Academics Navigation
Academics
You are here
Courses
Campus | Bryn Mawr |
Semester | Fall 2020 |
Registration ID | MATHB295001 |
Course Title | Topics in Mathematics-Enumerative Combinatorics |
Credit | 1.00 |
Department | Environmental Studies |
Instructor | Myers,Amy N. |
Times and Days | MTh 02:40pm-04:00pm
|
Room Location | |
Additional Course Info | Class Number: 2357 This is a topics course. Course content varies. Not all topics are open to first year students.; Current topic description: Enumerative combinatorics is a collection of techniques for enumerating a set of objects (saying how many) without listing all the possibilities. Combinatorial techniques are often applied to questions of probability in situations when all outcomes are equally likely. For example, in a game of poker, any combination of five cards is equally likely to be dealt from a well-shuffled deck. What is the probability that any particular set of five cards form a full house (three of one rank and two of another)? To answer this question, we divide the number of full-house combinations by the total number of five-card combinations. To obtain these two numbers without listing all the possibilities, we use combinatorics. Although combinatorial problems can often be stated in the language of puzzles and games, the results have applications throughout mathematics, both pure and applied. Topics include: permutations, combinations, binomial identities, generating functions, recurrence relations, inclusion-exclusion, and Polya’s enumeration formula. The official prerequisite for this course is Math 203: LInear Algebra. Proof-writing experience (such as Math 206: Transition to Higher Mathematics) is strongly recommend, but not required. Course content includes counting techniques and methods of proof such as: the pigeonhole principle, mathematical induction, permutations, combinations, binomial identities, compositions, partitions, the sieve method, and generating functions. Graph theory will be introduced if time permits. Approach: Quantitative Methods (QM); Haverford: C: Physical and Natural Processes (C), Does not satisfy Haverford QU (NO_QU) Enrollment Limit: 25; Enrollment Criteria: Major/Minor/Concentration; Prerequisite: MATH B203 or permission from instructor. Asynchronous online lectures and written homework submitted online. Group work either online or in-person (depending on group members' preferences). Class time (MTh 2:40pm - 4pm) for a fraction of the class to meet with the professor in person. Class meetings will be recorded for others not present to view. The frequency with which students meet with the professor depends on the number of students in the class and the size of the classroom. |
Miscellaneous Links |