Introduction to the theory and applications of combinatorics. Enumeration of combinatorial structures (permutations, integer partitions, set partitions). Bijections, inclusion-exclusion, ordinary and exponential generating functions.TEXTBOOK:
The course text is Herb Wilf's freely available generatingfunctionology.LECTURES and QUIZZES:
Lectures will be posted on Canvas in the Assignments tab. They will be available by the regularly scheduled lecture time. Quizzes are integrated with lectures. Lecture notes and videos (no quizzes) are hosted in a shared Google Drive folder; the links are in Announcements on Canvas.DISCUSSION SECTIONS:
Discussion sections will take place on Zoom starting in Week 2. A poll will be held the first week to decide on times, which will be announced. They will be focused on homework help. They will be scheduled on Canvas in the Zoom LTI Pro tab.OFFICE HOURS:
Office hours will take place on Zoom starting in Week 2. Times will be announced. They will be scheduled on Canvas in the Zoom LTI Pro tab.HOMEWORK:
Homework is the most important component of this course. The vast majority of learning advanced mathematics occurs while struggling with difficult problems and discussing them with others. Consequently, you are strongly encouraged to work on the homework with each other. However, you must write up your solutions separately. You are not allowed to use resources which simply give you answers---doing so completely defeats the purpose of the homework and is a serious Academic Integrity violation.
Homework will be posted weekly on Canvas; see the calendar for due dates. They will be turned in on GradeScope; see the assignments themselves for further directions. Your lowest homework score will be dropped.
You will be graded partly on style. You must use complete English sentences, standard notation, legible writing, etc. Certain parts of homework will be marked "bonus". You should think of these as opportunities to make up for lost points on other homework assignments.
You are strongly encouraged to type up your homework in LaTeX---this is an invaluable skill used daily by every working mathematician, and it's never too early to start learning. To encourage this, .tex source code for each homework will be provided. You are welcome to ask typesetting questions on Piazza, during lecture or discussion sections, and during office hours.CATALAN PROJECT:
You will be assigned groups of roughly 4-5 people and each group will be tasked with writing an exposition of a well-known combinatorics topic. Further details will be provided early in the quarter.EXAMS:
We will not have traditional exams this quarter.GRADING:
The components of the course will be weighted as follows:
While I may adjust the scale to be more lenient, I guarantee that the grade corresponding to a given percentage will not be lower than specified by the above scale.PIAZZA:
We will use Piazza for class announcements and discussions.
Post on Piazza whenever you're confused about homework, quizzes, the lecture, the textbook, course logistics, or anything relevant to the course. Do not let yourself be silenced by the fear of looking stupid. Your classmates, the TA's, and I will answer. You have the option of posting anonymously to classmates, though I encourage you to post as yourself to foster a sense of community with your classmates.
You are strongly encouraged to post messages on Piazza instead of emailing me or the TA's directly. Private posts can be made if needed.GRADESCOPE: We will use GradeScope for homeworks, projects, returning graded work, and regrade requests. Regrade requests are for when the rubric has been marked incorrectly. They are not for arguing with the rubric. More details will be announced during the quarter.