Algebra

based on Professor F.W.Levi's book, University of Calcutta, 1942 INTRODUCTORY REMARKS 3.2 Galois Fields 0.1 Odd and even numbers 3.3 The fields K(t) 0.2 Mathematical Induction 3.4 lrreducibility of polynomials 0.3 Permutations 3.5 Symmetric polynomials I Algebra 3-6. Solution of special equations by radicals: 1.1 Introduction - A dialogue 3.7 Resultants 1.2 n-vectors 3.8 Closed fields 1.3 Vector Spaces IV Continued Fractions 1.4 Matrices. Method of sweep out 4.1 General properties of continued fractions 1.5 Orthogonality. Homogeneous linear equations 4.2 Representation of positive numbers by continued fractions 1.6 Systems of non-homogeneous linear equations 4.3 Periodic continued fractions with integral coefficients 1.7 Method of orthogonalization 4-4. Applications to the theory of numbers: 1.8 Determinants 4.5 Continued fractions with elements f(x) 1.9 Minors of a determinant 4.6 Continued fractions with rational elements 1.10 Solution of systems of linear equations by means of determinants V Approximation of Roots l-11 Linear transformations 5.0 Introduction: Another dialogue II Fundamentals of General Algebra 5.1 Horner's scheme 2.1 Principal notions 5.2 Roots of real polynomials 2.2 Fields 5.3 Graeffe's Method 2.3 Polynamials 5.4 Roots of complex polynomials. 2.4 Factorisation 5.5 Interpolation 2.5 The fundamental theorem of General Algebra VI Matrices 2.6. Extension of a field 6.1 Addition and multiplication of matrices of degree n 2.7 Repeated extension of a field 6.2 Transformation of vector spaces III General Algebra. Specific Theory 6.3 The characteristie polynomial of a matrix 3.1 Cyclotomic Polynomials

Index