tag:blogger.com,1999:blog-84465040896846853992015-04-28T10:48:01.775-04:00Ashland Math/CS NewsAshlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.comBlogger118125tag:blogger.com,1999:blog-8446504089684685399.post-45505620552710951782015-04-28T10:48:00.000-04:002015-04-28T10:48:01.783-04:00Math 450 Senior Seminar Presents "Optimal Bluffing Strategies in Poker" today, Tuesday, April 28<div class="separator" style="clear: both; text-align: center;"></div>Bluffing is a very important aspect of the popular card game poker, however, knowing when to bluff can be difficult. This talk will briefly discuss how to play poker, what the classical bluffing situation is, and then apply game theory in order to optimize betting strategies. As part of this analysis the expected returns of each player and the ideal frequency of bluffing and calling will be found. However, while exact probabilities for situations such as the opponent having the winning hand can be determined,<br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-sUee_DqZDEs/VT-cAZGpWJI/AAAAAAAAAlQ/pI9cnAx0xAA/s1600/bluffing-poker.jpg" imageanchor="1" style="clear: right; display: inline !important; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://4.bp.blogspot.com/-sUee_DqZDEs/VT-cAZGpWJI/AAAAAAAAAlQ/pI9cnAx0xAA/s1600/bluffing-poker.jpg" height="219" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Compliments of Bing Images</td></tr></tbody></table>it is often time-consuming and not realistic to do so during a game. As such, this method will rely on estimated probabilities that a player has the winning hand.<br /><br /><div style="text-align: center;"><span style="color: #351c75;"><span style="background-color: white;"><b>Math 450 Senior Seminar Presents</b></span></span></div><div style="text-align: center;"><span style="color: #351c75;"><span style="background-color: white;"><b>"Optimal Bluffing Strategies in Poker"</b></span></span></div><div style="text-align: center;"><span style="color: #351c75;"><span style="background-color: white;"><b>by: Joel Moseman</b></span></span></div><div style="text-align: center;"><span style="color: #351c75;"><span style="background-color: white;"><b>Tuesday, April 28, 4:30 p.m.</b></span></span></div><div style="text-align: center;"><span style="color: #351c75;"><span style="background-color: white;"><b>in Patterson 301</b></span></span></div>Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-58610098806758411622015-04-16T11:28:00.001-04:002015-04-16T11:28:23.297-04:00Math 450 Senior Seminar Presents "Computing Determinants Using the Dodgson Condensation Method" on Tuesday, April 21<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-3XeOHO9sCrU/VS_R6IyWVEI/AAAAAAAAAkw/c554EKPkB10/s1600/LewisCarrollSelfPhoto.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-3XeOHO9sCrU/VS_R6IyWVEI/AAAAAAAAAkw/c554EKPkB10/s1600/LewisCarrollSelfPhoto.jpg" height="200" width="134" /></a></div><a href="http://1.bp.blogspot.com/-Y_lVZ7G719o/VS_R2GWVnUI/AAAAAAAAAko/INNnRsT_bjg/s1600/alice-in-wonderland.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://1.bp.blogspot.com/-Y_lVZ7G719o/VS_R2GWVnUI/AAAAAAAAAko/INNnRsT_bjg/s1600/alice-in-wonderland.jpg" height="200" width="146" /></a>Every square matrix has a determinant but computing a matrix that is larger than<br />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. <i>Alice's Adventure in Wonderland's </i>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.<br /><br /><div style="text-align: center;"><span style="color: #351c75;"><b>Math 450 Senior Seminar Presents</b></span></div><div style="text-align: center;"><span style="color: #351c75;"><b>"Computing Determinants Using the Dodgson Condensation Method"</b></span></div><div style="text-align: center;"><span style="color: #351c75;"><b>by Kylee Bogner</b></span></div><div style="text-align: center;"><span style="color: #351c75;"><b>Tuesday, April 21, 4:30 p.m.</b></span></div><div style="text-align: center;"><span style="color: #351c75;"><b>in Patterson 301</b></span></div><div style="text-align: left;"><span style="color: #351c75;"><b><br /></b></span></div><div style="text-align: left;"><b>All are Welcome!