Find one other student in 6120a. Exchange one proof each. Do not talk. Simply write: "I don't understand line 4" or "You assumed the conclusion." This external feedback fixes blind spots faster than solo study.
| Day | In‑class activity | Homework | |-----|------------------------------------------------|----------------------------------------------| | Mon | Simple induction (sum of integers) | Prove sum of squares formula | | Wed | Strong induction (Fibonacci, binary rep) | Prove every n > 1 has prime factor (strong) | | Fri | Recurrence from recursion (factorial, Towers) | Solve T(n) = T(n−1) + n, T(1)=1 by induction|
All homework graded for proof structure using the fixed template. False equivalences : “And” vs
This document integrates fixes for common errors found in standard textbooks (e.g., Rosen, Epp) and previous course offerings:
| Concept | Fixed Notation | |-----------------------|------------------------------| | Natural numbers | ℕ = 0, 1, 2, … (specify if 1‑based) | | Empty set | ∅ | | Set difference | A \ B (not A − B) | | Complement (relative) | ∁_U A or ~A when U is clear | | Power set | 𝒫(A) | | Tuple | (a₁, a₂, …, aₙ) | | Relation composition | R ∘ S | | Floor/ceiling | ⌊x⌋, ⌈x⌉ | | Graph G | (V, E) | | Binomial coefficient | (\binomnk) (not C(n,k) unless specified) | | Implication | P → Q (not P ⇒ Q) for object language | | Logical equivalence | P ≡ Q | Find one other student in 6120a
All proof exercises must use this fixed notation.
Warning: 6120a students overuse this. Use only when the statement asserts "not" or "no". Template: | Day | In‑class activity | Homework |
Fix for misuse: If you can write a direct proof in 3 lines, do not write a 10-line contradiction. Contradiction doesn't "look smarter."