# Core Modules (CMs)

Note: these material posts were delivered through Canvas (the LMS we used; closed to external traffic). They were reproduced here after the conclusion of the course for documentary purposes. Hence the publication dates of the posts are not accurate; they are in fact intentionally ordered in reverse, so that the posts can show chronologically.

First Week Slides (Intro, Logistics, Survey Results) | |||

CM 1: Logic | Reading Guide/Completion Requirements | Slides | Recitation/Assignment |

CM 2: Proof Methods | Reading Guide/Completion Requirements | Slides | Recitation/Assignment |

CM 3: Math Tools | Reading Guide/Completion Requirements | Slides I, Slides II | Recitation/Assignment |

CM 4: Sets, Functions, and Relations | Reading Guide/Completion Requirements | Slides | Recitation/Assignment |

CM 5: Inductions | Reading Guide/Completion Requirements | Slides | Recitation/Assignment |

CM 6: Graph Fundamentals | Reading Guide/Completion Requirements: Part I, Part II | Slides I, Slides II | Recitation/Assignment |

CM 7: Combinatorics | Reading Guide/Completion Requirements | Slides | Recitation/Assignment |

CM 8: Probability | Reading Guide/Completion Requirements: Part I-II, Part III | Slides I, Slides II | Recitation/Assignment |

Last Day Slides (Recap) |

Every CM is 2-3 class meetings long. 3-meetings modules will be paired with an exam day to make two full weeks. A module typically contains:

## Prepare (? hours)

- Every CM introduces some new math concepts. You will be assigned textbook chapters (sometimes other online resources) as required reading.
*We only use textbooks that are completely free and available.*We will mainly use chapters from the following three textbooks:- AIDMA: Charles A. Cusack,
*An Active Introduction to Discrete Mathematics and Algorithms* - MCS: Eric Lehman, F Thomson Leighton, and Albert R Meyer,
*Mathematics for Computer Science* - MFADM: Jean Gallier and Jocelyn Quaintance,
*Mathematical Foundations And**Aspects of Discrete Mathematics*

- AIDMA: Charles A. Cusack,
- To evaluate your understanding of the required reading, there is usually a lightweight quiz in Canvas that you can attempt for
~~three~~an unlimited number of times (with a~~1-hour~~15-minute cooldown period between consecutive attempts). This quiz mainly tests your proficiency in the basic concepts, and it is encouraged to attempt it with your required reading open on the side. You will not need to show any work for the answers. - Both the required reading and the quiz are “due” the midnight before the first class meeting of the CM.
*That merely means we recommend you finish them by that point. There is no penalty if you complete them later than that point – the real penalty lies in that you will not get to enjoy the class meetings as much as your peers who have completed the reading and quiz.* - As mentioned in the Course Description, this prepare process allows people from diverse math backgrounds to take as much time as necessary to get comfortable with the concepts. Therefore, the amount of time it takes may greatly vary from person to person and from module to module. We could have said that this is supposed to take 1-1.5 hours in total, but really there is no informative estimate.

## Class meetings (2-3 class meetings of 75 minutes each)

The class meetings are a mix of the following:

- Motivating why we need to learn the topic
- Comparing and contrasting between how different textbooks address the topics, and pointing out any inconsistencies (this happens more often than you’d expect)
- (In later CMs) Refer back to earlier CMs and explicitly connecting the mathematical structures/concepts together
- Peer work: Interactive problem-solving on trickier concepts (more advanced than prepare quizzes); similar in nature to CS201’s WOTOs and CS216’s peer instructions.
- (In some CMs) More material that required readings do not cover
- Talking about mathematical communication in the context of the CM

**Do not show up to class unprepared hoping to pick up all the basic concepts on-the-fly.** That should happen in the prepare phase, in your own preferred pace, at your most convenient time and place.

## Recitation (one 75-minute session)

In the small-group, TA-led recitation sessions, you will engage in group activities with your peers. This is a place for you to get more direct and customized feedback from the teaching team. Some parts of the assignments directly build on the work completed in recitation. This is also a place for you to practice oral math communication.

We will not take attendance, but the work is required. Put another way, we believe you get the exposure if you attend (and thus don’t even bother checking your work), but you will need to submit your work if you miss the recitation.

## Assignment (? hours)

Assignments examine your mastery of the concepts in each individual CM. There are two kinds of assignments (typically a CM has both kinds, but some only have one):

**Autograded practice questions on PrairieLearn**to be completed**individually**. This is a platform on which you can attempt the same type of questions over and over for an unlimited number of times until (the results show that) you have mastered the concepts. (Some CMs’ practice quizzes are also administered on PrairieLearn.)**Manually graded questions on Gradescope**that can be completed**in pairs**. (Edit: we allowed groups of 3 for the last two CMs.) This is where we (the teaching team) read your work and give you feedback on not only the mathematical correctness but also the quality (concision, rigor, etc.) of your mathematical communication. The complete feedback loop is as follows:- The first (initial) due date is roughly a week after the end of the recitation.
- The teaching team will give you feedback within one week (i.e., by the first due date of the next CM’s assignment).
- The feedback is by question. If there is nothing to revise, the feedback will just indicate so.
- This will happen strictly before any exam that covers this CM.

- You will then have some time (typically slightly less than a week) to revise your work based on the feedback and resubmit.
- For 3 out of the 8 CMs, this timespan will overlap with the corresponding exam; the idea is that the first round of feedback should sufficiently prepare you for the exam. In case it does not, you have the chance to retake any exam later in the finals week.

- Ideally, we would then implement a second round of feedback and a third round of submission, and so on. However, we do not have enough guaranteed resources to make this promise. We might add it if we end up having the resources. Edit: we ended up deciding to handle all outstanding revisions past round two via instructor interaction.

- Collaboration is allowed and encouraged (see Community Policies for detailed instructions on collaboration) but
**you should not work with the same assignment partner for consecutive CM assignments.**This is for you to work with as many of your peers as possible and learn from each other.