Topics: first-order login, logical seeing, number, number structures, points, lines, structure of real numbers, set theory, relations, structures, geometry, definable elements, definable constants, minimal structure, order-minimal structures, definable sets, complex numbers, first-order properties, symmetries, logical visibility

Topics: Communication, Fourier series, Fourier transform, signal symmetry, modulation, amplitude modulation, amplitude modulation large carrier

Topics: Crystal Structures, Unit cells, crystal systems, Symmetry, Lattice planes, Miller indices, carbon graphite, inorganic chemistry, crystalline solids

Topics: Materials science, Metallurgy, Metallography, Crystal physics, Neumann’s symmetry principle, Equilibrium thermodynamics, phase diagrams, Gibbs phase rule

Topics: Gas laws, Gas, Boyle's law, Charles law, Gay-Lussac's law, Dalton's law, general gas equation, ideal gas, Avogardo's law, kinetic theory, Boltzmann distribution, intermolecular distribution, Vander Waal's equation, viscosity, dilute solution, molarity, mole fraction, colligative properties, osmotic pressure, thermodynamics, internal energy, heat change, heat capacity, isothermal process, phase change, adiabatic process, adiabatic reversible expansion, thermodynamic equilibrium, chemical equilibrium, thermochemistry, heat of reaction, heat of formation, heat of combustion, bond energy, chemical equilibrium, dynamic equilibrium, law of mass action, solubility, chemical kinetics, chemical reaction, reaction rate, rate laws, differential rate laws, integrated rate laws, activation energy, action complex, activated complex, ionic equilibrium, electrolytes, acid, bases, Bronsted-Lowry theory, Lewis theory, dissociation constant, hydrolysis, buffer solution, buffer capacity, crystals, crystalline phases, polymorphism, amorphous, crystal growth, nucleation, crystal systems, cubic structures, mirror symmetry

Topics: Calculus, linear coordinate systems, absolute value, inequalities, rectangular coordinate systems, lines, circles, parabolas, ellipses, hyperbolas, conic sections, functions, limits, continuity, continuous function, derivative, delta notation, chain rule, inverse functions, implicit differentiation, tangent lines, normal lines, critical numbers, relative maximum relative minimum, cure sketching, concavity, symmetry, points of inflection, vertical asymptotes, trigonometry, trigonometric functions, inverse trigonometric functions, rectilinear motion, circular motion, differentials, Newton's method, antiderivatives, definite integral, sigma notation, natural logarithm, exponential functions, logarithmic functions, L'hopital's rule, exponential growth, decay, half-life, integration by parts, trigonometric integrands, trigonometric substitutions, improper integrals, parametric equations, curvature, plane vectors, curvilinear motion, polar coordinates, infinite sequences, infinite series, geometric series, power series, uniform convergence, Taylor's series, Maclaurin series, partial derivatives, total differential, differentiability, chain rules, space vectors, directional derivatives, vector differentiation, vector integration, double integrals, iterated integrals, centroids, triple integrals, Separable Differential Equations, Homogeneous Functions, Integrating Factors, Second-Order Equations

Topics: organic molecule, stereochemistry, alkyl halide, alkene, alkyne, alcohol, infrared spectroscopy, mass spectrometry, nuclear magnetic resonance spectroscopy, ether, epoxide, thioether, orbital symmetry, ultraviolet spectroscopy, aromatic compound, ketone, aldehyde, amine, carboxylic acid, carbohydrate, nucleic acid, amino acid, peptide, protein, lipid, synthetic polymer

Topics: Echinoderm Symmetry, Asteroidea, sea stars, Ophiuroidea, brittle stars, Echinoidea, sea urchins, Holothuroidea, sea cucumbers, Crinoidea, sea feathers, Water Vascular System, Tube Feet, Hemal Canal, Protostome, Deuterostome, Echinoderm Development, Asteroidea Anatomy, Echinoid Anatomy, Aristotle’s Lantern, Holothuroidea Anatomy, Crinoid Anatomy

Topics: Enantiomers, Chirality, Asymmetric Carbon, Stereocenters, Symmetry

Topics: Properties of gases, mixtures, chemical equilibrium, quantum theory, atomic structure, atomic spectra, molecular structure, molecular symmetry, molecular spectroscopy, magnetic resonance, statistical thermodynamics, molecular interactions, solids, chemical kinetics, reaction dynamics