「mathematics」の検索結果

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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Expert-level discrete mathematics knowledge. Use when working with logic, set theory, combinatorics, graph theory, relations, functions, induction, recursion, boolean algebra, or discrete probability. Also use when the user mentions 'combinatorics', 'permutations', 'combinations', 'pigeonhole principle', 'inclusion-exclusion', 'generating functions', 'recurrence relations', 'graph theory', 'trees', 'logic', 'propositional calculus', or 'boolean algebra'.

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Performs exact symbolic mathematics with SymPy for algebra, calculus, equation solving, symbolic linear algebra, physics, and lambdify or LaTeX code generation. Use when a task needs symbolic results, explicit assumptions, or exact arithmetic; use NumPy or SciPy for purely numerical workloads.

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Discovers and evaluates scientific datasets, models, methodology posts, and Spaces through the Hugging Science catalog. Used when selecting scientific ML resources in biology, chemistry, genomics, materials, climate, physics, astronomy, medicine, mathematics, protein design, single-cell analysis, or PDE modeling, and when checking their actual datasets, Transformers, native-runtime, Inference Providers, or Gradio interfaces.

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Chinese K-12 core-literacy course design for a single OpenMAIC classroom. Use when a teacher asks for 中小学课程、核心素养、素养导向、2022 课标、真实情境、任务群、表现性评价, or wants a grade-and-subject lesson designed around authentic tasks rather than content delivery. Covers Chinese, mathematics, languages, science, humanities, technology, arts, PE and labor education across primary, junior-high and senior-high stages.

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Work on one hard mathematics problem in rounds: each round a judge writes a few self-contained questions, independent workers answer them, and the judge keeps a ledger of what is proved, refuted and open, until the judge concludes or the rounds run out, and then a proof.md says plainly what is and is not proved. A run takes hours and dozens of worker runs. Usage: /math-proof:siege [NAME=value settings] <the problem, stated in full, or the path of a file holding it>.

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Work on one hard mathematics problem in this session yourself, with no sub-agents: reason in stages, record each settled step in a notes file so that nothing written is lost if a response is cut off, and end with a self-contained proof.md. Usage: /math-proof:solo <the problem, stated in full, or the path of a file holding it>.

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Writes and reviews structured Lean 4 proofs and designs Lean libraries following Mathlib conventions. Use when proving theorems in Lean, formalizing mathematics or specifications in Lean 4, defining new types or definitions in a Lean library, reviewing Lean proofs for readability and maintainability, refactoring long tactic proofs into lemmas, filling in sorry placeholders in a Lean development, setting up CI or linters for a Lean project, diagnosing slow proofs or maxHeartbeats timeouts, or writing custom tactics, macros, or linters.

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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.

日本語の概要は準備中です。原文の説明を表示しています。

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.

日本語の概要は準備中です。原文の説明を表示しています。

Expert in formal logic, model theory, computability, and foundations of mathematics

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Master discrete mathematics, logic, formal proofs, and computational thinking. Build the mathematical foundation for all computer science.

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Search arXiv physics, math, and computer science preprints using natural language queries. Powered by Valyu semantic search.

日本語の概要は準備中です。原文の説明を表示しています。

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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Review academic papers for correctness, quality, and novelty using OpenJudge's multi-stage pipeline. Supports PDF files and LaTeX source packages (.tar.gz/.zip). Covers 10 disciplines: cs, medicine, physics, chemistry, biology, economics, psychology, environmental_science, mathematics, social_sciences. Use when the user asks to review, evaluate, critique, or assess a research paper, check references, or verify a BibTeX file.

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Design a variation theory task using contrast, separation, and fusion to teach critical features of a concept. Use when students confuse similar concepts or fail to discern key distinctions.

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Design a Concrete-Pictorial-Abstract learning sequence for a mathematical concept using manipulatives. Use when teaching maths through Singapore method or when students struggle with abstraction.

日本語の概要は準備中です。原文の説明を表示しています。

AMM liquidity provision mathematics including constant-product, concentrated liquidity, price impact, and LP share calculations

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Search arXiv preprint repository for papers in physics, mathematics, computer science, quantitative biology, and related fields

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Applies the Neoplatonic and mathematical reasoning of Hypatia of Alexandria. Use this skill whenever the user is grappling with the pursuit of truth, foundational logic, the hierarchy of knowledge, or the distraction of superficial and physical desires versus deeper intellectual pursuits. Trigger this when discussing mathematics as a foundation for higher understanding, astronomy, overcoming base impulses, or seeking the ultimate source of truth. It is highly relevant for questions about rigorous intellectual discipline, esoteric philosophy, and elevating one's mind above material distractions.

日本語の概要は準備中です。原文の説明を表示しています。

Design a variation theory task using contrast, separation, and fusion to teach critical features of a concept. Use when students confuse similar concepts or fail to discern key distinctions.

日本語の概要は準備中です。原文の説明を表示しています。

Design a Concrete-Pictorial-Abstract learning sequence for a mathematical concept using manipulatives. Use when teaching maths through Singapore method or when students struggle with abstraction.

日本語の概要は準備中です。原文の説明を表示しています。

Conjecture generation, sequence analysis, and experimental mathematics for mathematical discovery. Covers sequence analysis (OEIS lookups, recurrence relations, generating functions), pattern detection methods (finite differences, ratio analysis, modular patterns), conjecture generation workflow, classical integer sequences (Fibonacci, Catalan, partition numbers, Bernoulli numbers), combinatorial identities, the probabilistic method (Erdos, expected value arguments, Lovasz Local Lemma), AI-assisted discovery (FunSearch, Ramanujan Machine), and confidence calibration with cautionary tales (Mertens conjecture, Polya conjecture). Use when discovering patterns, analyzing sequences, generating conjectures, or working with combinatorial identities.

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Calculus, series, numerical methods, and optimization for computational mathematics. Covers limits (epsilon-delta, L'Hopital, squeeze theorem), derivatives (rules, optimization, related rates), integrals (Riemann sums, Fundamental Theorem of Calculus, integration techniques), series (convergence tests, Taylor and Maclaurin expansions), differential equations (separable, linear, exact), numerical methods (Newton-Raphson, Euler method, Simpson's rule), and computational pitfalls (floating-point arithmetic, catastrophic cancellation, numerical stability). Use when computing derivatives, integrals, limits, series, solving differential equations, or analyzing numerical accuracy.

日本語の概要は準備中です。原文の説明を表示しています。