介绍一套代数学初步的优秀教材

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)：

1. Set-Theoretic and Combinatorial Background
2. Integers and Residues
3. Polynomials and Simple Field Extensions
4. Elementary Functions and Power Series Expansions
5. Ideals, Quotient Rings, and Factorization
6. Vectors
7. Duality
8. Matrices
9. Determinants
10. Euclidean Spaces
11. Projective Spaces
12. Groups
13. Descriptions of Groups
14. Modules over a Principal Ideal Domain
15. Linear Operators
16. Bilinear Forms
17. Quadratic Forms and Quadrics
18. Real Versus Complex
19. Hermitian Space s
20. Quaternions and Spinors
21. Hints to Selected Exercises

然后是第二卷(355 pages)：

1. Tensor Products
2. Tensor Algebras
3. Symmetric Functions
4. Calculus of Arrays, Tableaux, and Diagrams
5. Basic Notions of Representation Theory
6. Representations of Finite Groups in Greater Detail
7. Representations of Symmetric Groups
8.  -Modules
9. Categories and Functors
10. Extensions of Commutative Rings
11. Affine Algebraic Geometry
12. Algebraic Manifolds
13. Algebraic Field Extensions
14. Examples of Galois Groups
15. Hints to Some Exercises