Title page for ETD etd-042706-133106

Document Type	thesis
Author Name	Palmacci, Matthew Stephen
Email Address	mspalmacci at msn.com
URN	etd-042706-133106
Title	Escher's Problem and Numerical Sequences
Degree	MS
Department	Mathematical Sciences
Advisors	Brigitte Servatius, Advisor
Keywords	sequences Escher Catalan Collatz integer
Date of Presentation/Defense	2006-04-18
Availability	unrestricted
Abstract Counting problems lead naturally to integer sequences. For example if one asks for the number of subsets of an $n$-set, the answer is $2^n$, or the integer sequence $1,~2,~4,~8,~ldots$. Conversely, given an integer sequence, or part of it, one may ask if there is an associated counting problem. There might be several different counting problems that produce the same integer sequence. To illustrate the nature of mathematical research involving integer sequences, we will consider Escher's counting problem and a generalization, as well as counting problems associated with the Catalan numbers, and the Collatz conjecture. We will also discuss the purpose of the On-Line-Encyclopedia of Integer Sequences.
Files	palmacci.pdf

Browse by Author | Browse by Department | Search all available ETDs