Claude Skills by jeffreytse

Use when updating beliefs from evidence, estimating probabilities under uncertainty, or making decisions where prior knowledge and new data must be combined

Use when a curve is a circle, ellipse, parabola, or hyperbola — classifying a general second-degree equation into standard form and applying its focus, directrix, and eccentricity properties to a physical problem, such as orbital mechanics, parabolic reflector/antenna design, or optical mirror focusing.

Use when modeling or solving differential equations — classifying ODE/PDE type, selecting analytical or numerical solution methods, validating solutions, and interpreting the physical or mathematical meaning of the result.

Use when analyzing networks, relationships, or connectivity problems using graph theory — including graph representation, traversal algorithms, shortest path, minimum spanning tree, centrality measures, and community detection.

Use when deciding what kind of evidence a question actually requires — before running an experiment, trusting an observational correlation, or reasoning about "what would have happened if" — by classifying the question as associational (what is?), interventional (what if I do X?), or counterfactual (what if I had done X instead?), since each rung requires a different type of evidence or model and no amount of data at a lower rung can answer a question posed at a higher one.

Use when solving systems of linear equations, decomposing matrices, analyzing transformations, or working with eigenvalues and eigenvectors in applied mathematics, data science, physics, or engineering contexts.

Use when drawing a conclusion, trend, or explanation from a small number of observations — a short streak, a handful of test results, a few data points on a dashboard — before treating the pattern as reliable, because small samples produce extreme, memorable-looking results by chance far more often than intuition expects, and apparent reversion afterward is a statistical artifact, not a new causal effect.

Use when reporting statistical estimates that require quantified uncertainty bounds for scientific, clinical, or policy decision-making

Use when working with probability distributions — identifying the correct distribution for a phenomenon, computing probabilities and quantiles, fitting distributions to data, and checking distributional assumptions statistically.

Use when designing a numerical simulation — including Monte Carlo, finite difference, finite element, or agent-based models — specifying convergence criteria, uncertainty quantification, validation strategy, and computational resource requirements.

Use when formulating and solving an optimization problem — defining the objective function, constraints, variable types, and selecting an appropriate solver for linear, nonlinear, integer, or stochastic programming.

Use when selecting an approach for constructing a mathematical proof or verifying a conjecture

Use when solving mechanics, fluid dynamics, or electromagnetism problems by applying conservation of energy, momentum, angular momentum, or charge — identifying the system boundary, the conserved quantity, and the conditions under which conservation applies.

Use when deriving relationships between physical quantities, checking equations for consistency, or scaling physical models to different sizes or conditions

Use when solving electromagnetic field problems — the field of a charge distribution, the field of a current-carrying conductor, induced EMF from changing flux, or displacement current in a capacitor — by matching the problem's symmetry to the correct form of Gauss's law, Faraday's law, or the Ampère-Maxwell law, rather than attempting a direct force calculation on every source charge or current element.

Use when calculating how measurement uncertainties propagate through mathematical operations — computing combined uncertainty for sums, products, powers, and general functions using partial derivative methods or Monte Carlo propagation.

Use when reporting physical measurements that require quantified uncertainty estimates for scientific or metrological purposes

Use when analyzing the thermodynamic efficiency of heat engines, refrigerators, power cycles, or chemical processes — applying the first and second laws of thermodynamics, Carnot efficiency, entropy analysis, and exergy to identify losses and optimization targets.

Use when designing an experimental circuit — applying Ohm's law, Kirchhoff's laws, Thevenin/Norton equivalents, and RC/RL/RLC transient analysis to select components, calculate expected behavior, and plan measurements safely.

Use when planning a physics experiment that requires controlling variables to isolate causal relationships between physical quantities

Use when designing a physics experiment or laboratory investigation requiring control of variables and uncertainty quantification

Use when designing an optical system — including lenses, mirrors, apertures, and detectors — applying geometric optics (ray tracing), the thin lens equation, aberration analysis, and diffraction limits to achieve target imaging performance.

Use when a coach wants to build a team or individual athlete culture that treats setbacks as learning opportunities, effort as controllable, and improvement as the primary measure of success — to prevent fixed-mindset responses to failure and adversity.

Use when a coach needs to have a conversation with an athlete who is resistant to change, low on motivation, or ambivalent about committing to a training or behavioral goal — to build intrinsic motivation rather than imposing external direction.

