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BSMA1003 - Mathematics for Data Science II
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BSMA1003 - Mathematics for Data Science II
476 words
2 min read
| Field | Value |
|---|---|
| Course Code | BSMA1003 |
| Level | Foundational Level Course |
| Credits | 4 |
| Type | Foundational |
| Pre-requisites | BSMA1001 - Mathematics for Data Science I |
| Videos | YouTube Playlist |
📖 Description
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.
🗓️ Weekly Syllabus
| Week | Topic |
|---|---|
| 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 mat | |
| Week 3 | Introduction to vector spaces - |
| Introduction to vector spaces; | |
| Some properties of vector spaces; | |
| Linear dependence; | |
| Linear independence - Part | |
| Week 4 | Basis and dimension - |
| What is a basis for a vector space?; | |
| Finding bases for vector spaces; | |
| What is the rank/dimension for a vector space; | |
| Ran | |
| 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 n | |
| Week 6 | Linear transformation, Kernel and Images - |
| Linear transformations, ordered bases and matrices; | |
| Image and kernel of linear transformations; | |
| Exa | |
| Week 7 | Equivalent and Similar matrices; |
| Introduction to inner products - | |
| Equivalence and similarity of matrices; | |
| Affine subspaces and affine mappings | |
| Week 8 | Orthogonality, Orthonormality; |
| Gram-schmidt method - | |
| Orthgonality and linear independence; | |
| What is an orthonormal basis? | |
| Projections using inner prod | |
| Week 9 | Multivariable functions, Partial derivatives, |
| Limit, continuity and directional derivatives - | |
| Multivariable functions : visualization; | |
| Partial | |
| Week 10 | Directional ascent and descent, |
| Tangent (hyper) plane, | |
| Critical points - | |
| The directional of steepest ascent/descent; | |
| Tangents for scalar-valu | |
| Week 11 | Higher order partial derivatives, |
| Hessian Matrix and local extrema, | |
| Differentiability - | |
| Higher order partial derivatives and the Hessian matri |
📎 Reference Documents
📚 Books & Resources
Reference Documents / Books
Linear Algebra DOWNLOAD
📝 About the Instructors
Sarang S Sane
Assistant Professor,
Department of Mathematics,
IIT Madras
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.
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