Review — Difficulty 2/10

Abstract algebra · Optional capstone

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 √7 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 √9 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._

___________________________ ___________________________ ___________________________ ___________________________ ___________________________

Skills checklist

• [ ] Writes complete proofs
• [ ] Uses definitions precisely

___________________________ ___________________________ ___________________________ ___________________________