Math 205, Spring 2003
Prof. Lynnell Matthews , lynnell@math.upenn.edu
Course webpage:
http://www.math.upenn.edu/~lynnell/205/
Office hours: Monday 11am-12pm, Wednesday 11:00-12:00pm in DRL
4E3.
Office Phone: 215-898-4828
Lecture 301: T 1:30pm-3:00pm in DRL 3C4
Lecture 302: Th 1:30pm-3:00pm in DRL 3C4
Course : Seminar
Assignment #1, DUE: wk of 1/27/03 Given in class
Assignment #2, DUE: wk of 2/3/03 posted 1/30/03:
1. Describe a setting which is counted by the Catalan numbers not
discussed in class. Illustrate the 4th Catalan number, C_4=14 of this
setting.
2. Def: A group G is said to be abelian if
a*b=b*a for all a,b
in G. Given this definition show that a group of order 5 must be
abelian.
3. Determine if the following sets G with the operation
indicated form a group. If not, state the group axiom that fails.
(a) G = set of all integers, a*b = a - b.
(b) G = set of all integers, a*b = a + b + ab.
(c) G = set of all nonnegative integers, a*b = a + b.
(d) G = set of all rationals with denominator divisible by 5
(written so that numberator and denominator are relatively prime),
a*b = a + b.
(e) G a set having more than one element, a*b = a for all
a,b in G.
Assignment #3, DUE: wk of 2/10/03 posted 2/8/03:
1. Describe a bijection between Dyck Paths and triangulation of an n+2-gon counted by the Catalan numbers.
2. Describe a bijection between planar trees and binary trees counted by the Catalan numbers.
3. List the elements of S_4, the Symmetric group on 4 elements.
4. Find a subgroup of S_4, you must prove it is a
subgroup.
Assignment #4, DUE: wk of 3/24/03 Given in class
Important Dates:
Last Day to Drop a Course: Friday,
Spring Break (no class): March 10-14
Last Day to Withdraw from a Course: Friday,
Last Day of Class: Thursday, March 24