Unit 0: Admin & Proof Techniques

This is an archived version of this module from Fall 2022.
Click here for the current iteration.

This unit covers:

• organization of the module (administrative part)
• strategies for mathematical proofs
• mathematical induction
• loop invariants

Learning outcomes

1. Know logical proof strategies for proving implications, set inclusions, set equality, and quantified statements.
2. Be able to use mathematical induction in simple proofs.
3. Know techniques for proving termination and correctness of procedures.

Material

• slides on administrativa

• slides on proof techniques

• lecture notes on administrativa

• lecture notes on proof techniques

• Video 0-1 (2022-09-26): Welcome, teaching mode, overview, assessment, Campuswire, prior knowledge survey

• Video 0-2 (2022-09-28): §0.1 Random shuffle motivation, logical statements

• Video 0-3 (2022-09-28): §0.2 Proof templates, random shuffle motivation

• Video 0-4 (2022-09-28): §0.3 Mathematical induction, Towers of Hanoi

• Video 0-5 (2022-09-28): §0.4 Correctness proofs (part 1)

• Video 0-6 (2022-10-03): §0.4 Correctness proofs (part 2): example

Further reading and sources

A much more in-depth introduction to proof techniques, with many examples and exercises can be found, e.g., here:

• Velleman: How to Prove It, 2nd ed. (2006), Cambridge University Press

The loop invariants are the center piece of Hoare Logic for program verification. More background on Hoare Logic is given for example here:

• Gordon: Lecture Notes on Hoare Logic

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Syllabus  ⋅  Unit 1