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Mathematics
Decade:
2010-2019
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UNT Scholarly Works
Continued Fractions and Sturmian Words: Discover the Power of Mathematics!
Date: April 14, 2011
Creator: Allen, Andrew & Cherry, William, 1966-
Description: This presentation discusses research on continued fractions as an alternative to decimal expansions. Abstract: Continued fractions are an alternative to decimal expansions for representing numbers. For a "random" number, if its decimal expansion is simple, its continued fraction expansion is probably complicated; conversely, if a number has a simple continued fraction, its decimal expansion usually appears random. The author's research involves examining numbers with nice patterns in both their decimal (or binary) expansions an din their continued fraction expansions. To explain this further, the authors the authors introduce some terminology: a "word" on the alphabet {0,1} is a possibly infinite string of 0's and 1's, e.g. 010101... The authors may also consider such a word as a binary decimal, e.g. 0.010101... A piece of a word is called a "subword." A word which is not periodic but still has as few subwords as possible is called a Sturmian word. The authors will explain how one can find simple patterns in the continued fraction expansions of some of these numbers.
Contributing Partner: UNT Honors College
Permallink:digital.library.unt.edu/ark:/67531/metadc93224/
An Elementary Characterization of the Orders of Non-Abelian Groups
Date: 2011
Creator: Anghel, Nicolae
Description: In this article, the author presents an elementary proof of a result due to Dickson characterizing those integers n admitting non-abelian groups of order n.
Contributing Partner: UNT College of Arts and Sciences
Permallink:digital.library.unt.edu/ark:/67531/metadc146578/
O generalizare a problemei piesei de 5 lei a lui Ţiţeica
Date: November 2012
Creator: Anghel, Nicolae
Description: The '5 lei coin' problem of Titeica is generalized to circles of arbitrary radii.
Contributing Partner: UNT College of Arts and Sciences
Permallink:digital.library.unt.edu/ark:/67531/metadc152461/
Legătura dintre sumele Stieltjes şi sumele simetrice elementare
Date: February 2012
Creator: Anghel, Nicolae
Description: This paper studies the relationship between the Stieltjes sums and the elementary symmetric sums.
Contributing Partner: UNT College of Arts and Sciences
Permallink:digital.library.unt.edu/ark:/67531/metadc152460/
A Tiling Game and Its Properties in the Plane: Discover the Power of Mathematics
Date: April 14, 2011
Creator: Bach, Kevin & Schlutzenberg, Farmer
Description: This presentation discusses research on a tiling game in which two players alternate placing dominoes over a chessboard pattern of a given size (possibly infinite). Play continues until no more tiles can be placed. Player 1, blocker, wins if less than a certain percentage of a board is tiled, while player 2, tiler, wins if that percentage or more of the board is tiled. When the percentage is 100, there are simple strategies for winning. When the percentage is less than 100, the minimum percentage of the board that can be tiled by the end of play must be determined in order for the winning percentage for tiler to not be trivial. In discovering this, many properties of the tiled space under the rules of the game can be found. This presentation focuses on these properties and their relationship to the game.
Contributing Partner: UNT Honors College
Permallink:digital.library.unt.edu/ark:/67531/metadc93225/
Continued Fractions: Discover the Power of Mathematics!
Date: April 14, 2011
Creator: Beardslee, Jordan & Cherry, William, 1966-
Description: This presentation discusses research on predictable patterns in continued fractions and decimal expansions. Abstract: A continued fraction is a representation of a number by series of fractions inside fractions, such that the numerator of every fraction is a one. Decimal expansion is another way to express a number. Many times in mathematics when we have two different ways to write the same expression, we look for connections between the two notations. When trying to express a number, we encounter an interesting anomaly between continued fractions and decimal expansions. A randomly chosen number, with a predictable decimal pattern, will have an unpredictable continued fraction. Furthermore, a randomly chosen continued fraction, with predictable partial quotients, will have an unpredictable decimal expansion. However, there are those few exceptions, one of which the author is studying in depth. It is a binary sequence closely tied with the Fibonacci numbers, a series of numbers that often occur in nature. Through the author's research, the author hopes to find an understanding to this aforementioned anomaly and bridge continued fractions and decimals. In this presentation, the author will show where predictability lies and furthermore where there is chaos still to be settled.
Contributing Partner: UNT Honors College
Permallink:digital.library.unt.edu/ark:/67531/metadc93226/
Autonomous Robot Localization Using WiFi Fingerprinting
Date: April 14, 2011
Creator: Bunkley, Terrence; Wright, Alex & Namuduri, Kamesh
Description: This paper discusses autonomous robot localization using WiFi fingerprinting. Abstract: We are using widely available 802.11 wireless networks to determine the location of autonomous robots. Before a robot can accomplish a simple task such as moving to a specific coordinate, it must accurately know its current location with-in a certain degree of accuracy. Humans often take their eye sight and spatial awareness for granted. For a robot, the computational difficulty of solving the same problem becomes apparent. Our implementation creates a database of wireless signal strengths of a given area and uses the current signal strength reading within the area to find a weighted signal space distance. The "closest" point in the database should also correlate with the current position of the robot. Given the robots correct location, the authors can successfully navigate around any area with sufficient Wi-Fi coverage.
Contributing Partner: UNT Honors College
Permallink:digital.library.unt.edu/ark:/67531/metadc94281/
Descriptive Set Theory: Why Should We Study It?
Date: April 14, 2011
Creator: Gilton, Thomas D. & Krueger, John
Description: In this presentation, the author will briefly introduce the subject of Descriptive Set Theory and the motivation for its study. The author will discuss the idea of a projective set and also define the mathematical notion of a "tree" as an example of a projective set. The author will conclude with a brief mention of a significant result that can be proved using the notion of a tree.
Contributing Partner: UNT Honors College
Permallink:digital.library.unt.edu/ark:/67531/metadc93250/
Parent's Education and Children's Test Scores
Date: April 19, 2012
Creator: Jennings, Garrett & Verrill, Diane
Description: This poster discusses research on correlations between parent's education and children's test scores. Parents can have an enormous amount of influence on their children's education. Many factors can change how heavily the influence is and if the effect is positive or negative. Children will typically be dealt with in different ways based on factors out of their control and these will impact their performance and their teachers' performances. For this project, the author would like to explore the correlation between the education of parents and the test scores of their children. The author will do that by analyzing data that has already been amassed by the College Board through their standardized tests and the questionnaires that come along with them.
Contributing Partner: UNT Honors College
Permallink:digital.library.unt.edu/ark:/67531/metadc86717/