IITM BS Mathematical Thinking (BSMA2001): Syllabus and Tips

Mathematical Thinking (BSMA2001) is a 4 credit elective at the degree level of the IITM BS in Data Science. It teaches you to read and write proofs, through number theory, counting, graphs and the basics of real analysis. It has no prerequisites. The instructors are Prof. Amritanshu Prasad and Prof. Sankaran Viswanath, mathematicians at The Institute of Mathematical Sciences, Chennai.

The course aims to move you from using maths methods to understanding why they work, so you are ready for more advanced mathematics.

Three things to check

• Length of the course. The course page says "8 weeks of coursework" in its assessment line, but it lists topics for 12 weeks. The handbook says all 4 credit courses run for 12 weeks. Expect 12 weeks unless your term calendar says otherwise.
• Level. The handbook says a 2xxx code means a level 2 course, yet it puts this course in the degree level table, tagged SE. It does not explain SE. Ask support how it counts toward your BSc elective credits before you rely on it.
• When it runs. The March 2026 table marks it as offered only in September 2026, out of May 2026, September 2026 and January 2027.

What you learn

• Weeks 1 and 2: numbers, sets and infinity. Sums and sequences, Peano's axioms for the natural numbers, sets as the language of maths, bijections and the size of infinite sets (the Hilbert Hotel), Cantor's diagonal argument, the real numbers and the completeness axiom, and mathematical logic.
• Weeks 3 to 5: number theory. Divisibility, the GCD and the Euclidean algorithm with its proof, Fermat's little theorem, the fundamental theorem of arithmetic, modular arithmetic, why there are infinitely many primes, the inclusion and exclusion principle, the pigeonhole principle, the sieve of Eratosthenes and gaps between primes.
• Weeks 6 and 7: counting and graphs. Binomial coefficients and the binomial theorem, lattice paths, permutations, random sampling, then graphs, connectedness, adjacency matrices, trees, Sperner's lemma and graph colouring.
• Weeks 8 to 12: analysis. Limits of sequences, continuity, the intermediate value theorem, the limit behind the Fibonacci numbers, derivatives, Riemann integrals, the mean value theorem, uniform continuity and the fundamental theorem of calculus.

How it is assessed

The course page lists weekly online assignments, 2 in-person invigilated quizzes and 1 in-person invigilated end term exam. It does not mention an OPPE or a project.

Where it counts

• Degree level elective. It is in the DS degree level course table with 4 credits and the SE tag. See the full DS electives list.
• BSc elective credits. The BSc level has 8 elective credits after the five core courses. Confirm with support that this course can fill them, given the level question above. See the BSc degree level.
• No minor. It is not part of any minor in the current handbook.

Who finds it hard and how to prepare

It can be hardest if your strength in school maths was fast calculation. Here, a right answer without a reason earns little. You write arguments in sentences. The analysis weeks (8 to 12) are the most abstract, because they prove facts about limits and continuity that school calculus took for granted.

• Learn four proof styles first. Direct proof, proof by contradiction, proof by contrapositive and induction. Write one short proof in each before the term starts.
• Rebuild each proof. After a lecture, close the video and write the main proof from memory. Where you get stuck is the step you did not really understand.
• Try small cases. Before proving a claim about primes or sums, test it for n = 1 to 10. Patterns show up fast.
• Write in full sentences. A proof is an argument for a reader, not a chain of symbols.
• Use the suggested books. Mathematical Thinking: Problem-Solving and Proofs by D'Angelo and West, and Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand, Polimeni and Zhang.

What to take before and after

• Before: nothing is required. The graph theory weeks of Maths 1 give you a head start on week 7. See the Maths 1 guide.
• With or after: Discrete Mathematics. Both cover sets, logic, Cantor's diagonal argument, inclusion and exclusion, the pigeonhole principle, graphs and trees. Taking Mathematical Thinking first should make Discrete Mathematics easier. Taking both means some repeated ground, so choose on purpose.

Common questions

Is Mathematical Thinking useful for a data science career?

It is not a tools course. What it trains is careful reasoning and reading proofs. That helps in theory heavy electives such as Sequential Decision Making, where much of the work is proving how well an algorithm does.

Do I need Maths 2 before this course?

No prerequisite is listed. The course starts from natural numbers and sets and builds up. If you are comfortable with Maths 1, you have enough to begin.

Is there any coding in this course?

The course page mentions no programming, OPPE or project. The work is written maths: assignments, two quizzes and an end term exam.