BSMA1003 · 4 credits · Foundation
Mathematics for
Data Science 2
Linear algebra done properly, then multivariable calculus. The single most load-bearing course in the Foundation level — every machine learning course in the Diploma is built on top of it.
- Lectures
- 111 · 32 h
- Prerequisite
- Maths 1
- Bonus marks
- up to 6
- Unlocks
- Stats 2 (co-req)
What this course actually asks
Definitions you can use, not definitions you can reciteMaths 2 is taught by Sarang S Sane of the IIT Madras mathematics department, and it is the first course in the programme that is taught like a university mathematics course. Weeks 3 to 8 are about vector spaces: definitions, proofs that something is or is not a basis, arguments about dimension.
That is a real change of gear. In Maths 1 you computed. Here you are asked things like "is this set linearly independent" and "what is the kernel of this map", and the answer is an argument, not a number. The students who struggle are usually the ones trying to memorise the definitions rather than use them on small examples.
Everything here returns. Rank, nullity, orthogonality, Gram–Schmidt, gradients and the Hessian are the working vocabulary of Machine Learning Foundations and Techniques. Time spent here is repaid twice.
Weeks 9 to 11 change subject again, to multivariable calculus — partial derivatives, directional derivatives, the tangent plane, critical points and the Hessian. That block is the direct ancestor of gradient descent.
The eleven weeks
Topics quoted from the official course pageTwo blocks: weeks 1–8 are linear algebra, weeks 9–11 are multivariable calculus. The course page describes this as "eleven weeks of coursework", one fewer than the other Foundation courses.
Vectors and matrices. Vectors; matrices; systems of linear equations; determinants.
Solving linear equations. Cramer's rule; solutions with an invertible coefficient matrix; echelon form; row reduction; Gaussian elimination.
Vector spaces. Introduction, properties, linear dependence, linear independence.
Basis and dimension. What a basis is, finding bases, rank and dimension.
Rank and nullity of a matrix; introduction to linear transformation.
Linear transformations, kernel and image.
Equivalent and similar matrices; introduction to inner products.
Orthogonality and orthonormality; the Gram–Schmidt method.
Multivariable functions. Partial derivatives; limit, continuity and directional derivatives.
Directional ascent and descent, the tangent (hyper)plane, critical points.
Higher order partial derivatives, the Hessian matrix and local extrema, differentiability.
A wording mismatch worth knowing about
The course page lists eleven weeks. The May 2026 grading document still carries the standard line that "W11/W12 contents will be included for the final exam". Treat week 11 as fully examinable and check your course announcements for whether a twelfth revision week exists this term.
Weeks 1 to 6, in one picture
Determinant, rank, nullity and invertibility are one factA 2×2 matrix is a thing that moves the plane. Blue is the standard basis, orange is where the matrix sends it, and the shaded area is the image of the unit square. Drag the entries until the determinant hits zero and watch all four numbers change at once — that is the theorem the course spends six weeks proving.
Try "singular". The whole plane collapses onto a line: the columns are multiples of each other, the determinant is 0, the rank drops to 1, and a whole line of vectors gets sent to the origin. Rank + nullity = 2 always, which is the rank–nullity theorem in week 5.
How it is graded
May 2026 grading document · confirm against your course pageThe standard formula, with the largest bonus in the Foundation level:
capped at 100, where B is out of 6
The six bonus marks
Three extra activities, 2 marks each, released on the portal during the term. Unlike Statistics, these are straightforward submissions — no peer review requirement is listed. Six marks for three pieces of work is the best return available anywhere in Foundation.
The eligibility gate
Average of the best 5 of 8 — the first seven weekly assignments plus Mock Quiz 1 — must be 40/100 or more, and you must attend at least one quiz. The gate closes at week 7, which here is inner products.
The multivariable block sits outside the gate
Weeks 9 to 11 — partial derivatives, gradients, the Hessian — count for nothing in eligibility and a great deal in the end term. They are also the part the Diploma needs most.
Where the marks actually go
My read, from this course and from what people ask aboutMemorising definitions instead of testing them
"Linearly independent" is not a phrase to recall, it is a check to run. Take any definition in weeks 3 and 4 and immediately try it on a set of two vectors in the plane. If you cannot, you do not have it yet.
Arithmetic slips in row reduction
Week 2's Gaussian elimination is the tool used in half the later questions, and it is pure arithmetic under time pressure. Practise until it is boring; a single sign error invalidates everything downstream.
Gram–Schmidt, forgotten
Week 8 lands after the eligibility window and just before the quiz-2 cut-off, so it gets squeezed from both sides. It is also the most mechanical procedure in the course — pure marks if you have done it five times.
Confusing the Hessian's role
In week 11 the gradient finds the critical point and the Hessian classifies it. People compute one and answer the other question.
Everything worth opening
Official first, then the free things that genuinely helpEvery link here was opened and checked on 23 September 2026.
Official
- Course page BSMA1003 on study.iitm.ac.in The week list, the instructor, and the Linear Algebra volume.
- Lectures Mathematics for Data Science II — full playlist All 111 official lectures on the programme's own channel.
For the linear algebra (weeks 1–8)
- Video 3Blue1Brown · Essence of linear algebra Watch the whole thing in week 1, before the definitions arrive. It is the picture that every later proof is describing.
- Course MIT 18.06 · Gilbert Strang The standard first linear algebra course, free, with problem sets and exams. Use it when a definition in weeks 3–5 will not land.
- Free book Interactive Linear Algebra · Georgia Tech A free textbook with figures you can drag. Its chapters on span, independence, bases and rank map almost exactly onto weeks 3–5.
For the calculus (weeks 9–11)
- Notes Paul's Online Math Notes · Calculus III Partial derivatives, directional derivatives, tangent planes and critical points, with fully worked practice problems.
- Free book Mathematics for Machine Learning Free PDF. Chapters 2 to 5 are this course, written for the reason you are taking it. Read it if you want to see where all of this is going.
What to do in week one
Term starts 2 October 2026- Watch Essence of linear algebra firstAll fifteen videos, before week 3. Three hours that change how the next eight weeks feel.
- Drill row reduction until it is dullTen systems by hand. Week 2's technique is used in weeks 4, 5, 6 and 8.
- Find the three bonus activitiesSix marks, and the easiest six in Foundation. Put the deadlines in your calendar as they appear.
- Test every definition on two vectorsWhen "linearly independent" is defined, immediately check a dependent pair and an independent pair by hand.
- Do not let weeks 9–11 driftThey are outside eligibility, heavily examined, and the direct prerequisite for gradient descent later.
- Check your course page's grading sectionEverything here is from the May 2026 document. The September 2026 one was not published when this was written.