'math' 검색 결과

Translate a complete mathematical modeling contest problem sentence by sentence into precise modeling language, preserve every substantive condition and definition, expose hidden constraints, draw a mandatory Mermaid cross-question flowchart, audit omissions, and deliver one easy-to-open Markdown report. For Huawei Cup (CPGMCM) graduate-contest problems, additionally prepend a plain-language layer that rewrites the background and questions as a primary-school word problem with a mandatory term-mapping table. Optionally render the finished report as one standalone HTML page on request. Use whenever a user supplies a CUMCM, CPGMCM, or other modeling problem and asks to interpret, translate, unpack, read closely, identify requirements, or avoid missing details before modeling.

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Query the bundled BZD mathematical-modeling dictionary for a user-selected model, explain its assumptions, inputs, outputs, limitations and validation, then judge whether it fits the current competition problem and data. Use when a user asks whether a proposed model is appropriate, requests model feasibility review, or wants dictionary-based alternatives for a modeling task.

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Review a mathematical-modeling paper's model-assumption section against the complete problem statement. Diagnose whether each assumption is necessary, evidence-based, compatible with the task, appropriately simplified, and usable by the later model. Use for assumption review, not automatic full-paper review or unsupported assumption generation.

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Generate or review mathematical-modeling competition AI tool usage statements and the anonymous AI工具使用详情.pdf. Use when users provide real AI usage records, or when checking a paper, statement, details PDF, code, and AI records for completeness, anonymity, and consistency.

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Review mathematical modeling competition papers from a complete problem and paper, with an optional strict bzd-paper-format-checker audit, itemized problem-specific scoring, a bottom-up low-score safeguard, and CUMCM award calibration by problem type, division, region, school and advisor. Generate a Chinese HTML judge report.

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Review a complete mathematical-modeling competition paper with an atomic checklist covering abstract readability, page structure, typography, headings, pagination, figures, tables, equations, anonymity, metadata, visual balance, and page allocation. Return the review in chat or Markdown by default, and provide the bundled single-sheet checklist when the user requests a reusable form. Use when the user provides a PDF or Word paper and asks for a full-paper format and writing-compliance audit; do not replace technical model correctness review.

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Review a Chinese mathematical-modeling problem-analysis section against the original problem, checking task classification, data reasoning, cross-problem linkage, model-choice rationale, validation planning, chapter boundaries, and the overall solution framework. Use for diagnosis, not automatic full rewriting.

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Generate a compliant Chinese mathematical-modeling problem-restatement chapter from a complete problem statement, or review a user's restatement against the original problem. Covers research background, problem review, and research overview; does not perform the separate problem-analysis chapter.

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Review the model establishment, numerical solution, result analysis, model validation, and sensitivity or robustness sections of a mathematical-modeling paper against the complete problem. Use for core-model-section diagnosis, not automatic full-paper scoring or unsupported recomputation.

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Verifies math-heavy code for algorithmic correctness and numerical stability. Use when reviewing scientific algorithms, ML models, or numerical code.

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Use when reviewing mathematical validity, evidence, reproducibility, figures or a submission draft.

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Plugin shim for the mathmodel-skill competition workflow. Use when Codex invokes this plugin for a CUMCM, MCM/ICM, or Diangong Cup modeling-contest task, including problem selection, modeling, robustness, contest-paper writing, compliance, or final submission review. Do not use for generic data analysis or non-competition paper review.

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Think and work like an expert Mathematical Modeler. Use when a task calls for Mathematical Modeler judgment. Reasons from nondimensionalization, conservation/positivity laws, and minimal-viable model structure through mechanistic ODE/PDE, stochastic, and agent-based formulations, profile-likelihood and Fisher-information identifiability, and Sobol/Morris sensitivity analysis, while treating sloppy unidentifiable parameters, structural model uncertainty, and out-of-regime extrapolation as first-class failure modes.

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Think and work like an expert Mathematical Statistician. Use when a task calls for Mathematical Statistician judgment. Reasons from LAN, empirical processes, and influence functions; proves M/Z-estimator limits, minimax rates (Fano/Le Cam/Assouad), and semiparametric efficiency while validating with ADEMP simulations and treating naive bootstrap, non-Donsker classes, and debiasing sparsity violations as first-class failure modes.

