December 2025 against December 2023
What one sitting asked that the other did not — as a share of each paper, because December 2025 carries 98 subject questions and December 2023 carries 96. Comparing raw counts across papers of different sizes invents a trend in every row.
Asked more in December 2025
- Singularities and Residues+3.0 pp
4.1% (4) in December 2025 · 1.0% (1) in December 2023
- The Real Line+3.0 pp
7.1% (7) in December 2025 · 4.2% (4) in December 2023
- Topology+2.0 pp
3.1% (3) in December 2025 · 1.0% (1) in December 2023
- Groups+2.0 pp
5.1% (5) in December 2025 · 3.1% (3) in December 2023
- Eigenvalues and Canonical Forms+1.9 pp
7.1% (7) in December 2025 · 5.2% (5) in December 2023
Asked more in December 2023
- Continuity and Differentiation-4.2 pp
2.0% (2) in December 2025 · 6.3% (6) in December 2023
- Rings and Fields-3.2 pp
3.1% (3) in December 2025 · 6.3% (6) in December 2023
- Hypothesis Testing-2.1 pp
3.1% (3) in December 2025 · 5.2% (5) in December 2023
- Vector Spaces and Linear Maps-2.1 pp
3.1% (3) in December 2025 · 5.2% (5) in December 2023
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
- Linear Programming · 1
- Metric Spaces · 1
Only in December 2023
- — none
Every topic, both papers
| Topic | December 2025 | December 2023 | Change |
|---|---|---|---|
| ProbabilityProbability, Statistics & Linear Programming | 7.1% (7) | 7.3% (7) | -0.1 pp |
| Eigenvalues and Canonical FormsAnalysis & Linear Algebra | 7.1% (7) | 5.2% (5) | +1.9 pp |
| Linear Models and MultivariateProbability, Statistics & Linear Programming | 5.1% (5) | 6.3% (6) | -1.1 pp |
| The Real LineAnalysis & Linear Algebra | 7.1% (7) | 4.2% (4) | +3.0 pp |
| Rings and FieldsComplex Analysis, Algebra & Topology | 3.1% (3) | 6.3% (6) | -3.2 pp |
| Partial Differential EquationsODE, PDE & Applied Mathematics | 5.1% (5) | 4.2% (4) | +0.9 pp |
| EstimationProbability, Statistics & Linear Programming | 5.1% (5) | 4.2% (4) | +0.9 pp |
| Continuity and DifferentiationAnalysis & Linear Algebra | 2.0% (2) | 6.3% (6) | -4.2 pp |
| Hypothesis TestingProbability, Statistics & Linear Programming | 3.1% (3) | 5.2% (5) | -2.1 pp |
| Vector Spaces and Linear MapsAnalysis & Linear Algebra | 3.1% (3) | 5.2% (5) | -2.1 pp |
| Ordinary Differential EquationsODE, PDE & Applied Mathematics | 4.1% (4) | 4.2% (4) | -0.1 pp |
| GroupsComplex Analysis, Algebra & Topology | 5.1% (5) | 3.1% (3) | +2.0 pp |
| Limit Theorems and Markov ChainsProbability, Statistics & Linear Programming | 4.1% (4) | 3.1% (3) | +1.0 pp |
| Inner Product Spaces and FormsAnalysis & Linear Algebra | 3.1% (3) | 3.1% (3) | -0.1 pp |
| Numerical AnalysisODE, PDE & Applied Mathematics | 3.1% (3) | 3.1% (3) | -0.1 pp |
| Calculus of VariationsODE, PDE & Applied Mathematics | 3.1% (3) | 3.1% (3) | -0.1 pp |
| Linear Integral EquationsODE, PDE & Applied Mathematics | 3.1% (3) | 3.1% (3) | -0.1 pp |
| Sampling and Design of ExperimentsProbability, Statistics & Linear Programming | 3.1% (3) | 3.1% (3) | -0.1 pp |
| Analytic FunctionsComplex Analysis, Algebra & Topology | 2.0% (2) | 3.1% (3) | -1.1 pp |
| Functions of Several VariablesAnalysis & Linear Algebra | 2.0% (2) | 3.1% (3) | -1.1 pp |
| IntegrationAnalysis & Linear Algebra | 3.1% (3) | 2.1% (2) | +1.0 pp |
| Singularities and ResiduesComplex Analysis, Algebra & Topology | 4.1% (4) | 1.0% (1) | +3.0 pp |
| Cauchy TheoryComplex Analysis, Algebra & Topology | 2.0% (2) | 2.1% (2) | -0.0 pp |
| TopologyComplex Analysis, Algebra & Topology | 3.1% (3) | 1.0% (1) | +2.0 pp |
| Lebesgue Measure and IntegrationAnalysis & Linear Algebra | 1.0% (1) | 2.1% (2) | -1.1 pp |
| Classical MechanicsODE, PDE & Applied Mathematics | 1.0% (1) | 2.1% (2) | -1.1 pp |
| Zeros and MappingsComplex Analysis, Algebra & Topology | 1.0% (1) | 2.1% (2) | -1.1 pp |
| Sequences and Series of FunctionsAnalysis & Linear Algebra | 2.0% (2) | 1.0% (1) | +1.0 pp |
| Linear ProgrammingProbability, Statistics & Linear Programming | 1.0% (1) | 0.0% (0) | +1.0 pp |
| Metric SpacesAnalysis & 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.