'math' 검색 결과

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/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 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 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 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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Performs numerical and symbolic mathematics using NumPy, SciPy, SymPy, and mpmath. Use when the user needs linear algebra, arrays, optimization, integration, ODEs, symbolic expressions, equation solving, or arbitrary-precision arithmetic.

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Use this skill when working with symbolic mathematics in Python. This skill should be used for symbolic computation tasks including solving equations algebraically, performing calculus operations (derivatives, integrals, limits), manipulating algebraic expressions, working with matrices symbolically, physics calculations, number theory problems, geometry computations, and generating executable code from mathematical expressions. Apply this skill when the user needs exact symbolic results rather than numerical approximations, or when working with mathematical formulas that contain variables and parameters.

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Create mathematical animations in ManimGL using Python, with guidance for equations, graphs, 3D scenes, and camera movement. Includes interactive development workflows, examples, and templates for testing changes and rendering scenes to video.

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• Animate equations and mathematical derivations
• Visualize functions and graphs
• Build 3D scenes with camera movement

Use SymPy to simplify expressions, solve equations, and calculate derivatives, integrals, and matrices with exact symbolic results. Specify assumptions, verify solutions, and turn mathematical expressions into numerical functions, source code, or LaTeX output.

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• Solving equations and checking their solutions
• Calculating symbolic derivatives, integrals, and limits
• Finding matrix eigenvalues with exact arithmetic

Prepare GRPO reinforcement learning configurations for tasks with programmatically checkable answers, such as math, code, and structured output. Design and inspect reward functions, then select training variants when runs show instability or exploit flaws in scoring.

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• Preparing GRPO training for tasks with automatic correctness checks
• Designing rewards for output format and correctness
• Inspecting reward scores before training

Convert Markdown documents into HTML for web pages, documentation, or previews. Covers single files, batch conversion, and static site workflows, with guidance on tables, code blocks, math rendering, and handling untrusted content safely.

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• Convert Markdown documentation into HTML
• Batch-convert multiple .md files
• Build static sites from Markdown

Build three-tier bookings forecasts from sales opportunities and historical conversion data. Project recurring revenue by customer cohort, assess the reliability of each sales stage, and present forecast numbers alongside their assumptions.

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• Preparing a quarterly bookings forecast for the board
• Projecting annual recurring revenue for the next 4–8 quarters
• Finding customer cohorts with declining revenue retention

Add formatting, arithmetic, text processing, and translated labels to json-render specifications. This skill explains ready-made directives, or value-processing rules, how to combine them, and how to define custom rules for application-specific transformations.

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• Format dates, currencies, and percentages
• Calculate totals from prices and quantities
• Shorten text and join lists of tags

Develop mathematical proofs for machine learning and AI theory by checking assumptions, intermediate results, and edge cases. Produce a complete proof, a corrected claim with its proof, or a report explaining the unresolved gap.

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• Draft a proof of a theorem or lemma
• Expand a proof sketch into justified steps
• Check for hidden assumptions and counterexamples

Shape broad mathematical interests into precise research questions. Search prior work on definitions and theorems, record traceable sources, map supporting and conflicting evidence, and identify gaps that could lead to testable conjectures.

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• Tracing a theorem’s variants and related work
• Checking prior work on an integer sequence
• Defining search terms and the scope of a research question

Combine specialized language models without retraining using mergekit. The skill explains how to choose merging methods, configure each model’s contribution, compare resulting variants, and prepare a merged model for evaluation and deployment.

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• Combine math, coding, and conversation capabilities
• Compare model variants with different merge weights
• Choose a method for merging several models

Plan advertising budget allocation, bidding, and spending pace using goals, financial constraints, and evidence about additional spending returns. Compare options and produce a plan with amounts, timing, owners, success measures, and triggers for reversing changes.

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• Reviewing budget allocation across advertising campaigns
• Deciding whether to increase or reduce advertising spend
• Reviewing bidding targets and spending pace

Calculate advertising costs, revenue relative to ad spend, break-even targets, and budget forecasts. The skill makes inputs and formulas explicit, checks inconsistent data, and compares base, downside, and upside scenarios when uncertainty affects the decision.

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• Calculating advertising acquisition costs and returns
• Setting break-even targets for advertising
• Comparing budget and revenue forecasts across scenarios

Turn mathematical modeling reports into DrawIO diagrams showing solution steps, model structures, and data processing flows. Produce editable source files, export PDFs for papers when DrawIO is available, and record diagram choices and export results.

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• Illustrate the overall approach in a modeling paper
• Draw solution flows for individual subproblems
• Show model structure and variable relationships

Implements mathematical models from a design report as reproducible code, runs calculations, and checks results. It records methods and validation findings in a results report and produces data-based PDF charts for papers.

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• Implementing models from a modeling report
• Checking constraints and evaluating prediction errors
• Creating PDF charts from computed results