Course Syllabus

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Welcome to 18.200! 

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) 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.

In addition to the lectures (MWF at 2PM in-person in 2-190), there will be a 1h recitation with compulsory attendance. The recitations will focus on the mathematical concepts seen in lectures and on effective mathematical writing. The recitations will be on Thursdays:

Staff. Lectures will be given by Peter Shor. The writing component of the course will be coordinated by Michael Maune and Susan Ruff, in collaboration with Peter. We also have a grad TA [TBA].

Modules:  This is where you can find lecture notes, and other resources and course materials.

Semester schedule This is the schedule of lecture and recitation topics, exams, homeworks, and term paper deadlines

Office hours.

  • Mitali Bafna: Thursday, 3-4pm. Room 4-251.
  • Peter Shor: Monday, 3-4pm. Room 2-375.
  • Shivam Nadimpalli : Friday, 9-10am. Room 2-376. 

Office Hours to discuss WRITING (one-on-one) Talking about writing is easiest one-on-one, so we encourage you to contact us to make an appointment.

18.062/6.042 vs 18.200. If you have already taken 18.062, you should not be taking 18.200 (or 18.200A), but instead more advanced subjects 18.2xx. If you take/pass both 18.200 and 6.042, 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 CIM. 

Limited Enrollment. This course has limited enrollment (because of the CI-M component). Please contact Theresa Cummings for registration questions. In case you were allowed to (and did) register for 18.200 but you have decided to drop it, we (and your fellow students on the waiting list) would much appreciate if you could let us and Theresa Cummings know as soon as possible.

Grading. The grade will be made up of:

  • Problem sets (most likely 10 of them, for a total of 30%; these will include both writing and non-writing assignments; psets will not all be equally weighted as some of the psets 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—due April 4—and second draft—due April 18—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—May 12.
  • two in-class quizzes (15% 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 on March 14 and May 2. 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.

Homework. Assignments will be posted on Gradescope, and must be submitted on Gradescope (the only exceptions are the pre-recitation assignments). 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 psets 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.

Late Policy on Problem Sets. You can submit any problem set 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 pset will be allowed after solutions are posted without a note from S3. As writing exercises will often be followed by a revision, it is quite disruptive when a writing piece is not submitted on time (eg 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. The website https://psetpartners.mit.edu/ is useful to form pset (or study) groups; we encourage you to sign up there. 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.

Recitations. There is a 1-hour weekly recitation in which we will both discuss communication and further explain the course material. Attendance in this recitation is mandatory. You are allowed two unexcused absences from recitation without penalty. The next two will cost you 1/4 of a percent from your grade each. After that, the cost will go up to 1/2 a percent. For many of the recitations, there will be a pre-recitation assignment.

You need to attend the section you are assigned to. You can try to change your section in Section Signup; this will not work if the recitation you are trying to change to is full (in which case you would have to wait until a spot frees up). If you have a conflict for a specific week, please inform the recitation instructor that you cannot make it and are attending a different section. 

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

Piazza. We will be using piazza for discussions. We encourage all of you not only to post questions, but also to provide answers or advice on other students' questions.

Pset Partners. If you want to find somebody to do psets with, I have added this class to Pset Partners: https://psetpartners.mit.edu/   I encourage you to use this site.

Generative AI. The guidelines 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 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.

Accommodations. Given the pandemic, we have to plan for contingencies. For the teaching staff, we will do our best to hold lectures, recitations, quizzes in-person, and our plan is to rotate responsibilities if one of us has to stay away from campus.

If you are dealing with a personal or medical issue (eg covid) that is impacting your ability to attend class (lecture or recitation), complete work, or take one of the exams, please discuss this with Student Support Services (S3) and they will contact all your professors. You may contact S3 by email s3-support@mit.edu or phone 617-253-4861. We will provide videotaped lectures to those students who will be unable to attend a few lectures (because of covid, some other illness, or some other personal issue), and provide accommodations for the relevant assignments. If you have a lecture conflict with another subject offered at the same time as 18.200 (we do not recommend this), you should contact us during the first week of class for accommodations. There will be no accommodations for the two in-class quizzes for conflicts with another class, or for unexcused reasons.

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. Because Gradescope does not support uploading of .tex files, we will only ask you to upload the .pdf file. However, please keep the original .tex file in your records: it can come handy if you are interested in appealing later on.

 

Course Schedule (subject to change):

 

Course Summary:

Course Summary
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