Institutional Subscription. Free Shipping Free global shipping No minimum order. Functions 1. Sets 2. Functions 3. Mathematical Induction 1.
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Positive Integers and the Mathematical Induction 2. Permutations 1. Permutations 2. Combinations 1. Combinations 2. Properties of the Function nk 3. Newton's Multinomial Formula 1. Newton's Binomial Formula 2. Multiplication of Permutations 1. Definition 2. Factorization of a Permutation into Cycles 3. Transpositions III.
Fields 1. Number Fields 2. General Fields 3. Isomorphism of Fields 4. Field of Real Numbers 5. Properties of Complex Numbers 1. Geometric Interpretation of Complex Numbers 2. The Modulus and Conjugate Complex Numbers 3. Roots of Complex Numbers 1. Square Roots of Complex Numbers 2. Roots of Higher Degree of Complex Numbers 3. Primitive Roots of Unity 4. Definition of a Determinant 1.
Inversions 3. Applications of Inversions to the Theory of Permutations 4. Definition of a Matrix 5.
Laplace Expansion 1. Minors 2. Examples 1. Simple Examples 2. Example of a Cyclic Determinant 3. Vandermonde Determinant 4. Cauchy's Theorem and its Generalizations 1. Cauchy's Theorem 2. Cyclic Determinant 3. Generalization of Cauchy's Theorem V. Vector Spaces 1. Linear Independence 3.
Higher-Dimensional Algebra VI: Lie 2-Algebras
Linear Subspaces 4. Rank of a Matrix 1. Simplest Properties 2. Investigation of the Rank of a Matrix by means of Minors 3. Linear Equations 1. General Systems of Linear Equations 2. Axiomatic Definition of the Determinant VI. Operations on Polynomials 1. Polynomials 2.
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Differentiation of Polynomials 3. The Arithmetic of the Ring K[x] 1. The Arithmetic of Integers 2. Division of Polynomials 3. Roots of a Polynomial 1. Multiple Roots 2. Divisibility of a Polynomial by Linear Factors 3. Interpolation Formulae 1. Lagrange's Formula 2. Newton's Interpolation Formula 3.
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