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 good-faith completion, not correctness. We'll give you some choice about which problem to write up, but we will exclude some easy warm-up 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 | Big-O + Algorithms |
Do these discussion manual problems: 13.1ab, 14.1ac Do these big-O 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: 1a-e, 2a, 3abc, 4a-f, 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.