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 (usually on Monday night). If you miss tutorial, feel free to consult with friends and staff.
Tutorial groups will be assigned randomly and stay stable for the whole term. If your group is working out badly, please contact your instructor.
Each week, you should do the 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.
As motivation, you will need to submit a typed answer to one study problem. These answers will be typed directly into a PrairieLearn editing window (not uploaded as pdf) so that you can get used to the editor before you have to use it on examlets. Although study problems come with answers, we're expecting to see your answer written in your own words. This will be graded for goodfaith completion, not correctness. We'll give you some choice about which problem to write up, but we will exclude some easy warmup problems.
When writing equations in PrairieLearn, it's often helpful to know some basic latex commands. Here is a brief guide
You may freely consult friends and/or course staff for help checking your answers and for hints if you get stuck. You can also post questions on piazza. However, significant pieces of solutions should be posted only privately to the course staff.
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.
This schedule is somewhat tentative: tutorial problems will appear and study problems will be finalized around the start of each week. Study problems are due on the Saturday at the end of each week.
Week  Topic  Tutorial problems  Study problems 

Week 1  Prerequisites + Logic 
Get to know the rest of your team Do this problem Do problem 1.5 in the discussion manual 
Turn in a logic problem, not a prerequisites problem 
Week 2 
Proofs 
Do problems 1.2bc, 1.3d, 1.4a, 2.2ab, 2.3a, and 2.4a in the discussion manual 
Pick any problem other than number theory #1 or #6 
Week 3  Labor Day  
Week 4 
Modular arithmetic 
Do 2.1 in the discussion manual. For 2.1a, include at least three positive and three negative values. 
Turn in set theory problem 2, 3, or 4 
Week 5  Relations  Do these problems 
Pick any problem 
Week 6  Functions 
Do discussion manual problems 5.1bd, 5.2, 5.4, 7.3, 7.5c 
Pick any problem 
Week 7 
Graphs 
Discussion manual problems (it looks like a lot but most are short): 8.1a, 8.3b, 8.4, 8.5, 9.2b, 9.1b, 9.3a, 10.2d, 10.1b Do this problem 
Pick any problem 
Week 8  Induction 
Do these discussion manual problems: 11.1bc, 11.2, 11.4 

Week 9  Recursive Definition  Do these discussion manual problems: 12.1d, 12.2ac Do this problem Do discussion manual problem 12.3abcd Do this problem 
Pick any problem except induction #2 and the unrolling problem 
Week 10 
Trees 
Discussion manual problems: 13.3b, 13.2a, 13.4 
Turn in problem 1, 2, or 3 
Week 11  BigO + Algorithms 
Do these discussion manual problems: 13.1ab, 14.1ac Do these bigO problems 
recursion trees Pick any problem 
Week 12  Algorithms + NP 
Do these discussion manual problems: 15.5, 15.3, 15.2, 15.4 
Pick any problem 
Week 13  Collections of Sets  Do these discussion manual problems from section 17: 1ae, 2a, 3abc, 4af, 5ae, 6ab Do these problems 
Turn in problem 1, 2, or 3 
Break  
Week 14  Contradiction State Diagrams 
Do these discussion manual problems: 2.2a (using proof by contradiction), 16abc, 18.1, 18.2 Do this problem 
Pick any problem except state diagrams #1 
Week 15  State Diagrams Countability 
Do these discussion manual problems: 19.1, 19.2 Do this problem 
Pick any problem 
Attendance will be taken in class. We may adjust these methods as we decide what works best.