This text is intended for a one- or two-semester undergraduate course in ...
This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly.
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Table of Contents Preliminaries The Integers Groups Cyclic Groups Permutation Groups Cosets and Lagrange's Theorem Introduction to Cryptography Algebraic Coding Theory Isomorphisms Normal Subgroups and Factor Groups Homomorphisms Matrix Groups and Symmetry The Structure of Groups Group Actions The Sylow Theorems Rings Polynomials Integral Domains Lattices and Boolean Algebras Vector Spaces Fields Finite Fields Galois Theory
A First Course in Linear Algebra is an introductory textbook aimed at ...
A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically students will have taken calculus, but it is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Determinants and eigenvalues are covered along the way.
Table of Contents Systems of Linear Equations Vectors Matrices Vector Spaces Determinants Eigenvalues Linear Transformations Representations Preliminaries Reference
Access also available here: http://linear.ups.edu/