Browsing OSU - Honors College by Author "Fili, Paul A."

Now showing items 1-5 of 5

    • Absolute Galois group as a profinite group 

      Burkhart, Ryan (2016-04-25)
      In this paper we will discuss the absolute Galois group, the Galois group of Q where Q is an algebraic closure of Q. We will begin with a discussion of Galois groups and Galois theory and why they are important. Then we ...

    • Congruent number problem and elliptic curves 

      Schroeder, Harrison (2015-04-24)
      This paper explores the congruent number problem, which asks which rational numbers are areas of triangles with rational side lengths. We define a rational non-zero number that is the area of a rational triangle as a ...

    • Enigma cipher machine 

      Hurlbut, Anna (2018-11-27)
      The Enigma cipher machine was invented in the early 1920s to help businesses protect commercial secrets, but the German military soon saw its potential application to military communications. By the mid-1930s, every branch ...

    • Internal set theory approach to nonstandard analysis 

      Beauregard, Gregory (2016-04-25)
      Although epsilon-delta analysis has enjoyed great success in giving rigor to modern mathematics, nonstandard analysis can be used to rigorously reformulate modern arguments with infinite and infinitesimal arguments. The ...

    • P-adic numbers and the local-to-global principle 

      Hull, Kelsea (2017-05-04)
      We introduce the notion of p-adic absolute value on the rationals. We prove up to equivalence that these and the Euclidean absolute value are the only non-trivial absolute values. Then we discuss the completion of the ...