# Mathematics

# Resources

• Calculus Made Easy (1914)
• Interactive Linear Algebra
• Calculus Explained with GIFs and Pics
• Calculus for the Curious
• Mathigon – an interactive, personalized mathematics textbook
• Immersive Linear Algebra
• Linear Algebra by Jim Hefferon – free textbook
• Ask HN: How to self-study mathematics from the undergrad through graduate level?
• Calculus with Julia
• Overview of differential equations - video
• How category theory is applied
• Applied Category Theory
• Mathematics all-in-one cheat-sheet - 2013 - pdf
• Ask HN: Are there books for mathematics like Feynman's lectures on physics?
• Ask HN: Best way to relearn basic math?
• Calculus for Beginners and Artists
• Math Basics for Computer Science and Machine Learning from UPenn - pdf
• A 2020 Vision of Linear Algebra
• An Intuitive Guide to Linear Algebra
• Mathematics for the Adventurous Self-Learner

Physics:

• Taking Census of Physics
• Simulation-based high school physics course notes
• Intuitive Guide to Maxwell's Equations https://hn.premii.com/#/comments/23700295

Basic/Interesting question to solve:

The diameter of earth is 12,756 km. Know that we know that:

• What is the circumference of Earth at the equator?
• What is the circumference of Earth at the 42nd latitude?
• What's the volume of earth?
• What's the surface area?
• A plane travels at 900km per hour
  • how long does it take to fly from top to bottom?
  • It flies at 12.7km from the surface. How long now?
  • It has acceleration of 1 m/s^2. How long now?
• Calculate the volume of each:
  • 0–35km Crust
  • 35–2,890km Mantle
  • 2,890–5,150km Outer core
  • 5,150–6,360km Inner core

Gravity

• How much gravitational force does the moon have on the earth?
• How much does the sun have?
• What are the tides different? Earth friction? Positioning of moon + sun? Natural dissonance of tides compounding?

Relativity

• I am standing at a clock tower (hint: twin paradox)
  • I travel for 1 hour at the speed of light away from the clock. I look at my watch. What is the time on my watch? I look at the clock. What is the time on the clock?
  • I travel for 1 hour at the speed of light back to the clock. I look at my watch. What is the time on my watch? I look at the clock. What is the time on the clock?