Let’s play a game. I toss a coin twice and ask you, what is the probability of landing two heads? I claim that my coin is a fair coin. Considering I might be lying, what probability should you guess?

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# Random Coin

# The Isomorphism Theorems

# An Idealized Programming Language

# Is Ordered Square Path Connected?

# CS70 Resources

Let’s play a game. I toss a coin twice and ask you, what is the probability of landing two heads? I claim that my coin is a fair coin. Considering I might be lying, what probability should you guess?

Continue reading “Random Coin”

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We learned about quotient groups and four Isomorphism Theorems in my algebra class. My professor refers the four Isomorphism Theorems as “four siblings of Isomorphism Theorems” (of course, that made me laugh; it always makes me happy when people describe math in lively terms). I’ll write about my understanding of them in this post.

Imagine this: you write a program, compile it and you start to run the program. It has been running for one minute (“this is not a incredibly fast program”, you think;) five minutes (“oh, it’s kind of slow”), one hour (“okay it’s *very *slow”), one hour (you start to become impatient) and after one day, it’s still running. You start to wonder,

“would it *ever* stop running?”

I’ll start my blog with one thing I love about mathematics, which is although intuition is helpful lots of the times, we should also try not to get fooled by our intuition.

In many aspects, CS70 plays an important role in my undergraduate study.

Over the past three semesters, I’ve written some resources that can be found here.