find the area of a lattice polygon – whether it be as simple as
the former or as convoluted as the latter – in a matter of seconds. The theorem
obviates the need to trudge through the tedious set of calculations that would
otherwise be required to find the area of a polygon, and all we have to do is
count the lattice points it encompasses.

Sounds easy enough,
right?

Although the result itself is straightforward,
proving that it holds for all polygons is anything but. Drawing from three
classic papers on topics closely related to Pick’s Theorem, this presentation
will take a deep dive into the intriguing foundations upon which Pick’s famous
result is built.

*Liu, Alex. “Lattice Points and Pick’s Theorem.” Mathematics Magazine 52.4 (1979): 232-235. JSTOR. Web. 31 August 2015.*

*Graver, Jack, and Yvette Monachino. “A Colorful Proof of Pick’s Theorem.” Math Horizons 18.2 (2010): 14-16. JSTOR. Web. 5 September 2015.*

*Funkenbusch, W.W. "From Euler's Formula to Pick's Formula Using an Edge Theorem." The American Mathematical Monthly 81.6 (1974): 647-648. JSTOR. Web. 31 August 2015.*

*Niven, Ivan, and H.S. Zuckerman. “Lattice Points and Polygonal Area.” The American Mathematical Monthly 74.10 (1967): 1195-1200. JSTOR. Web. 31 August 2015.*

**Math 450 Seminar Presents**

**"Primitive Triangles and Pick's Theorem**

**by: Charlie Michel**

**Tuesday, September 29, 1:40 p.m.**

**in Patterson 301**

**Come join us! All are welcome.**

## Monday, September 21, 2015

### Alumni News

**Caitlin Music '13**completed the two year Master of Statistics program at Miami University. She started her career at AcuSport in Bellefontaine, OH. She is a Supply Planning Analyst. In this position, she is responsible for analyzing POS data and providing insight into inventory, fill rate, etc. Join the Math/CS department in congratulating Caitlin on her success.

### Problem Solving Group

The Problem Solving Group's first meeting is Tuesday, September 22, at 7:00 p.m. in Patterson 324. PSG will meet Bi-Weekly at 7:00 p.m. in Patterson 324. Call Dr. Chris Swanson for details.

**Come Join Us! We look forward to seeing you there!**

## Wednesday, September 16, 2015

### Math 450 Senior Seminar Presents "Colorful Symmetries"

Quiz!!

1. How
many ways can you paint your fingernails with three different colors?

2. How
many ways are there to color a disk divided into three equal parts with one of
two colors per section?

3. How
many ways can you color an icosahedron with one of

*n*colors per face?
Asking simple questions that are
difficult to answer is common in mathematics. The first question seems pretty
straight forward. Yet the second
requires a bit more understanding, one of basic geometry, group theory and
combinatorics.

Using Burnside’s Lemma, sometimes, called
the orbit-counting theorem, we will explore this question and others like it,
considering
the much needed rotation of an object,
looking at it from all sides.

By solving a much simpler problem, we will
build to the question of the icosahedron, showing with the proper ‘tools’, the
problem-solving approach needed is not that hard after all.

Bargh, B. Chase, J. Wright, M. (2014). Colorful Symmetries.

*Math Horizons,*April 2014, pp 14-17**Math 450 Senior Seminar Presents**

**"Colorful Symmetries"**

**by: Brenda Forbes**

**Tuesday, September 22, 1:40 p.m.**

**in Patterson 301**

## Tuesday, September 15, 2015

### Math 450 Senior Seminar Presents "Evaluating Risk in the Board Game 'Risk'"

In the board game

*RISK*, players attempt to conquer the world by capturing all territories on the board, with battle outcomes determined by dice rolls. Let A be the number of attacking armies and D be the number of defending armies in two adjacent territories. This talk will present the probability the defending territory will be captured and the expected number of armies lost by the attacking territory in the capture.**Math 450 Senior Seminar Presents**

**"Evaluating Risk in the Board Game**

*Risk*"**by: Dr. Christopher N. Swanson**

**Tuesday, September 15, 1:40 p.m.**

**in Patterson 301**

## Monday, August 31, 2015

### Math Club

Math Club is starting soon. The first meeting is Tuesday, September 1, 2015 at 7:00 p.m. in Patterson 324.

