TM Preparation Guide
Study Timeline
3 Weeks Before
- Review all lecture notes
- Create concept maps
- List all theorems and definitions
- Identify weak areas
2 Weeks Before
- Practice proofs daily
- Form study group
- Create flashcards
- Attend office hours
1 Week Before
- Review session
- Practice problems
- Memorize key definitions
- Sleep well
Proof Techniques
| Type | When to Use | Example |
|---|---|---|
| Direct | Straightforward implication | If n even, then n² even |
| Contradiction | Proving impossibility | ℝ uncountable |
| Contrapositive | Negation easier | If f not injective, ∃x,y |
| Induction | Properties of ℕ | Sum formula |
| Construction | Existence claims | Bijection A → B |
What to Memorize
Set Theory
- 9 set laws (commutative, associative, distributive, etc.)
- Power set: |𝒫(A)| = 2^|A|
- Cantor’s theorem statement
- Schroeder-Bernstein statement
Relations
- 5 relation properties
- Equivalence ↔ partition theorem
- Function composition: (g ∘ f)(x) = g(f(x))
- Poset properties
Boolean Algebra
- Boolean laws (≈18)
- DNF/CNF definitions
- Functional completeness: {AND, OR, NOT}, {NAND}, {NOR}
- Gate symbols
Logic
- Truth tables for connectives
- Natural deduction rules
- Soundness vs completeness
- Quantifier negation: ¬∀x P(x) ≡ ∃x ¬P(x)
Study Strategies
- Active recall: Don’t just read—recite
- Spaced repetition: Review multiple times
- Practice proofs: Write them out completely
- Explain to others: Best way to test understanding
- Use whiteboards: Work through problems standing up
Resources
- Lecture slides
- Textbook chapters
- Homework solutions
- Review session notes
- Study group
- Office hours
Common Mistakes
- Circular reasoning in proofs
- Using “obvious” without justification
- Confusing necessary vs sufficient
- Mixing quantifier order
- Incomplete case analysis
Day Before
- Light review (no cramming)
- Get 8 hours sleep
- Eat well
- Review flashcards once
- Stay calm