Math
Some personal notes on mathematics
Set
- Set Theory
- Empty Set
- Subsets
- Improper Subsets
- Proper Subsets
- Empty Set
- Universe Set
- Complement Set
- Union, Intersection, and Difference
- Union
- Intersection
- Difference Set
- Equal Sets
- Disjoint Sets
- Power Set
- Set Partitions
- Upper and Lower Bounds (majorants and minorants)
- Maximum and Supremum (Least Upper Bound)
- Minimum and Infimum (Greatest Lower Bound)
- Extremes
- Cartesian Product
- Relations
- Set Collections
- Open and Closed Sets
Geometry
- Geometry
- Lines
- Plane
- Triangle
- Circumnference
- Conic sections
- Similarity
- Criteria for Triangle Similarity
- Similarity Criteria for Polygons with the Same Number of Sides
- Golden Ratio
- The Pythagorean Theorem
- The Extended Pythagorean Theorem
- Radius of an Inscribed Circle in a Triangle
Algebra
Functions
Linear Algebra
Sequences in Mathematics
Statistics
Matrices
- Matrices
- Square matrix
- Matrix addition
- Matrix multiplication
- Multiplying matrices by scalars
- Identity matrix
- Zero matrix
- Matrix power
- Determinant of square matrix
- Matrix rank
- Invertible and inverse matrices
- Row equivalent matrices
- Pivot operations in a matrix
- Complementary minor in a matrix
- Characteristic polynomial
- The Bordered Theorem ( Kronecker's theorem )
- Gauss' Method of elimination
Vectors
- Vectors
- Adding vectors
- Vector subtraction
- Scalar multiplication of a vector
- Dot product
- Cross product
- Norm
- Angle between two vectors
- Linear Combination of Vectors
- Zero vector
- Opposite vector
- Parallel vectors
- Equivalent vectors
- Decomposing a vector
- Linear dependence and independence of Vectors
- Vector representation of a line
- Vector representation of a plane
Complex numbers
Vector space
- Vector spaces
- Basis of a vector space
- Coordinates (or Weights)
- Uniqueness of the Linear Combination of a Basis
- Dimension of the Basis
- Codimension
- Grassmann's Formula
- Orthogonal vectors
- Orthogonal Basis
- Orthonormal Basis
- Converting Any Basis to Orthogonal
- Converting an Orthogonal Basis to Orthonormal
- Orthogonal Projection of a Vector onto a Subspace
- Orthogonal Complement
- Linear span
- Generators of a vector space
- Vector Subspace
- Subspaces Generated by a Set of Vectors
- Union of Subspaces
- Intersection of Vector Subspaces
- Sum of Vector Subspaces
- Direct Sum
- Complementary Subspaces
- Decomposition of Vector Space
Topology
- Topology
- Topological Spaces
- Topology of Open Sets
- Open Sets
- Trivial Topology (or Minimal Topology)
- Discrete Topology
- Finite Complement Topology
- Example of Topology
- Particolar Point Topology
- Excluded Point Topology
- Basis of Topology
Abstract Algebra
Modular Arithmetic
Group Theory
- Groups
- Group Theory
- Identity Element in a Group
- Inverse Elements
- Power of an Element
- Centre
- Compositions in Symmetric Groups
Logic
Numerical Computation
Category Theory
Physics
