高等線性代數二   (90年度 下學期)

1.Infinite Dimensional Vector Spaces (including Zorn's Lemma, Existence of Bases, Invariance of Dimensionality, Finite Topology) 2.Bilinear Forms (including Symmetric and Skew Symmetric Bilinear Forms, Groups Preserving Bilinear Forms) 3.Ring of Linear Transformations (including Ideals in This Ring. Dense Subrings, Schur's Lemma, Density Theorem) 4.Algebras over a Field (including Division Algebras, Simple Algebras, Semisimple Algebras) 5.Tensor Products (including Free Vector Spaces, Tensor Products of Vector Spaces, Tensor Products of Algebras, Grassmann Algebras) 6.Selected Topics (1) Metric Vector Spaces. (2) Hilbert Spaces. (3) Operator Algebras. (4) Affine Geometry.

1. Douglas R. Farenick, Algebras of Linear Transformations. 2. Kenneth Hoffman and Ray Kunze, Linear Algebra. 3. Nathan Jacobson, Lectures in Abstract Algebra, vol. 2, Linear Algebra. 4. Steven Roman, Advanced Linear Algebra.

原則上以期中考與期末考平均為準。 四.其他