CS173: Discrete Structures
Tutorials and Study Problems


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.

Study problems

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
Get to know the rest of your team
Do this problem
Do problem 1.5 in the discussion manual

math prerequisites

Turn in a logic problem, not a prerequisites problem

Week 2

Number theory

Do problems 1.2bc, 1.3d, 1.4a, 2.2ab, 2.3a,
and 2.4a in the discussion manual

number theory

Pick any problem other than number theory #1 or #6

Week 3 Labor Day    

Week 4

Modular arithmetic
Set theory

Do 2.1 in the discussion manual. For 2.1a, include at least three positive and three negative values.
Do these problems
Do 3.1, 3.2, and 3.3b in the discussion manual

modular arithmetic
set theory

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
Do this problem


Pick any problem

Week 7

Two-way bounding

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

two-way bounding

Pick any problem

Week 8 Induction

Do these discussion manual problems: 11.1bc, 11.2, 11.4
In this other textbook, do problem 5.16acdefh. (it's on p170 of the pdf, p162 by printed numbers)
- or this hopefully-clearer rewriting of the above textbook problem
Do this problem

easier induction
Pick any problem
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


Discussion manual problems: 13.3b, 13.2a, 13.4

tree induction

Turn in problem 1, 2, or 3

Week 11 Big-O
Do these discussion manual problems: 13.1ab, 14.1ac
Do these big-O problems

recursion trees
inequality induction

Pick any problem

Week 12 Algorithms
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

collections of sets

Turn in problem 1, 2, or 3

Week 14 Contradiction
State Diagrams
Do these discussion manual problems: 2.2a (using proof by contradiction), 16abc, 18.1, 18.2
Do this problem

state diagrams

Pick any problem except state diagrams #1

Week 15 State Diagrams
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.