| Chapter 1 NUMBERS AND SETS 1.1 Sets 1.2 Mappings ,Cardinality 1.3 The Number sequence 1.4 Finite and countable (denumerable)sets 1.5 partitions Chapter 2 GROUPS 2.1 The concept of a group 2.2 subgrougs 2.3 compleses.cosets 2.4 Isomorphisms and automorphisms 2.5 Homomorphisms ,normal subgroups,and factor groups Chapter 3 RINGS AND FIELDS 3.1 Rings 3.2 Homomorphism and Isomorphism 3.3 The concept of a field quotients 3.4 Polynomial rings 3.5 Ideals,residue class rings 3.6 divesibility .prime ideals 3.7 Euclidean rings and principal ideal rings 3.8 Factorization Chapter 4 VECTOR SPACES AND TENSOR SPACES 4.1 Vector spaces 4.2 Dimensional invariance 4.3 The dual vector space 4.4 Linear equations in a skew field 4.5 Linear transformations 4.6 Tensors 4.7 Antisymmetric multilinear forms and determinants 4.8 Tensor products,contraction,and trace Chapter 5 POLYNOMIALS 5.1 Differentiation 5.2 The zeros of a polynomial 5.3 Interpolation formulae 5.4 Factorixation 5.5 Irrdeucibility criteria 5.6 Factorixation in a finite number of steps 5.7 symmetric functions 5.8 the resultant of two polynomials 5.9 the resultant as a symmetric function of the roots 5.10 partial fraction decomposition Chapter 6 THEORY OF FIELDS Chapter 7 CONTINUATION OF GROUP THEORY Chapter 8 THE GALOIL THEEORY Chapter 9 ORDERING AND WELL ORDERING OF SETS Chapter 10 INFINITE FIELD EXTENSIONS Chapter 11 REAL FIELDS INDEX |
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