Algebra, Topology, Differential Calculus, and Optimization Theory For Computer Science and Engineering

In the First four chapters, the basic algebraic structures (groups, rings, fields, vector spaces) are reviewed, with a major emphasis on vector spaces. Basic notions of linear alge- bra such as vector spaces, subspaces, linear combinations, linear independence, bases, quo- tient spaces, linear maps, matrices, change of bases, direct sums, linear forms, dual spaces, hyperplanes, transpose of a linear maps, are reviewed.