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  • 1.
    Lundin, Edvin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Logic and Representation Theory.
    Erdős-Kaplansky Satsen2023Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Inom linja ̈r algebra har varje vektorrum ett s ̊a kallat dualrum, vilket är ett vektorrum bestående av alla linjära funktioner från det ursprungliga rummet till sin kropp. Att beräkna dimensionen av ett dualrum tillhörande ett ändlig-dimensionellt vektorrum är relativt enkelt, för oändlig-dimensionella vektorrum är det mer komplicerat. Den sats vi ska diskutera, Erdős–Kaplansky Satsen, ämnar lösa den frågan med påståendet att ett dualrum tillhörande ett oändlig-dimensionellt vektorrum har dimension lika med sin kardinalitet. 

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  • 2.
    Fors Rosén, Ellen
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Galoisteori och Abel-Ruffinis sats2023Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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  • 3.
    Karlsson, Edward
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Characterisation of countably infinitely categorical theories2023Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This thesis looks at characterising countably infinitely categorical theories. That is theories for which every countably infinite model is isomorphic to every other countably infinite model. The thesis looks at the Lindenbaum-Tarski algebra, Henkin theories, types and then ends with the Ryll-Nardzewski theorem which provides several equivalences to a theory being countably infinitely categorical.

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  • 4.
    Sundgren, Hampus
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Logic and Representation Theory.
    Elementary proof of the Riemann—Roch Theorem2023Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This thesis will cover an elementary proof of the Riemann–Roch Theorem for planecurves. We will introduce the notions of divisors, which is a convenient way of com-puting multiplicities of rational function, then continuing by introducing differentials.Furthermore we will introduce the K-vector space L(D), consisting of rational func-tions which are controlled by a divisor D. This is followed by presenting some moreresults before we arrive at an elementary proof of the Riemann–Roch Theorem.

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    Elementary Proof of The Riemann–Roch Theorem
  • 5.
    Bengtsson, Niclas
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Logic and Representation Theory.
    Abstract Logics and Lindström's Theorem2023Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    A definition of abstract logic is presented. This is used to explore and compare some abstract logics, such as logics with generalised quantifiers and infinitary logics, and their properties. Special focus is given to the properties of completeness, compactness, and the Löwenheim-Skolem property. A method of comparing different logics is presented and the concept of equivalent logics introduced. Lastly a proof is given for Lindström's theorem, which provides a characterization of elementary logic, also known as first-order logic, as the strongest logic for which both the compactness property and the Löwenheim-Skolem property, holds.

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  • 6.
    Perman, Zoe
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Probability Theory and Combinatorics.
    On Minimizing Properties of Geodesics2022Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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  • 7.
    Sköldberg, Linus
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Logic and Representation Theory.
    The 0-1 Law and quantifier elimination in finite structures2022Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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  • 8.
    Löfgren, Simon
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Logic and Representation Theory.
    The Eisenstein integers and cubic reciprocity2022Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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  • 9.
    Norlén Jäderberg, Mika
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Logic and Representation Theory.
    Triangulated Categories2022Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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  • 10.
    Alverbro, Miranda
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Logic and Representation Theory.
    An Overwiev Of The Rado Graph2022Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This paper examines the Rado graph, the unique, countably infinite, universalgraph. Many of the central properties are covered in detail, and various constructionsare provided, using results from a variety of fields of mathematics. A variantof the Rado graph was initially constructed by Ackermann. The actual Rado graphwas studied later, by Erdős and Rényi, before Rado rediscovered it from a differentperspective. A multitude of other authors have since then contributed to the subject.

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  • 11.
    Wredh, Felix
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Logic and Representation Theory.
    Impossible Constructions Within Euclidean Geometry2022Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    One of the most important mathematicians of all time was Euclid. Even though his books laid thegroundwork for plane geometry, they did have some limitations. In this paper we show why some importantconstructions are impossible, as well as giving Swedish mathematics teachers some ideas on how to implementthis in their lessons.

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  • 12.
    Drakengren, Saga
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Logic and Representation Theory.
    Subsemigroups and congruences for classical transformation semigroups2022Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    In this thesis we study and classify all isolated and completely isolatedsubsemigroups and congruences in classical finite transformationsemigroups.

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  • 13.
    Solig, Tim
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Logic and Representation Theory.
    A Semantic Approach to Computation: Representing the Partial Recursive Functions in Lambda Calculus2022Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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  • 14.
    Holm, Sanna
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Napoleons sats: Napoleon's Theorem2022Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Denna uppsats behandlar en matematisk sats, oftast benämnd som Napoleons sats. I uppsatsen presenteras och bevisas denna sats med hjälp av ett flertal olika bevismetoder. Det presenteras även bevis för att satsen kan utvidgas till att gälla för fler geometriska objekt än en triangel, vilken är det objekt som satsen ursprungligen utgår från. Texten inleds med en kort redogörelse för historien bakom satsen. 

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  • 15.
    Hendi, Haya
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Fibonaccitalen och matristeori: Fibonacci Numbers and Matrix Theory2022Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Syftet med denna uppsats är att studera kopplingar mellan Fibonaccitalen och matristeori. Det matematiska innehållet utgår till största delen från artikeln A contribution to the connections between Fibonacci numbers and matrix theory, skriven av Miriam Farber och Abraham Berman. Texten innehåller även litet biografi över den kände matematikern Leonardo Fibonacci som skrev ned Fibonaccitalen i form av ett klassiskt samhällsproblem, utan att veta om om deras oändliga egenskaper. Relationen mellan Fibonaccitalen och matristeori studeras i olika sammanhang.

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  • 16.
    Johansson Melin, Emma
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Hurwitz 1-, 2-, 4-, 8-sats2021Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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