Mathematics Commons^™

The Mathematics Teacher Educator’S Reflection On Edtpa: The Basics And The Complexity Of Georgia’S Implementation, Lynn Stallings, Woong Lim

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Beginning in fall 2015, Georgia will require that all teacher candidates pass the edTPA, a performance-based assessment, as a requirement for initial certification. With the potential to impact teacher preparation programs in a profound way, the questions and issues related to the implementation of edTPA merit some critical reflection. In this article, we introduce the brief history of the instrument and review the basics of edTPA with a particular interest in middle grades mathematics. Furthermore, drawing upon our experience with edTPA during a pilot program and the extensive knowledge base of edTPA rubrics and scoring process, we present issues related …

Riemannian Submersions And Lagrangian Isometric Immerson 1, Yun Myung Oh

Faculty Publications

In [1], it has shown that if a Riemannian manifold admits a non- trivial Riemannian submersion with total geodesic fibers, then it cannot be isometrically immersed in any Riemannian manifold of non-positive sectional curvature as a minimal submanifold. In this paper, we consider a nontrivial Riemannian submersion and investigate some properties on Lagrangian iso- metric immersions using the submersion invariant.

Einstein Metrics On Piecewise-Linear Three-Spheres, Kyle Pitzen

Dissertations and Theses @ UNI

Einstein metrics on manifolds are in some ways the "best" or most symmetric metrics those manifolds will allow. There has been much work on these metrics in the realm of smooth manifolds, and many results have been published. These results are very difficult to compute directly, however, and so it is helpful to consider piecewise-linear approximations to those manifolds in order to more quickly compute and describe what these metrics actually look like. We will use discrete analogues to powerful preexisting tools to do analysis on two particular triangulations of the three dimensional sphere with the intent of finding Einstein …

Singular Value Inequalities: New Approaches To Conjectures, Peter Chilstrom

UNF Graduate Theses and Dissertations

Singular values have been found to be useful in the theory of unitarily invariant norms, as well as many modern computational algorithms. In examining singular value inequalities, it can be seen how these can be related to eigenvalues and how several algebraic inequalities can be preserved and written in an analogous singular value form. We examine the fundamental building blocks to the modern theory of singular value inequalities, such as positive matrices, matrix norms, block matrices, and singular value decomposition, then use these to examine new techniques being used to prove singular value inequalities, and also look at existing conjectures.

On The Persistence Properties Of The Cross-Coupled Camassa-Holm System, David Henry, Darryl Holm, Rossen Ivanov

Articles

In this paper we examine the evolution of solutions, that initially have compact support, of a recently-derived system of cross-coupled Camassa-Holm equations. The analytical methods which we employ provide a full picture for the persistence of compact support for the momenta. For solutions of the system itself, the answer is more convoluted, and we determine when the compactness of the support is lost, replaced instead by an exponential decay rate.

Particle Trajectories In Extreme Stokes Waves Over Inifinte Depth, Tony Lyons

Articles

We investigate the velocity field of fluid particles in an extreme water wave over infinite depth. It is shown that the trajectories of the particles within the fluid and along the free surface do not form closed paths over the course of one period, but rather undergo a positive drift in the direction of wave propagation. In addition it is shown that the wave crest cannot form a stagnation point despite the velocity of the fluid being zero there.

Mathematical Modelling At Secondary School: The Macsi-Clongowes Wood College Experience, J.P.F. Charpin, S. O'Hara, Dana Mackey

Articles

In Ireland, to encourage the study of STEM (science, technology, engineering and mathematics) subjects and particularly mathematics, the Mathematics Applications Consortium for Science and Industry (MACSI) and Clongowes Wood College (County Kildare, Ireland) organized a mathematical modelling workshop for senior cycle secondary school students. Participants developed simple mathematical models for everyday life problems with an open-ended answer. The format and content of the workshop are described and feedback from both students and participating teachers is provided. For nearly all participants, this workshop was an enjoyable experience which showed mathematics and other STEM components in a very positive way.

Weyl-Titchmarsh Type Formula For Periodic Schrodinger Operator With Wigner-Von Neumann Potential, Sergey Simonov, Pavel Kurasov

Articles

Schroedinger operator on the half-line with periodic background potential perturbed by a certain potential of Wigner-von Neumann type is considered. The asymptotics of generalized eigenvectors for the values of the spectral parameter from the upper half-plane and on the absolutely continuous spectrum is established. Weyl-Titchmarsh type formula for this operator is proven.

Mass Transfer From A Vertical Flat Plate Due To Natural Convection With A Constant Counterflow, David Mcdonnell, Brendan Redmond, Lawrence J. Crane

Articles

This paper first examines the mass transfer from a vertical flat surface of a soluble material due to natural convection. A perturbation term is then introduced into the stream function to model the introduction of a constant counterflow. The effect this counterflow has on both the overall mass transfer and the overall velocity profile is studied in detail.

