Lectures

Each week has a set of lecture videos and their associated notes. These assume that you have already done the posted reading assignment from the textbook. So they do not walk through basic definitions but, rather, concentrate on aspects of the topic that you probably didn't fully understand after doing the readings. (The first-week videos are more comprehensive because we are just getting started.)

Tutorials

Many of our tutorial problems will be taken from this manual of discussion problems. Additional problems will be posted below, as needed. Answers to tutorial problems will be posted in the evenings after tutorial.

You will work with the people sitting near you; feel free to sit near the same people each week or to move around and meet new people.

Additional study problems

We encourage you to do the additional study problems listed below. You should write up a solution to each problem on your own, as if you were taking an exam or turning in a graded homework, before checking your answers against the posted solutions. Writing up the answers is important, since it forces you to work through the details and practice composing a polished proof.

Additional practice problems, sample exams, etc may be found on the web pages for previous offerings of this course. There are differences from term to term and online exams are obviously a bit different from paper ones, but you'll find that the basic techniques and concepts are similar.

The last column includes some demo solutions to some past examlet problems. The content in this column is optional, and aims to help you see sample solutions to problems, as well as how to write a clean and rigorous proof. Videos in this column will be added gradually during the semester. For each demo, like any other practice problem, you are encouraged to solve the problem first before watching the solution.

Week	Topics	Readings	Lecture notes	Tuesday lectures	Additional problems	Additional videos
Week 1 Aug 25–29	Logic	1.1–1.4, 1.7, 2.*	Intro Logic 1 Logic 2 Logic 3	slides	prereqs logic	conditionals quantifiers
Week 2 Sep 1–5	Proofs & Number Theory	3.*, 4.1–4.11	Proofs 1 Proofs 2 Numbers 1 Numbers 2	problems	proofs number_theory modular_arithmetic
Week 3 Sep 8–12	Basic Set Theory	4.12–4.14, 5.*	Numbers 3 Sets 1 Sets 2	problems solutions	set_theory	Sp 20 Examlet 3
Week 4 Sep 15–19	Collections of Sets	7.1, 18.*	COS 1 COS 2 COS 3	Problems solutions	collections_of_sets
Week 5 Sep 22–26	Functions	7.*, 8.*	Functions 1 Functions 2 Functions 3 Functions 4	problems solutions	functions
Week 6 Sep 29–Oct 3	Graphs & Two-way Bounding	9.*, 10.*	Graphs 1 Graphs 2 Bounding	problems Problems with Solutions	graphs two-way_bounding	A confusion about two-way bounding for graph coloring
Week 7 Oct 6–10	Induction	1.5–1.6, 11.*	Induction 1 Induction 2 Induction 3 Induction 4 Optional: Fall`20's intro	problems solutions	easier_induction	A worked example (notes)
Week 8 Oct 13–17	Recursion	12.*	Rec. Defn 1 Rec. Defn 2 Rec. Defn 3		unrolling induction	Demo: induction to justify a closed form Demo: Unrolling & Induction (ignore mentions of a  "previous demo")
Week 9 Oct 20–24	Trees & Grammars	chapter 13	Trees 1 Trees 2 Trees 3		tree_induction	Demo: Recursion Trees
Week 10 Oct 27–31	Algorithms & Asymptotics	14.*, 15.1–15.8	Algorithms 1 Algorithms 2 Algorithms 3		recursion_trees inequality induction
Week 11 Nov 3–7	Algorithms	15.9 optional: 16.*	Algorithms 4 optional: Algorithms 5		algorithms
Week 12 Nov 11–14	Contradiction	17.*	contradiction 1 contradiction 2		contradiction
Week 13 Nov 17–21	State Diagrams	19.*	state diagrams 1 state diagrams 2 state diagrams 3		state_diagrams
Fall break Nov 22–30
Week 14 Dec 1–5	Countability	20.*	countability 1 countability 2 countability 3 countability 4		countability
Week 15 Dec 8–10	no tutorial
Finals Week	sign up on PrairieTest