# # 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?

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