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 not be posted. 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 moodle 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 moodle, 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 | Study Problems | Tutorial problems | Comments |
---|---|---|---|---|

Week 1 | Prerequisites and Logic | math prerequisites logic |
Get to know the rest of your team Do problem 1.5 in the discussion manual Do this problem |
Turn in a logic problem, not a prerequisites problem. |

Week 2 | Proofs Number theory |
proofs number theory |
Do problems 1.2bc, 1.3d, 1.4a, 2.2ab, 2.3a, and 2.4a in the discussion manual. Don't worry if you don't finish - treat the rest as extra study problems (but don't turn them in) |
Turn in one of the proof problems. Do not turn in problem 1 or 6 in the number theory problems. |

When writing up a study problem on moodle, indicate clearly which problem you are solving. That is, which topic section of the study problems and which problem number, e.g. "number theory 3". | ||||

Week 3 | Modular arithmetic Set theory |
modular arithmetic set theory |
Do 2.1 in the discussion manual. For 2.1a, include at least three positive and three negative values. |
Turn set theory problem 2, 3, or 4 |

Week 4 | Relations | relations | Do these problems | any relations problem |

Week 5 | Functions | functions | Do discussion manual problems 5.1bd, 5.2, 5.4, 7.3, 7.5c Do this problem |
any functions problem |

Week 6 | Graphs Two-way bounding |
graphs two-way bounding |
Do these discussion manual problems (it looks like a lot but most are much shorter problems than usual): 8.1a, 8.3b, 8.4, 8.5, 9.1b, 9.2bc, 9.3a, 10.2d, 10.1b |
Turn in any graphs or two-way bounding problem |

Week 7 | Induction | easy induction |
Do these discussion manual problems: 11.1bcd, 11.2, 11.4 |
Turn in either induction problem |

Week 8 | Recursive Definition | unrolling induction |
Do these discussion manual problems: 12.1d, 12.2ac |
Turn in an induction problem other than problem 2 (so NOT induction #2 and NOT the unrolling problem) |

Week 9 | Trees, Grammars | tree induction | Do these discussion manual problems: 13.3b, 13.2a, 13.4 | Turn in tree induction problem 1, 2, or 3. |

Week 10 | Big-O Algorithms |
recursion trees inequality induction |
Do these discussion manual problems: 13.1ab, 14.1ac |
Turn in a recursion tree or inequality induction problem |

Week 11 | Algorithms NP |
algorithms | Do these discussion manual problems: 15.5, 15.3, 15.2, 15.4 | Turn in either algorithms study problem. |

Week 12 | Collections of Sets | collections of sets | Do these discussion manual problems from section 17: 1a-e, 2a, 3abc, 4a-f, 5ae, 6ab Do these problems |
Turn in Collections of Sets problem 1, 2, or 3 |

Week 13 | Contradiction State Diagrams |
contradiction state diagrams |
Do these discussion manual problems: 2.2a (justify your answer using proof by contradiction), 16abc, 18.1, 18.2 |
Do not turn in State Diagram problem 1. |

Week 14 | State Diagrams Countability |
countability | Do these discussion manual problems: 19.1, 19.2 Do this problem |
Turn in either countability problem. |