Ziyi Handbook
Ziyi Handbook of Mathematics (自怡数学手册) is:
- An upgrade version of my mathematics notebook;
- A personal effort to integrate elementary, college, Olympic, recreational, and modern mathematics;
- A systemization of what I have learned about mathematics.
(Not-yet-finalized) Contents and (Not-yet-finished) Online Version
Frontmatter
- Mathematical Logic
- Sets
- Partial Order
- Categories
- Groups
- Rings
- Polynomials
- Fields
- Matrices
- Linear Spaces and Mappings
- Modules
- Sequences
- Point Set Topology
- Algebraic Topology
- Real Numbers
- Elementary Functions
- Functional Equations
- Inequalities
- Univariate Calculus
- Multivariate Calculus
- Function Series
- Functions of Complex Variables
- Lebesgue Measure and Integration
- Ordinary Differential Equations
- Partial Differential Equations
- Divisibility and Congruence
- Diophantine Equations
- Algebraic Number Theory
- Analytical Number Theory
- Vectors and Geometric Transformations
- Planar Geometry
- Solid Geometry
- Spherical geometry
- Conics and Quadrics
- Curves
- Surfaces
- Probability Theory
- Random Processes
- Enumerative Combinatorics
- Graph Theory
- Design Theory
- Discrete Geometry
- Recreational Mathematics
- Languages and Automata
- Computability
- Computational Complexity
- Algorithms
- Computational Geometry
- Symbolic Computing
- Optimization Theory