: Review

Review Sheet

Getting Started
- Problem Orientation–What is the context of the problem?
- Simplifying assumptions–can you make the problem easier and learn from this?
- Test examples looking for ideas.
- Look for partial solutions or stepping stones toward a solution.
- Consider Cases–Even obvious ones!
- Carefully consider definition of the things that you are given and the items that you are trying to show.
- Ask What is special about ...
Methods of Arguments
- Direct: if p → q, and q → r then p → r
- Contradiction: Make sure to formulate the starting hypothesis carefully. p → q ≡ p ∧ q → F
- Induction: Is there someway to induce a sequence of statements and to make an inductive step?
- Cases: How can the problem be split up?
Miscellaneous
- Draw pictures
- Recast the problem in a different context. Graph theory, Algebraic, Calculus, ...
Tactics
- Look for symmetry: Geometric, Algebraic,
- Consider the extreme principle: What make these extreme special? (Can contradiction be use?)
- Pigeon Hole Principle: Look for this along the way in problems.
- Invariants: odd/even, linear algebra items (determinate, eigenvalues,etc.), Others that you know.