Machine Learning Foundations
Linear algebra, probability and optimisation lenses on machine learning — the mathematical foundations before the algorithms.
§ 1Calendar
- Quiz 1—
- Quiz 2—
- End-term examination—
§ 2Previous Year Questions
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MLF weekwise and quizwise papers
Past papers sorted by week and by quiz, May 2022 to Sep 2025.
23f3004032.github.ioby Ankit Kumar
§ 3Resources
Course material2
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Supplementary content
Extra material shared on Google Drive.
drive.google.comIITM login required -
Course YouTube channel
All lecture videos.
youtube.com
Notes7
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MLF weekwise notes
Week-by-week notes for the whole course.
giri-subrahmanya.github.ioby B R Giri Subrahmanya -
MLF weekwise summary
Short weekly summaries written by a TA.
22f3001517.github.ioby Anant Kumar -
MLF notes (Karthik's site)
Full course notes.
notes.karthikthiagu.comby Karthik Thiagarajan -
MLF notes (course site)
A second set of full course notes.
bsc-iitm.github.ioby Karthik Thiagarajan -
MLF notes on Medium
Written notes for the Diploma MLF course.
medium.comby Pratham Bhalla -
Course notes
Notes and study material for this course.
iitmbsdegree.inby IITM BS Students' Corner -
Topic-wise notes
Topic-wise notes on ML Study Hub.
degreedost.comby ML Study Hub
Books2
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MLF textbook
The course textbook as a PDF.
drive.google.comby B R Giri SubrahmanyaIITM login required -
Books folder
Reference books for the course.
drive.google.comIITM login required
TA resources3
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Activity questions
Activity questions shared by the MLF TA team.
drive.google.comIITM login required -
Maths 2 Linear Algebra recap
Quick revision of the linear algebra needed for MLF.
drive.google.comIITM login required -
TA session recordings (Jan 2026 term)
Sheet of TA sessions with dates, topics and recordings.
docs.google.comIITM login required
Syllabus
The official course syllabus, transcribed from the IITM BS Data Science & Applications course booklet.
§ 1Course Description
This course lays the foundation for subsequent machine learning courses by covering essential concepts that, while not strictly part of machine learning, are crucial for a comprehensive understanding of the field
Lectures-Tutorials-Practicals-Credits: 4-0-0-4
§ 2Faculty
- Prof. Harish G. Ramaswamy, Wadhwani School of Data Science, IIT Madras
- Prof. Arun Rajkumar, Wadhwani School of Data Science, IIT Madras
- Prof. Prashanth LA, Wadhwani School of Data Science, IIT Madras
§ 3Week-by-week
Week 1: Introduction to ML - data, models, tasks; Supervised (regression, classification); Unsupervised (dimensionality reduction, density estimation); Applications.
Week 2: Sets and functions; Calculus - univariate (derivatives, applications), multivariate (lines, planes, approximations).
Week 3: Four fundamental subspaces; Orthogonality and orthogonal subspaces; Projections; Least squares and projections onto subspaces.
Week 4: Linear and polynomial regression; Eigenvalues and eigenvectors; Matrix diagonalization; Orthogonal diagonalization.
Week 5: Complex matrices; Hermitian and unitary matrices; Diagonalization.
Week 6: SVD; Examples and applications; Positive definiteness; Geometric interpretation.
Week 7: Principal Component Analysis - variance maximization; High-dimensional data; Applications.
Week 8: Optimization - gradient descent; Taylor series; Multivariate methods; ML foundations.
Week 9: Constrained Optimization and Lagrange multipliers. Projected gradient descent; Convexity - convex sets and functions; Properties of convex functions.
Week 10: Convex optimization - properties, applications; Primal-dual problems; Karush-Kuhn-Tucker conditions; Linear programming.
Week 11: Continuous random variables - conditional pdf, expectation; Multiple and independent variables; Transformations; Common distributions.
Week 12: Multivariate distributions; MLE; GMM and EM; Laws of large numbers and CLT.