#### Looking forward to seeing you. Come Join Us!

### ACM Student Club

Logo of ACM |

#### Come join us! We look forward to seeing you!

## Friday, August 28, 2015

### Drop-In Tutoring Fall 215

### Drop-In tutoring Available for Math Courses

Ashland University's Center for Academic Support provides tutors and
other tools to help students succeed. Drop-In sessions are available for
several Math classes in Kettering 219. Below are the classes and times
for drop in tutoring.

Do not struggle. Drop-In and see a tutor. All below tutor sessions are available from

**7:00-9:00 p.m**.**in Kettering 219**.**Elementary Statistics (M208) - Mondays, Tuesdays, Wednesdays and Thursdays**

**Theory of Arith. & Geom. (M217) - Mondays**

**Geometry for Middle Grades (M218) - Mondays**

**Note: Calc. with Application (M201), The Calculus (M205), and Discrete Math 1 (M223) have individual tutors only.**

####
**Please see your professor, first, for help!!!**

## Wednesday, June 3, 2015

### Alumni News - Joel Moseman '15 Congratulations!

Congratulations to

Congratulations, Joel. We wish you the best in your future.

**Joel Moseman**(15'). He accepted a position with Motorists Insurance Group as an actuarial analyst. He will assist in pricing their personal and commercial Property and Casualty lines.Congratulations, Joel. We wish you the best in your future.

## Tuesday, April 28, 2015

### Math 450 Senior Seminar Presents "Optimal Bluffing Strategies in Poker" today, Tuesday, April 28

Compliments of Bing Images |

**Math 450 Senior Seminar Presents**

**"Optimal Bluffing Strategies in Poker"**

**by: Joel Moseman**

**Tuesday, April 28, 4:30 p.m.**

**in Patterson 301**

## Thursday, April 16, 2015

### Math 450 Senior Seminar Presents "Computing Determinants Using the Dodgson Condensation Method" on Tuesday, April 21

Every square matrix has a determinant but computing a matrix that is larger than

2 x 2 can be difficult. Most students learn the Laplace expansion and Gaussian method for computing these determinants. These methods are effective but are prone to many mistakes especially when fractions show up in the Gaussian method.

2 x 2 can be difficult. Most students learn the Laplace expansion and Gaussian method for computing these determinants. These methods are effective but are prone to many mistakes especially when fractions show up in the Gaussian method.

*Alice's Adventure in Wonderland's*author, Lewis Carroll, invented a method to compute the determinants for these large matrices. It is named after his given name, Charles Lutwidge Dodgson. The Dodgson Condensation comes across some issues when working with zeroes in the matrix. This talk will cover the original method, theorem and solution for the zero issue. Then it can be determined whether the Dodgson Condensation is an easier method for computing these determinants.**Math 450 Senior Seminar Presents**

**"Computing Determinants Using the Dodgson Condensation Method"**

**by Kylee Bogner**

**Tuesday, April 21, 4:30 p.m.**

**in Patterson 301**

**All are Welcome!**

## Friday, April 10, 2015

### Math 450 Senior Seminar Presents "Markov Chains and the Risk Board Game" on Tuesday, April 14

Markov chains have been used in a wide variety of areas such as computer, science, linguistics and finance. After an overview of Markov chains is presented, the talk will focus on the application of Markov chains to the popular board game

*RISK*. Specifically, this talk will look at the probability of winning a territory given the size of the defending army and size of the attacking army. Further discussion will involve the expected losses of both armies in the battle based on the probabilities generated. By analyzing the results, an answer to the question, "When should I attack?" will be provided.

