MATH 630. Enumerative Combinatorics

Fall, 2020, MWF 12:00 A.M.- 12:50 p.m. ETB 1020 & ZOOM

All Communication will go through eCampus

    Instructor: Dr. Catherine Yan

    Office: BLOCKER 513F

    E-mail:, and

    Class: MWF 12:00--12:50, ETB 1020 & ZOOM

    Office hours: eCampus discussion board and/or by appointment via ZOOM (or by appointment)

    Grade Policy: Grade is determined by Homeworks (including participation).

    Level : Graduate

    Prerequisites : Math 302 (Discrete Mathematics), or Math 431 (Structures and methods in Combinatorics), or equivalent will be sufficient.

    Course Description : This course will be an introduction at graduate level to the fundamental ideas and results of combinatorics. The course moves quickly but does not assume prior study in combinatorics. It is intended for graduate students from mathematics or related areas wanting a good one-semester background in fundamental and applicable discrete mathematics. It also provides solids preparation for advanced combinatorics and for various courses in computer sciences.

    The course will cover structures and methods of combinatorics, including basic counting techniques, sieve methods, generating functions, hypergeometric summation, and special topics on Catalan structures and symmetric functions. One emphasis of the course will be bijective proofs illustrating the frequent, and often surprising, interrelations between these structures. The prerequisite for this course is an undergraduate discrete mathematics course or permission of the instructor.

    Text: : A Course in Enumeration , by Martin Aigner, Springer. ISBN: 978-3-540-39032-9 (Print) 978-3-540-39035-0 (Online)

    Grading: Tne plan is to cover the first eight chapters of Aigner's textbook, on Basics and Methods, together two Topics chapters on the Catalan Connection and Symmetric Functions, We will have homework assignments every couple of weeks, depending on our progress in class. As exercise is an important part of combinatorics, anyone who misses three homework sets fails the course automatically. No late home work will be accepted except for university-approved excuses.

    The grade will be determined by the homework assignments (90%) and in-class participation (10%).
    The standard cutoffs for letter grades will be used:
    A 90/100; B 80/100; C 70/100; D 60/100.

    Homework Assignments

    Useful Identities This list will be updated periodically.

    Homework will be assigned every couple of weeks, depending on how much we cover in lectures. The following due dates are tentative.
    Homework Assignments and Solutions will be communicated through eCampus. Due date are subject to change.

    Lecture Schedule

    (subject to change without notice)

    Fundamental Coefficients, Stirling numbers, permutation statistics, set and integer partitions. twelve-fold way, lattice paths: 3 wks

    Formal Series and Infinite Matrices: 1 wk

    Generating Functions, tree counting, Lagrange inversion formula: 2.5 wk

    Hypergeometric Summmation: 0.5 wk, maple sheet.

    Sieve Methods, Mobius inversion, involution principle, Gessel-Viennot Lemma: 3 wk

    Number of patterns and Polya counting: 1 wk

    Catalan numbers and structures: 1.5 wk

    Optional topics: 1.5 wk

    MAKE-UP POLICY: Make-ups for missed quizzes and exams will only be allowed for a university approved excuse in writing. Wherever possible, students should inform the instructor before an exam or quiz is missed. Consistent with University Student Rules , students are required to notify an instructor by the end of the next working day after missing an exam or quiz. Otherwise, they forfeit their rights to a make-up.

    POLICY FOR ABSENCES: Attendance on a regular basis is expected. While there are occasionally good reasons for you to choose to miss class, my experience has been that there is a strong correlation between attendance (as long as you are awake and listening) and performance in the course.

    For absence related to injure or illness, students who are absent from class three or more days should provide instructors with confirmation from a medical provider for an excused absence.

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