Essays about: "pure mathematics"

Showing result 1 - 5 of 12 essays containing the words pure mathematics.

  1. 1. Students' perception of the role of mathematics in their physics education

    University essay from Uppsala universitet/Fysikundervisningens didaktik

    Author : Johan Walfridsson; Anders Arvidson; [2023]
    Keywords : Didactics; Physics education;

    Abstract : The deep interdisciplinarity between physics and mathematics is not always easy to grasp for students. Transferring mathematical skills to a physical context is demanding, and students mainly use mathematics tools (i.e., formulas) for pure calculations rather than as a basis for reasoning. READ MORE

  3. 2. An Introduction to Hitchin Systems

    University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

    Author : Manuel Neumayer; [2023]
    Keywords : Mathematics and Statistics;

    Abstract : This thesis aims to introduce the tools that are needed to understand — and historically led to the inception of — Hitchin systems. We lay out a basic theory of Hamiltonian systems on symplectic manifolds, and prove the Liouville-Arnold theorem, which states that integrable Hamiltonian systems admit coordinates in which their solution is basically linear. READ MORE

  4. 3. Perron-Frobenius' Theory and Applications

    University essay from Linköpings universitet/Algebra, geometri och diskret matematik; Linköpings universitet/Tekniska fakulteten

    Author : Karl Eriksson; [2023]
    Keywords : Positive matrices; nonnegative matrices; Perron-Frobenius; linear dynamical systems; Leslie matrices; Markov chain; Google s PageRank algorithm; Positiva matriser; icke-negativa matriser; Perron-Frobenius; linjära dynamiska system; Leslie matris; Markov-kedja; Google s PageRank algoritm;

    Abstract : This is a literature study, in linear algebra, about positive and nonnegative matrices and their special properties. We say that a matrix or a vector is positive/nonnegative if all of its entries are positive/nonnegative. First, we study some generalities and become acquainted with two types of nonnegative matrices; irreducible and reducible. READ MORE

  5. 4. Cyclotomic Fields and Fermat's Last Theorem

    University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)

    Author : Samuel Runyeon Odeberg; [2021]
    Keywords : pure mathematics; number theory; algebra; algebraic number theory; cyclotomic fields; cyclotomic rings; cycltomic integers; Fermat s last theorem; Mathematics and Statistics;

    Abstract : Number theory is in a sense among the oldest disciplines of mathematics. A running theme is that many number theoretic problems are very easy to state and understand. However, actually solving these problems often requires much work or some very clever trick. READ MORE

  6. 5. From Relations to Simplicial Complexes: A Toolkit for the Topological Analysis of Networks

    University essay from KTH/Matematik (Avd.)

    Author : Johan Lord; [2021]
    Keywords : applied algebraic topology; complex networks; topological data analysis; brain network analysis;

    Abstract : We present a rigorous yet accessible introduction to structures on finite sets foundational for a formal study of complex networks. This includes a thorough treatment of binary relations, distance spaces, their properties and similarities. READ MORE