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,
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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.
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. 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"
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.
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.
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.
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 firstname.lastname@example.org or visit the website www.beanactuary.com.
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.
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.