Sökning: "algebraic number theory"
Visar resultat 1 - 5 av 9 uppsatser innehållade orden algebraic number theory.
1. Profinite groups
Master-uppsats, Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/MatematikcentrumSammanfattning : This thesis provides a comprehensive study of profinite groups, which are fascinating mathematical objects that have attracted significant interest in modern algebraic research. Profinite groups are infinite generalizations of finite groups and share many similarities with them. LÄS MER
2. Cyclotomic Fields and Fermat's Last Theorem
Kandidat-uppsats, Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)Sammanfattning : 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. LÄS MER
3. Scheme Theory & Weak Mordell-Weil for Elliptic Curves Over Number Fields
Kandidat-uppsats, Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)Sammanfattning : We provide an introduction to scheme-theoretic algebraic geometry, which studies spaces that are in essence locally solutions to systems of polynomial equations, and prove the weak Mordell-Weil theorem. The weak Mordell-Weil theorem states that for an elliptic curve $E$ over a number field $K$, the quotient $E(K)/mE(K)$ is finite for all $m\geq 2$. LÄS MER
4. Klassgruppen Introduktion, faktorisering och implementation
Kandidat-uppsats, KTH/Skolan för teknikvetenskap (SCI)Sammanfattning : Givet ett heltal n så utforskar denna text olika sätt att hitta ns faktorer, med fokus på Shanks Klassgruppmetod, även om korta beskrivningar av Pollards p -1- och rho-algoritmer ges. Klassgruppen introduceras som en mängd av ekvivalensklasser av fraktionsideal i imaginära kvadratiska talkroppar, varpå en isomorfi till en mängd av ekvivalensklasser av binära kvadratiska former av given diskriminant D ges. LÄS MER
5. Degree Project in Engineering Physics, First Level Department of Mathematics KTH Royal Institute of Technology
Kandidat-uppsats, KTH/Skolan för teknikvetenskap (SCI)Sammanfattning : The study of elliptic curves is an important part of the elds of algebraic geometry and number theory, with many applications in areas such as cryptography. While much of the groundwork has already been laid out, the results often times fall short of giving an easily digestible overview of the subject as a whole. LÄS MER