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Think and work like an expert Mathematical Analyst. Use when a task calls for Mathematical Analyst judgment. Reasons from function-space topology, convergence modes, and constant-dependent inequalities (Hölder, Sobolev, Gronwall) through compactness theorems (Rellich-Kondrachov, Banach-Alaoglu), Calderon-Zygmund and Schauder estimates, and Lax-Milgram while treating limit-integral swaps without dominated convergence, boundary-degenerating constants, weak-versus-classical regularity gaps, and concentration-compactness loss as first-class failure modes.

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Think and work like an expert Applied Mathematician. Use when a task calls for Applied Mathematician judgment. Reasons from formulation-first modeling, Buckingham scaling, and asymptotics (matched expansions, boundary layers) through FEM/FVM numerics (FEniCS, PETSc, LAPACK), Tikhonov inverse problems, and ASME/Sandia V&V while treating ill-posed inversion, stiffness, and numerical diffusion as first-class failure modes.

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Use when 高教社杯/CUMCM mathematical modeling papers need lightweight literature search, citation verification, method/background references, standards or policy sources, Chinese-English source routing, DOI/BibTeX checks, or claim-to-citation mapping without fabricated sources.

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Use when 高教社杯/CUMCM mathematical modeling work needs lightweight reusable paper assets, national-prize style paragraph templates, section controls, per-question code/plot/test scaffolds, evidence registries, paper fragments, reproduction scripts, or safe reuse of prior contest project structure without copying old problem-specific content.

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Use when 高教社杯/CUMCM/电工杯 mathematical modeling abstracts, keywords, highlights, first-page claims, or high-density summaries need drafting, revision, audit, or style diagnosis, especially when feedback mentions too many numbers, weak focus, process-listing, empty official prose, buzzwords, missing structure, weak keywords, unsupported values, or first-page claim verification.

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Use when solving CUMCM, MCM, ICM, or other mathematical modeling tasks that need contest problem intake, model selection, Python solving, figures, paper writing, quality audit, and packaged deliverables.

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Solve competition math problems (IMO, Putnam, USAMO, AIME) with adversarial verification that catches the errors self-verification misses. Activates when asked to 'solve this IMO problem', 'prove this olympiad inequality', 'verify this competition proof', 'find a counterexample', 'is this proof correct', or for any problem with 'IMO', 'Putnam', 'USAMO', 'olympiad', or 'competition math' in it. Uses pure reasoning (no tools) — then a fresh-context adversarial verifier attacks the proof using specific failure patterns, not generic 'check logic'. Outputs calibrated confidence — will say 'no confident solution' rather than bluff. If LaTeX is available, produces a clean PDF after verification passes.

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Explains DSP math concepts to developers who need the theory behind an algorithm. Use whenever the user asks how a signal-processing concept works, wants intuition behind a formula, or hits a math-shaped bug. Trigger on phrases like "how does a Fourier transform work", "explain z-transforms", "what is convolution", "why does my biquad ring", "what is windowing for", "what causes aliasing", or "how do I convert gain to dB". Also trigger when the user pastes DSP code and asks why it behaves a certain way.

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Verify and write proofs using the Acorn theorem prover for mathematical and cryptographic formalization. Use when working with Acorn proof files (.ac), verifying theorems, formalizing mathematical or cryptographic protocols, or writing proofs in the Acorn language. Triggers on: (1) Creating or editing .ac files, (2) Running acorn verify commands, (3) Formalizing math or crypto proofs, (4) Questions about Acorn syntax or standard library.

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Expert in visualizing and explaining braid theory, knot mathematics, and topological concepts for educational purposes. Use for creating interactive visualizations, explainer cards, step-wise animations, and translating abstract algebra into intuitive understanding. Activate on keywords: braid theory, knot visualization, σ notation, crossing diagrams, Yang-Baxter, topological education. NOT for general math tutoring, pure knot invariant computation, or non-educational knot theory research.

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