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Advanced Physics I: Orders of Magnitude

Explores the triumph of determinism in modern mechanics and the methodology of scientific development, with practical exercises on estimating surgical mask usage and analyzing atomic bomb energy.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Integral on S-up

Covers the properties of the integral on S-up, including linearity and monotony.

Magnetic Order: Symmetry Breaking

Covers the transition from order to disorder and the significance of scalar fields in breaking the electroweak symmetry.

Notation in Multivariable Calculus

Reviews the notation used in multivariable calculus, emphasizing accurate translation between different forms of integrals.

Residue Theorem: Calculating Integrals on Closed Curves

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Path Integral for Harmonic Oscillator

Covers the path integral for the harmonic oscillator, including classical action and fluctuation determinant.

Lorentz-Minkowski Spacetime

Covers Lorentz-Minkowski spacetime, speed of light interpretation, isometries, and special relativity principles.

Quantum Fluids: Cross Section & Lifetime

Covers the concepts of cross section and lifetime in quantum fluids, focusing on transition and differential probabilities.

Quadratic Forms and Symmetric Bilinear Forms

Explores quadratic forms, symmetric bilinear forms, and their properties.

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Matricizations and Alternating Least Squares

Covers matricizations, ALS method, and tensor decomposition, emphasizing the alignment of fibers in matrices.

Laws of Transformation of Velocities and Accelerations

Covers the laws of transformation of speeds and accelerations, including the rotation of points and dynamic movement principles.

Classification of Quadratic Forms

Explores the classification of quadratic forms based on eigenvalues and orthogonal diagonalization of symmetric matrices.

Linear Quadratic (LQ) Optimal Control: Proof of Theorem

Covers the proof of the recursive formula for the optimal gains in LQ control over a finite horizon.

Asymptotic States and S-matrix: Operators

Explores asymptotic states, S-matrix, and operators in quantum field theory, emphasizing the role of discrete symmetries and complete sets of states.

Particle Detection: Stable Particles and Lifetime

Explores the detection of stable particles in particle physics experiments, covering observed and unobserved particles, their lifetimes, and the impact of Lorentz boost.

Dynamics on Homogeneous Spaces and Interactions with Number Theory

Delves into Oppenheim's conjecture on quadratic forms and their connection to number theory.