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Solve problems in viscoelasticity, plasticity, high-temperature creep, fracture and fatigue, linking atomistic behavior of crystalline solids to their continuum mechanical response.
Prices and markets allocate scarce resources: model supply and demand, consumer choice, production and costs, competitive firms, monopoly and oligopoly, and capital markets.
Learn microeconomic theory and its empirical testing: consumer choice, demand functions, general equilibrium, comparative advantage, externalities, risk and signaling, applied to policy debates like the minimum wage.
Learn how point defects govern diffusion in solids: microscopic diffusion mechanisms, chemical strengthening of glass by ion exchange, and charge carrier concentrations via the Brouwer approximation.
Learn how phase transformation kinetics shape microstructure: crystal nucleation, vapor-liquid-solid nanowire growth, precipitate growth from a binary solution, and dendritic growth from a melt.
Apply statistical mechanics to materials phenomena: derive the entropy of a solid solution quantum mechanically, explain heat capacity trends, and use the canonical distribution for Curie's law.
Predict surface energy along crystalline planes, see how it is exploited in nanoparticle synthesis, and explain Ostwald ripening in solid solutions.
Explore philosophy of mind: weigh arguments for and against machine thinking, compare theories of mental states and physical states, and confront the hard problem of consciousness.
Compare DNA replication in prokaryotes and eukaryotes, trace enzymatic repair and damage-tolerance mechanisms, infer function from protein structures, and design and interpret replication experiments.
Compare transcription in prokaryotes and eukaryotes, work through mechanisms of transposition, infer protein function from structure, and design experiments to interpret molecular data.
Compare translation in bacteria and eukaryotes, examine protein–RNA interactions and RNA turnover mechanisms, and design experiments to interpret data from translation and RNA processing studies.
Learn to reason rigorously about ethical questions, exploring well-being, objectivity, key historical figures and approaches, and what we owe to others.
Extend the derivative to higher dimensions: visualize functions with level curves and surfaces, compute partial derivatives, directional derivatives and gradients, and optimize under constraints.
Learn how step-growth and chain-growth polymerizations work, and how molecular weight, dispersity, topology, temperature and solvent choice control polymer properties for engineering materials.
Prove Cantor's Theorem, the Banach-Tarski Theorem and Gödel's Theorem, and reason rigorously about infinity and paradoxes where standard mathematical tools break down.
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