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Introduction to algebra
Book I
Algebra basics
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A. I. Kostrikin
On this page
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I.1 · Origins of algebra
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I.2 · Matrices
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I.3 · Determinants
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I.4 · Groups. Rings. Fields.
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I.5 · Complex numbers and polynomials
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I.6 · Polynomial roots
Chapter I.1
Origins of algebra
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Section I.1.1
Brief algebra
Section I.1.2
Some model problems
Section I.1.3
Systems of linear equations. First steps
Section I.1.4
Determinants of low orders
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Section I.1.5
Sets and mappings
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Section I.1.6
Equivalence relations. Factorization of mappings
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Section I.1.7
The principle of mathematical induction
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Section I.1.8
Permutations
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Section I.1.9
Arithmetic of integers
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Chapter I.2
Matrices
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Section I.2.1
Row and column vector spaces
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Section I.2.2
Matrix rank
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Section I.2.3
Linear mappings. Operations with matrices
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Chapter I.3
Determinants
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Section I.3.1
Determinants: construction and basic properties
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Section I.3.2
Further properties of determinants
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Section I.3.3
Applications of determinants
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Section I.3.4
Towards the construction of the theory of determinants
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Chapter I.4
Groups. Rings. Fields.
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Section I.4.1
Sets with algebraic operations
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Section I.4.2
Groups.
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Section I.4.3
Rings and fields
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Chapter I.5
Complex numbers and polynomials
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Section I.5.1
The field of complex numbers
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Section I.5.2
Polynomial ring
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Section I.5.3
Polynomial ring factorization
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Section I.5.4
Field of quotients
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Chapter I.6
Polynomial roots
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Section I.6.1
General properties of roots
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Section I.6.2
Symmetric polynomials
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Section I.6.3
Algebraic closure of the field
C
\mathbb{C}
C
Section I.6.4
Polynomials with real coefficients
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