Please enable JavaScript.

Coggle requires JavaScript to display documents.

Math Topics Tree - Coggle Diagram

- - - - It measures the chance for a event to occur divided by the total number of possibles outcomes.
    - - It’s basically what we can measure from our experiments. This is the number of times the event occurs divided by the total number of samples
    - - P(AUB) = P(A) + P(B) - P(A∩B)
        
        Multiplication Rules
        
        Independent Events
        
        P(Head, Head) = P(Head ∩ Head) = P(Head) P(Head) "(Also known as joint probability)"
        P(A∩B) = P(A) P(B)
        
        General Multiplication Rule
        
        Given two events A and B:
        P(A∩B) = P(A) * P(B|A)
        or
        P(A∩B) = P(B) * P(A|B)
        
        1 more item...
        
        Dependent Events
        
        Conditional probability: P(B | B)
        P(B∩B) = P(B) + P(B | B)
  - - - Union (⋃)
      - Intersection (∩)
      - Substraction (-)
  - - - Discrete Random Variable
        
        Probability Mass Function (PMF)
        
        Cumulative Distribution Function (CDF)
    - - Continuous Random Variable
        
        for any number c, P(X=c) = 0
        
        Probability Density Function (PDF)
        
        P(a <= X <= b) = f(x)dx
        
        Where f(x) is
        
        Cumulative Distribution Function (CDF)
        
        F(x) = P (X <= x) = dominio de x a -infinito f(y)dy
        
        For any two numbers a and b where a < b
        P(a <= X <= b) = F(b) - F(a)
        
        Normal Distribution: in practice, when working with continuous random variables, it’s quite common to approximate it’s true probability distribution with a Normal Distribution
        
        Normal Distribution: PDF
- - - - Functions: Also called Relation, Transformation or Mapping
    - - A single number
    - - A series of numbers
        
        Types
        
        Row Vectors
        
        Column Vectors
        
        Representation
        
        Usually represented with a lowercase alphabetical character with an arrow pointing to the right on top of it
        
        Norms
        
        Also known as the length of a vector, is the distance between its "Origin" and its "End"
        
        Popular Norms used in Machine Learning
        
        Euclidean Norm (L2)
        
        Manhattan Norm (L1)
        
        Distance = d(x,y) := || x-y ||
    - - A two-dimensional array of numbers arranged in rows and columns
      - Matrix Multiplication
      - Well-known types of matrices
        
        Dense: It has all of its values
        
        Sparse: Is missing some values
        
        Sparse in COOrdinate format: Same as sparse but values are also coordinates to the sparse values
        
        Transpose Matrix
        
        Lower triangular matrix & Upper triangular matrix: the values compose a triangle of values, either upper or lower. The rest is zeros only.
        
        Symmetric matrix: All of values are mirrors of their counter position
        
        Anti symmetric matrix: All of values are negative mirrors of their counter position
        
        Identity Matrix: Diagonal 1's
        
        Matrix Inverse: Is a matrix that when multiplies another matrix from either the left or right side , returns the identity matrix (Not all matrices have an inverse)
    - - A Matrix with more than two axes
    - - A group of linear equations (Equations that only involves adding and subtracting one or more variables to the first power)
        
        Ax = b
        
        Solving Methods
        
        Substitution
        
        Reduction
        
        Gauss-Jordan
        
        Cramer
        
        Others
- - - - Numerical Aproximations
        
        Fordward
        
        Backward
        
        Central Difference
    - - Although all derivatives could be computed using the definition of derivative as a limit, there are well-established rules, known as derivative calculus theorems, which allow one to compute the derivative of many functions according to their composition without necessarily having to compute the limit. Such rules are a direct consequence of the definition of derivative and previous limit theorems.