URL study guide
https://tue.osiris-student.nl/onderwijscatalogus/extern/cursus?cursuscode=1CM57&collegejaar=2025&taal=enDescription
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.
Objectives
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