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id ▼ slug title subtitle preview image video category tags date status confidence importance state
1 cauchy-riemann-equations Understanding the Cauchy-Riemann Equations A deep dive into the conditions for complex differentiability. Explore how the Cauchy-Riemann equations govern holomorphic functions in the complex plane. https://i.ytimg.com/vi/DxREm3s1scA/maxresdefault.jpg https://cdn.krisyotam.com/videos/cauchy-riemann.mp4 Complex Analysis ["holomorphic functions", "CR equations", "complex variables"] 2025-04-30 Finished certain 7 active
2 galois-theory-fundamentals Exploring Galois Theory Fundamentals Foundations of the symmetry groups underlying polynomial solvability. An introduction to Galois groups and their role in solving polynomial equations. https://i.ytimg.com/vi/DxREm3s1scA/maxresdefault.jpg https://cdn.krisyotam.com/videos/galois-theory.mp4 Algebra ["field theory", "group theory", "symmetry"] 2025-04-30 Finished highly likely 6 active
3 riemann-hypothesis-explained The Riemann Hypothesis Explained Unpacking the famous unsolved conjecture in analytic number theory. A survey of the Riemann zeta function and its implications for primes. https://i.ytimg.com/vi/DxREm3s1scA/maxresdefault.jpg https://cdn.krisyotam.com/videos/riemann-hypothesis.mp4 Number Theory ["zeta function", "prime distribution", "unsolved problems"] 2025-04-30 In Progress possible 9 active
4 intro-topological-manifolds An Intro to Topological Manifolds Exploring the local Euclidean nature of abstract spaces. Learn what it means for a space to be a manifold and why it matters. https://i.ytimg.com/vi/DxREm3s1scA/maxresdefault.jpg https://cdn.krisyotam.com/videos/topological-manifolds.mp4 Topology ["manifolds", "topological spaces", "geometric structures"] 2025-04-30 Finished likely 5 active
5 measure-theory-lebesgue-integral Measure Theory and the Lebesgue Integral The rigorous framework for modern integration. An introduction to sigma-algebras and Lebesgue integrals. https://i.ytimg.com/vi/DxREm3s1scA/maxresdefault.jpg https://cdn.krisyotam.com/videos/measure-theory.mp4 Measure Theory ["integration", "sigma algebra", "real analysis"] 2025-04-30 Finished certain 6 active
6 spectral-theorem-basics Spectral Theorem Basics Diagonalizing operators on inner-product spaces. A walkthrough of self-adjoint operators and their spectra. https://i.ytimg.com/vi/DxREm3s1scA/maxresdefault.jpg https://cdn.krisyotam.com/videos/spectral-theorem.mp4 Linear Algebra ["eigenvalues", "operators", "inner product spaces"] 2025-04-30 Finished likely 5 active
7 intro-sheaves-schemes Introduction to Sheaves and Schemes Bridging algebra and geometry with local data. Overview of sheaves, schemes, and their geometric significance. https://i.ytimg.com/vi/DxREm3s1scA/maxresdefault.jpg https://cdn.krisyotam.com/videos/sheaves-schemes.mp4 Algebraic Geometry ["sheaves", "schemes", "varieties"] 2025-04-30 Notes possible 7 hidden
8 sobolev-spaces-simplified Sobolev Spaces Simplified Function spaces for PDEs and beyond. Understanding Sobolev embeddings and applications. https://i.ytimg.com/vi/DxREm3s1scA/maxresdefault.jpg https://cdn.krisyotam.com/videos/sobolev-spaces.mp4 Functional Analysis ["Sobolev spaces", "partial differential equations", "normed spaces"] 2025-04-30 Finished likely 5 active
9 godels-theorems-depth Gödel's Theorems in Depth Limits of formal axiomatic systems. Exploring Gödel's first and second incompleteness theorems. https://i.ytimg.com/vi/DxREm3s1scA/maxresdefault.jpg https://cdn.krisyotam.com/videos/godel-theorems.mp4 Logic ["incompleteness", "formal systems", "proof theory"] 2025-04-30 Finished certain 8 active
10 overview-lie-algebra-theory An Overview of Lie Algebra Theory Structures that underlie continuous symmetries. A survey of Lie algebras and their representations. https://i.ytimg.com/vi/DxREm3s1scA/maxresdefault.jpg https://cdn.krisyotam.com/videos/lie-algebra.mp4 Lie Theory ["Lie groups", "algebras", "representation theory"] 2025-04-30 Finished likely 6 active

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CREATE TABLE videos (
  id INTEGER PRIMARY KEY AUTOINCREMENT,
  slug TEXT UNIQUE NOT NULL,
  title TEXT NOT NULL,
  subtitle TEXT,
  preview TEXT,
  image TEXT,
  video TEXT,
  category TEXT,
  tags TEXT,
  date TEXT,
  status TEXT DEFAULT 'Draft',
  confidence TEXT DEFAULT 'possible',
  importance INTEGER DEFAULT 5,
  state TEXT DEFAULT 'active'
);