Proof techniques for IE

Proof techniques:

• What is a theorem or lemma?

• How to formulate a theorem or lemma?

• What is a proof?

• Why do we prove?

• What do we prove?

• How do we prove?

• Direct proof

• Proof by induction

• Proof by transposition

• Proof by contradiction

• Proof by exhaustion

• Proof by construction

• Nonconstructive proof

• Probabilistic proof/sample path

• Proof nor disproof

• When is a proof finished?

• Writing proofs

• Evaluating proofs

Analysis:

• To illustrate the different techniques topics like real numbers, axioms, rows, limits, continuity, differentiability, and convexity will be dealt with. Applicability to IE problems is touched upon.

PhD student

• can formulate theorems

• can distinguish several proof techniques

• can apply these techniques in a basic setting

• gains first insight in usefulness of different proof techniques in IE setting