**Math 450 Senior Seminar Presents**

**"Markov Chains and the RISK Board Game"**

**by William Horn**

**Tuesday, April 14, 4:30 p.m.**

**in Patterson 301**

**All are Welcome!**

## Tuesday, April 7, 2015

### The Seventy-fifth Annual William Lowell Putnam Mathematical Competition

The seventy-fifth annual William Lowell Putnam Mathematical Competition was held on Saturday, December 6, 2014. The results are in: Ashland University had two students receive non-zero scores. They were

**Paul Pernici**and

**Grace McCourt**. Pernici received a score of 18 and McCourt received a score of 2. Pernici holds the record for the highest score by an Ashland University student. Cara Smith, a 2010 graduate, previously held the highest score with a score of 12.

The William Lowell Putnam Mathematical Competition began in 1938 and is designed to stimulate a healthy rivalry in mathematical studies in the colleges and universities of the United States and Canada. Mr. William Lowell Putnam, a member of the Harvard class of 1882, believed in the "merits of an intellectual intercollegiate competition." Elizabeth Lowell Putnam created a fund in 1927 in honor of her late husband known as the William Lowell Putnam Intercollegiate Memorial fund. The first competition was in the field "of English and then a few years later another competition was held in mathematics between two institutions." It was not until after her death in 1935 that "the examination assumed its present form and was placed under the administration of the Mathematical Association of America" (The Mathematical Association of America, Exam Brochure).

This year a total of 4,320 students from 577 colleges and universities in Canada and the United States participated in the competition. Pernici did better than 76.1% of students taking the exam and McCourt did better than 42.4% of students taking the exam. Andrew Rowe, a 2006 graduate, still holds the record for the highest percentile rank, doing better than 76.2% of students taking the exam.

This year's top 5 teams were: 1.) MIT, 2.) Harvard, 3.) Rensselaer Polytechnic, 4.) Waterloo, and 5.) Carnegie Mellon. Thank you to all of the AU students who participated in this year's exam.

### Math 450 Senior Seminar Presents "Is a .833 Hitter Better Than a .338 Hitter?" on Tuesday, April 7

**Math 450 Senior Seminar Presents**

**"Is a .833 Hitter Better Than a .338 Hitter?"**

**by Ashely Palmer**

**Tuesday, April 7, 4:30 p.m.**

**in Patterson 301**

**All are Welcome!**

## Monday, April 6, 2015

### Moseman Passes Exam P

Joel Moseman Passes Exam P |

**Joel Moseman Passes Exam P**

**Joel Moseman (15') has passed the Society of Actuaries' Probability Exam (Exam P). The exam tests the candidate's knowledge of the fundamental probability tools for quantitatively assessing risk. Exam P is one of the exams required to achieve professional status as an actuary.**

Actuaries are professionals who provide expert advice and relevant solutions for business and societal problems that involve economic risk. The actuarial profession is consistently ranked as one of the top 5 careers in the United States.

Congratulations, Joel, and good luck!

For more information about the actuarial Science Program, contact Dr. Christopher Swanson, at cswanson@ashland.edu or visit the website www.beanactuary.com.

### Math 450 Senior Seminar Presented "Welcome to Prime Time" on Tuesday, March 31

**Alex Lillich**presented

*Welcome to Prime Time*at the Senior Seminar held on Tuesday, March 31. Lillich's presentation focused on the prime integers and all the work that is done with them. As many know the prime numbers are still somewhat of a mystery to us and mathematicians are constantly at work to learn more about them. Lillich covered the basics of what a prime number is and started out with proofs of primes. He also discussed how the prime numbers are laid out throughout the number line and how arithmetic progressions can relate to the primes. Another topic that was discussed was twin primes and how they are studied and utilized. He also shared a couple of the more interesting theorems he found and worked out how the proofs of those theorems work. Lillich ended the presentation with some details on the current research done with primes.

