Mathematics Honors ThesesCopyright (c) 2021 Ithaca College All rights reserved.
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Recent documents in Mathematics Honors Thesesen-usFri, 27 Aug 2021 13:33:29 PDT3600Internal Rays of the Mandelbrot Set
https://digitalcommons.ithaca.edu/math_honors_theses/11
https://digitalcommons.ithaca.edu/math_honors_theses/11Thu, 21 Apr 2016 10:09:26 PDT
This paper will investigate a method for seeing the internal structure of individual hyperbolic components of the Mandelbrot set by mapping the unit to disc to individual components. This will be used to explain how two components are connected to each other.
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Walter HannahDeletion and Contraction Games: Chromatic Polynomial Proofs and Making Sense of an Apple Tree
https://digitalcommons.ithaca.edu/math_honors_theses/10
https://digitalcommons.ithaca.edu/math_honors_theses/10Thu, 21 Apr 2016 10:05:44 PDT
Using the deletion contraction algorithm we can find the chromatic polynomials for graphs. Similar to combinatorial proofs, we can apply this algorithm in different ways to the same graph to derive polynomial identities. Also, we will be looking at a couple of results from a previous paper and provide alternate proofs. Lastly, we will give a formula for the chromatic polynomial of an Apple Tree. Roughly, an Apple Tree is a tree with cycles attached at its vertices.
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Donny TangDynamical Plan Structures in the Parameter Plane of Cosine-Root Family
https://digitalcommons.ithaca.edu/math_honors_theses/9
https://digitalcommons.ithaca.edu/math_honors_theses/9Thu, 21 Apr 2016 08:54:25 PDTMaksim SiposGeneralization of the Genocchi Numbers to their q-analogue
https://digitalcommons.ithaca.edu/math_honors_theses/8
https://digitalcommons.ithaca.edu/math_honors_theses/8Thu, 21 Apr 2016 08:37:05 PDT
In the study of functions, it is often useful to derive a more generalized form of a given function and study it in order to shed new light on the original function, which is a special case of the object under study. One way in which to construct such generalizations is through the use of q-series. In this note, we will discuss some of the tools necessary for constructing these q-analogues of classical functions, their purpose, and then demonstrate one such construction on the Genocchi numbers and its close relative, the Euler numbers. Two methods of generation for the Genocchi numbers will be given, and a verification of the relationship between the Genocchi numbers and the Euler numbers will be discussed in each case. Following that, the generalization to a q-analogue of each series will be discussed and the preservation of the relationship between the two series will be verified.
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Matthew RogalaCornered Circles
https://digitalcommons.ithaca.edu/math_honors_theses/7
https://digitalcommons.ithaca.edu/math_honors_theses/7Thu, 21 Apr 2016 08:31:15 PDT
The circle, the set of points equal distance from a given point, is a round, perfectly symmetrical object in two dimensional Euclidian Space. What if we redefined distance, the metric, in such a way that circles were not circles, but rather cornered circles? What would happen to the circumference? Of course, because circumference is dependent on measuring distance the change in metric would also affect the circumference measurement. Given a symmetric convex set, it is possible to define a metric space that has the boundary of the set as a unit circle. The main result of this paper is to find the circumference of every even edged regular polygon unit circle in the corresponding metric space.
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Samuel ReedMinimization via the Subway Metric
https://digitalcommons.ithaca.edu/math_honors_theses/6
https://digitalcommons.ithaca.edu/math_honors_theses/6Thu, 21 Apr 2016 08:26:02 PDT
The Subway Metric is a variant of the well-known Taxicab Metric in which a subway, in the form of a line in the plane, is used to alter walking distance within a city grid. In this work, we discuss where to place such a subway line in order to miminize the greatest walking distance within various city layouts.
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Carly O'BrienAn Axiomatic Formulation of Quantum Mechanics
https://digitalcommons.ithaca.edu/math_honors_theses/5
https://digitalcommons.ithaca.edu/math_honors_theses/5Thu, 21 Apr 2016 08:22:26 PDT
Von Neumannâ€™s axiomatic treatment of non-relativistic quantum mechanics is the archetypal example of the dual interaction between physical theories and the development of mathematical ideas. We examine this interaction by first building up the necessary parts of the theory of unbounded self-adjoint operators on a Hilbert space, emphasizing the physical intuition that motivates the mathematical concepts. We then present a version of the Dirac-von Neumann axioms on a quantum system and deduce some of their elementary consequences, illustrating the converse effect of the mathematical formalism on the physical theory.
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Matthew MastroeniOperations Research
https://digitalcommons.ithaca.edu/math_honors_theses/4
https://digitalcommons.ithaca.edu/math_honors_theses/4Thu, 21 Apr 2016 08:18:12 PDTJihyun Rachel LeeDynamics of a cosine-root family
https://digitalcommons.ithaca.edu/math_honors_theses/3
https://digitalcommons.ithaca.edu/math_honors_theses/3Thu, 21 Apr 2016 08:11:29 PDTMatt Halsteadq-Series
https://digitalcommons.ithaca.edu/math_honors_theses/2
https://digitalcommons.ithaca.edu/math_honors_theses/2Thu, 21 Apr 2016 08:04:32 PDTMichael GriffithExploring a Connection between Transformational Geometry and Matrices
https://digitalcommons.ithaca.edu/math_honors_theses/1
https://digitalcommons.ithaca.edu/math_honors_theses/1Thu, 21 Apr 2016 07:58:27 PDTDanielle Dobitsch