Mathematics
http://hdl.handle.net/10211.8/17
Sun, 21 Jan 2018 02:32:07 GMT2018-01-21T02:32:07ZData of Modular Curves
http://hdl.handle.net/10211.3/198862
Data of Modular Curves
Newberg, Steven
A moduli problem seeks to find a bijection between a class of objects and a topological space that describes the parameters of the class of objects. We will present the moduli problem for a type of curve used in cryptography, elliptic curves.
The topological space describing elliptic curves is the quotient of the complex plane by the action of matrices in SL_2(Z), which we call a modular curve. Taking a quotient of the upper half of the complex plane by subgroups of SL_2(Z) also give moduli spaces of elliptic curves but include some extra structure. There are special points on modular curves, which we will discuss and give methods for finding.
Thu, 14 Dec 2017 00:00:00 GMThttp://hdl.handle.net/10211.3/1988622017-12-14T00:00:00ZInhomogeneous Bond Percolation for Regular Infinite Trees and on a Square Lattice with an N-Periodic Inhomogeneity
http://hdl.handle.net/10211.3/198860
Inhomogeneous Bond Percolation for Regular Infinite Trees and on a Square Lattice with an N-Periodic Inhomogeneity
Hernandez Hernandez, Jesus
This thesis explores bond percolation on r-ary trees and then moves on to 3-regular infinite trees. The last chapter explores bond percolation on the square lattice where horizontal bonds are open in a periodic fashion.
Wed, 13 Dec 2017 00:00:00 GMThttp://hdl.handle.net/10211.3/1988602017-12-13T00:00:00ZEnglish Translation of the Sphaerica of Menelaus
http://hdl.handle.net/10211.3/158652
English Translation of the Sphaerica of Menelaus
Hermiz, Rani
The SPHAERICA (in English: Spherics) of Menelaus of Alexandria (dating to roughly 100 AD) is among the oldest known works on spherical geometry and trigonometry. Spherical geometry is the study of geometric objects on the surface of a sphere and spherical trigonometry is the study of relationships among sides and angles in triangles on a sphere, where the sides are arcs of “great circles.” The SPHAERICA was originally written in Koiné Greek, but editions in this language are no longer extant. One of the oldest complete editions still available is Abu Nasr Mansur’s “improved” edition in Arabic. Other editions exist in Arabic, Hebrew, Latin, and German, but none in English. In this thesis I give an English translation of Abu Nasr Mansur’s edition, and discuss certain aspects of the text from a modern point of view.
Wed, 16 Dec 2015 00:00:00 GMThttp://hdl.handle.net/10211.3/1586522015-12-16T00:00:00ZRanking the Players in a Tournament
http://hdl.handle.net/10211.3/158617
Ranking the Players in a Tournament
Caldwell, James David
This paper examines the problem of rank ordering a set of players or objects on the basis of a tournament arising from a complete set of pairwise comparisons.
Mon, 14 Dec 2015 00:00:00 GMThttp://hdl.handle.net/10211.3/1586172015-12-14T00:00:00Z