# Math for Machine Learning

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## Statistics Roadmap <a href="#id-0d46" id="id-0d46"></a>

**1. STATS BASICS**

* Types of Data: Nominal, Ordinal, Discrete, Continuous
* Descriptive vs Inferential Stats
* Moments
* Mean, Median, Mode
* Skewness
* Kurtosis
* Range, IQR
* Percentiles, Quartiles
* Mean Deviation
* Standard Deviation
* Variance
* Quartile Deviation
* Standard Error

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**2. CHARTS**

* Frequency Distribution Table
* Line Chart
* Bar Chart
* Histogram
* Frequency Polygon
* Pie Chart
* Ogives

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**3. PROBABILITY DISTRIBUTION FUNCTIONS**

* Random Variables
* Multivariate random variables
* Discrete random variables
* Continuous random variables
* Law of Large Numbers
* Expectation
* PMF — Probability Mass Function
* PDF — Probability Density Function
* CDF — Cumulative Density Function
* Bernoulli Distribution
* Binomial Distribution
* Geometric Distribution
* Poisson Distribution
* Exponential Distribution
* Uniform Distribution
* Gaussian / Normal Distribution
* Chi-Square Distribution
* Power Law Distribution
* Pareto Distribution
* Box-Cox Transformation
* Log-Normal Distribution
* Kernel Density Estimation
* Q-Q plot

**4. PROBABILITY**

* Basic Probability
* Joint Probability
* Conditional Probability
* Independent Events
* Mutually Exclusive Events
* Bayes’ Theorem

**5. TESTS / SAMPLING / POPULATION**

* Sampling, Sample Mean & Distribution
* Central Limit Theorem
* Point estimate, Interval estimate
* Confidence Interval
* Population, Population Mean & Distribution
* Hypothesis Testing
* P-value
* Population Proportions
* Critical Value
* Significance Level
* Rejection regions
* Type I vs Type II errors
* One tail vs Two tail
* Z-Test
* T-Test
* ANOVA
* F-Test
* Chi-Square Test
* Monte Carlo Simulation
* A/B Testing

**6. RELATIONS / REGRESSION**

* Causality
* Covariance
* Covariance Matrix
* Correlation
* Scatter Plots
* Pearson Correlation Coefficient
* Rank / Spearman Correlation Coefficient
* R2 score
* Linear Regression
* OLS
* Factor Analysis
* Logistic Regression

## Linear Algebra Roadmap <a href="#id-87b4" id="id-87b4"></a>

**1. LINEAR EQUATIONS**

* Systems of Linear Equations
* Gaussian Elimination
* Echelon Form
* Linear Combination
* Span
* Homogeneous Linear System
* Linear Independence
* Subspace
* Basis
* Affine space
* Linear Transformation

**2. MATRIX**

* Matrix transformations
* Matrix multiplication
* Inverse Matrix
* Transpose of a matrix
* Rank of a matrix
* Symmetric Matrix
* Orthogonal Matrix
* Adjoint Matrix
* Singular Matrix
* Determinant of a matrix
* Trace of a Matrix

**3. VECTORS**

* Components of Vector
* Vector Space
* Norm of a vector
* Lengths and distances
* Euclidean Norm
* Manhattan Norm
* Minkowski Distance
* Scalar Multiplication
* Dot Product
* Inner Product
* Cross Product
* Orthogonality
* Orthonormal
* Rotations

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**4. FACTORIZATION**

* Matrix Decomposition
* LU Decomposition
* QR Decomposition
* Cholesky Decomposition
* Eigen Decomposition
* Eigen Values
* Eigen Vector
* Singular Value Decomposition
* Principal Component Analysis

## Calculus Roadmap <a href="#id-7309" id="id-7309"></a>

**1. CALCULUS BASICS**

* Functions
* Derivatives
* Maxima Minima
* Product and Chain Rule Differentiation
* Composite functions
* Partial Derivatives
* Higher-order derivatives
* Integrals
* Limits
* Infinite series summation

**2. OPTIMIZERS**

* Gradient Descents
* Optimizers
* Loss Functions
* Taylor’s Series
* Constrained Optimization (Lagrange Multiplier)
* Newton’s method in Optimization
* Convex Optimization

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## **Free YouTube resources:** <a href="#af9a" id="af9a"></a>

Credits to 3Blue1Brown, Khan Academy, StatQuest with Josh Starmer.