Use when an athlete or coach needs to build a reliable, repeatable preparation sequence that consistently produces optimal arousal and focus before competition or high-stakes performance

Use when a coach, club, or national federation needs to structure a long-term plan for developing athletes from youth through elite levels — matching training content, competition volume, and specialization timing to each developmental stage.

Use when a coach needs to structure the days and weeks leading into a major competition — covering the taper, logistics, mental preparation, and pre-competition routine to ensure athletes arrive physically fresh, tactically confident, and mentally ready.

Use when a coach needs to build a consistent approach to giving athletes skill-improvement feedback — covering timing, specificity, frequency, and ratio of positive-to-corrective messages to accelerate learning without damaging confidence.

Use when a coach or team leader needs to build or repair team unity, trust, and collective identity to improve both performance and athlete satisfaction

Use when a coach needs to systematically evaluate an athlete's performance, provide structured feedback, and set goals for the next training phase

Use when a coach needs to structure and deliver an effective group training session — planning objectives, time allocation, transitions, and coaching interventions to maximize athlete development and engagement within a fixed time window.

Use when a coach needs to use recorded footage to identify tactical patterns, technical errors, or opponent tendencies and translate them into actionable coaching points

Use when an athlete needs a hydration strategy for training or competition — to prevent dehydration-induced performance decline, avoid overhydration risk, and maintain electrolyte balance across varying sweat rates and environmental conditions.

Use when an athlete is considering adding dietary supplements — to identify those with strong performance evidence, evaluate risk of contamination or banned substance presence, and avoid wasting money on ineffective or harmful products.

Use when an athlete or sports dietitian needs to calculate individualized daily protein, carbohydrate, and fat targets to support their sport demands, body composition goals, and training phase.

Use when an athlete needs a nutrition plan for the 24-48 hours and the final hours before a competition — to maximize glycogen stores, avoid GI distress, and arrive at the start line fueled and comfortable.

Use when an athlete needs to optimize post-exercise nutrition to accelerate glycogen resynthesis, stimulate muscle protein synthesis, and restore fluid and electrolyte balance — particularly when recovery between sessions is <24 hours.

Use when an athlete or sports dietitian needs to align nutritional intake with training phases, competition schedule, and recovery demands to maximize performance and body composition outcomes

Use when an athlete in a weight-class sport (wrestling, boxing, MMA, rowing, judo, weightlifting) needs a structured plan to reach competition weight safely, with the most effective rehydration and refueling strategy to restore performance before competing.

Use when an athlete needs to accelerate post-training recovery using evidence-based heat, cold, or contrast therapy protocols

Use when an athlete needs to improve sleep quality and duration to accelerate recovery, enhance cognitive performance, and reduce injury risk — including strategies for sleep extension, jet lag, pre-competition insomnia, and travel disruption.

Use when an athlete wants to use foam rolling, massage, or myofascial release techniques to reduce post-exercise muscle soreness, improve ROM, or prepare tissue for training — with appropriate technique and timing for each method.

Use when a coach or athlete needs to objectively measure an athlete's recovery status before a training session — to decide whether to train as planned, reduce load, or rest based on physiological and subjective readiness indicators.

Use when an athlete needs a structured low-intensity recovery session between hard training blocks to accelerate adaptation without adding fatigue

Use when a coach, strength trainer, or sports medicine professional needs to implement a structured warm-up and movement program that reduces injury incidence in athletes

Use when an athlete needs strategies to mentally recover from a poor performance, competitive setback, significant loss, or period of burnout — to prevent rumination from compounding into ongoing performance anxiety or identity crisis.

Use when an athlete is recovering from an injury and needs a structured, criteria-based progression back to full training and competition — to minimize reinjury risk without unnecessarily prolonging absence.

Use when an endurance or strength athlete needs to peak for a major competition — reducing training volume systematically over 1-3 weeks to dissipate fatigue while preserving the fitness built during the training block.

Use when athletes need to travel across time zones or endure long travel days for competition — to minimize jet lag, manage sleep disruption, and arrive physically and mentally prepared to perform.

Use when a coach needs to make tactical, personnel, or strategic adjustments during a competition — at halftime, between periods, or during play stoppages — to respond to what the opponent or the game is revealing.