### Math 450 Senior Seminar Presented "The Monty Hall Problem" on Tuesday, March 24

**Sean Burns**presented the

*Monty Hall Problem*at the Senior Seminar held on Tuesday, March 24. The Monty Hall Problem has an infamous reputation for its counter intuitive solution. You have a choice between three doors; one contains a car, the others contain goats. After you pick a door the host, Monty Hall, opens a different door revealing a goat. He then offers you a chance to switch doors. Do you switch? The answer is that switching increases your odds of winning. This solution has been so paradoxical that the problem is arguably more famous than the show, Let's Make a Deal, that it came from. This has inspired several proofs to show just why this is the case. This undying fascination with the Monty Hall Problem has created many variations. One of these is the Progressive Monty Hall Problem, with more doors hiding goats and more chances to switch. Another is a generalization of the Monty Hall Problem with arbitrary numbers of cars, doors, doors that you pick, and doors that Monty reveals.

## Friday, March 27, 2015

### Drop-In Tutoring Changes Spring 2015

**Due to lack of need, the following Math Courses will no longer have a drop-in tutoring session:**

**Calc. Mgmt. Life & Soc. Sci. II (M202)**

**The Calculus II (M206)**

**Theory of Arith. & Geom. (M217)**

**Geometry for Middle Grades (M218)**

**If you find you are in need of a tutor for one of these courses, please see your professor.**

The following courses will still have drop-in Tutoring from 7:00 - 9:00 p.m. in Kettering 219:

**Elementary Statistics (M208) - Mondays, Tuesdays, and Wednesdays**

**Discrete Math II (M224) - Wednesdays**

## Friday, March 13, 2015

### Math 450 Senior Seminar Presents "The Probability of Winning a Point, Game, and Set" on Tuesday, March 17

In a sweaty, heated game of racquetball there seems to be little time to think about the mathematics behind the fast-paced game. However, when one steps back from the life threatening sport of racquetball and looks at the probabilities that are incorporated into the game, it makes the sport that much more interesting. Throughout this talk, we will be looking at some of the research of Tom Brown and Brian Pasko and their discoveries of relations of mathematical probabilities to winning a point, a game, and a set in racquetball. Using geometric series and combinations, it is possible to show a player, whether he is better, worse or equally as good as his opponent, and the probability he has of winning a point, a game, and a set.

**Math 450 Senior Seminar Presents**

**"The Probability of Winning a Point, Game, and Set"**

**by Jacob Ackerman**

**Tuesday, March 17, 4:30 p.m.**

**in Patterson 301**

### All are Welcome!

## Thursday, March 12, 2015

### Happy Pi Day!

Celebrate National Pi Day this Saturday, March 14. Pi Day was created by physicist Larry Shaw at San Francisco's Exploratorium in 1988. It wasn't until 2009 that the U.S. House of Representatives officially recognized March 14 as National Pi Day.

"Pi, an infinite number with no pattern, has been calculated to over 1 trillion digits beyond its decimal point. This year is especially significant since the date, year and time (3/14/15 at 9:26 a.m. and 53 seconds) corresponds with the first 10 digits of Pi (3.141592653...), an occurrence that only happens once a century" (http://northofboston.wickedlocal.com/article/20150311/NEWS/150319900).

###
**Enjoy Pi Day, Saturday, March 14!**

### Math 450 Senior Seminar Presented "Ford Circles, Continued Fractions, and Rational Approximation" on Tuesday, March 10

The presentation focused on the material presented by Ian Short in his article "Ford Circles, Continued Fractions, and Rational Approximations," which was published in

*The American Mathematical Monthly*in February 2011. Ford Circles are a geometric representation of the relationship between continued fractions and approximation of real numbers by rational numbers. An introduction to some of these essential concepts were presented before delving into the material Short presented which further illuminated the mathematics behind rational approximation of real numbers. Short proves two major theorems along with a series of lemmas and corollaries. By proving these statements,**Charles Michel**ultimately showed that several of the key properties of continued fraction expansion and Diophantine approximations can be proven using Ford Circles and rewritten in terms of relationships between tangential Ford Circles, at the Math 450 Senior Seminar that was held on Tuesday, March 10.## Monday, February 23, 2015

### Undergraduate Research and Creative Activity Symposium

This symposium is an opportunity for students to present their scholarly and creative work.

