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	New topic	Readings	Lecture notes	Lecture videos	Tutorial problems (work on these in class; no need to turn it in)	Additional study problems	(optional) Videos with worked examples
Week 1 Aug 21-25	Logic	1.1-1.4, 1.7; chapter 2	Intro Logic 1 Logic 2 Logic 3	Intro Logic 1 Logic 2 Logic 3	Get to know the rest of your team Do this problem Do problem 1.5 in the discussion manual	math prerequisites logic
Week 2 Aug 28 - Sep 1	Proofs + Number Theory	Chap. 3, 4.1-4.11	Proofs 1 Proofs 2 Numbers 1 Numbers 2	Proofs 1 Proofs 2 Numbers 1 Numbers 2	Do problems 1.2bc, 1.3d, 1.4a, 2.2b, 2.3a, 2.4a, and 2.2a in the discussion manual	proofs number theory
Week 3 Sep 4-8	Modular Arithmetic + Sets	4.12-4.14, chapter 5	Numbers 3 Sets 1 Sets 2	Numbers 3 Sets 1 Sets 2	Do 2.1 and 3.1 in the discussion manual. For 2.1a, include at least two positive and two negative values. Do these problems Do 3.2 and 3.3b in the discussion manual	modular arithmetic set theory	Sp 20 Examlet 3
Week 4 Sep 11-15	Relations	chapter 6	Relations 1 Relations 2	Relations 1 Relations 2	Do these problems	relations
Week 5 Sep 18-22	Functions	chapters 7 and 8	Functions 1 Functions 2 Functions 3 Functions 4	Functions 1 Functions 2 Functions 3 Functions 4	Do discussion manual problems 5.1bd, 5.2, 5.4, 7.3, 7.5c Do this sanity check for 7.5c Do this problem	functions
Week 6 Sep 25-29	Graphs + 2-way bounding	chapters 9 and 10	Graphs 1 Graphs 2 Bounding	Graphs 1 Graphs 2 Bounding	Discussion manual problems:  8.1a, 8.3b, 8.4, 8.5, 9.2b, 9.1b, 9.3a, 10.2d, 10.1b Do this problem	graphs two-way bounding	A confusion about two-way bounding for graph coloring
Week 7 Oct 2-6	Induction	1.5-1.6; chapter 11	Induction 1 Induction 2 Induction 3 Induction 4 Optional: Fall`20's intro	Induction 1 Induction 2 Induction 3 Induction 4 Optional: Fall`20's intro	Do these discussion manual problems: 11.1b, 11.2, 11.4 Do this problem and this problem	easier induction	A worked example (notes)
Week 8 Oct 9-13	Recursive Definition	chapter 12	Rec. Defn 1 Rec. Defn 2 Rec. Defn 3	Rec. Defn 1 Rec. Defn 2 Rec. Defn 3	Do these discussion manual problems: 12.1d, 12.2ac Do this problem Do discussion manual problems 12.3abcd and 14.1d	unrolling induction	Demo: induction to justify a closed form Demo: Unrolling & Induction (ignore mentions of a  "previous demo")
Week 9 Oct 16-20	Trees + Grammars	chapter 13	Trees 1 Trees 2 Trees 3	Trees 1 Trees 2 Trees 3	Discussion manual problems: 13.3b, 13.2a, 13.4	tree induction	Demo: Recurion Trees
Week 10 Oct 23-27	Big-O + Algorithms	chapter 14; 15.1-15.8	Algorithms 1 Algorithms 2 Algorithms 3	Algorithms 1 Algorithms 2 Algorithms 3	Discussion manual problem 13.1ab (use the recursions trees method; not unrolling!) Do this big-O problem Discussion manual problem 14.1ac	recursion trees inequality induction
Week 11 Oct 30 - Nov 3	Algorithms	15.9 optional: chapter 16	Algorithms 4 optional: Algorithms 5	Algorithms 4 optional: Algorithms 5	Discussion manual problems: 15.5, 15.3, 15.4, 15.2	algorithms
Week 12 Nov 6-10	Collections of Sets	chapter 18	COS 1 COS 2 COS 3	COS 1 COS 2 COS 3	Discussion manual problems from section 17: 1a-e, 2a, 3abc, 4a-f, 5ae, 6ab Do these problems	collections of sets
Week 13 Nov 13-17	Contradiction State Diagrams	chapter 17, 19.1-19.6	contradiction 1 contradiction 2 state diagrams 1 state diagrams 2	contradiction 1 contradiction 2 state diagrams 1 state diagrams 2	Discussion manual problems: 18.1, 18.2, this problem, 16abc, 2.2a (using proof by contradiction)	contradiction state diagrams
Fall break Nov 20-24
Week 14 Nov 27 - Dec 1	State Diagrams Countability	19.7-19.8, chapter 20	state diagrams 3 countability 1 countability 2 countability 3 countability 4	State Diagrams 3 Countability 1 Countability 2 Countability 3 Countability 4	Discussion manual problems: 19.1, 19.2 Do this problem	countability
Week 15 Dec 4-8	(no tutorial)					inequality induction (solution)
Finals Week	Final is TBD; sign up starting TBD

"A room with dozens of tables and at each table students are working collaboratively on a math problem, impressionist style", by DALL-E (+Ben)