来自隔壁乎:https://www.zhihu.com/pin/862467594530222080
900页(在数学教材里面比起讲到的内容和深度来说一点都不厚)的两卷本,从代数学的基本结构讲到代数几何的一些基本内容,文风单刀直入,讲解明白并且透彻,Exercises和没有答案的Problems十分丰富。
(目前本菜鸡读到第三章,问题是本身内容就不简单xd
先放上第一卷的目录(545 pages):
- Set-Theoretic and Combinatorial Background
- Integers and Residues
- Polynomials and Simple Field Extensions
- Elementary Functions and Power Series Expansions
- Ideals, Quotient Rings, and Factorization
- Vectors
- Duality
- Matrices
- Determinants
- Euclidean Spaces
- Projective Spaces
- Groups
- Descriptions of Groups
- Modules over a Principal Ideal Domain
- Linear Operators
- Bilinear Forms
- Quadratic Forms and Quadrics
- Real Versus Complex
- Hermitian Space s
- Quaternions and Spinors
- Hints to Selected Exercises
然后是第二卷(355 pages):
- Tensor Products
- Tensor Algebras
- Symmetric Functions
- Calculus of Arrays, Tableaux, and Diagrams
- Basic Notions of Representation Theory
- Representations of Finite Groups in Greater Detail
- Representations of Symmetric Groups
- -Modules
- Categories and Functors
- Extensions of Commutative Rings
- Affine Algebraic Geometry
- Algebraic Manifolds
- Algebraic Field Extensions
- Examples of Galois Groups
- Hints to Some Exercises