Review — Difficulty 5/10

Complex analysis · Conformal mapping and advanced topics

Review skills for this standard. Write answers where shown.

Together with a parent

1. Prove: the sum of two even integers is even. ___ 2. Give a direct proof that √10 is irrational (outline key step). ___ 3. Prove by induction: 1 + 2 + … + n = n(n+1)/2

Written review

1. Prove: the sum of two even integers is even. ___ 2. Give a direct proof that √12 is irrational (outline key step). ___ 3. Prove by induction: 1 + 2 + … + n = n(n+1)/2 4. State the contrapositive of: if n² is even, then n is even ___ 5. Find a counterexample if false: every continuous f is differentiable 6. Write a ε-δ style argument outline for a limit. ___

_See printable PDF for diagram._

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Skills checklist

• [ ] Writes complete proofs
• [ ] Uses definitions precisely
• [ ] Selects appropriate proof techniques

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