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Full-Text Articles in Physical Sciences and Mathematics
Magic Squares Of Squares Of Order 4 Over Certain Finite Fields, Drew O’Neill
Magic Squares Of Squares Of Order 4 Over Certain Finite Fields, Drew O’Neill
Theses, Dissertations and Culminating Projects
A magic square of order n over a commutative ring R is an n x n matrix such that all the rows, columns, and the two diagonals add up to a fixed sum, which is called the magic sum. If all of the numbers in a magic square are perfect squares in R, it is called a magic square of squares. The rings under consideration in this thesis are either Z or Zp where p is a prime. In this thesis I present methods of constructing magic squares of squares of order 4 from selected ones of order 3. A …
Teaching Social Justice Mathematics In A Privileged Setting, Rick Mcnamee
Teaching Social Justice Mathematics In A Privileged Setting, Rick Mcnamee
Theses, Dissertations and Culminating Projects
This practitioner action research using qualitative techniques of gathering data looks at the experiences of students in a mostly white, upper-middle class suburb who enrolled in a class that integrated mathematics with social justice issues. The researcher designed the curriculum and co-taught the one semester course. The data were collected from pre-interviews, beginning and end of class questionnaires, quick writes, field notes, and end of class focus group interviews with all the students. The author chose a practitioner action research design because he wanted to be an integral part of the study. The cyclical nature of action research allowed him …
Number Theory Applications In Cryptography, Francesca Pizzigoni
Number Theory Applications In Cryptography, Francesca Pizzigoni
Theses, Dissertations and Culminating Projects
This thesis provides a unique cryptosystem comprised of different number theory applications. We first consider the well-known Knapsack Problem and the resulting Knapsack Cryptosystem. It is known that when the Knapsack Problem involves a superincreasing sequence, the solution is easy to find. Two cryptosystems are designed and displayed in this thesis that allow two parties often called Alice and Bob use a common superincreasing sequence in the encryption and decryption process. They use this sequence and a variation of the Knapsack Cryptosystem to send and receive binary messages. The first cryptosystem assumes that Alice and Bob agree on a shared …
Variations Of The Combinatorial Game Tron, Miriam Parnes
Variations Of The Combinatorial Game Tron, Miriam Parnes
Theses, Dissertations and Culminating Projects
The combinatorial game Tron is a two player game played on a graph, in which players move to adjacent vertices, but cannot move to any vertex which is currently occupied or which has been occupied by either player earlier in the course of the game. It was introduced by Hans Bodlaender, inspired by the Disney movie of the same name. Bodlaender and, later, Tillmann Miltzow considered the complexity of the question of whether a player has a winning strategy in the game. Miltzow also considered an extremal question regarding the ratio of the vertices taken by the second player over …
Proper Connection Of Bipartite Circulant Graphs, Melissa Marie Fuentes
Proper Connection Of Bipartite Circulant Graphs, Melissa Marie Fuentes
Theses, Dissertations and Culminating Projects
The study of proper edge-colorings of graphs has been a popular topic in graph theory since the work of Vizing. While the proper edge-colorings of entire graphs was the topic of interest when the subject began decades ago, more recent works have focused on the study of properly colored subgraphs, as opposed to proper colorings of graphs as a whole. The types of properly colored subgraphs that we will be most concerned with are paths. The topic of finding certain types of properly colored paths within larger edge-colored graphs, though seemingly specific in nature, has been a topic of much …