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Applications Of Leggett Williams Type Fixed Point Theorems To A Second Order Difference Equation, Charley Lockhart Seelbach
Applications Of Leggett Williams Type Fixed Point Theorems To A Second Order Difference Equation, Charley Lockhart Seelbach
Online Theses and Dissertations
Using extensions of the Leggett-Williams fixed-point theorem, we prove the existence of solutions for a class of second-order difference equations with Dirichlet boundary conditions. We present these fixed point theorems and then show what conditions have to be met in order to satisfy the theorem. Finally, we provide specific examples to show the hypotheses of the theorems do not contradict one another.
Effective Methods Of Formative Assessment, Chelse Rae Bugg
Effective Methods Of Formative Assessment, Chelse Rae Bugg
Online Theses and Dissertations
The purpose of this research is to explore the implementation of formative assessment in the mathematics classroom. Formative assessment is considered to be any data-driven activity that an educator uses to help guide and improve instruction. While there is an abundance of research that concludes that formative assessment does indeed improve student achievement, practical methods of implementation are not thoroughly discussed. To partially determine which methods of formative assessment most positively impact student achievement, a study was conducted at Lafayette High School. The researcher compared two popular methods of formative assessment: daily exit slips and unit probing (pre-, middle-, and …
Increasing Automaticity, Sara Burns
Increasing Automaticity, Sara Burns
Online Theses and Dissertations
Automaticity is defined as the process of developing fluency in mathematics and the ability to answer a basic math problem routinely. Automaticity is one of the most important skills that a student can possess in mathematics. While there are many ways that an educator can implement strategies to increase automaticity in the classroom, the purpose of this study was to determine which of these methods of implementation is more effective: requiring students to practice automaticity three times per week or requiring students to practice automaticity five times per week.
Gaussian Amicable Pairs, Ranthony Ashley Clark
Gaussian Amicable Pairs, Ranthony Ashley Clark
Online Theses and Dissertations
Amicable pairs are two integers where the sum of the proper divisors of one is the other and vice versa. Since the Gaussian integers have many of the properties of the regular integers, we sought to discover whether there exist any pairs of Gaussian integers with the same property. It turns out that they do exist. In fact, some of the normal amicable pairs carry over as Gaussian amicable pairs. Also discovered are pairs that have a complex part.
Positive Solutions, Existence Of Smallest Eigenvalues, And Comparison Of Smallest Eigenvalues Of A Fourth Order Three Point Boundary Value Problem, Sarah Schulz King`
Positive Solutions, Existence Of Smallest Eigenvalues, And Comparison Of Smallest Eigenvalues Of A Fourth Order Three Point Boundary Value Problem, Sarah Schulz King`
Online Theses and Dissertations
The existence of smallest positive eigenvalues is established for the linear differential equations $u^{(4)}+\lambda_{1} q(t)u=0$ and $u^{(4)}+\lambda_{2} r(t)u=0$, $0\leq t \leq 1$, with each satisfying the boundary conditions $u(0)=u'(p)=u''(1)=u'''(1)=0$ where $1-\frac{\sqrt{3}}{3}\le p < 1$. A comparison theorem for smallest positive eigenvalues is then obtained. Using the same theorems, we will extend the problem to the fifth order via the Green's Function and again via Substitution. Applying the comparison theorems and the properties of $u_0$-positive operators to determine the existence of smallest eigenvalues. The existence of these smallest eigenvalues is then applied to characterize extremal points of the differential equation $u^{(4)} + q(t)u = 0$ satisfying boundary conditions $u(0) = u'(p) = u''(b) = u'''(b)= 0$ where $1-\frac{