Elementary Theory Of Equations

Dickson, Leonard Eugene

History

Franklin Classics

<p>Of enormous historical importance, this classic offered the first public formulation of Dickson's theory of invariants for modular forms and linear transformations. In many sections of the five lectures included here, Dickson aimed not at complete generality, but at an illumination of typical and suggestive topics. The introductory lecture is followed by sections on seminvariants of algebraic and modular binary forms; invariants of a modular group and formal invariants and covariants of modular forms; modular geometry and covariantive theory of a quadratic form in m variables, modulo 2; and a theory of plane cubic curves with a real inflexion point valid in ordinary and in modular geometry. 1914 ed.<br></p>

On Invariants and the Theory of Numbers (Dover Phoenix Editions)

Science & Math

Mathematics

Dover Publications

Hailed as a milestone in the development of modern algebra, this classic exposition of the theory of groups is well within the range of graduate students. Its particular value lies in its attention to practical applications: the theory of the solvability of equations, theory of differential equations, complex number systems, and the foundations of geometry, where Euclidean or parabolic geometry, elliptic geometry, and hyperbolic geometry can be completely characterized by groups. The first of the two-part treatment consists of an extensive presentation of the theory of Galois Fields, with a wealth of examples and theorems; the second part features a discussion of linear groups in a Galois Field, with a survey of the known simple groups of finite composite order. 1901 ed.

Linear Groups with an Exposition of Galois Field Theory (Dover Phoenix Editions)

On invariants and the theory of numbers.

Dover `

The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This first volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to the subjects of divisibility and primality. It can be read independently of the succeeding volumes, which explore diophantine analysis and quadratic and higher forms.Within the twenty-chapter treatment are considerations of perfect, multiply perfect, and amicable numbers; formulas for the number and sum of divisors and problems of Fermat and Wallis; Farey series; periodic decimal fractions; primitive roots, exponents, indices, and binomial congruences; higher congruences; divisibility of factorials and multinomial coefficients; sum and number of divisors; theorems on divisibility, greatest common divisor, and least common multiple; criteria for divisibility by a given number; factor tables and lists of primes; methods of factoring; Fermat numbers; recurring series; the theory of prime numbers; inversion of functions; properties of the digits of numbers; and many other related topics. Indexes of authors cited and subjects appear at the end of the book.

History of the Theory of Numbers, Volume I: Divisibility and Primality (Dover Books on Mathematics)

The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This second volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to the subject of diophantine analysis. It can be read independently of the preceding volume, which explores divisibility and primality, and volume III, which examines quadratic and higher forms.Featured topics include polygonal, pyramidal, and figurate numbers; linear diophantine equations and congruences; partitions; rational right triangles; triangles, quadrilaterals, and tetrahedra; the sums of two, three, four, and n squares; the number of solutions of quadratic congruences in n unknowns; Liouville's series of eighteen articles; the Pell equation; squares in arithmetical or geometrical progression; equations of degrees three, four, and n; sets of integers with equal sums of like powers; Waring's problem and related results; Fermat's last theorem; and many other related subjects. Indexes of authors cited and subjects appear at the end of the book.

History of the Theory of Numbers, Volume II: Diophantine Analysis (Dover Books on Mathematics)

Linear Groups: With an Exposition of the Galois Field Theory

Wentworth Press

Introduction to the Theory of Algebraic Equations

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Books by Dickson, Leonard Eugene