Most preparation advice for this exam is a list of books. Books are the easy part. What decides the result is what you do with the sixty attempts you are allowed, and a plan should be built backwards from that.
The three things that actually move the score
1. Depth beats coverage. Part C is all-or-nothing and carries 95 of 200 marks. Twenty topics you can close completely will outscore fifty you half-remember. Every hour spent adding a new topic instead of closing an existing one is a bet that pays only if the paper is kind.
2. Previous-year questions are the syllabus. The official syllabus tells you what may be asked; past papers tell you what is asked, in what style, with which traps. Reading the syllabus without working past papers is preparing for a different exam.
3. Selection is a skill, and it is trainable. Choosing which sixty of the 120 to attempt is worth marks by itself, and it can only be practised on a full paper with the real limits enforced.
A six-month structure
Months 1–2 — Unit 1, properly. Analysis and linear algebra are roughly 60 marks and the most predictable questions on the paper. Do not move on until you can close standard questions here without hesitation. Use the syllabus map topic by topic; each subtopic has curated lectures and exam-focus pointers.
Month 3 — Unit 2. Complex analysis and algebra. Algebra especially is patterned — Sylow counting, group actions, quotient checks, irreducibility tests recur endlessly. Learn the patterns, not individual problems.
Month 4 — Units 3 and 4. Broad and shallow. Aim for competence across the standard questions rather than mastery. Unit 4 is where most candidates are weakest, which makes modest effort unusually profitable.
Month 5 — Previous-year questions, by trap type. Switch from topics to patterns. Work the tagged PYQ bank and drill categories: converse fails, boundedness dropped, closed-and-bounded-is-not-compact. When you can name why an option is wrong before computing, you are ready.
Month 6 — Full papers under time. Sit full-length papers with the real 15/25/20 limits. Review every paper properly: for each question you got wrong, decide whether it was knowledge, a trap, or selection. Those three failures have three different fixes, and treating them all as "revise more" is why scores plateau.
Reviewing a mock properly
The mark is the least useful output. What matters is the classification:
- Knowledge gap — you did not know the result. Go back to the topic.
- Trap — you knew the result and still chose wrong. Add it to your counterexample list; this is the most valuable category and the most ignored.
- Selection error — you spent attempts on questions you could not close while closable ones went unread. Fix by changing your first-pass discipline, not by studying.
A note on counterexamples
A large share of Part B and Part C questions turn on knowing one standard counterexample: a function that is differentiable but not continuously so, a set that is closed and bounded without being compact, a connected space that is not path-connected. Collect them deliberately — ours are in the counterexample bank, and the interactive visuals let you watch several of them fail.
What not to do
Do not collect resources. A candidate with three video courses, five books and two test series who has worked one past paper is worse prepared than one with a single source and ten worked papers. Choose, then commit.