01 MATH40003 OVER ANCHORING DIAGNOSIS
English review edition prepared on 4 October 2026 from a preserved source copy. It is a later presentation, not the historical study interface. Source checks and difficulty judgements describe the original material author's own process; they do not indicate Imperial College London endorsement.
Source SHA-256: 42dacdc1d5b61003ba281de147462e390101aa6e60ca9723a2c803302f5bdd00Source date: 2026-08-06
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Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
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1. diagnostic report on excessive anchoring
why the old six papers cannot serve as the final training version
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Conclusion. The earlier materials were not wholly ineffective. However, their generation logic repeatedly expanded the entry points, method sequences and combinations of the four 2026 questions, and mistook the presence of identically named knowledge points for effective coverage. Reviewing question entry points, first key steps and complete course-method sequences gives the old six papers A=77, B=64, C=35 and D=18 across 194 historical ability units. Effective coverage A+B is 141/194=72.7%. Category C is label-only apparent coverage and is excluded from that rate.
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the most serious structural issue :
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1. Paper 1 almost follows the four 2026 questions one by one: D/G kernels and images, even/odd operators, unitary real blocks, and conjugacy classification. Paper 6 again uses function spaces, operator polynomials, spectral decomposition and a progression of permutation questions.
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2. Old M2Q3 and M4Q3 both practise QR/SVD. Old M2Q4, M4Q4 and M3Q4 repeat the abstract group-theory sequence. These repeated questions reduce the capacity to practise high-mark 2025 abilities.
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3. Stabilisation of ascending chains in 2025 Q2, transfer of function-space structure in Q3, the two-way rank–minor proof in Q4, and the full classification of integer orthogonal matrices in Q5 were not practised consecutively in a 2025 bridging paper.
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4. The old report claimed full coverage by counting 67 knowledge-point labels. Reviewing 194 marking clusters shows that a name appearing does not establish that its entry point, first step and proof sequence have been practised.
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Revision principles. The 2026 paper fixes only the two-hour duration, 80 marks, four questions, overall workload and A/B/C/D progression. Question types and method sequences are drawn from the seven years 2020–2026. The final six papers respectively address the current structure, a 2025 bridge, 2023–2024 abilities, 2020–2022 abilities, seven-year gaps and mixed transfer.
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Material scope. This session could access seven years of formal questions, official solutions, marking categories and examiner comments, plus the old practice papers and solutions. No separate lecture notes, problem sheets, tutorial or assignment files were found. The course-method audit therefore uses the main methods in official solutions and their seen/similar/unseen labels; no unavailable lecture-note page numbers were invented. Tony's 2025 handwritten script and question-level marks were also unavailable. The only feedback was that he could not solve the 2025 paper. This triggered structural revision but cannot replace question-by-question marking evidence.