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On Degree Bound For Syzygies Of Polynomial Invariants, Zhao Gao
On Degree Bound For Syzygies Of Polynomial Invariants, Zhao Gao
Senior Independent Study Theses
Suppose G is a finite linearly reductive group. The degree bound for the syzygy ideal of the invariant ring of G is given in [2]. We develop the theory of commutative algebra and give the proof from [2] that the ideal of relations of the minimal set of generators of invariant ring of a finite linearly reductive group G is generated in degree at most 2|G|.
Building A Course Recommender System For The College Of Wooster, Nan Jiang
Building A Course Recommender System For The College Of Wooster, Nan Jiang
Senior Independent Study Theses
The goal of this project is to investigate the approaches for building recommender systems and to apply them to implement a course recommender system for the College of Wooster. There are three main objectives of this project. The first is to understand the mathematics and computer science aspects behind it. The mathematic concepts built into this project include probability, statistics and linear algebra. The final product is consist of two components: a collection of Python scripts containing the implementation code of the course recommender system, and a simple user interface allowing people to use the recommender system without typing commands. …
The Search For Gto: Determining Optimal Poker Strategy Using Linear Programming, Stuart Young
The Search For Gto: Determining Optimal Poker Strategy Using Linear Programming, Stuart Young
Senior Independent Study Theses
This project applies techniques from game theory and linear programming to find the optimal strategies of two variants of poker. A set of optimal poker strategies describe a Nash equilibrium, where no player can improve their outcome by changing their own strategy, given the strategies of their opponent(s). We first consider Kuhn Poker as a simple application of our methodology. We then turn our attention to 2-7 Draw Poker, a modern variant onto which little previous research is focused. However, the techniques that we use are incapable of solving large, full-scale variants of poker such as 2-7 Draw. Therefore, we …
Pretending To Be Human: An Automated Theorem Prover To Write Mathematical Proofs, Khoa Nguyen
Pretending To Be Human: An Automated Theorem Prover To Write Mathematical Proofs, Khoa Nguyen
Senior Independent Study Theses
This project explores the theories of automated theorem proving and lambda calculus, and seeks to improve upon a current implementation of an automated theorem prover that produces human-like output. This software component is based on a published article titled “A Fully Automatic Theorem Prover with Human-Style Output” by M. Ganesalingam and W.T. Gowers [7], which outlines a program called robotone containing a first-order logic system (with a few modifications) able to automatically write simple direct proofs. It is designed to mimic different strategies that a human mathematician would use when facing a problem, and to write human-style proofs. The current …