Linear Algebra and Matrix Operations

• Matrices
• Eigenvalues and Eigenvectors
• LU Decomposition
• QR Decomposition
• Singular Value Decomposition (SVD)
• Orthogonalization
• Diagonalization
• Non- Negative Matrix Factorization
• Vectors
• Vector Spaces and Subspaces
• Linear Mappings

Regression Analysis

• Linear Regression
• Logistic Regression
• Bayesian Linear Regression
• Ridge and lasso Regression
• Normal Equation in Linear Regression
• Maximum Likelihood Estimation (MLE)
• Mean Squared Error

Statistics

• Mean, Standard Deviation and Variance
• Sample Error and True Error
• Confidence Intervals
• Correlation and Covariance
• Correlation Coefficient
• Pearson Correlation Coefficient
• Covariance Matrix
• Hypothesis Testing

                     • Null and Alternative Hypothesis

                     • Type 1 and Type 2 Errors

                     • p-value interaction

• Parametric Methods

                     •  T-test

                     •  Paired Samples t-test

                     • ANOVA Test

• Non-Parametric Methods

                      • Mann-Whitney U test

                      • Wilcoxon signed-rank test

                      • Kruskal-Wallis test

                      • Friedman test

• Bias Vs Variance and Its Trade-Off
• Bootstrap method
• Normal Probability Plot
• Q-Q Plot
• Curve Fitting
• Residuals Leverage Plot

Geometry

• Vector Norms
• Inner Product
• Outer Product
• Dot and Cross Product
• Euclidean Distance
• Manhattan Distance
• Minkowski Distance
• Cosine Similarity
• Jaccard Similarity
• Orthogonality and Projections

Calculus

• Fundamental Calculus Concepts

                       • Differentiation

                       • Partial Derivatives

                       • Gradient Descent

                       • Chain Rule

                       • Jacobian and Hessian Matrices

• Inverse Trigonometric Functions Differentiation
• Partial Differentiation
• Higher-Order Derivatives
• Optimization Techniques using Gradient Descent
• Uni-variate Optimization

Vector Calculus

• Gradient
• Divergence and Curl
• Line Integrals
• Laplacian Operator

Probability and Distributions

• Probability
• Bayes’ Theorem
• Joint, Conditional and Marginal Probability
• Discrete Probability Distributions

                           • Discrete Uniform Distribution

                           • Bernoulli Distribution

                           • Binomial Distribution

                           • Poisson Distribution

• Continuous Probability Distributions

                           • Continuous Uniform Distribution

                           • Exponential Distribution

                           • Normal Distribution

                           • Beta Distribution

                           • Gamma Distribution

• Sampling Distributions

                          • Chi-Square Distribution

                          • F - Distribution

                          • t - Distribution

• Central Limit Theorem

Dimensionality Reduction

• Introduction to Dimensionality Reduction
• Principal Component Analysis (PCA)
• Linear Discriminant Analysis (LDA)
• Generalized Discriminant Analysis (GDA)
• t-SNE Algorithm