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Articles 1 - 7 of 7
Full-Text Articles in Number Theory
Optimizing Buying Strategies In Dominion, Nikolas A. Koutroulakis
Optimizing Buying Strategies In Dominion, Nikolas A. Koutroulakis
Rose-Hulman Undergraduate Mathematics Journal
Dominion is a deck-building card game that simulates competing lords growing their kingdoms. Here we wish to optimize a strategy called Big Money by modeling the game as a Markov chain and utilizing the associated transition matrices to simulate the game. We provide additional analysis of a variation on this strategy known as Big Money Terminal Draw. Our results show that player's should prioritize buying provinces over improving their deck. Furthermore, we derive heuristics to guide a player's decision making for a Big Money Terminal Draw Deck. In particular, we show that buying a second Smithy is always more optimal …
Divisibility Probabilities For Products Of Randomly Chosen Integers, Noah Y. Fine
Divisibility Probabilities For Products Of Randomly Chosen Integers, Noah Y. Fine
Rose-Hulman Undergraduate Mathematics Journal
We find a formula for the probability that the product of n positive integers, chosen at random, is divisible by some integer d. We do this via an inductive application of the Chinese Remainder Theorem, generating functions, and several other combinatorial arguments. Additionally, we apply this formula to find a unique, but slow, probabilistic primality test.
Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang
Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang
Electronic Theses and Dissertations
While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and Paul Loya. In this thesis, we reproduce the Kirsten and Loya approach to …
Applying The Data: Predictive Analytics In Sport, Anthony Teeter, Margo Bergman
Applying The Data: Predictive Analytics In Sport, Anthony Teeter, Margo Bergman
Access*: Interdisciplinary Journal of Student Research and Scholarship
The history of wagering predictions and their impact on wide reaching disciplines such as statistics and economics dates to at least the 1700’s, if not before. Predicting the outcomes of sports is a multibillion-dollar business that capitalizes on these tools but is in constant development with the addition of big data analytics methods. Sportsline.com, a popular website for fantasy sports leagues, provides odds predictions in multiple sports, produces proprietary computer models of both winning and losing teams, and provides specific point estimates. To test likely candidates for inclusion in these prediction algorithms, the authors developed a computer model, and test …
Introduction Aux Méthodes D’Intégrale De Chemin Et Applications, Nour-Eddiine Fahssi
Introduction Aux Méthodes D’Intégrale De Chemin Et Applications, Nour-Eddiine Fahssi
Nour-Eddine Fahssi
These lecture notes are based on a master course given at University Hassan II - Agdal in spring 2012.
On Generalized Hurwitz-Lerch Zeta Distributions, Mridula Garg, Kumkum Jain, S. L. Kalla
On Generalized Hurwitz-Lerch Zeta Distributions, Mridula Garg, Kumkum Jain, S. L. Kalla
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we introduce a function which is an extension to the general Hurwitz-Lerch Zeta function. Having defined the incomplete generalized beta type-2 and incomplete generalized gamma functions, some differentiation formulae are established for these incomplete functions. We have introduced two new statistical distributions, termed as generalized Hurwitz-Lerch Zeta beta type-2 distribution and generalized Hurwitz-Lerch Zeta gamma distribution and then derived the expressions for the moments, distribution function, the survivor function, the hazard rate function and the mean residue life function for these distributions. Graphs for both these distributions are given, which reflect the role of shape and scale …
Convergence Of Random Walks On The Circle Generated By An Irrational Rotation, Francis E. Su
Convergence Of Random Walks On The Circle Generated By An Irrational Rotation, Francis E. Su
All HMC Faculty Publications and Research
Fix . Consider the random walk on the circle which proceeds by repeatedly rotating points forward or backward, with probability , by an angle . This paper analyzes the rate of convergence of this walk to the uniform distribution under ``discrepancy'' distance. The rate depends on the continued fraction properties of the number . We obtain bounds for rates when is any irrational, and a sharp rate when is a quadratic irrational. In that case the discrepancy falls as (up to constant factors), where is the number of steps in the walk. This is the first example of a sharp …