code2video/json_files/long_video_topics_list.json

[
  "Euler's Formula and e^(πi) = -1",
  "Limits, L'Hôpital's rule, and epsilon-delta definitions",
  "Proof of Snell's law",
  "Space-filling curves and the relationship between infinite and finite mathematics",
  "The inscribed square or rectangle problem in topology",
  "Planar graph duality and Euler's Characteristic Formula",
  "The Borsuk-Ulam theorem and stolen necklace problem",
  "Space-filling curves",
  "Fractal dimension",
  "Linear transformations and matrices",
  "Cross products and their relationship to geometric intuition and linear transformations",
  "Geometric interpretation of non-square matrices as transformations between dimensions",
  "Eigenvectors, eigenvalues, and eigenbasis",
  "Change of basis",
  "Basics of linear algebra and vectors",
  "Dot products and duality",
  "Three-dimensional linear transformations",
  "Geometric interpretation of linear systems, inverse matrices, column space, and null space",
  "Abstract vector spaces",
  "Superposition and quantum states in quantum mechanics",
  "Matrix multiplication as composition of linear transformations",
  "Geometric intuition in linear algebra",
  "The determinant",
  "Eigenvalues of 2x2 matrices",
  "Span, linear combinations, linear dependence, and bases",
  "History and definition of π",
  "Euler's formula and e^{pi i} = -1",
  "Riemann zeta function",
  "Numerical algorithms for solving 2D equations, winding numbers, and domain coloring",
  "Uncertainty Principle in the Context of Fourier Transforms",
  "Infinite sums, convergence and divergence, 2-adic metric in mathematics",
  "Holomorphic dynamics and iterated complex functions",
  "Basel problem and its geometric proof",
  "Origin of π in the normal distribution and the Gaussian integral",
  "Pure Fourier series",
  "Topology",
  "Prime patterns, pi approximations, and Dirichlet's theorem",
  "Alternate notation for powers, logarithms, and roots",
  "Interconnections in number theory: π, primes, complex numbers, and prime regularities",
  "Newton's method and Newton's fractal in root-finding",
  "Euler's formula e^{iπ}",
  "Fourier Transform",
  "Fourier series and their connection to the heat equation and circular representations",
  "Central Limit Theorem",
  "Bayes' theorem and the geometry of changing probabilistic beliefs",
  "Information theory and entropy in solving Wordle",
  "Binomial distributions",
  "256-bit hash security",
  "Likelihood Ratios and Bayes Factors in Medical Testing",
  "Bayes' theorem and independence in probability",
  "Sum of normal distributions, Gaussian + Gaussian = Gaussian",
  "Adding Random Variables and Convolution in Probability",
  "Probability density functions",
  "Intuition for e^(πi) = -1 using group theory and Euler's formula",
  "Exponential growth and logistic growth",
  "SIR models and epidemic simulation",
  "DP-3T algorithm for contact tracing",
  "Attention mechanism in transformers and large language models",
  "Neural networks: structure, neurons, layers, underlying mathematics",
  "How multilayer perceptrons in transformers may store facts",
  "Neural network learning and intuitive backpropagation",
  "Discrete convolutions and their applications",
  "Cost functions and gradient descent in neural network training",
  "Large Language Models and Transformers in Deep Learning",
  "Backpropagation calculus",
  "Diffusion models, CLIP, and the mathematics of text-to-image generation in AI",
  "Mathematical principles of cryptocurrencies and Bitcoin",
  "Qubits, state vectors, and Grover's algorithm in quantum computing",
  "Error correction codes and Hamming codes",
  "Hamming error correction codes",
  "Large Language Models",
  "Ternary counting, constrained Towers of Hanoi, and Sierpinski triangle graph traversal",
  "High-dimensional spheres",
  "Grover's algorithm in quantum computing",
  "The Brachistochrone Problem",
  "Binary counting and its application to the Towers of Hanoi puzzle",
  "Criteria for effective mathematical explanation",
  "Optimal Wordle starting strategies and algorithmic analysis",
  "Generating functions and complex numbers in combinatorial counting",
  "Impossible chessboard puzzle and information theory",
  "Music and Measure Theory",
  "Moser's circle problem",
  "Putnam mathematics competition problem-solving",
  "Geometry puzzles involving dimensional shifts",
  "Dandelin spheres and conic sections",
  "Windmill problem",
  "Cross products in 2D and 3D",
  "Pythagorean triples and their connection to complex numbers",
  "Wallis product for pi",
  "Sphere surface area and its relationship to projected shadow",
  "How wiggling charges give rise to light and the barber pole effect",
  "Fundamental constants and mathematical structure in turbulence",
  "Refraction and the behavior of light in different media",
  "Block collision problem and its relation to calculating digits of pi",
  "Origin and color dependence of the index of refraction",
  "The physics of pi arising from colliding blocks",
  "Barber pole effect with polarized light in sugar water",
  "Unexpected answer to a counting puzzle involving collisions and pi",
  "Principles of Holography and Diffraction",
  "Partial differential equations",
  "Boundary conditions and Fourier series in solving the heat equation",
  "Ordinary Differential Equations",
  "Matrix exponentials",
  "The essence of calculus",
  "Implicit differentiation",
  "Borwein integrals and their surprising patterns",
  "Higher order derivatives",
  "Transformational view of derivatives",
  "Instantaneous rate of change and the derivative",
  "Chain rule and product rule in calculus",
  "Divergence and curl in vector calculus",
  "Taylor polynomials and Taylor series",
  "Relationship between integrals and derivatives",
  "Derivative formulas and geometric intuition",
  "Euler's number e and exponential functions in calculus",
  "Cramer's rule explained geometrically",
  "Integration, the Fundamental Theorem of Calculus, and the inverse relationship between integrals and derivatives"
]