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About 24 results
  • 3.2: Colorings and Quandles
    https://math.libretexts.org/Bookshelves/Abstract_and_Geometric_Algebra/Open_Algebra_and_Knots_(Salomone)/03%3A_Knots_and_Algebra/3.02%3A_Colorings_and_Quandles
  • 1: Rational Tangles
    https://math.libretexts.org/Bookshelves/Abstract_and_Geometric_Algebra/Open_Algebra_and_Knots_(Salomone)/01%3A_Rational_Tangles
    Calculate the fraction of a rational tangle in two different ways, and argue for why the fraction is an invariant of rational tangles. As we discovered in our first class, crossings are one of the fir...Calculate the fraction of a rational tangle in two different ways, and argue for why the fraction is an invariant of rational tangles. As we discovered in our first class, crossings are one of the first ways for us to understand the connections between knots and algebra: somehow, if we can say "enough" about how a strand crosses itself, we can characterize the essential nature of a knot.
  • TitlePage
    https://math.libretexts.org/Bookshelves/Abstract_and_Geometric_Algebra/Open_Algebra_and_Knots_(Salomone)/00%3A_Front_Matter/01%3A_TitlePage
    Open Algebra and Knots
  • 4.1: Project Overview
    https://math.libretexts.org/Bookshelves/Abstract_and_Geometric_Algebra/Open_Algebra_and_Knots_(Salomone)/04%3A_Workshop_Project/4.01%3A_Project_Overview
    This, principally, highlights both a connection and a distinction between quantitative reasoning, which emphasizes concrete, contextual, and critical uses of number skills, and mathematical reasoning,...This, principally, highlights both a connection and a distinction between quantitative reasoning, which emphasizes concrete, contextual, and critical uses of number skills, and mathematical reasoning, which exposes the abstract, fundamental, and logical principles of which the former is one special case.
  • Front Matter
    https://math.libretexts.org/Bookshelves/Abstract_and_Geometric_Algebra/Open_Algebra_and_Knots_(Salomone)/00%3A_Front_Matter
  • 3.4: Invariant Polynomials
    https://math.libretexts.org/Bookshelves/Abstract_and_Geometric_Algebra/Open_Algebra_and_Knots_(Salomone)/03%3A_Knots_and_Algebra/3.04%3A_Invariant_Polynomials
    3.5.1 The Alexander Polynomial
  • 2.3: Colorings of Knots
    https://math.libretexts.org/Bookshelves/Abstract_and_Geometric_Algebra/Open_Algebra_and_Knots_(Salomone)/02%3A_Knots_and_Numbers/2.03%3A_Colorings_of_Knots
    2.4.1 Colorability as an Invariant 2.4.2 Colorability as an Algebra Problem
  • 5.1: Seminar Videos
    https://math.libretexts.org/Bookshelves/Abstract_and_Geometric_Algebra/Open_Algebra_and_Knots_(Salomone)/05%3A_Knot_Your_Average_Algebra/5.01%3A_Seminar_Videos
    The following are videos of "Knot Your Average Algebra," presented at the Bridgewater State University mathematics department seminar on March 22, 2018.
  • 4: Workshop Project
    https://math.libretexts.org/Bookshelves/Abstract_and_Geometric_Algebra/Open_Algebra_and_Knots_(Salomone)/04%3A_Workshop_Project
  • Index
    https://math.libretexts.org/Bookshelves/Abstract_and_Geometric_Algebra/Open_Algebra_and_Knots_(Salomone)/zz%3A_Back_Matter/10%3A_Index
  • 2.4: Colorings of Tangles
    https://math.libretexts.org/Bookshelves/Abstract_and_Geometric_Algebra/Open_Algebra_and_Knots_(Salomone)/02%3A_Knots_and_Numbers/2.04%3A_Colorings_of_Tangles
    2.5.1 An Integer Coloring Scheme for Rational Tangles 2.5.2 Coloring as a Rational Tangle Invariant

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