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Elements of Abstract and Linear Algebra by E. H. Connell

MathSchoolinternational.com contain houndreds of Free Math e-Books. Which cover almost all topics of mathematics. To see an extisive list of Abstract Algebra eBooks . We hope mathematician or person who’s interested in mathematics like these books.

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Elements of Abstract and Linear Algebra written by E. H. Connell . This is an other great mathematics book cover the following topics.

  • Chapter 1. Background and Fundamentals of Mathematics
    Sets, Cartesian products, Relations, partial orderings, Hausdorff maximality principle, equivalence relations, Functions, bijections, strips, solutions of equations, right and left inverses, projections, Notation for the logic of mathematics, Integers, subgroups, unique factorization

  • Chapter 2. Groups
    Groups, scalar multiplication for additive groups, Subgroups, order, cosets, Normal subgroups, quotient groups, the integers mod n, Homomorphisms, Permutations, the symmetric groups, Product of groups,

  • Chapter 3. Rings
    Rings, Units, domains, fields, The integers mod n, Ideals and quotient rings, Homomorphisms, Polynomial rings, Product of rings, The Chinese remainder theorem, Characteristic, Boolean rings

  • Chapter 4. Matrices and Matrix Rings
    Addition and multiplication of matrices, invertible matrices, Transpose, Triangular, diagonal, and scalar matrices, Elementary operations and elementary matrices, Systems of equations, Determinants, the classical adjoint, Similarity, trace, and characteristic polynomial

  • Chapter 5. Linear Algebra
    Modules, submodules, Homomorphisms, Homomorphisms on Rn, Cosets and quotient modules, Products and coproducts, Summands, Independence, generating sets, and free basis, Characterization of free modules, Uniqueness of dimension, Change of basis, Vector spaces, square matrices over fields, rank of a matrix, Geometric interpretation of determinant, Linear functions approximate differentiable functions locally, The transpose principle, Nilpotent homomorphisms, Eigenvalues, characteristic roots, Jordan canonical form, Inner product spaces, Gram-Schmidt orthonormalization, Orthogonal matrices, the orthogonal group, Diagonalization of symmetric matrices
  • Chapter 6. Appendix
    The Chinese remainder theorem, Prime and maximal ideals and UFDs, Splitting short exact sequences, Euclidean domains, Jordan blocks, Jordan canonical form, Determinants, Dual spaces

  • Read online Elements of Abstract and Linear Algebra by E. H. Connell
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