- Dr. Maduka Rupasinghe, Assistant Professor of Mathematics, will sponsor Garrett Tresch. Garrett Tresch is a Mathematics and Actuarial Science major. Tresch will present
*Sieve Bootstrap-Based Prediction Intervals for GARCH Processes,*during Oral Session III, 10:30 - 11:30 a.m. in the Faculty Room. Time Series deals with observing a variable - interest rates, exchange rates, rainfall, etc. - at regular intervals of time. The main objective of Time Series analysis are to understand the underlying processes and effects of external variables in order to predict future variables. This presentation uses the Sieve Bootstrap for computing prediction intervals. - Dr. Paul Cao, Associate Professor of Computer Science, will sponsor Paul Pernici. Paul Pernici is a Computer Science and Mathematics major. Pernici will present
*Comparing Feature Extraction and Feature Selection Algorithms in Pattern Recognition,*during Oral Session IV, 2:00 - 3:00 p.m. in the Trustees Room. Pattern recognition is the science of discovering the inherent properties of large sets of data. A popular approach used an artificial neural network (ANN), which is a biologically inspired machine learning model capable of mimicking human cognitive functions. - Dr. Gordon Swain, Professor of Mathematics, will sponsor Joseph Scott Glorioso. Joseph Scott Glorioso is a Mathematics and Chemistry major. Glorioso will present
*Constant Speed or Constant Effort: Which is the More EfAcient Way to Run?",*during Oral Session VI, 3:15 - 4:15 p.m. in the Trustees Room. The problem examined was whether it is more beneficial to run 5000 meters at constant speed or at constant effort while minimizing the time. The model, based on human data from literature, takes an input of runner's speed, wind speed, and incline and gives an output of volume of oxygen consumed. Using a simple conversion, VO2 was then converted to Calories expended.

## Tuesday, February 17, 2015

### AU Alumni News - Clay Harris

Congratulations to

**Clay Harris**(15'). Harris is an Ashland University Actuarial Science major. Harris has accepted a position as Credit Risk Analyst with Key Bank. His job will involve risk management and will incorporate significant financial statement analysis. Congratulations, Clay, we wish you all the best in your new job!

## Monday, February 16, 2015

### Math 450 Senior Seminar Presents "Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy" on Tuesday, February 17

In 1968, Edward Altman developed a model to predict bankruptcy up to three years before the event. This model is known as The Altman Z-Score and was developed using in-depth statistical techniques. This talk will focus on an introduction to traditional ratio analysis and how Altman combined this with statistics to predict bankruptcy. An overview of the multiple regression techniques used to create the model will be discussed, along with the overall results of the model. Further discussion will be on the application of the The Altman Z-Score in today's economic environment, as well as the application to some well-known companies.

###

**Math 450 Senior Seminar Presents**

**"Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy"**

**by Leslie Johnson**

**Tuesday, February 17, 4:30 p.m.**

**in Patterson 301**

###
**All are Welcome!**

## Friday, February 6, 2015

### Math 450 Senior Seminar Presents "The Dangers of Gambling in American Roulette" on Tuesday, February 10

### Have you ever wondered what your chances of winning at the roulette table are?

If you are familiar with American casinos then you are familiar with the game of roulette. As one of the most popular gambling games in the U.S. roulette is a game of probabilities. While everyone should know the casino is always favored, one might not realize how bad the odds are that the gambler walks away with a particular sum of money. In this exploration of roulette we will discuss the different types of bets the gambler can make and look at probability models as well as matrix models that should help convince you to keep your money in banks and not in casinos.**Math 450 Senior Seminar Presents**

