Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session


18.310 Principles of Discrete Applied Mathematics or 6.042J / 18.062J Mathematics for Computer Science; 18.06 Linear Algebra, 18.700 Linear Algebra, or 18.701 Algebra I; or permission of instructor.


This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic.

This course fulfills the Communication Intensive in the Major Requirement


Most student lectures will be given from this textbook:
Aigner, Martin, Günter M. Ziegler, and Karl Heinrich Hofmann. Proofs from THE BOOK. Springer, 2014. ISBN: 9783662442043. [Preview with Google Books]

Students may give other lectures, pending instructor approval.


Each student in the course is expected to do the following:

  • Give three 35 minute lectures.
  • Write a short paper on an assigned topic. This will be a 2 to 4 page paper which will be assigned in the beginning of the term.
  • Write a final paper on the topic of the last talk. This will include handing in a paper outline, a first draft, a second draft (if necessary) and a final draft. Papers must be written in LaTeX.
  • Attend all the meetings and give feedback on other students' talks. Students who miss more than one meeting will be required to write a short paper describing the lectures given there.
  • There is no final exam.


In additional to the assistance you will receive from your peers and instructor, help with presenting and writing is available from the department's mathematical communication specialist. A lecturer in Writing, Rhetoric, and Professional Communication is also available to help you. General help with writing and presenting (not specific to mathematics) is available from MIT's Writing Center. [Note: Not available to OCW users.]


1 Introduction, Lectures by instructor
3 Student lectures start
5 Short paper due
12 Final paper proposal due
14 Final paper outline due & Very short paper due
18 Final paper first draft due
21 Final paper second draft due
23 Final paper due


  • Each talk will be worth 15%; 7% for the depth and correctness of the mathematics, 7% for communication, and 1% for the audience's performance in the quiz. Any points lost on communication may be regained in subsequent lectures by improving the relevant issues.
  • The short paper will be worth 7%.
  • The very short paper will be worth 3%.
  • The final paper will be worth 25%.
  • Participation will count for 20%. Half of these points will be given for correctly solving the quizzes at the ends of the lectures, and half for giving helpful feedback to the speaker.


Collaboration on preparing lectures is encouraged, as is the reading and deciphering of material. However, papers have to be written individually. Students are strongly discouraged to commit plagiarism. It is forbidden to copy any complete sentence from another source, including work submitted in past years or other courses. It is furthermore not acceptable to copy a proof, rewriting each line. A good strategy for writing a proof that appears elsewhere is to read and understand the source, and then write it from scratch the next day.

Some guidelines of what is and isn't allowed are available from Math Comm, including some examples.