</b></div><br />Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-89721066656938584932015-04-10T10:22:00.003-04:002015-04-10T10:34:34.764-04:00Math 450 Senior Seminar Presents "Markov Chains and the Risk Board Game" on Tuesday, April 14<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-UV-RF3TE3Xc/VSfc8-BDaFI/AAAAAAAAAkU/FvfeWOaCmDc/s1600/Risk%2BBoard%2BGame.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-UV-RF3TE3Xc/VSfc8-BDaFI/AAAAAAAAAkU/FvfeWOaCmDc/s1600/Risk%2BBoard%2BGame.jpg" height="134" width="200" /></a></div><a href="http://4.bp.blogspot.com/-t2ugxmgBH1s/VSfc6_CP3BI/AAAAAAAAAkM/Bbq_nACchtA/s1600/Markov%2BChain.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-t2ugxmgBH1s/VSfc6_CP3BI/AAAAAAAAAkM/Bbq_nACchtA/s1600/Markov%2BChain.jpg" height="149" width="200" /></a><br /><br />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 <i>RISK</i>. 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.<br /><br /><div style="text-align: center;"><span style="color: #351c75;"><span style="background-color: white;"><b>Math 450 Senior Seminar Presents</b></span></span></div><div style="text-align: center;"><span style="color: #351c75;"><span style="background-color: white;"><b>"Markov Chains and the RISK Board Game"</b></span></span></div><div style="text-align: center;"><span style="color: #351c75;"><span style="background-color: white;"><b>by William Horn</b></span></span></div><div style="text-align: center;"><span style="color: #351c75;"><span style="background-color: white;"><b>Tuesday, April 14, 4:30 p.m.</b></span></span></div><div style="text-align: center;"><span style="color: #351c75;"><span style="background-color: white;"><b>in Patterson 301</b></span></span></div><div style="text-align: center;"><span style="color: #351c75;"><span style="background-color: white;"><b><br /></b></span></span></div><div style="text-align: left;"><span style="background-color: white;"><b>All are Welcome!</b></span></div>Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-58410738745955833002015-04-07T10:23:00.002-04:002015-04-07T10:23:15.917-04:00The Seventy-fifth Annual William Lowell Putnam Mathematical Competition<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-M5mEYSrTTLE/VSK4-tZiySI/AAAAAAAAAjg/siTnDKW-gD4/s1600/2014%2B75th%2BAnnual.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://1.bp.blogspot.com/-M5mEYSrTTLE/VSK4-tZiySI/AAAAAAAAAjg/siTnDKW-gD4/s1600/2014%2B75th%2BAnnual.JPG" height="171" width="320" /></a></div><br />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 <b>Paul Pernici </b>and <b>Grace McCourt</b>. 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.<br /><br />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).<br /><br />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.<br /><br />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.Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-50726823127352885972015-04-07T10:01:00.002-04:002015-04-07T10:01:52.209-04:00Math 450 Senior Seminar Presents "Is a .833 Hitter Better Than a .338 Hitter?" on Tuesday, April 7<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-6llDuLRP75c/VSPfSn7j6CI/AAAAAAAAAj0/moLycFQFzCY/s1600/AU%2BPlayer%2BBatting%2BAvg.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://3.bp.blogspot.com/-6llDuLRP75c/VSPfSn7j6CI/AAAAAAAAAj0/moLycFQFzCY/s1600/AU%2BPlayer%2BBatting%2BAvg.jpg" height="211" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><br /></td></tr></tbody></table>With baseball right around the corner it is time to get in the Spirit. In this presentation we will be discovering if you can actually determine a player's true abilities just based off of their batting average. Throughout the presentation we will be using formulas to measure a player's true ability, the variance in batting averages, and mean of ability to gather all the information needed for the problem. In the end, we will be able to conclude if in fact a player with a .833 batting average is a better player than the player with the lower batting average of .388.<br /><br /><div style="text-align: center;"><span style="color: #351c75;"><b>Math 450 Senior Seminar Presents</b></span></div><div style="text-align: center;"><span style="color: #351c75;"><b>"Is a .833 Hitter Better Than a .338 Hitter?"