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18.200 | Spring 2024 | Undergraduate

# Principles of Discrete Applied Mathematics

### Course Meeting Times

Lectures: 2 sessions/week, 1.5 hours/session

Recitations: 1 session/week, 1 hour/session

### Prerequisites

None. Corequisite: 18.06 Linear Algebra

Note: Corequisites are subjects that must be taken concurrently.

### Course Description

This course will teach you illustrative topics in discrete applied mathematics, including counting, generating functions, probability, linear optimization, algebraic structures, basic number theory, information theory, and coding theory. Prior exposure to linear algebra is definitely helpful for linear optimization and coding theory. This course is also a CI-M (Communication Intensive in the Major) course and thus includes a writing component. This component will take the form of writing assignments (often proofs) in homework problems; one of the assignments is a relatively long term paper whose writing will take a few iterations (with feedback along the way) between late February and the end of the term.

#### 18.062J/6.042J vs. 18.200

If you have already taken 18.062J/6.042J Mathematics for Computer Science, you should not be taking 18.200, but instead more advanced subjects 18.2xx. If you take/pass both 18.200 and 18.062J/6.042J, only one of them will count towards your course 18 or 18C requirements, even though both will count for your unit count beyond the GIRs, and 18.200 will count as a course 18 CI-M.

#### Limited Enrollment

This course has limited enrollment (because of the CI-M component).

### Recitations

In addition to the lectures, there will be a one-hour recitation each week with compulsory attendance. The recitations will focus on the mathematical concepts seen in lectures and on effective mathematical writing. For many of the recitations, there will be a pre-recitation assignment.

### Homework

You must clearly mark your recitation number on each problem you turn in. Homework will typically be posted on Mondays, a week before the due date. Writing assignments must be word processed (see the LaTeX section below) and should be submitted in PDF format. Hand-drawn figures are permitted, except for the final version of the term paper. You may draw your figures on the printed output and scan it in, or scan in your figures and include them in your document. If you do the non-writing problem sets by hand, you must write them legibly, and scan them with enough resolution for them to be easily legible. If they are barely legible, the graders are not required to accept them.

#### LaTeX

We require all writing assignments to be written in LaTeX. LaTeX is a document preparation system which is very good at handling mathematical equations, and which has become a standard in many fields, including mathematics, physics, and computer science. We have provided resources to help you learn it. In LaTeX, you edit a .tex file, and the software produces a .pdf file.

#### Late Policy on Problem Sets

You can submit any problem set up to 24 hours late, subject to a 10% decrease in your grade. We will not apply any penalty either if you are less than one hour late (enough time to fix internet issues) or if you are excused. After 24 hours, we may upload solutions; no problem set will be allowed after solutions are posted without a note from Student Support Services. As writing exercises will often be followed by a revision, it is quite disruptive when a writing piece is not submitted on time (e.g., if you submit your first or second draft of the term paper or some other writing exercise late, you may not receive timely feedback, impacting follow-up assignments and revisions.)

#### Collaboration Policy

Collaboration on homework is permitted, but you should first think about the problems on your own. You must write the solutions yourself; no copying is allowed. This policy will be strictly enforced. For the writing assignments, you may seek feedback from classmates and others, but the writing must be your own. You must list the names of your collaborators on your submitted homework and writing assignments, or state that you had none. Please also acknowledge any other source you may have consulted. We ask that you not refer to solutions from previous years, or from solution banks.

#### Tutoring

In addition to attending office hours, the Math Learning Center is also a good resource for students who need additional help.

#### Generative AI

The guideline for the use of large language models is the same as that for collaboration—you can use AI to help you figure out the solutions, but you should write up your solutions on your own. Note on the assignment that you used it, and how you used it. If you want to use AI to polish your first draft, or if you want to use AI to write a first draft, and then modify it, please talk to us about this first.

Two caveats: First, in a previous CI-M class, the instructors tried giving students rough drafts of a paper and having them revise them, and they observed that not only were the results worse than if the students had written the first draft themselves, but many students found revising somebody else’s draft was just as much work as writing their own first draft and revising it. Second, large language models often do a good job of finding a proof of a theorem if there are numerous proofs of it already on the web, but for theorems they haven’t “seen,” they are very likely to come up with nonsensical proofs.

### Grading

The grade will be based on the following elements:

- Problem sets (most likely 10 of them, for a total of 30%; these will include both writing and non-writing assignments; problem sets will not all be equally weighted as some of the problem sets will be longer than others).
- Term paper (35%, of which 20% is for the final paper, 5% is for the first draft, 5% is for the second draft, and 5% is for a peer review of other students’ papers). The grades for the first draft and second draft are effort grades—did you turn a draft in, and did you put a reasonable amount of effort into it? The final paper is due on the last day of classes.
- Three in-class quizzes (10% each) and participation in recitations (5%).

Some of the writing assignments will have to be revised after we give comments on them. The quizzes will take place in class during lecture. We will do our best to try to let you know how well you are doing during the semester, but your final grade will depend holistically on your performance during the semester. Your final letter grade is not a simple mathematical formula based on all your numerical scores and cutoffs. For example, if you skip the last quiz (unexcused), or do not complete the term project, expect that this will be reflected in your final grade. Also, for the same numerical score, we prefer to see students whose performance improves during the semester rather than the opposite.

## Course Info

##### Instructors

- Prof. Ankur Moitra
- Prof. Peter Shor
- Susan Ruff

##### Departments

- Mathematics

##### As Taught In

Spring 2024

##### Level

Undergraduate

##### Topics

- Mathematics
  - Applied Mathematics
  - Discrete Mathematics
  - Probability and Statistics
- Social Science
  - Communication

##### Learning Resource Types

theaters Lecture Videos
notes Lecture Notes
assignment Problem Sets
Editable Files

Browse Resources

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