i. Linear Algebra (30 Hrs)
• Vectors, definition, scalars, addition, scalar multiplication, inner product (dot product), vector projection, cosine similarity, orthogonal vectors, normal and ortho-normal vectors, vector norm, vectors pace, linear combination, linear span, linear independence, basis vectors
• Matrices definition, addition, transpose, scalar multiplication, matrix multiplication, matrix multiplication properties, hadamard product, functions, linear transformation, determinant, identity matrix, invertible matrix and inverse, rank, trace, popularity of matrices-symmetric, diagonal, orthogonal, ortho-normal, positive definite matrix
• Eigen values & eigen vectors, concept, intuition, significance, how to find Principle component analysis, concept, properties, applications
• Singular value decomposition, concept, properties, applications
ii. Calculus (20 Hrs)
• Function scalar derivative, definition, intuition, common rules of differentiation, chain rule, partial derivatives, Gradient, concept, intuition, properties, directional derivative
• Vector and matrix calculus, how to find derivative of scalar-valued, vector-valued function with respect to scalar, vector} four combinations- Jacobian
• Gradient algorithms, local/global maxima and minima, saddle point, convex functions, gradient descent algorithms-batch, mini-batch, stochastic, their performance comparison