The official syllabus is divided into four units. They are not equally weighted, and planning as though they are is a common and expensive mistake.
Unit 1 — Analysis and Linear Algebra · roughly 60 marks
The largest unit, and the one that rewards preparation most reliably.
Real analysis (sequences, series, continuity, differentiability, Riemann integration, sequences and series of functions), metric spaces and their topology, measure theory and Lebesgue integration, and linear algebra (vector spaces, linear transformations, eigenvalues, canonical forms, inner product spaces and quadratic forms).
If time is short, this is the unit to secure first — it is the largest and its questions are the most predictable in style. Open Unit 1.
Unit 2 — Complex Analysis, Algebra and Topology · roughly 50 marks
Complex analysis (analytic functions, Cauchy's theorem, Laurent series and residues, conformal maps, Rouché's theorem), group theory (Sylow theorems, group actions, permutation groups), rings and fields (ideals, PID/UFD, field extensions, Galois theory) and general topology.
Algebra here is highly patterned: the same handful of arguments — counting elements of a given order, applying Sylow, checking a quotient — recur constantly. Open Unit 2.
Unit 3 — ODE, PDE and Applied Mathematics · roughly 45 marks
Ordinary differential equations (existence and uniqueness, Wronskian, systems, Sturm–Liouville), partial differential equations (classification, characteristics, the standard three equations), numerical analysis, calculus of variations, integral equations and classical mechanics.
Broad but shallow: many topics, each asking a limited set of standard questions. Open Unit 3.
Unit 4 — Probability and Statistics · roughly 45 marks
Probability (distributions, limit theorems, Markov chains), statistical inference (sufficiency, UMVUE, testing, Neyman–Pearson), linear models and regression, sampling theory and design of experiments.
The unit candidates most often abandon — and therefore the one where a modest effort buys the most marks relative to competition. Open Unit 4.
How to read those weights
Unit 1 plus Unit 2 is around 110 of 200 marks. A candidate who is genuinely strong in those two and merely competent in the other two is in a comfortable position; one who is uniformly average across all four usually is not.
That said, Part C's exact-set marking means depth beats coverage. Twenty questions you can close completely will out-score forty you half-remember.
Study it, rather than reading about it
Every subtopic above is mapped to curated video lectures, exam-focus pointers, notes and solved previous-year questions on the syllabus and video map — free, and no account needed.