Expert-level abstract algebra knowledge. Use when working with groups, rings, fields, modules, Galois theory, representation theory, or algebraic structures. Also use when the user mentions 'group', 'ring', 'field', 'homomorphism', 'isomorphism', 'normal subgroup', 'quotient group', 'Sylow theorem', 'Galois theory', 'polynomial ring', 'ideal', 'module', 'vector space', or 'representation theory'.

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Expert-level acoustics knowledge. Use when working with sound waves, acoustic propagation, resonance, standing waves, Doppler effect, room acoustics, ultrasound, noise control, musical acoustics, or architectural acoustics. Also use when the user mentions 'sound wave', 'decibel', 'frequency', 'resonance', 'standing wave', 'Doppler effect', 'acoustic impedance', 'reverberation', 'ultrasound', 'noise control', 'harmonics', or 'sound intensity'.

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Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.

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Expert-level air quality engineering covering pollutant sources, atmospheric dispersion, air quality standards, emission controls, and air quality modeling.

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Expert-level aircraft structures covering structural design philosophy, wing and fuselage analysis, fatigue and damage tolerance, composite structures, and certification.

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Expert-level algorithms and complexity theory covering sorting, searching, graph algorithms, dynamic programming, greedy algorithms, NP-completeness, and algorithm design paradigms.

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