</b></span></div><div style="text-align: center;"><span style="color: #351c75;"><b>by Ashely Palmer</b></span></div><div style="text-align: center;"><span style="color: #351c75;"><b>Tuesday, April 7, 4:30 p.m.</b></span></div><div style="text-align: center;"><span style="color: #351c75;"><b>in Patterson 301</b></span></div><div style="text-align: left;"><span style="color: #351c75;"><b><br /></b></span></div><div style="text-align: left;"><b>All are Welcome!</b></div>Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-59315790009214384512015-04-06T12:44:00.001-04:002015-04-06T12:44:13.892-04:00Moseman Passes Exam P<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-aiK2AgKzi5A/VSK18xZmaEI/AAAAAAAAAjU/zb8nA6Ft_10/s1600/Joel%2BMoseman.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://3.bp.blogspot.com/-aiK2AgKzi5A/VSK18xZmaEI/AAAAAAAAAjU/zb8nA6Ft_10/s1600/Joel%2BMoseman.jpg" height="200" width="200" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Joel Moseman Passes Exam P</td></tr></tbody></table><b>Joel Moseman Passes Exam P</b><br /><b><br /></b>Joel Moseman 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.<br /><br />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.<br /><br />Congratulations, Joel, and good luck!<br /><br />For more information about the actuarial Science Program, contact Dr. Christopher Swanson, at cswanson@ashland.edu or visit the website www.beanactuary.com.Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-76351608844878749232015-04-06T12:31:00.001-04:002015-04-06T12:31:34.421-04:00Math 450 Senior Seminar Presented "Welcome to Prime Time" on Tuesday, March 31<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-oXZyHm8gOZI/VSKyx4eXMUI/AAAAAAAAAjI/vONMXklUk_o/s1600/Prime%2BIntegers.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-oXZyHm8gOZI/VSKyx4eXMUI/AAAAAAAAAjI/vONMXklUk_o/s1600/Prime%2BIntegers.jpg" /></a></div><b>Alex Lillich</b> presented <i>Welcome to Prime Time</i> 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.Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-62533137950373382002015-04-06T12:20:00.000-04:002015-04-06T12:20:51.490-04:00Math 450 Senior Seminar Presented "The Monty Hall Problem" on Tuesday, March 24<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-dGazZu_5-1s/VSKoYjHHWzI/AAAAAAAAAi4/62Iw5ZOcqhE/s1600/Monty%2BHall%2BProblem.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://1.bp.blogspot.com/-dGazZu_5-1s/VSKoYjHHWzI/AAAAAAAAAi4/62Iw5ZOcqhE/s1600/Monty%2BHall%2BProblem.jpg" height="150" width="200" /></a></div><b>Sean Burns </b>presented the <i>Monty Hall Problem </i>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.Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-36266171639383192332015-03-27T10:29:00.003-04:002015-03-27T10:29:45.198-04:00Drop-In Tutoring Changes Spring 2015<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-s--hEvO4QiU/VRVnaUKDXNI/AAAAAAAAAig/3Nf3s3imi_k/s1600/Cartoon%2Bstudy-group.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-s--hEvO4QiU/VRVnaUKDXNI/AAAAAAAAAig/3Nf3s3imi_k/s1600/Cartoon%2Bstudy-group.jpg" height="180" width="320" /></a></div><br /><div><b>Due to lack of need, the following Math Courses will no longer have a drop-in tutoring session: </b></div><div><br /></div><div><b>Calc. Mgmt. Life & Soc. Sci. II (M202)</b></div><div><b>The Calculus II (M206)</b></div><div><b>Theory of Arith. & Geom. (M217)</b></div><div><b>Geometry for Middle Grades (M218)</b></div><div><br /></div><div><b><span style="color: red;">If you find you are in need of a tutor for one of these courses, please see your professor.</span></b></div><div><br /></div><div>The following courses will still have drop-in Tutoring from 7:00 - 9:00 p.m. in Kettering 219:</div><div><br /></div><div><b>Elementary Statistics (M208) - <span style="color: red;">Mondays, Tuesdays, and Wednesdays</span></b></div><div><b>Discrete Math II (M224) - <span style="color: red;">Wednesdays</span></b></div><div><b><br /></b></div>Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-48219712893739870862015-03-13T10:38:00.000-04:002015-03-13T10:38:24.848-04:00Math 450 Senior Seminar Presents "The Probability of Winning a Point, Game, and Set" on Tuesday, March 17<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-cLFgHYPJLT0/VQLytSy6fFI/AAAAAAAAAiI/Sr6InpExkcA/s1600/racquetball-3.