2010: Research Experience for Undergraduates

Permanent link for this collectionhttps://hdl.handle.net/2022/13433

Browse

Browsing 2010: Research Experience for Undergraduates by Issue Date

Filter results by year or month
Now showing 1 - 7 of 7
  • Thumbnail Image
    Item
    Evolution of mutation rates in a population
    (Indiana University Department of Mathematics, 2010) Anselmi, Michael
  • Thumbnail Image
    Item
    Torsion Subgroups of CAT(0) Groups
    (Indiana University Department of Mathematics, 2010) Ghadyali, Hamza; Dowlin, Nathan
    Given a CAT(0) group G acting geometrically on a proper CAT(0) space, we attempt to demonstrate that any torsion subgroup of G has nite cardinality.
  • Thumbnail Image
    Item
    Moduli spaces of square-tiling deformations and single-tile real line tilings
    (Indiana University Department of Mathematics, 2010) Proffitt, Garrett
    Classifying Single-Tile Periodic Tilings of the Real Line and Realizing the Deformation Spaces of Two and Three Square Periodic Tilings of the Plane through Combinatorial Structure.
  • Thumbnail Image
    Item
    On the Combinatorics of Schubert Calculus
    (Indiana University Department of Mathematics, 2010) Truong, Linh
  • Thumbnail Image
    Item
    Average time until fixation of a mutant allele in a given population
    (Indiana University Department of Mathematics, 2010) Messan, Komi
    One of the important problems in population genetics is how long it takes for a gene to go to fixation (become established). A mutant gene in a given population will eventually be lost or established. The particular interest of this research is to know the mean time for a mutant gene to become fixed in a population, and we will exclude the case when this gene is lost. A diploid population of N individuals will be considered with a forward and backward mutation of u and v respectively per basis. Using a set of nonlinear equations, we will first calculate the genotype frequencies which will allow us to find the equilibrium points for the infinite population. With the diffusion theory, we will approximate the time to fixation for finite populations. We will then proceed with a numerical approximation using C++ to see a close result for the problem.
  • Thumbnail Image
    Item
    The Links Between Smale’s Mean Value Conjecture and Complex Dynamics
    (Indiana University Department of Mathematics, 2010) Miles-Leighton, Hayley
    In this paper we study the links between Smale’s Mean Value Conjecture (SMVC) and the convergence of critical points under iteration. We begin by introducing SMVC and discussing what progress has been made towards proving this conjecture. From there we give a brief introduction to a few concepts in Complex Dynamics and Complex Analysis including conjugacy, conjugations by 1/z, and orbits. We then show that conjugacy conserves SMVC. At this point, we go through the quadratic case to show the patterns that we are looking for as well as to show a basic structure of how this problem is being looked at. From there we look at the cubic case, going through SMVC for the cubic polynomial. We then introduce the Petal Theorem and show how it is used for the cubic case specifically. We conclude with the connections between the SMVC in the cubic case and the convergence of the same critical points explained and discuss future work.
  • Thumbnail Image
    Item
    Systems of Natural Logic with Adjectives and Their Completeness
    (Indiana University Department of Mathematics, 2010) Kammer, Elizabeth
    In natural logic, the goal is to create a system of logic that is as sim- ilar to natural language as possible. In order to build a natural logic, simple sentence forms are considered, slowly incorporating more language throughout time. As background, we rst consider the fragments of the form All X are Y and then add No X are Y , where X and Y are nouns. We will look at the rules of logic and completeness of their proof sys- tems. Next, we will introduce the idea of intersecting adjectives which are adjectives with meaning separate from the noun being modifying. For example, the plural noun red cars means the intersection of everything red and everything that is a car. This paper will then present versions of the simple systems that contain intersecting adjectives and will discuss their completeness.