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Equilibrium in 3D: System Isolation and Constraints

Covers the equilibrium conditions in 3D, system isolation, free-body diagrams, and constraints.

A Conjecture of Erdös: Proof by Moreira, Richter and Robertson

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

Symmetry in Modern Geometry

Delves into modern geometry, covering transformations, isometries, and symmetries.

Dynamical Approaches to Spectral Theory of Operators

Explores ergodic theory, spectral operators, and almost periodic factors in dynamical systems and spectral theory.

Scaling & Renormalization in Statistical Mechanics

Explores scaling and renormalization in statistical mechanics, emphasizing critical points and invariant properties.

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.

Isometries & Orientation in Modern Geometry

Explores true angle magnitude, reflections, isometries, and symmetries in modern geometry, with practical CAD applications.

Introduction to Quantum Chaos

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Linear Maps and the Duality Principle in Mathematics

Covers the duality principle in linear algebra and its implications in mathematics.

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Geometric Transformations: Translation and Homothety

Explores geometric transformations like translation and homothety in the plane.

Determinantal Point Processes and Extrapolation

Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

Molecular dynamics under constraints

Explores molecular dynamics simulations under holonomic constraints, focusing on numerical integration and algorithm formulation.

Isometries in Euclidean Spaces

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.

Stochastic Block Model

Covers the Stochastic Block Model and its application in community detection, exploring its mathematical formulation and challenges.

Isometries and Orthonormal Bases

Discusses isometries and orthonormal bases in mathematics.

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Analytical Mechanics: Lagrange Formalism

Covers the limitations of Lagrange formalism and the transition to Hamiltonian formalism for dynamic variables.

Translations and Homotheties

Covers translations, homotheties, and geometric transformations using vectors and matrices.

Dynamical Systems: Maps and Stability

Explores one-dimensional maps, periodic solutions, and bifurcations in dynamical systems.