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Explains Pareto efficiency, social planner's problem, and optimal consumption allocation in complete markets.

Explores utility functions and risk management in asset pricing under uncertainty.

Covers the structure theorem for state-space representations and companion forms.

Covers advanced topics in Quantum Field Theory, including quantization of fields and the organization of fields into irreducible representations.

Explores asset pricing models, risk-free assets, portfolio choice, and stochastic discount factors in PhD classes.

Explores the synthesis of spinning particles and proper vertices for 2-point functions in quantum field theory.

Explores expected utility theory, risk-aversion, utility functions, and decision-making under uncertainty.

Introduces real numbers, including equations like x²=2 with no rational solutions.

Explores Ward identities in Quantum Field Theory, emphasizing classical and quantum cases, symmetry generators, and perturbation theory.

Covers the concept of party wavefunctions and the reduction formulae.

Explores equilibrium and Pareto optimality in asset pricing theory, emphasizing market equilibrium conditions and welfare theorems.

Explores Pareto efficiency, social welfare, and asset pricing optimization in complete and incomplete markets.

Presents a structured approach to discussing key concepts and emphasizes the importance of each point for comprehensive understanding.

Covers the quantization of spin in Quantum Field Theory, focusing on induced representations and unitary irreps.

Explores turning points, quantization, and tunneling in quantum mechanics.

Covers wave functions, De Broglie wavelength, and quantization in quantum mechanics.

Covers the organization of real numbers, axioms, and bounds, including infimum and supremum.

Covers the basics of group theory, including sets, applications, and examples like permutations and rotations.

Explains the representation for evolution in quantum mechanics and the application of path integrals.

Explores dynamic programming for optimizing portfolio choices and asset pricing theory.