Mathematics for Data Science II
This course aims to introduce the basic concepts of linear algebra, calculus and optimization with a focus towards the application area of machine learning and data science.
Course ID: BSMA1003
Course Credits: 4
Course Type: Foundational
Recommended Pre-requisites: None
What you’ll learn VIEW COURSE VIDEOS
Course structure & Assessments
12 weeks of coursework, weekly online assignments, 2 in-person invigilated quizzes, 1 in-person invigilated end term exam. For details of standard course structure and assessments, visit Academics page.
| WEEK 1 | Vector and matrices - Vectors; Matrices; Systems of Linear Equations; Determinants (part 1); Determinants (part 2) |
| WEEK 2 | Solving linear equations - Determinants (part 3); Cramer's Rule; "Solutions to a system of linear equations with an invertible coefficient matrix"; The echelon form; Row reduction; The Gaussian elimination method |
| WEEK 3 | Introduction to vector spaces - Introduction to vector spaces; Some properties of vector spaces; Linear dependence; Linear independence - Part ; Linear independence - Part 2 |
| WEEK 4 | Basis and dimenstion - What is a basis for a vector space?; Finding bases for vector spaces; What is the rank/dimension for a vector space; Rank and dimension using Gaussian elimination |
| WEEK 5 | Rank and Nullity of a matrix; Introduction to Linear transformation - The null space of a matrix : finding nullity and a basis - Part 1; The null space of a matrix : finding nullity and a basis - Part 2; What is a linear mapping - Part 1; What is a linear mapping - Part 2; What is a linear transformation |
| WEEK 6 | Linear transformation, Kernel and Images - Linear transformations, ordered bases and matrices; Image and kernel of linear transformations; Examples of finding bases for the kernel and image of a linear transformation |
| WEEK 7 | Equivalent and Similar matrices; Introduction to inner products - Equivalence and similarity of matrices; Affine subspaces and affine mappings; Lengths and angles; Inner products and norms on a vector space |
| WEEK 8 | Orthogonality, Orthonormality; Gram-schmidt method - Orthgonality and linear independence; What is an orthonormal basis? Projections using inner products; The Gram-Schmidt process; Orthogonal transformations and rotations |
| WEEK 9 | Multivariavle functions, Partial derivatives, Limit, continuity and directional derivatives - Multivariable functions : visualization; Partial derivatives; Directional derivatives; Limits for scalar-valued multivariable functions; Continuity for multivariable functions; Directional derivatives in terms of the gradient |
| WEEK 10 | Directional ascent and descent, Tangent (hyper) plane, Critical points - The directional of steepest ascent/descent; Tangents for scalar-valued multivariable functions; Finding the tangent hyper(plane); Critical points for multivariable functions |
| WEEK 11 | Higher order partial derivatives, Hessian Matrix and local extrema, Differentiability - Higher order partial derivatives and the Hessian matrix; The Hessian matrix and local extrema for f(x,y); The Hessian matrix and local extrema for f(x,y,z); Differentiability for Multivariable Functions; Review of Maths - 2 |
About the Instructors
I completed my B.Stat. (Hons.) and M.Stat. from the Indian Statistical Institute, Kolkata in 2004 and my Ph.D. from TIFR, Mumbai in 2010. I was a postdoctoral fellow in TIFR, a visiting assistant professor in the University of Kansas and very briefly an INSPIRE faculty fellow in IISc, Bengaluru before I joined the mathematics department in IITM in 2015.