IITM BS Maths 1: A Week-by-Week Survival Guide

Maths 1 (Mathematics for Data Science I, code BSMA1001) is a 4 credit foundation course with 12 weeks of content. It moves from sets and straight lines to polynomials, exponentials and logarithms, then to limits, derivatives and integrals, and ends with graph algorithms. Falling behind hurts most in weeks 5 to 9, where each week builds on the one before. The fix is steady practice by hand, every week.

The topics below come from the official course page. Quiz 1 tests weeks 1 to 4 and Quiz 2 tests weeks 1 to 8. For a short overview of the subject, see our Maths 1 subject page.

Weeks 1 to 4: sets, lines, quadratics, polynomials

This is the content you studied during the qualifier. Revise it anyway, because Quiz 2 and the end term still cover these weeks.

How to practise:

• For relations, take a small set such as 1, 2 and 3, and write the pairs by hand. Check reflexive, symmetric and transitive one at a time.
• For lines, find the slope first. The line through (1, 2) and (3, 8) has slope (8-2)/(3-1) = 3. A parallel line also has slope 3. A perpendicular line has slope -1/3, since the two slopes multiply to -1.
• For quadratics, the vertex is at x = -b/(2a). For f(x) = x^2-6x+5, that is x = 3, and f(3) = -4. The x^2 term is positive, so -4 is the minimum.
• For polynomials, use the factored form. In (x-2)^2(x+1), the graph touches the x-axis at 2 (even power) and crosses it at -1.

Weeks 5 and 6: functions, exponentials and logarithms

• Order matters in composition. If f(x) = x+1 and g(x) = x^2, then f(g(2)) = 5 but g(f(2)) = 9.
• A function has an inverse only if it passes the horizontal line test. The inverse of f(x) = 2x+3 is (x-3)/2. Check by putting one inside the other.
• Learn three log rules until they are automatic: log(ab) = log(a)+log(b), log(a/b) = log(a)-log(b), and log(a^n) = n log(a).
• Solve 2^x = 32 by writing 32 as 2^5, so x = 5.
• Logs work only for positive inputs. Test every answer, because an equation can give a value you must throw out.

Weeks 7 to 9: limits, derivatives and integrals

• A 0/0 form is not the end. The limit of (x^2-1)/(x-1) as x goes to 1 is 2, because the expression simplifies to x+1.
• For critical points, set the derivative to 0, then test each side. For f(x) = x^3-3x, f'(x) = 3x^2-3, which is 0 at x = 1 and x = -1. The sign of f' shows a local max at -1 and a local min at 1.
• For integrals, draw the region first. The area under y = 2x from 0 to 3 is a triangle with base 3 and height 6, so 9. Use pictures like this to check your answers.

If calculus is new to you, give these weeks extra hours. Maths 2 builds on them.

Weeks 10 to 12: graph theory and revision

Week 11 covers Dijkstra, Bellman-Ford and Floyd-Warshall for shortest paths, and Prim and Kruskal for spanning trees.

• Run each algorithm by hand on a graph of 5 or 6 nodes. Write the queue (BFS) or the stack (DFS) at every step.
• Topological sorting works only on a directed graph with no cycles.
• Dijkstra's algorithm assumes no negative edge weights. Bellman-Ford can handle them.
• For Kruskal, list the edges by weight and add them one by one, skipping any edge that makes a cycle.

This part has little algebra. Careful, written steps score well here.

How to use the official material

• The handbook says each week has self-tests after the videos and a practice assignment with solutions. Try every practice question before you look at the solution.
• The course page offers three reference volumes to download: Sets and Functions, Calculus, and Graph Theory. Its suggested book is Introductory Algebra: a real-world approach by Ignacio Bello.
• The lecture videos are also on YouTube as a public playlist, so you can rewatch on your phone.

Do your graded assignments yourself. Sharing or copying answers breaks the honour code.

Common questions

I failed Maths 1. What should I change on the second try?

Start with the part where you lost the most marks, not week 1. Redo the question types you got wrong every weekend. Take fewer courses that term so Maths 1 gets its full share of hours. Our post on recovering after a failed course has a plan.

Which courses need Maths 1?

Maths 2 lists Maths 1 as its prerequisite. The Stats 2 course page lists Maths 1 and Stats 1 as prerequisites. See taking Maths 2 and Stats 2 together.

Can I manage Maths 1 without Class 12 maths?

It starts from basics like number systems and sets, so yes, with extra time for weeks 5 to 9. Our post on IITM BS with weak maths covers this.

Which weeks carry the most marks?

The handbook does not give marks by week. Quiz 1 covers weeks 1 to 4, Quiz 2 covers weeks 1 to 8, and the end term is half of your course score. Your grading document gives the exact weights.