____________________________________________________>>中文版

what is mathematics?

0.set and category

  0.1.set

  0.2.category

1.group, ring, module, field

  1.1. group

         a.1.1.1. finite permutation groups

  1.2. ring

  1.3. module

  1.4. field 

         a.1.4.1. finite field

2.linear structure

  2.1.finite dimension linear space

  2.2.multilinear algebra

3.analysis on infinite and order

  3.1.realization and description

  3.2.basic analysis technology

  3.3.integration

4.analysis of function and equation

  4.1.elemental function, complex function

  4.2.differential equation

  4.3.mathematical physics function and equation

  4.4.function space and function analysis

5.topology: beyond classical analysis

  5.1.general topology

  5.2.dimension theory

6.the view of geometry: from real space to manifold

  6.1.curve and surface

  6.2.manifold

7.analysis on manifold

  7.1.Riemann manifold

  7.2.Finsler manifold

8.representations of group and algebra

9.algebraic geometry

10.noncommutative geometry