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Access Rights: Public
Department: Mathematics
Resource Type: Presentation
Language: English
Collection: UNT Scholarly Works
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### 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

### 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

### 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

### 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

### The Effects of Technology on Achievement in Mathematics in Middle School

Date: March 30, 2006
Creator: Rooth, Heather M. & Tunks, Jeanne L.
Description: This presentation discusses a research study on the effect of technology on achievement in mathematics in middle school. This presentation discusses the research, which analyzes how these concepts, ideas, and problems have been discussed in the past in order to form a solid platform that will support technology in schools in the future.
Contributing Partner: UNT Honors College

### Fear Math? Fear No More! Analysis of Math Anxiety in MATH 1010 Students

Date: April 3, 2008
Creator: Draznin, Sara & Brand, Neal E.
Description: This presentation discusses research on mathematics anxiety. The author describes the current state of research and understanding of math anxiety, expounds upon this information with independent research conducted at UNT, evaluates this research, and suggests a plan for improved results in mathematics education.
Contributing Partner: UNT Honors College