Most book lists for this exam are inventories. They name twenty titles, say nothing about which to open first, and leave you with a shelf instead of a plan. This one is deliberately short, and the recommendation that matters most is at the bottom.
Before the list: the mistake almost everyone makes
Collecting books feels like preparation. It is not. The exam does not test whether you have read Rudin; it tests whether, under time pressure, you can tell that a closed bounded set need not be compact in an infinite-dimensional space.
Two books you have worked through beat eight you have skimmed, by a wide margin. If you are choosing between buying another text and solving fifty more previous-year questions, solve the questions.
Unit 1 — Analysis and Linear Algebra
This unit carries the most weight and rewards depth more than any other.
Real analysis. Bartle and Sherbert, Introduction to Real Analysis is the right starting point if your foundations are shaky — it explains, rather than compresses. Rudin, Principles of Mathematical Analysis is the standard, and it is terse on purpose; use it once the ideas are familiar and you want them sharpened. Reading Rudin first is a common and demoralising mistake.
Metric spaces. Covered adequately in both of the above. Simmons, Introduction to Topology and Modern Analysis is worth it if metric-space questions keep catching you out.
Measure theory. Royden, Real Analysis is the usual choice. Be strategic here: the exam asks a narrow set of things — convergence theorems, (L^p) inclusions, measure-zero subtleties — and you do not need the whole book.
Linear algebra. Hoffman and Kunze is the standard and matches the exam's taste for canonical forms and minimal polynomials closely. Friedberg, Insel and Spence is gentler. Axler, Linear Algebra Done Right is excellent but avoids determinants for most of the book, which is a poor fit for a paper that asks about them directly.
Unit 2 — Complex Analysis, Algebra and Topology
Complex analysis. Conway, Functions of One Complex Variable is the reference; Churchill and Brown is the friendlier route if you want computation before theory. Residues, Rouché and the argument principle appear year after year.
Algebra. Dummit and Foote is comprehensive and the one to own. Gallian is easier and better for a first pass through group theory. Herstein, Topics in Algebra is compact and still excellent for Sylow theory.
Topology. Munkres is the standard and there is no real competitor. The exam stays in the first half — connectedness, compactness, separation axioms, quotients.
Unit 3 — ODE, PDE and Applied Mathematics
This unit is where a good book saves the most time, because the material is broad and shallow.
ODE. Simmons, Differential Equations with Applications and Historical Notes reads well. Coddington is the more rigorous option for existence and uniqueness.
PDE. Sneddon, Elements of Partial Differential Equations covers what the exam asks — first-order equations, characteristics, classification.
Numerical analysis. Jain, Iyengar and Jain is the standard Indian text and is well matched to the questions asked.
Calculus of variations. Gelfand and Fomin is short and complete for this syllabus.
Classical mechanics. Goldstein is the reference, but it is far more than you need. For this exam, Lagrangian and Hamiltonian formulations and Poisson brackets are the whole story.
Unit 4 — Probability and Statistics
Probability. Ross, A First Course in Probability for intuition; Rohatgi and Saleh for the measure-theoretic framing the exam sometimes leans on.
Statistical inference. Hogg, McKean and Craig is the reliable choice. Casella and Berger is deeper and worth it if inference is your strong suit and you want to make it decisive.
Sampling and design. Cochran, Sampling Techniques and Montgomery, Design and Analysis of Experiments. Both are heavier than the exam requires — use them as references, not readings.
How to actually use these
Pick one book per topic and finish it. Use the second only when a specific idea refuses to land.
Read with a pen and a purpose: after each section, close the book and try a previous-year question on it. If you cannot, you have not learned it yet — and you will discover that in minutes rather than in the exam hall.
Most importantly, stop reading earlier than feels comfortable. The gap between candidates who clear this exam and those who do not is rarely knowledge. It is practice under the marking scheme, where Part C gives you nothing unless every option is right.