**"The Dangers of Gambling in American Roulette"**

**by James Harris**

**Tuesday, February 10, 4:30 p.m.**

**in Patterson 301**

### Come and find out your chances. All are Welcome!

## Friday, January 30, 2015

### Dr. Paul Cao Awarded the Senior Faculty Study Leave Grant

Dr. Paul Cao was awarded the Senior Faculty Study Leave Grant for the Fall 2015 semester. During this sabbatical leave, he will focus on the development of cyber security courses such as information security and network security. He will visit the Computer Science Department at Ohio State University and collaborate with Professor Dong Xuan. Professer Xuan is an expert on security and networks. Also during his study leave, Dr. Paul Cao, will collaborate with the Xuan Group on several data analysis projects using machine learning and data mining techniques.

### 2014 Math and Computer Science News Available

The Math and Computer Science Department has put the 2014 Newsletter on their website. Click here to read the fall 2014 newsletter for the Ashland University Mathematics and Computer Science Department.

You will find information about student activities, student accomplishments, Math Lab Renovation, Alumni News, and Faculty News. You can also read about Dr. Iyad Ajwa's participation in the Fullbright U.S. Scholar Program. Look inside to discover who the new chair of the department is.

Additional news is posted on the Math and Computer Science department page throughout the year. You can even sign up to receive new postings by email on the department blog site.

## Wednesday, January 28, 2015

### Math 450 Senior Seminar Presents "How Many Regions Are Created in a Two-Dimensional Plane?" on Tuesday, January 27

What is the distinct number of regions possible when using parallel lines, concurrent lines, and lines that are neither parallel nor concurrent? Attend senior science/chemistry major,Scott Glorioso's,senior seminar talk and he will show you proofs to determine the distinct number of regions.

Math 450 Senior Seminar Presents

"How Many Regions are Created in a Two-Dimensional Plane?"

by Scott Glorioso

Tuesday, January 27

4:30 p.m.

in Patterson 301

### All are Welcome!

### Math 450 Senior Seminar Presents "Euler's Perfection of Sound," Tuesday, February 3

Why do certain sounds appear pleasant and others do not? Attend integrated math senior Brenda Forbes senior seminar talk and find out!

Euler's musical theory explained how certain sounds appear pleasant and others do not. This is noted by sequence numbers in scale and specific order, which he called "perfection of sound." He stated that where there is perfection, there is necessary order.

Math 450 Senior Seminar Presents

"Euler's Perfection of Sound"

by Brenda Forbes

Tuesday, February 3

4:30 p.m.

in Patterson 301

#### All are Welcome!

Euler's musical theory explained how certain sounds appear pleasant and others do not. This is noted by sequence numbers in scale and specific order, which he called "perfection of sound." He stated that where there is perfection, there is necessary order.

## Tuesday, January 27, 2015

### Math Club Meeting

## Thursday, January 8, 2015

### Drop-In Tutoring Spring 2015

### Drop-In tutoring Available for Math Courses

Ashland University's Center for Academic Support provides tutors and other tools to help students succeed. Drop-In sessions are available for several Math classes in Kettering 219. Below are the classes and times for drop in tutoring.

Do not struggle. Drop-In and see a tutor. All below tutor sessions are available from

**7:00-9:00 p.m**.**in Kettering 219**.**Calc. Mgmt. Life & Soc. Sci. II (M202) - Mondays**

**The Calculus II (M206) - Wednesdays**

**Elementary Statistics (M208) - Mondays, Tuesdays and Wednesdays**

**Theory of Arith. & Geom. (M217) - Thursdays**

**Geometry for Middle Grades (M218) - Tuesdays**

**Discrete Math II (M224) - Wednesdays**

### Please also see your professor for help!!!

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