Fundamentals of AI/ML

Where the field came from, the mathematics underneath it, and how to tell whether a model is any good.

मूलं हि शस्यं वर्धते नितान्तं
मूलं हि विद्या वर्धते नितान्तम्।
मूलं हि सर्वस्य भवन्ति मूलं
मूलं न सन्देहकृतं हि लोके॥

mūlaṁ hi śasyaṁ vardhate nitāntaṁ
mūlaṁ hi vidyā vardhate nitāntam |
mūlaṁ hi sarvasya bhavanti mūlaṁ
mūlaṁ na sandehakṛtaṁ hi loke ||

Just as the root is essential for the growth of a plant, the fundamentals of knowledge are crucial for its development. The root is the basis of everything; there is no doubt about this in the world.

Course information

Instructor

Jitin Singla · jsingla@bt.iitr.ac.in

Lectures

Mon & Thu · 4:05–5:00 PM
Fri · 5:05–6:00 PM

Venue

GB-003

Office hours

To be announced
Room 211, BSBE Department

Discussion

Piazza

Objectives

Comprehend the historical evolution and foundational concepts of AI/ML.
Build mathematical intuition for machine learning principles.
Explore core theoretical frameworks and evaluation strategies.

Prerequisites

Python programming

Course content

Historical development and evolution of AI/ML
Key terminology
Linear algebra and probability review
Theoretical underpinnings of learning from data
How energy functions and loss functions guide model training and evaluation
Various loss functions
First-order optimization: gradient descent (GD) and stochastic gradient descent (SGD)
Basics of constrained optimization and its relevance in training
Hyperparameter tuning strategies
Validation techniques to assess model generalization
Evaluation metrics to measure and compare models
Bayesian inference in machine learning

Schedule

#	Topic	Slides	Essential reading	Additional	Homework
0	Kick-off	Slides	—	The course in one picture	—
1	History of AI and machine learning	Slides	Kolter & Do, Linear Algebra Review & Reference (CS229) §1–2 · Boyd & Vandenberghe, Introduction to Applied Linear Algebra (VMLS) Ch. 1–3	The Imitation Game · Turing machine — short	—
LA1	Notation & basic objects; vector/matrix products; properties of matrix multiplication	—	Kolter & Do §1–2	3Blue1Brown, Essence of Linear Algebra · Deisenroth, Faisal & Ong, Mathematics for Machine Learning, Ch. 2–4	—
LA2	Transpose, symmetric matrices, trace; norms, Cauchy–Schwarz & cosine similarity	—	Kolter & Do §3.2–3.5	Demo: ℓₚ unit balls · Demo: cosine similarity	—
LA3	Matrix inverse; span, range & linear independence	—	Kolter & Do §3.6–3.9	—	—
LA4	Linear projection & least squares	—	Kolter & Do §3.9, §4.4	Demo: least-squares line fitting	—
LA5	Determinant; condition number & numerical sensitivity	—	Kolter & Do §3.10 · condition number is supplementary — see Trefethen & Bau, Numerical Linear Algebra	—	—
LA6	Quadratic forms; symmetric & positive (semi)definite matrices	—	Kolter & Do §3.11	—	—
LA7	Eigenvalues & eigenvectors; diagonalization & the spectral theorem; eigenvalues as optimisation	—	Kolter & Do §3.12–3.13, §4.6	Demo: eigenvectors as fixed directions · Demo: rotate, scale, rotate · Setosa, Eigenvectors & Eigenvalues, Explained Visually	Practice-1
LA8	SVD; PCA; matrix calculus (self study)	—	Kolter & Do §4.1–4.3	Demo: PCA playground · Setosa, Principal Component Analysis, Explained Visually · Petersen & Pedersen, The Matrix Cookbook	Practice-2

References and resources

Recommended text

Probabilistic Machine Learning: An Introduction, Kevin Murphy. MIT Press, 2022.

Supplementary

Machine Learning — Andrew Ng, Coursera

Watch

The Imitation Game (2014)

Evaluation

30% Continuous assessment (CWS)Announced and surprise quizzes

30% Mid-term exam (MTE)

40% End-term exam (ETE)

Tentative.

Question papers

Autumn 2025–26 — MTE · ETE

All courses