Mathematics for Machine Learning

SPECIALIZATION ELECTIVE

Credit Hour: 3

Pre-Requisite: Discrete Mathematics

Course Content

Topic 1: Introduction

Topic 2: Linear Algebra

• System of Linear Equations

• Matrices

• Solving Systems of Linear Equations

• Vector Spaces

• LInear Independence

• Basis and Rank

• Linear Mappings

• Affine Spaces

Topic 3: Analytic Geometry

• Norms

• Inner Product

• Length and Distances

• Angle & Orthogonality

• Orthonormal Basis

• Orthogonal Complement

• Inner Product of Functions

• Orthogonal Projects

• Rotations

Topic 4: Matrix Decomposition

• Determinant and Trace

• Eigenvalues and Eigenvectors

• Cholesky Decomposition

• Eigen Decomposition and Diagonalization

• Singular Value Decomposition

• Matrix Approximation

Topic 5: Vector Calculus

• Differentiation of Univariate Functions

• Partial Derivation and Gradients

• Gradients of Vector-Valued Functions

• Gradients of Matrices

• Useful Identities for Computing Gradients

• Backpropagation and Automatic Differentiation

• Higher-Order Derivative

• Linearization and Multivariate Taylor Series

Topic 6: Continous Optimization

• Optimization Using Gradient Descent

• Constrained Optimization and Lagrange Multipliers

• Convex Optimization

Prepared By:

Assoc. Prof. Ts Dr. Amiza Amir