A history of Galois fields
This paper stresses a specific line of development of the notion of finite field, from Evariste Galois's 1830 ''Note sur la theorie des nombres,'' and Camille Jordan's 1870 Traite des substitutions…
Algorithms for sorting by reversals or transpositions, with application to genome rearrangement : Algoritmos para problemas de ordenação por reversões ou transposições, com aplicações em rearranjo de genomas
- Physics, Computer Science
Muitas variacoes do problema da ordenacao por rearranjo that envolvem esses rearranjos tem sido atacadas na literatura e, para a maior parte delas, os melhores algoritmos conhecidos sao aproximacoes ou heuristicas.
On Dedekind’s “Über die Permutationen des Körpers aller algebraischen Zahlen"
An Analysis of Students' Difficulties in Learning Group Theory
ABSTRACT. Research in mathematics education and anecdotal data suggest that undergraduate students often find their introductory courses to group theory particularly difficult. Research in this area,…
Galois' Remarkable Subgroups
Abstract Mathematics is a creative process, and unfortunately, that process is often hidden from students of the discipline. This is certainly the case in the area of mathematics commonly referred…
Dedekind's Treatment of Galois Theory in the Vorlesungen
We present a translation of §§160–166 of Dedekind’s Supplement XI to Dirichlet’s Vorlesungen uber Zahlentheorie, which contain an investigation of the subfields of C. In particular, Dedekind explores…
Symmetric Polynomials in the Work of Newton and Lagrange
A modern paraphrase of Newton’s remark might be that it is valuable to have “several different ways of looking at things.” Although we will work with quadratic equations instead of the cubics Newton…
Field Theory: From Equations to Axiomatization
7. THE ABSTRACT DEFINITION OF A FIELD. The developments we have been describing thus far lasted close to a century. They gave rise to important "concrete" theories-Galois theory, algebraic number…
SHOWING 1-10 OF 29 REFERENCES
Vorlesungen über Zahlentheorie
Vorwort 1. Von der Theilbarkeit der Zahlen 2. Von der Congruens der Zahlen 3. Von den quadratischen Resten 4. Von den quadratischen Formen 5. Bestimmung der Anzahl der Classen Supplemente.
Carl Friedrich Gauss Werke / herausgegeben von der Königlichen Gesellschaft der Wissenschaften zu Göttingen
Opere matematiche di Paolo Ruffini : Publicate sotto gli auspici del Circolo matematico di Palermo
Galois and Group Theory
Every mathematician knows of EVARISTE GALOIS, and of his tragic career. But there are few who could give more than a vague description of his influence on mathematical thought. In order to understand…