Unit 1 Vectors and Matrices

6 lecture hours

• Matrix Introduction
• Matrix Addition
• Matrix Multiplication
• Transpose of a Matrix
• Inverse of a Matrix
• Matrix Multiplication using Python
• Matrix factorization
• Diagonalization Vector introduction
• Basis and Dimension
• Vector Spaces
• Vector Operations
• Vector Spaces and Sub spaces
• Eigenvalues and Eigenvectors

Unit 2 Statistics

6 lecture hours

• Standard Deviation, and Variance
• use NumPy Arrays
• Sample Error and True Error Bias Vs Variance and Its Trade-Off Hypothesis Testing T-test Paired T-test
• Confidence Intervals
• Correlation and Covariance
• Correlation Coefficient
• Program Name: Master of Engineering Level: PG Branch: Information Technology Course / Subject Code : ME01000691 Subject Name: Maths for Machine Learning Covariance Matrix
• Normal Probability Plot
• Residuals Leverage Plot
• Hypothesis Testing
• Null and Alternative Hypothesis
• Type 1 and Type 2 Errors p-value interaction
• Parametric Hypothesis Testing
• Paired Samples t-test
• ANOVA Test
• Non-Parametric Hypothesis Testing
• Mann-Whitney U test
• Wilcoxon signed-rank test

Unit 3 Estimation Methods

6 lecture hours

• Bayesian Estimation
• Least Square Estimation
• Maximum Likelihood Estimation
• Likelihood Function and Log-Likelihood Function Properties of Estimation
• Confidence Intervals

Unit 4 Vector Operations

7 lecture hours

• Cross Products
• Distance Between Two Points
• Distance Measures
• Euclidean Distance
• Manhattan Distance
• Minkowski Distance
• Chebysev Distance
• Similarity Measures
• Cosine Similarity
• Jaccard Similarity
• Pearson Correlation Coefficient
• Spearman’s Rank Correlation Measure
• Orthogonality and Orthogonal Projections
• Orthogonality and Orthonormal Vectors
• Orthogonal Projections

Unit 5 Calculus

7 lecture hours

• Inverse Trigonometric Functions Differentiation
• Logarithmic Differentiation
• Partial Differentiation
• Advanced Differentiation
• Mathematical Intuition Behind Gradients and their usage
• Implementation of Gradients using Python
• Optimization Techniques using Gradient Descent
• Higher-Order Derivatives
• Multivariate Taylor Series
• Application of Derivation
• Application of Derivative – Maxima and Minima
• Absolute Minima and Maxima
• Constrained Optimization
• Unconstrained Optimization
• Constrained Optimization – Lagrange Multipliers
• Newton’s Method
• Uni-variate Optimization
• Multivariate Optimization
• Convex Optimization
• Lagrange’s Interpolation
• Area Under Curve

Unit 6 Probability

7 lecture hours

• Chance and Probability
• Addition Rule for Probability
• Law of total probability
• Bayes’ Theorem
• Discrete Probability Distributions
• Discrete Uniform Distribution
• Bernoulli Distribution
• Binomial Distribution
• Poisson Distribution
• Continuous Probability Distributions
• Continuous Uniform Distribution
• Exponential Distribution
• Normal Distribution
• Beta Distribution
• Beta Distribution of First Kind
• Beta Distribution of Second Kind Program Name: Master of Engineering Level: PG Branch: Information Technology Course / Subject Code : ME01000691 Subject Name: Maths for Machine Learning
• Gamma Distribution
• Sampling Distributions
• Chi-Square Distribution
• Central Limit Theorem
• Implementation of Central Limit Theorem
• Law of Large Numbers
• Change of Variables/Inverse Transformation

Unit 7 Introduction to Dimensionality Reduction

• Mathematical Intuition Behind PCA, PCA implementation in Python 6 10