IITM BS Mathematics for Data Science II (BSMA1003): Syllabus and Tips

Mathematics for Data Science II (BSMA1003), usually called Maths 2, is a 4 credit foundation course. Most of it is linear algebra: matrices, solving equations, vector spaces, linear maps and orthogonality. The last three weeks cover calculus with many variables, ending with how to find maxima and minima. You need Maths 1 (BSMA1001) first. Maths 2 is also the corequisite for Statistics 2.

The instructor is Sarang S Sane, Assistant Professor in the Department of Mathematics, IIT Madras.

One small mismatch

The course page says 11 weeks of coursework, and its week list ends at week 11 with a review of the course. The handbook says all 4 credit courses run for 12 weeks. Follow the calendar for your term. The prerequisite (Maths 1) is the same in both places.

What you learn

• Weeks 1 and 2: matrices and equations. Vectors, matrices, determinants, Cramer's rule, echelon form, row reduction and Gaussian elimination.
• Weeks 3 to 6: vector spaces. Linear dependence and independence, basis, rank and dimension, the null space and nullity, and linear transformations with their kernel and image.
• Weeks 7 and 8: lengths, angles and orthogonality. Equivalent and similar matrices, affine subspaces, inner products and norms, orthonormal bases, projections, the Gram-Schmidt process and rotations.
• Weeks 9 to 11: calculus with many variables. Partial and directional derivatives, limits and continuity, the gradient and the direction of steepest ascent or descent, tangent planes, critical points, the Hessian matrix and local extrema, and differentiability.

The page's outcome list is very practical. By the end you should be able to row reduce, test whether vectors are independent, find bases and ranks, measure distances and angles, run Gram-Schmidt, and find maxima and minima for one or many variables.

How it is assessed

The course page lists 11 weeks of coursework, weekly online assignments, 2 in-person invigilated quizzes and 1 in-person invigilated end term exam. There is no OPPE.

Where it counts

• Foundation level. It is one of the 8 foundation courses. All 8 must be done before any diploma level course. See the foundation level guide.
• Statistics 2. Maths 2 is its corequisite. Take it before Stats 2 or in the same term. See Statistics for Data Science II.
• Direct entry. If you enter the Data Science diploma through the direct entry qualifier, the handbook says you start with Maths 2 and Stats 2.
• Later courses. Machine Learning Foundations spends weeks 3 to 6 on linear algebra (least squares, eigenvalues, symmetric matrices, SVD) and weeks 7 to 9 on optimisation. Maths 2 is the ground under all of it.

Who finds it hard and how to prepare

Maths 1 is mostly about working out answers. Maths 2 also asks you to reason about ideas like "vector space" and "basis". Students who learn only the steps can do well in weeks 1 and 2 and then feel lost from week 3, when the definitions take over.

• Make row reduction automatic. Do Gaussian elimination by hand until you stop making sign errors. Rank, basis, null space and independence all come back to it.
• One example, one non-example. For every definition, write one case that fits and one that does not, with the reason. For example, a set that is a subspace and a set that is not.
• Draw it. Sketch projections and Gram-Schmidt in 2D and 3D. The formulas make sense once you see the picture.
• Revise Maths 1 calculus first. Weeks 9 to 11 assume you are at ease with limits and derivatives in one variable. See the Maths 1 week by week guide.
• Use the course notes. The page offers a Linear Algebra reference document to download.

What to take before and after

• Before: Maths 1.
• With it: Statistics 2, if your hours allow. Read Maths 2 and Stats 2 in the same term before you decide.
• After: the Diploma in Data Science courses, such as Machine Learning Foundations.

Common questions

Is Maths 2 harder than Maths 1?

It is different. There is less formula work and more reasoning with definitions. If you liked the graph theory weeks of Maths 1, you may find the abstract parts easier than you expect.

Do I need Maths 2 for the Diploma in Programming?

On the normal route, yes. The handbook says all 8 foundation courses must be complete before you register for any diploma level course. The direct entry route to the programming diploma follows different rules.

How is Maths 2 used in data science?

The course description says it focuses on linear algebra, calculus and optimisation for machine learning and data science. Data sets are stored as matrices, and training a model is often finding the minimum of a function of many variables.