6120a Discrete Mathematics And Proof For Computer Science Fix

Number theory proofs fail because students treat ≡ as =. They aren’t equal; they are equivalent modulo n.

Most computer science students are trained in procedural thinking (Step A → Step B → Step C). 6120a requires declarative and structural thinking (Why must Step B be true regardless of the data?). Number theory proofs fail because students treat ≡ as =

The "Fix" Mindset: Stop asking "What is the answer?" Start asking "What is the argument that guarantees the answer?" The Iron Template (fix for all induction):

When to use: Direct proof gets stuck (e.g., proving "If n² is odd, then n is odd"). The Fix: Instead of P → Q, prove ¬Q → ¬P. Fix for "Strong Induction": Use when P(k+1) depends

Most lost points come from:

The Iron Template (fix for all induction):

Fix for "Strong Induction": Use when P(k+1) depends on P(k-1) or P(0)...P(k). The template is identical, but IH becomes "Assume P(j) holds for all j ≤ k."

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