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Articles 1 - 7 of 7
Full-Text Articles in Education
Time As A Line: Helping Children Make Abstract Ideas Concrete, Rachel Mae Stenner
Time As A Line: Helping Children Make Abstract Ideas Concrete, Rachel Mae Stenner
WWU Honors College Senior Projects
This is a math education project that included research, a lesson plan, and actual in the classroom work with students. Under the advisement of Dr. Rebecca Borowski, I looked into how time, an abstract idea, is taught to young children who are just starting to learn what measurement is, and examined how teachers can better teach time as a more concrete topic. This focused on the idea of turning the abstract time concepts that are thrown at children into the more abstract ideas of both circular and then linear number lines, using physical materials to help guide the process.
Making Upper-Level Math Accessible To A Younger Audience, Allyson Roller
Making Upper-Level Math Accessible To A Younger Audience, Allyson Roller
WWU Honors College Senior Projects
Symmetry is all around us. It appears on fabrics and on the buildings that surround us. Believe it or not, there is actually quite a bit of math that goes into generating these patterns, which are known as the seven frieze patterns. In my work, I explain how each unique pattern is generated using different types of symmetries. I also created a PDF of a children’s book about frieze patterns to ensure that people of all ages have the opportunity to learn about seemingly complex patterns.
Conformal Geometry Of Polygons, Michael Albert
Conformal Geometry Of Polygons, Michael Albert
WWU Honors College Senior Projects
Conformal maps are functions from subsets of the complex plane to the complex plane that locally preserve angles. Our goal is to understand conformal maps that pass to and from polygonal domains. In order to do so, we derive some of the basic theory of harmonic functions on simply connected domains. In particular, our goal with the first few sections is to prove the Schwarz Reflection principle. Using this, as well as other tools from complex analysis, we give an in-depth explanation of Tao’s proof of the Schwarz-Christoffel formula. This is a differential equation that allows one to compute a …
Do Men Matter? In Statistics, Probably, Michael Kelly
Do Men Matter? In Statistics, Probably, Michael Kelly
WWU Honors College Senior Projects
In statistical genetics, there are several parameters of a dataset which a researcher might, but which are difficult to estimate in practice. In this paper, we will be focusing on allele frequencies, null alleles, inbreeding coefficients and, to a certain extent, beta values. A common technique for obtaining these values, developed by Amy Anderson and her co-workers, is to jointly estimate all of them using an EM-algorithm and the method of maximum likelihood. Despite this technique being effective in general, it is currently unable to deal with males at X-linked markers. The purpose of this project is to modify the …
Deblurring Images, Jamie Mcmullen
Deblurring Images, Jamie Mcmullen
WWU Honors College Senior Projects
Let the matrix B be a blurred version of a sharp image represented by the matrix X. Given B, we would like to recover X.
To accomplish this, we construct linear models of the blurring process that produced B from X. The idea is that we could then reverse the blurring to reproduce the original image.
For example, if the blurred image satisfies
B = CXRT
for some invertible matrices C and R, then we could recover X as
X = C-1B(RT)-1.
However, the blurring model …
The World Before Calculus: Historical Approaches To The Tangent Line Problem, Lindsay Skinner
The World Before Calculus: Historical Approaches To The Tangent Line Problem, Lindsay Skinner
WWU Honors College Senior Projects
Pierre de Fermat and René Descartes were two brilliant 17th century mathematicians who have had lasting impacts on modern mathematics. Descartes laid the groundwork for the Cartesian coordinate system that is frequently employed in modern mathematics and Fermat’s last theorem vexed the mathematics community until Wiles’ proof was published in 1995. Amidst their many ground-breaking accomplishments these two men produced solutions for another mathematical problem - developing a general method to find the tangent line to a curve.
In spite of their apparent genius, neither man’s method had the lasting impact of their other works. Descartes’ and Fermat’s methods were …
A Comparison Of Two Statistical Tests For Interaction In Genetic Data, Clair Smith
A Comparison Of Two Statistical Tests For Interaction In Genetic Data, Clair Smith
WWU Honors College Senior Projects
This paper focuses on statistical methods that test for the effect of a single gene in a way that accounts for interaction with other genes. Such tests of association can be difficult since there may be many genetic and environmental factors that contribute to an effect. A gene is a hereditary DNA sequence that codes for a specific protein. A locus is a gene’s location in the DNA sequence of nucleotides (A, T, G, and C) and an allele is a specific version of a gene that has multiple forms. The existence of interactions between loci makes it difficult to …