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://1.bp.blogspot.com/-cLFgHYPJLT0/VQLytSy6fFI/AAAAAAAAAiI/Sr6InpExkcA/s1600/racquetball-3.jpg" height="164" width="320" /></a></div>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.<br /><br /><div style="text-align: center;"><span style="color: #351c75;"><b>Math 450 Senior Seminar Presents</b></span></div><div style="text-align: center;"><span style="color: #351c75;"><b>"The Probability of Winning a Point, Game, and Set"</b></span></div><div style="text-align: center;"><span style="color: #351c75;"><b>by Jacob Ackerman</b></span></div><div style="text-align: center;"><span style="color: #351c75;"><b>Tuesday, March 17, 4:30 p.m.</b></span></div><div style="text-align: center;"><span style="color: #351c75;"><b>in Patterson 301</b></span></div><div style="text-align: center;"><span style="color: #351c75;"><b><br /></b></span></div><h3 style="text-align: left;"><span style="background-color: white;">All are Welcome!</span></h3>Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-37052541696109172402015-03-12T12:48:00.001-04:002015-03-12T12:48:24.705-04:00Happy Pi Day!<a href="http://2.bp.blogspot.com/-mTyV1AS_6Q0/VQHCnr_KuWI/AAAAAAAAAh0/T0Mocc2QYXw/s1600/Irrational%2BDay.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-mTyV1AS_6Q0/VQHCnr_KuWI/AAAAAAAAAh0/T0Mocc2QYXw/s1600/Irrational%2BDay.jpg" height="197" width="200" /></a><br />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.<br /><br /><br />"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" (<a href="http://northofboston.wickedlocal.com/article/20150311/NEWS/150319900" target="_blank">http://northofboston.wickedlocal.com/article/20150311/NEWS/150319900</a>).<br /><br /><h3><b><span style="background-color: white; color: #351c75;">Enjoy Pi Day, Saturday, March 14!</span></b></h3>Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-36370560713201711392015-03-12T12:12:00.003-04:002015-03-12T12:15:58.582-04:00Math 450 Senior Seminar Presented "Ford Circles, Continued Fractions, and Rational Approximation" on Tuesday, March 10<div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-epMZF9Z7r7U/VQG6X1VhcDI/AAAAAAAAAhk/uWqQj0FSuGs/s1600/Ford_circles_colour.svg.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://3.bp.blogspot.com/-epMZF9Z7r7U/VQG6X1VhcDI/AAAAAAAAAhk/uWqQj0FSuGs/s1600/Ford_circles_colour.svg.png" height="200" width="188" /></a></div>The presentation focused on the material presented by Ian Short in his article "Ford Circles, Continued Fractions, and Rational Approximations," which was published in <i>The American Mathematical Monthly</i> 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, <b>Charles Michel </b>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.Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-27579575180936920622015-02-23T12:44:00.001-05:002015-02-23T12:44:14.462-05:00Undergraduate Research and Creative Activity Symposium<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-M4TAM-hsQL0/VOtmc10ptEI/AAAAAAAAAhA/_9xogHfPOKk/s1600/Research%2C%2Bcreativity%2C%2Binnovation.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-M4TAM-hsQL0/VOtmc10ptEI/AAAAAAAAAhA/_9xogHfPOKk/s1600/Research%2C%2Bcreativity%2C%2Binnovation.jpg" height="147" width="320" /></a></div>The Undergraduate Research and Creative Activity Symposium will be held on April 8, 2015 in the John C. Myers Convocation Center. The Math and Computer Science Department congratulates and thanks Dr. Paul Cao, Dr. Maduka Rupasinghe and Dr. Gordon Swain for sponsoring students and representing our department at this symposium.<br /><br />This symposium is an opportunity for students to present their scholarly and creative work.<br /><br /><br /><ul><li>Dr. Maduka Rupasinghe, Assistant Professor of Mathematics, will sponsor Garrett Tresch. Garrett Tresch is a Mathematics and Actuarial Science major. Tresch will present <i>Sieve Bootstrap-Based Prediction Intervals for GARCH Processes, </i>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.