You can download the lectures here. We will try to upload lectures prior to their corresponding classes.

  • An introduction to 301
    tl;dr: We discuss the structure of the course, additional resources, grading policy, responsibilities, support in the first half. In the second half, we discuss what proofs are and why we need them.
    [slides]

    Suggested Readings: Chapter 0 of the textbook

  • Propositional logic
    tl;dr: In this lecture, we shall introduce propositional logic and we shall use it to analyze the forms of proofs.
    [slides]

    Suggested Readings: Section 1.1. of the textbook

    Extra exercises: PDF

  • Natural Deduction, Excluded Middle, and Truth Tables
    tl;dr: We shall introduce the inference rules of disjunction, contradiction and negation. We shall also talk about the semantics of (classical) propositional logic.
    [slides] [handout]

    Suggested Readings: Section 1.1. of the textbook

    Appendix D of the textbook

    Extra exercises: PDF

  • Propositions with Lean
    tl;dr: We use the proof assistant Lean as propositional logic.
    [Lean code]

    Open the attached lean code file with your favourite text editor. I recommend Sublime text or VSCode.

    Extras

  • First Order Logic -- Variables, Predicates, and Quantifiers
    tl;dr: We explore some of the limitations of the propositional logic. We see how the first order logic gives us the right tools to overcome these limitations.
    [slides]

    Suggested Readings: Sections 1.2 and 1.3 of the textbook

  • First Order Logic -- Natural Deduction
    tl;dr: We introduce natural deduction for first order logic.
    [slides]

    Suggested Readings: Sections 1.2 and 1.3 of the textbook

  • Proof Strategies
    tl;dr: We use natural deduction to get a bird's eye view of the structure of our mathematical proofs.
    [slides]
  • Sets (part I)
    tl;dr: We make the idea of collections and containment precise by introducing the notion of set.
    [slides] [handout]

    Suggested Readings: Chapter 2 of the textbook

  • Sets (part II)
    tl;dr: We make the idea of collections and containment precise by introducing the notion of set.
    [slides] [handout]

    Suggested Readings: Chapter 2 of the textbook

  • Sets (part III)
    tl;dr: We make the idea of collections and containment precise by introducing the notion of set.
    [slides] [handout]
    • Suggested Readings:
    • Chapter 2 of the textbook
  • Sets (part IV)
    tl;dr: We make the idea of collections and containment precise by introducing the notion of set.
    [slides] [handout]
    • Suggested Readings:
    • Chapter 2 of the textbook
  • Relations
    tl;dr: We introduce the notions of ordered sets, partially ordered sets, and equivalence relations with tons of examples.
    [slides]

    Suggested Readings: Chapters 3 and 5 of the textbook

  • Functions
    tl;dr: All about functions.
    [slides] [handout]

    Suggested Readings: Chapters 3 and 5 of the textbook

  • Isomorphisms
    tl;dr: When are two sets the same? Take 2
    [slides] [handout]

    Suggested Readings: Chapters 3 and 5 of the textbook

    Extras

  • Images and pre-images
    tl;dr: We learn about images, pre-images, and fibres of functions. We also learn about image factorization. In the second part, we encounter axiom of choice.
    [slides] [handout]

    Suggested Readings: Chapters 3 and 5 of the textbook

    Extras

    More to come …

  • Induction on natural numbers
    tl;dr: We learn about natural numbers and the principles of induction and least element.
    [notes]

    Suggested Readings: Chapter 4 of the textbook

  • Recursion
    tl;dr: We learn about recursion. We use recursion to define addition(+) and we prove 1+1=2.
    [slides] [handout]

    Suggested Readings: Chapter 4 of the textbook

    Cool stuff to do with recursion: Recursion ‘Super Power’ (in Python) - Computerphile

  • Integers
    tl;dr: We construct integers from natural numbers and define arithmetic operations on them.
    [slides] [handout]

    Suggested Readings: Section B.2 of the textbook

  • Rational numebrs
    tl;dr: We construct rational numebrs from integers in two ways and prove they are the same.
    [slides] [handout]

    Suggested Readings:

  • Real numbers
    tl;dr: We construct (Dedekind) real numbers from rational numbers.
    [slides] [handout]

    Suggested Readings:

  • Real numbers
    tl;dr: More on real numbers.
    [slides] [handout]

    Suggested Readings: