Session 1: Why Our Code Breaks (and What a Proof Is)

Overview

Orientation session. We look at software that passed its tests and failed anyway, then turn to what it means to prove something and what a well-written proof looks like on paper.

Lecturer

Jad Abou Hawili — Teaching Assistant (jka15@mail.aub.edu) (CS + Applied Math Alumnus)

Session Information

• Date and Time: Monday 21 September 2026 — 17:30-19:30
• Place: Nicely 212
• Online Meeting Link
  • Meeting Number: 2550 601 9224
• Session Recording (not available due to technical issues)

Core Concepts

• Course mechanics: structure, the five problem sets, certification, and the academic integrity policy
• Real-world software disasters: Ariane 5 ($370M, integer overflow), Therac-25 (race condition, patient deaths), and Heartbleed (buffer over-read) vulnerabilities
• The limits of testing: finite inputs vs infinite possibilities, Dijkstra’s principle, and a live demo
• Statements, hypotheses, conclusions; the anatomy of a proof
• True vs provable
• Basic set notation as vocabulary: ∈, ⊆, ∪, ∩, , ∅, and set-builder notation
• What a well-written proof looks like on paper and its “marking criteria”

Slides

Session 1 Slides: Download PDF

Credit: The above slides were prepared by Daniel Dia.

Readings

• Book of Proof (Hammack), Ch. 1
• Book of Proof (Hammack), Ch. 4, 5, 6

Exercises & Extra Steps

• Practice (not collected): write out, in full sentences, a proof that the sum of two even integers is even

Navigation

• Back to Course Overview
• Next: S2: Propositional Logic →

Questions? Reach out on the course WhatsApp!