</li><li>Dr. Paul Cao, Associate Professor of Computer Science, will sponsor Paul Pernici. Paul Pernici is a Computer Science and Mathematics major. Pernici will present <i>Comparing Feature Extraction and Feature Selection Algorithms in Pattern Recognition, </i>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.</li><li>Dr. Gordon Swain, Professor of Mathematics, will sponsor Joseph Scott Glorioso. Joseph Scott Glorioso is a Mathematics and Chemistry major. Glorioso will present <i>Constant Speed or Constant Effort: Which is the More EfAcient Way to Run?", </i>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.</li></ul><div><ul></ul></div>Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-76880270369237811172015-02-17T10:21:00.001-05:002015-02-17T10:21:02.744-05:00AU Alumni News - Clay Harris<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-aKmpvL9Nc5g/VONYvkS4aiI/AAAAAAAAAgc/_ZOamZLcGSI/s1600/Alumni%2BNews.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-aKmpvL9Nc5g/VONYvkS4aiI/AAAAAAAAAgc/_ZOamZLcGSI/s1600/Alumni%2BNews.jpg" height="153" width="200" /></a></div><br />Congratulations to Clay Harris. 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!Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-67301852717197239982015-02-16T10:29:00.001-05:002015-02-16T10:29:13.417-05:00Math 450 Senior Seminar Presents "Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy" on Tuesday, February 17<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-kJ9sYPDvaII/VOIKehivGCI/AAAAAAAAAgM/uer0QJaa8GQ/s1600/liquidity-ratio-analysis.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://2.bp.blogspot.com/-kJ9sYPDvaII/VOIKehivGCI/AAAAAAAAAgM/uer0QJaa8GQ/s1600/liquidity-ratio-analysis.png" height="251" width="320" /></a></div>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.<br /><br /><div style="text-align: center;"><b>Math 450 Senior Seminar Presents</b></div><div style="text-align: center;"><b>"Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy"</b></div><div style="text-align: center;"><b>by Leslie Johnson</b></div><div style="text-align: center;"><b>Tuesday, February 17, 4:30 p.m.</b></div><div style="text-align: center;"><b>in Patterson 301</b></div><div style="text-align: left;"><b><br /></b></div><h3 style="text-align: left;"><b>All are Welcome!</b></h3>Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-71013989918107234052015-02-06T10:57:00.001-05:002015-02-06T10:57:04.766-05:00Math 450 Senior Seminar Presents "The Dangers of Gambling in American Roulette" on Tuesday, February 10<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-r2vo_bDW0-k/VNThVTwcujI/AAAAAAAAAf8/OEEacKQ266E/s1600/american-roulette.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-r2vo_bDW0-k/VNThVTwcujI/AAAAAAAAAf8/OEEacKQ266E/s1600/american-roulette.gif" height="196" width="320" /></a></div><h3>Have you ever wondered what your chances of winning at the roulette table are?</h3>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.<br /><br /><div style="text-align: center;"><b>Math 450 Senior Seminar Presents</b></div><div style="text-align: center;"><b>"The Dangers of Gambling in American Roulette"</b></div><div style="text-align: center;"><b>by James Harris</b></div><div style="text-align: center;"><b>Tuesday, February 10, 4:30 p.m.</b></div><div style="text-align: center;"><b> in Patterson 301</b></div><div style="text-align: center;"><b><br /></b></div><h3 style="text-align: left;">Come and find out your chances. All are Welcome!</h3>Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-35186240826534623462015-01-30T11:13:00.002-05:002015-01-30T11:13:44.832-05:00Dr. Paul Cao Awarded the Senior Faculty Study Leave Grant<div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-O3dRLDmIhVQ/VMurF_kTRrI/AAAAAAAAAfo/AzT57jsv1Ns/s1600/Cao.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://3.bp.blogspot.com/-O3dRLDmIhVQ/VMurF_kTRrI/AAAAAAAAAfo/AzT57jsv1Ns/s1600/Cao.jpg" height="200" width="200" /></a></div>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.Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-71294543655815563472015-01-30T10:51:00.004-05:002015-01-30T10:51:54.513-05:002014 Math and Computer Science News Available<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-1zO-qg1IZKA/VMkYxniwlfI/AAAAAAAAAfY/SIoB5CdcvAo/s1600/Picture%2B2014%2BNewsletter.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-1zO-qg1IZKA/VMkYxniwlfI/AAAAAAAAAfY/SIoB5CdcvAo/s1600/Picture%2B2014%2BNewsletter.JPG" height="400" width="298" /></a></div><br /><br /><br />The Math and Computer Science Department has put the 2014 Newsletter on their website. <a href="https://www.ashland.edu/cas/file/final-newsletter-2014pdf-0" target="_blank">Click here</a> to read the fall 2014 newsletter for the Ashland University Mathematics and Computer Science Department.<br /><br />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.<br /><br />Additional news is posted on the Math and Computer Science <a href="https://www.ashland.edu/cas/departments/mathematics-and-computer-science" target="_blank">department page</a> throughout the year. You can even sign up to receive new postings by email on the <a href="http://aumathcs.blogspot.com/" target="_blank">department blog site</a>.Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-12720588473288896962015-01-28T11:58:00.003-05:002015-01-28T11:58:54.929-05:00Math 450 Senior Seminar Presents "How Many Regions Are Created in a Two-Dimensional Plane?" on Tuesday, January 27<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-EO80y1nY4xQ/VMkSgrUxs1I/AAAAAAAAAfI/r70m-Amg7W0/s1600/Lines%2B1.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-EO80y1nY4xQ/VMkSgrUxs1I/AAAAAAAAAfI/r70m-Amg7W0/s1600/Lines%2B1.jpg" height="224" width="320" /></a></div>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.<br /><br /><div style="text-align: center;">Math 450 Senior Seminar Presents</div><div style="text-align: center;">"How Many Regions are Created in a Two-Dimensional Plane?"</div><div style="text-align: center;">by Scott Glorioso</div><div style="text-align: center;">Tuesday, January 27</div><div style="text-align: center;">4:30 p.m.</div><div style="text-align: center;">in Patterson 301</div><h3 style="text-align: left;">All are Welcome!</h3>Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-82984126373507399212015-01-28T11:45:00.000-05:002015-02-17T10:50:24.612-05:00Math 450 Senior Seminar Presents "Euler's Perfection of Sound," Tuesday, February 3Why do certain sounds appear pleasant and others do not? Attend integrated math senior Brenda Forbes senior seminar talk and find out!<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-EnUHGLoHFO4/VMkPKspKb4I/AAAAAAAAAfA/5X53Ltowgww/s1600/classical-music%2B1.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-EnUHGLoHFO4/VMkPKspKb4I/AAAAAAAAAfA/5X53Ltowgww/s1600/classical-music%2B1.jpg" height="400" width="293" /></a></div><br /><div style="text-align: center;"><span style="font-size: large;">Math 450 Senior Seminar Presents</span></div><div style="text-align: center;"><span style="font-size: large;">"Euler's Perfection of Sound"</span></div><div style="text-align: center;"><span style="font-size: large;">by Brenda Forbes</span></div><div style="text-align: center;"><span style="font-size: large;">Tuesday, February 3</span></div><div style="text-align: center;"><span style="font-size: large;">4:30 p.m.</span></div><div style="text-align: center;"><span style="font-size: large;">in Patterson 301</span></div><div style="text-align: center;"><span style="font-size: large;"><br /></span></div><h4 style="text-align: center;"><span style="font-size: large;">All are Welcome!</span></h4><br />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.<br /><div><br /></div>Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-82180617834562095222015-01-27T12:40:00.001-05:002015-01-27T12:40:20.835-05:00Math Club Meeting<a href="http://3.bp.blogspot.com/-Nxe-7BwjafU/VMfNC8f6TgI/AAAAAAAAAek/GhSrHJG6EMY/s1600/Math%2BClub%2B1.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-Nxe-7BwjafU/VMfNC8f6TgI/AAAAAAAAAek/GhSrHJG6EMY/s1600/Math%2BClub%2B1.JPG" height="133" width="200" /></a><br /><br /><br />The first Math Club Meeting of the Spring 2015 is tonight, Tuesday, January 27 in Patterson 324. The theme will be Mathemagical TED Talks by Arthur Benjamin.Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-32974556087944724382015-01-08T12:06:00.001-05:002015-01-21T09:06:34.394-05:00Drop-In Tutoring Spring 2015<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-cGjFwf_nn-c/VK60jbjXioI/AAAAAAAAAeQ/Hblj6Cj-BbM/s1600/teachers-working-together.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-cGjFwf_nn-c/VK60jbjXioI/AAAAAAAAAeQ/Hblj6Cj-BbM/s1600/teachers-working-together.jpg" height="132" width="200" /></a></div><h3>Drop-In tutoring Available for Math Courses</h3><div>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. </div><div><br /></div><div>Do not struggle. Drop-In and see a tutor. All below tutor sessions are available from <span style="color: red;"><b>7:00-9:00 p.m</b>. <b>in Kettering 219</b>.</span></div><div><br /></div><div><b>Calc. Mgmt. Life & Soc. Sci. II (M202)<span style="color: #351c75;"> </span>- <span style="color: red;">Mondays</span></b></div><div><b><span style="color: red;"><br /></span></b></div><div><b>The Calculus II (M206) - <span style="color: red;">Wednesdays</span></b></div><div><b><span style="color: red;"><br /></span></b></div><div><b>Elementary Statistics (M208) - <span style="color: red;">Mondays, Tuesdays and Wednesdays</span></b></div><div><b><span style="color: red;"><br /></span></b></div><div><b>Theory of Arith. & Geom. (M217) - <span style="color: red;">Thursdays</span></b></div><div><b><span style="color: red;"><br /></span></b></div><div><b>Geometry for Middle Grades (M218) - <span style="color: red;">Tuesdays</span></b></div><div><b><span style="color: red;"><br /></span></b></div><div><b>Discrete Math II (M224) - <span style="color: red;">Wednesdays</span></b></div><div><b><span style="color: red;"><br /></span></b></div><h3>Please also see your professor for help!!!</h3>Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-72050565187258485892014-12-11T10:58:00.001-05:002014-12-11T10:58:21.823-05:0075th William Lowell Putnam Mathematical CompetitionSaturday, December 6, 2014, Grace McCourt, Scott Glorioso, Paul Pernici and Alex Lillich participated in the 75th William Lowell Putnam Mathematical Competition. The participants of the William Lowell Putnam Mathematical Competition work on 6 problems from 10 a.m. - 1 p.m. and then 6 additional problems from 3 p.m. - 6 p.m. Typically, 50% of the participants who enter this competition nationwide, and in Canada, receive 0 points on it. Based on conversations with the AU participants a couple will receive a non-zero score this year, having solved problem B1, the first problem for the afternoon session. All AU participants gleaned insights on at least one of the problems, therefore, maybe even more will receive a non-zero score. Good job AU participants!Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-17168714362829767652014-12-02T10:57:00.004-05:002014-12-02T10:57:52.541-05:00Fall Study Break set for December 4 and 5<h2><span style="font-family: inherit;"><i>Math and Computer Science Students you are Cordially invited!</i></span></h2><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-d2PCjyPbnMY/VH3hIbEA9WI/AAAAAAAAAdw/tWRs1I6fLGI/s1600/studybreak%2BFall%2B2014.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-d2PCjyPbnMY/VH3hIbEA9WI/AAAAAAAAAdw/tWRs1I6fLGI/s1600/studybreak%2BFall%2B2014.jpg" height="640" width="491" /></a></div><div><span style="font-family: inherit;"><i><br /></i></span></div>Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0tag:blogger.com,1999:blog-8446504089684685399.post-58233676266225051382014-12-02T10:48:00.003-05:002014-12-02T10:48:35.237-05:00Congratulations December Graduates<a href="http://3.bp.blogspot.com/-Q-QrV0GralE/VH3fAKjdSUI/AAAAAAAAAdk/ljAkOsaOsDg/s1600/graduation_image.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-Q-QrV0GralE/VH3fAKjdSUI/AAAAAAAAAdk/ljAkOsaOsDg/s1600/graduation_image.jpg" height="200" width="200" /></a><br /><br /><br />Congratulations to all December Graduates. The Math and Computer Science Department has two graduates graduating. Congratulations to Junjun Huang and Christopher Yocum. Both are Computer Science majors.Ashlandhttp://www.blogger.com/profile/01554946043456834618noreply@blogger.com0