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Algebra Calculus I Calculus II Calculus III Linear Algebra Differential Equations Partial Differential Equations Electromagnetism Probability & Statistics Engineering Statistics Discrete Mathematics

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Explore Challenges Review Leaderboard Groups Tutor

Discrete Mathematics/Computer Science

How Discrete Mathematics is used in Computer Science

Security

N = k^L, \qquad t = \frac{N}{2g}

How Long Would It Take to Guess Your Password?

The product rule

P(\text{no collision}) = \prod_{k=0}^{n-1}\left(1 - \frac{k}{N}\right) \approx e^{-n^2/(2N)}

The Birthday Problem and Hash Collisions

The product rule and the pigeonhole principle

Cryptography

c = m^e \bmod n, \qquad m = c^d \bmod n, \qquad d = e^{-1} \bmod (p-1)(q-1)

Sending a Secret with RSA

Modular exponentiation and inverses

Algorithms

T_{\text{simple}}(n) \approx \frac{n^2}{2}, \qquad T_{\text{merge}}(n) \approx n\log_2 n, \qquad \text{time} = \frac{T(n)}{v}

Why Fast Sorting Matters: n² vs n log n

Growth rates and big-O