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My name is Takashi, and I am a mathematics instructor at a technical college in British Columbia, Canada. I have been teaching various mathematics and statistics courses, mostly for undergraduate engineering programs. This blog is a collection of notes on various topics in mathematics and statistics. It is intended for undergraduate students and for instructors like me – who are not mathematicians but somehow ended up teaching the subject. I hope you will enjoy doing math with me.

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Three and a half Ways to Prove Euler's formula

Euler's formula $e^{i\theta} = \cos\theta + i\sin\theta$ is one of the most important formulae in engineering and science. See, for example, a beautifully done video about Euler's formula with $\theta=\pi$: 1. Maclaurin Series This is the most common proof you see on

Deriving the Volume and Surface Area of an n-dimensional Sphere

If you are in any of the STEM fields, you should be familiar with the formulae for the "volumes" and "surface areas" of "spheres" in 2D and 3D spaces. As you know, in 3D, \[\text{volume} = \frac{4\pi}{3} r^3 ~ \text{ and

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Three and a half Ways to Prove Euler's formula

Deriving the Volume and Surface Area of an n-dimensional Sphere