MFML Interactive ZC416 · Prof. Saurabh · BITS Pilani WILP
Mathematical Foundations for Machine Learning

Learn the math under the machine — by touching it.

by Prof. Saurabh · ZC416 · BITS Pilani WILP

All 16 sessions of MFML, rebuilt as interactive lessons: every idea told as a story first, every slide example worked in full, every concept something you can drag, zoom, and break. Read the intuition, play the widget, then pass the inline checks.

📐 15 topic units + finale 🎛 Interactive widgets in every unit ✅ Pause-and-predict checks

Part I · Linear Algebra

01

Systems of Linear Equations

A matrix is a machine that moves space. Three windows on Ax = b, the three fates, and elimination — the algorithm that never lies.

✓ Ready10 widgets (2 in 3D) · 9 checks · ~50 min
02

Vector Spaces

The universe where vectors live: groups, subspaces, span, independence, basis, dimension — the architecture of ML math.

✓ Ready6 widgets (span in 3D) · 10 checks · ~50 min
03

Analytic Geometry

The board gets its ruler: norms, inner products, angles, orthogonality — and Gram–Schmidt, the cleanest grid a geometry can have.

✓ Ready7 widgets (G–S in 3D) · 10 checks · ~50 min
04

Determinants, Eigenvalues & the Spectral Theorem

A matrix's fingerprints: the numbers and directions that survive the transformation.

Coming soon
05

Matrix Decompositions & SVD

Take one complicated matrix apart into simple honest pieces — the ladder from spectral to SVD to low-rank.

Coming soon

Part II · Calculus & Differentiation

06

Differentiation

Derivatives from scalars to tensors — the language of "which way is down?"

Coming soon
07

Backprop & Automatic Differentiation

The chain rule, industrialized: how a network computes a million derivatives for the price of two forward passes.

Coming soon
08

Taylor & MacLaurin Series

Polynomial impostors: approximating any function — and knowing exactly how big the lie (the remainder) is.

Coming soon

Part III · Optimization

09

Gradient Descent

Walk downhill in thick fog: steps, step sizes, and why a little noise helps you scale.

Coming soon
10

Optimization I — Gradients that Work

Nonlinear optimization and the minutiae that make or break gradient methods.

Coming soon
11

Optimization II — Five Ways Down One Valley

Momentum, AdaGrad, RMSProp, Adam — and the cliffs and valleys that defeat naive descent.

Coming soon

Part IV · Applications

12

PCA I — Foundations

Compress a thousand dimensions without losing the story: variance, projections, eigenvectors.

Coming soon
13

PCA II — In Action

Principal components at work — linear algebra earning its keep on real data.

Coming soon
14

SVM I — Constrained Optimization & Kernels

Lagrange multipliers, KKT conditions, duality, and the kernel trick — the math that draws the widest possible line.

Coming soon
15

SVM II — Solving the SVM

From primal to dual to solution — and soft margins for a messy world.

Coming soon
16

Session 16 · Finale

Awaiting slides — drop Lecture_16.pdf into the MFML folder and this unit joins the queue.

Awaiting slides