Mathematics

My mathematics notes:

Notes about differentiation

Notes about matrices

Notes about vectors - part 1

MLE of Poisson distribution ( external link)

Review of Asymptotic Complexity(Cornell)

Domain & Range of a function:

Domain of a function is the set of possible values for the variable.  

Range of a function is the set of possible outputs of the function.

Partitions:

Partition of a set groups the elements of the set into subsets. There is no empty subset. All elements of the set are present in the subsets, and each is present only once. 

Example :

S = {1,2,3,4}

S₀={{1}, {2}, {3}, {4}}  

S₁ = {{1}, {2, 3, 4}}

S₂ = {{1, 2}, {3, 4}}

S₃ = {{1, 2, 3}, {4}}

S₄ = {{1, 3}, {2, 4}}

S₅ = {{1, 4}, {2, 3}}

S₆ = {{1, 2, 4}, {3}}

S₇ = {{1, 3, 4}, {2}}

S₈ = {1,2,3,4} 

S₉ = {{1}, { 2}, {3, 4}}

S₁₀ = {{1, 2}, {3},{4}}

S₁₁ = {{1, 3}, {2},{4}}

S₁₂ = {{1, 4}, {2},{3}}

S₁₃ = {{1}, { 2, 3}, {4}}

S₁₄ = {{1}, { 2, 4}, {3}}