Unit materials

This page will be updated regularly once term has started.

All materials for the unit are hosted here. Files linked to on this page will require you to log in with your university username and password. Just click the link and you will be redirected to a login page, please check it starts with login.microsoftonline.com before entering any personal details!

See the schedule page for information on how best to plan and study for each session.

Logic and Proofs

Session 1, 22-23 September

• Topic: Booleans and Truth Tables
• Lecture notes
• Whiteboard
• Recording
• Worksheet
• Solutions

Session 2, 24-25 September

• Topic: Satisfiability, Validity, Entailment, and Equivalence
• Lecture notes
• Whiteboard
• Recording
• Worksheet
• Solutions

Session 3, 29-30 September

• Topic: Natural Deduction
• Lecture notes
• Whiteboard
• Recording
• Worksheet
• Solutions

Session 3 cont., 01-02 October

• Topic: Natural Deduction (cont.)
• Lecture notes
• Whiteboard
• Recording
• Worksheet
• Solutions

Session 4, 06-07 October

• Topic: Predicates and Quantifiers
• Lecture notes
• Whiteboard
• Recording
• Worksheet
• Solutions

Session 5, 08-09 October

• Topic: Natural Deduction for Quantifiers
• Lecture notes
• Recording
• Worksheet
• Solutions

Session 6: 13-14 October

• Topic: Informal Proofs
• Lecture notes
• Whiteboard
• Recording
• Worksheet
• Solutions

Session 7: 15-16 October

• Topic: Induction
• Lecture notes
• Recording
• Worksheet
• Solutions

Sets, Functions, and Relations

Session 9, 20-21 October

• Topic: Set Theory
• Lecture notes
• Lecture slides
• Recording
• Worksheet
• Solutions

Session 10, 22-23 October

• Topic: Set Theory
• Lecture notes
• Lecture slides
• Recording
• Worksheet
• Solutions

Session 11, 03-04 November

• Topic: Functions
• Lecture notes
• Lecture slides
• Recording
• Worksheet
• Solutions

Session 12, 05-06 November

• Topic: Relations
• Lecture notes
• Lecture slides
• Recording
• Worksheet
• Solutions

Session 13, 10-11 November

• Topic: Combinatorics
• Lecture notes
• Lecture slides
• Recording
• Worksheet
• Solutions

Session 14, 13-14 November

• Topic: Combinatorics
• Lecture notes
• Lecture slides
• Recording
• Worksheet
• Solutions

Probability

Session 15, 17-18 November

• Topic: Probability
  Outline

  • Sample Spaces & Events
  • Probability Spaces & Distributions
  • Uniform Distribution
  • Properties of Distributions
  • Probability Tables
  Further Reading

  • [Sheldon Ross, Chapter 2.1 - 2.5]
• Lecture notes
• Live notes
• Recording
• Worksheet
• Solutions

Session 16, 19-20 November

• Topic: Conditional Probability
  Outline

  • Conditional Probability Definition
  • Conditional Probability Properties
  • Bayes' Theorem & Bayesian Interpretation of Probability
  • Independence
  • Probability Tables Revisited
  Further Reading

  • [Sheldon Ross, Chapter 3]
• Lecture notes
• Live notes
• Recording
• Worksheet
• Solutions

Session 17, 24-25 November

• Topic: Random Variables
  Outline

  • Random Variables Motivation
  • Random Variables Definition
  • Notation, Mass Functions & Cumulative Distribution Functions
  • Joint Random Variables
  Further Reading

  • [Sheldon Ross, Chapter 4.1-4.2, 5.1]
• Lecture notes
• Live notes
• Recording
• Worksheet
• Solutions

Session 18, 26-27 November

• Topic: Expectation and Variance
  Outline

  • Discrete & Continuous Random Variables
  • Expected Value Definition
  • Expected Value Properties, Linearity
  • Variance Definition
  Further Reading

  • [Sheldon Ross, Chapter 4.3-4.5, 4.10, 5.2]
• Lecture notes
• Live notes
• Recording
• Worksheet
• Solutions

Session 19, 01-02 December

• Topic: Discrete Random Variables
  Outline

  • Binomial Distribution, Expectation and Variance
  • Poisson Distribution, Expectation and Variance
  • Geometric Distribution, Expectation and Variance
  Further Reading

  • [Sheldon Ross, Chapter 4.6-4.8]
• Lecture notes
• Live notes
• Recording
• Worksheet
• Solutions

Session 20, 03-04 December

• Topic: Continuous Random Variables
  Outline

  • Continuous Uniform Distribution, Expectation and Variance
  • Exponential Distribution, Expectation and Variance
  • Normal Distribution, Expectation and Variance (NOTE: This material is non-examinable)
  Further Reading

  • [Sheldon Ross, Chapter 5.3-5.5]
• Lecture notes
• Live notes
• Recording
• Worksheet
• Solutions