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Introduction to higher algebra
Introduction to Higher Algebra.
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| Main Authors: | , |
|---|---|
| Corporate Author: | |
| Other Authors: | |
| Format: | eBook |
| Language: | English Polish |
| Published: |
Oxford :
Pergamon Press,
1964.
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| Series: | International series of monographs in pure and applied mathematics ;
volume 37. |
| Physical Description: |
1 online resource (474 pages). |
| Subjects: | |
| Online Access: | Elsevier - Click here for access |
Contents:
- Front Cover; Introduction to Higher Algebra; Copyright Page; Table of Contents; CHAPTERI. INTRODUCTION; 1. Functions; 2. Mathematical induction; 3. Sums and products of an arbitrary number of terms; CHAPTERII. SOME COMBINATORIAL PROBLEMS; 1. Permutations; 2.k-permutations; 3. Combinations; 4. Newton's multinomial formula; 5. Multiplication of permutations; CHAPTERIII. COMPLEX NUMBERS; 1. Fields; 2. Introductory remarks on complex numbers; 3. Definition of complex numbers; 4. Properties of complex numbers; 5. Roots of complex numbers; CHAPTERIV. DETERMINANTS.
- 1. Definition of a determinant2. Laplace expansion; 3. Properties of determinants; 4. Examples; 5. Cramer's formulae; 6. General Laplace theorem; 7. Cauchy's theorem and its generalizations; CHAPTERV. VECTOR SPACES AND LINEAR EQUATIONS; 1. Vector spaces; 2. Rank of a matrix; 3. Linear equations; 4. Axiomatic definition ofdeterminant; CHAPTERVI. POLYNOMIALS IN ONE VARIABLE; 1. Operations on polynomials; 2. The arithmetic of the ringK; 3. Roots of a polynomial; 4. Interpolation formulae; 5. Rational functions; CHAPTERVII. RINGS OF REAL AND COMPLEX POLYNOMIALS.
- 1. The fundamental theorem of algebra2. Polynomials of the ring B[x]; 3. Quadratic equations in the domain of complex numbers; 4. Cubic equations; 5. Equations of the fourth degree; 6. Reciprocal equations; CHAPTERVIII. RING OF RATIONAL POLYNOMIALS ALGEBRAIC AND TRANSCENDENTAL NUMBERS; 1. Reduction of polynomials with rational coefficients to polynomialswith integral coefficients; 2. Polynomials irreducible in the field W; 3. Algebraic numbers; 4. Transcendental numbers; CHAPTERIX. POLYNOMIALS IN SEVERAL VARIABLES AND SYMMETRIC FUNCTIONS; 1. The arithmetic of the ringk.
- 2. Symmetric polynomialsCHAPTERX. THE THEORY OF ELIMINATION; 1. The resultant; 2. Systems of two equations in two unknowns; 3. Points of intersection of algebraic curves; CHAPTERXI. QUADRATIC AND HERMITIAN FORMS; 1. Introduction; 2. Linear transformations; 3. Quadratic forms; 4. Orthogonal transformations of quadratic forms; 5. Hermitian forms and unitary transformations; APPENDIX:SOME PROPERTIES OF MATRICES AND QUADRATIC FORMS; 1. Cofactor-matrix; 2. The case of a singular matrix; 3. The rank of the matrix formed by minors; 4. The rank of a symmetric matrix.
- 5. Sylvester's identity. Kronecker's and Jacobi's theoremson quadratic forms6. Gram matrices; 7. Cayley's and Hamilton's theorem; Index.