December 2025 against June 2024
What one sitting asked that the other did not — as a share of each paper, because December 2025 carries 98 subject questions and June 2024 carries 100. Comparing raw counts across papers of different sizes invents a trend in every row.
Asked more in December 2025
- Eigenvalues and Canonical Forms+3.1 pp
7.1% (7) in December 2025 · 4.0% (4) in June 2024
- Groups+2.1 pp
5.1% (5) in December 2025 · 3.0% (3) in June 2024
- Singularities and Residues+2.1 pp
4.1% (4) in December 2025 · 2.0% (2) in June 2024
- Integration+2.1 pp
3.1% (3) in December 2025 · 1.0% (1) in June 2024
Asked more in June 2024
- Continuity and Differentiation-3.0 pp
2.0% (2) in December 2025 · 5.0% (5) in June 2024
- Vector Spaces and Linear Maps-2.9 pp
3.1% (3) in December 2025 · 6.0% (6) in June 2024
- Rings and Fields-2.9 pp
3.1% (3) in December 2025 · 6.0% (6) in June 2024
- Cauchy Theory-2.0 pp
2.0% (2) in December 2025 · 4.0% (4) in June 2024
- Probability-1.9 pp
7.1% (7) in December 2025 · 9.0% (9) in June 2024
Present on one paper and absent from the other
Absent from one sitting is not absent from the syllabus. A topic carrying two questions one session and none the next has told you almost nothing.
Only in December 2025
- Metric Spaces · 1
- Lebesgue Measure and Integration · 1
Only in June 2024
- — none
Every topic, both papers
| Topic | December 2025 | June 2024 | Change |
|---|---|---|---|
| ProbabilityProbability, Statistics & Linear Programming | 7.1% (7) | 9.0% (9) | -1.9 pp |
| The Real LineAnalysis & Linear Algebra | 7.1% (7) | 7.0% (7) | +0.1 pp |
| Eigenvalues and Canonical FormsAnalysis & Linear Algebra | 7.1% (7) | 4.0% (4) | +3.1 pp |
| EstimationProbability, Statistics & Linear Programming | 5.1% (5) | 6.0% (6) | -0.9 pp |
| Linear Models and MultivariateProbability, Statistics & Linear Programming | 5.1% (5) | 5.0% (5) | +0.1 pp |
| Partial Differential EquationsODE, PDE & Applied Mathematics | 5.1% (5) | 4.0% (4) | +1.1 pp |
| Ordinary Differential EquationsODE, PDE & Applied Mathematics | 4.1% (4) | 5.0% (5) | -0.9 pp |
| Vector Spaces and Linear MapsAnalysis & Linear Algebra | 3.1% (3) | 6.0% (6) | -2.9 pp |
| Rings and FieldsComplex Analysis, Algebra & Topology | 3.1% (3) | 6.0% (6) | -2.9 pp |
| GroupsComplex Analysis, Algebra & Topology | 5.1% (5) | 3.0% (3) | +2.1 pp |
| Limit Theorems and Markov ChainsProbability, Statistics & Linear Programming | 4.1% (4) | 4.0% (4) | +0.1 pp |
| Inner Product Spaces and FormsAnalysis & Linear Algebra | 3.1% (3) | 4.0% (4) | -0.9 pp |
| Continuity and DifferentiationAnalysis & Linear Algebra | 2.0% (2) | 5.0% (5) | -3.0 pp |
| Singularities and ResiduesComplex Analysis, Algebra & Topology | 4.1% (4) | 2.0% (2) | +2.1 pp |
| Linear Integral EquationsODE, PDE & Applied Mathematics | 3.1% (3) | 3.0% (3) | +0.1 pp |
| Calculus of VariationsODE, PDE & Applied Mathematics | 3.1% (3) | 3.0% (3) | +0.1 pp |
| Hypothesis TestingProbability, Statistics & Linear Programming | 3.1% (3) | 3.0% (3) | +0.1 pp |
| Numerical AnalysisODE, PDE & Applied Mathematics | 3.1% (3) | 3.0% (3) | +0.1 pp |
| Cauchy TheoryComplex Analysis, Algebra & Topology | 2.0% (2) | 4.0% (4) | -2.0 pp |
| TopologyComplex Analysis, Algebra & Topology | 3.1% (3) | 2.0% (2) | +1.1 pp |
| Sampling and Design of ExperimentsProbability, Statistics & Linear Programming | 3.1% (3) | 2.0% (2) | +1.1 pp |
| IntegrationAnalysis & Linear Algebra | 3.1% (3) | 1.0% (1) | +2.1 pp |
| Sequences and Series of FunctionsAnalysis & Linear Algebra | 2.0% (2) | 2.0% (2) | +0.0 pp |
| Functions of Several VariablesAnalysis & Linear Algebra | 2.0% (2) | 2.0% (2) | +0.0 pp |
| Analytic FunctionsComplex Analysis, Algebra & Topology | 2.0% (2) | 1.0% (1) | +1.0 pp |
| Classical MechanicsODE, PDE & Applied Mathematics | 1.0% (1) | 2.0% (2) | -1.0 pp |
| Zeros and MappingsComplex Analysis, Algebra & Topology | 1.0% (1) | 1.0% (1) | +0.0 pp |
| Linear ProgrammingProbability, Statistics & Linear Programming | 1.0% (1) | 1.0% (1) | +0.0 pp |
| Metric SpacesAnalysis & Linear Algebra | 1.0% (1) | 0.0% (0) | +1.0 pp |
| Lebesgue Measure and IntegrationAnalysis & Linear Algebra | 1.0% (1) | 0.0% (0) | +1.0 pp |
21 of 30 topics moved by less than 1.5 percentage points and are greyed out — at four to thirteen questions a topic, a swing of one or two questions is noise, not a signal.