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Proofs about programs
The halting problem be damned - we can prove all kinds of things about programs, and we can even check those proofs with computers! In this chapter, we'll use a language called Lean to prove whether the famous Ackermann function always halts. Along the wa
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Rice's theorem
Turing famously showed that computers can't decide whether your code halts. But in 1951, Henry Rice proved a much more devastating result:
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Gödel's first incompleteness theorem
Back in 1931, Kurt Gödel published his first mathematical mic-drop:
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A/B Testing
In this chapter, you'll learn how to make decisions with A/B testing! The secret will be to think of your decision as a multi-armed bandit, model the bandit with the Beta distribution, and then sample it using Thompson sampling. Now let's learn what all t
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Differential Equations
In this chapter, you'll learn how to model systems using ordinary differential equations and Python. Along the way, you'll learn two famous systems of differential equations: the predator-prey model of ecosystems, and the Forbes model of metabolism (you m
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