Science

The physical and natural world.

Resources

Physics

• The Feynman Lectures on Physics
• Physics Info — mechanics, thermal, waves & optics, electromagnetic, etc.
• So You Want to Learn Physics — Collection of textbooks on different topics

Math

• Book of Proof — the methods of proving mathematical theorems
• Discrete Mathematics | An Open Introduction — free and available online

Mixed

• 3Blue1Brown Lessons
  • 3Blue1Brown lessons by topics (calculus, puzzles, Pi, neural networks, computer science, etc.)

Links

• Where the wood-wide web narrative went wrong (HN)
  • Wood-wide web: fungi spread out through forest soil, interconnecting tree roots
  • False claims or misinterpretations like the web signal danger, recognize offspring or share nutrients
  • How confirmation bias affects scientists and journalists amplify studies with emotional and seductive stories
• Matrices and Graphs (HN)
  • Matrices are graphs and graphs are matrices
  • Frobenius normal form: revealing cyclic subspaces and edges between the subspaces
• We are not empty
  • Atoms are 99% empty is a myth in popular science
  • Based on quantum theory, the nucleus delocalised into "continuous quantum clouds"
  • A long and detailed explanation of the structure of atoms with quantum theory
• YouTube: How the Most Useless Branch of Math Could Save Your Life | Veritasium
  • The knot theory, the knot equivalence problem and nowadays common knot applications in chemistry and biology
  • Invariants: crossing number, p-colorable, alexander polynomial, jones polynomial, HOMFLY-PT polynomial, etc.
• Introduction to Modern Statistics
  • An online book about stat, with examples using R
• The collapse of insects | Reuters Graphics
  • Nice graphic illustrating the global Insect Apocalypse
• Immersive Math
  • 10 chapters from basic geometry to vectors, to matrix, to eigenvalues and eigenvectors
• An animated introduction to Fourier series
  • Long form guide from circles, to sinusoids, to epicycles to Fourier series
• An Intuitive Guide to Maxwell's Equations
  • In depth, long form guide explaining the 4 Maxwell's equations, explaining equations with graphs
• Calculus with Julia
  • From the basic use of Julia, to limits, derivatives and integrals, ODEs and vector calculus

Numbers, riddles, conjectures

• 6174 | Wikipedia, Kaprekar's routine | Wikipedia
• Magic square | Wikipedia
  • Famous examples, properties, classification, enumeration, transformation, construction, etc.
• 3x + 1, Collatz Conjecture | Veritasium
  • The simplest math problem no one can solve

    It shows math is hard. If anything, it shows that all of the things we can solve are miracles. We have no right to have solutions for all these problems.

    -- Prof. Alex Kontorovich

• The Riddle That Seems Impossible Even If You Know The Answer | Veritasium
  • 100 Prisoners Riddle (Wikipedia)

Curves

• YouTube: The Beauty of Bézier Curves | Freya Holmér
  • Best explanation of Bézier curves I've seen
  • Things explained:
    • Lerp → Quadratic Bézier curve → Cubic Bézier curve
    • De Casteljau's algorithm, Bernstein Polynomial Form
    • 1st derivative (velocity, tangent & normals), 2nd derivative (acceleration), 3rd derivative (jerk)
    • Curvature, bounding box, arc length, arc length parameterization (LUT)
• Curves and Surfaces | Bartosz Ciechanowski
  • Interactive animations to understand how curves and surfaces are definied by limited set of poins
  • And an older article: Drawing Bézier Curves | Bartosz Ciechanowski
• A Primer on Bézier Curves
  • Free online book about Bézier curves
• Bézier Curves
  • Drawing Bézier curves in SVG/CSS and the logic behind the parameters