Bayesian Model Selection For Exponential Random Graph Models, Alberto Caimo, Nial Friel

Articles

Exponential random graph models are a class of widely used exponential family models for social networks. The topological structure of an observed network is modelled by the relative prevalence of a set of local sub-graph configurations termed network statistics. One of the key tasks in the application of these models is which network statistics to include in the model. This can be thought of as statistical model selection problem. This is a very challenging problem---the posterior distribution for each model is often termed ``doubly intractable'' since computation of the likelihood is rarely available, but also, the evidence of the posterior …

Endomorphisms Of Abelian Groups With Small Algebraic Entropy, D. Dikranjan, Ketao Gong, P. Zanardo

Articles

We study the endomorphisms ϕ of abelian groups G having a “small” algebraic entropy h (where “small” usually means ). Using essentially elementary tools from linear algebra, we show that this study can be carried out in the group , where an automorphism ϕ with must have all eigenvalues in the open circle of radius 2, centered at 0 and ϕ must leave invariant a lattice in , i.e., be essentially an automorphism of . In particular, all eigenvalues of an automorphism ϕ with must be roots of unity. This is a particular case of a more general fact known …

Equivalences Of Dessins D'Enfants, Rachel M. Volkert

Honors Program Theses

Dessins d'enfants are bipartite graphs with a cyclic ordering given to the set of edges that meet at each vertex. Merling and Perlis presented a method by which to construct pairs of dessins d'enfants using the permutations induced by the action of a finite group on the cosets of two locally conjugate subgroups of that group. They called these pairs of dessins Gassmann equivalent and investigated some of their properties. First, we discuss several properties of pairs of dessins that imply Gassmann equivalence. Then, using elementwise conjugate subgroups, we introduce and investigate a weaker type of equivalence of dessins, which …

Developing Crochet Patterns For Surfaces Of Non-Constant Curvature, Katherine Lea Pearce

Honors Program Theses

The purpose of this project is to develop an algorithm to create crochet patterns for a variety of surfaces. I start with surfaces of constant curvature: the Euclidean surface and the sphere. Then, I generate patterns for surfaces of revolution by calculating the change in circumference for each row of stitches. My methods suggest an approach to crochet more surfaces such as surfaces whose cross section is not a circle. This research demonstrates how crochet can act as a discrete model of differential geometry. Producing these patterns allows for further research into the surfaces themselves by providing accurate models as …

Estimasi Parameter Model Hybridizing Exponential Smoothing Dan Neural Network Pada Hasil Pengukuran Mean Sea Level Satelit Altimetri Jason 2, Novi Mara

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Nilai parameter dari suatu model peramalan dapat diestimasi dengan meminumkan ukuran evaluasi keakuratan peramalan seperti MSE, MAE, MAPE dan AIC. Pada penelitian ini telah dilakukan estimasi parameter hybridizing neural network dengan exponential smoothing dengan meminimumkan MSE, MAE, MPE dan MAPE. Estimasi parameter dibatasi untuk nilai mulai dari 0.01 sampai dengan 0.99. Estimator merupakan nilai yang memberikan model dengan ukuran keakuratan peramalan MAE dan MSE minimum. Dari algoritma program R yang telah dibuat, diperoleh estimator parameter yang meminimalkan MSE adalah 0.13. Estimtor parameter yang meminimumkan MAE adalah 0.01. Estimator parameter yang meminimumkan nilai MPE dan MAPE bernilai sama yakni 0.27. Ketiga …

Aplikasi Model Generalized Space Time Autoregressive Pada Data Pencemaran Udara Di Kota Surabaya, Dhoriva Urwatul Wutsqa, Suhartono Suhartono, Brodjol Sutijo

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Penelitian ini secara bertujuan mengaplikasan model Generalized Space Time Autoregressive (GSTAR) untuk mendapatkan model peramalan data pencemaran udara di Kota Surabaya. Data yang digunakan dalam penelitian ini adalah zat polutan PM 10 ang berasal dari tiga stasiun pemantau di kota Surabaya mulai Januari hingga Desember 2009. Tahap-tahap pembentukan model peramalan data pencemaran udara meliputi identifikasi order autoregresif dengan criteria AIC (Akaike Information Criterion), estimasi parameter yang terdiri atas estimasi bobot antar lokasi dengan normalisasi korelasi silang dan estimasi parameter autoregresif dengan metode kuadrat terkecil, uji signifikansi parameter melalui statistik uji Wald, serta uji kesesuaian model. Model yang dihasilkan merupakan model …

Sifat Kendala Pemrograman Kerucut Order Dua Dengan Norma ˆŽ, Caturiyati Caturiyati

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Masalah pemrograman kerucut order dua (Second Order Cone Programming/SOCP) dengan norma merupakan suatu masalah yang merupakan bentuk khusus dari masalah pemrograman kerucut order dua dengan norma 2. Pada makalah ini dikembangkan pengertian kerucut order dua (Second Order Cone/SOC) dengan norma dan sifat sifat kendala pemrograman kerucut order dua dengan Norma berdasarkan pada pengertian kerucut order dua dengan norma 2 dan pemrograman kerucut order dua dengan norma 2. Paper ini ditulis dengan menguraikan pengertian kerucut order dua dengan norma 2 dan pemrograman kerucut order dua dengan norma 2, dilanjutkan dengan mengembangkan pengertian kerucut order dua dengan norma …

Multi Traveling Salesman Problem (Mtsp) Dengan Algoritma Genetika Untuk Menentukan Rute Loper Koran Di Agen Surat Kabar, Fitriana Yuli Saptaningtyas

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Permasalahan pendistribusian oleh beberapa loper koran di suatu agen surat kabar pada pelanggan sering mengalami keterlambatan. Bagaimana menentukan rute optimum bagi beberapa loper koran di sebuah agen surat kabar akan dimodelkan secara matematis dan akan diselesaikan menggunakan algoritma genetika. Permasalahan ini masuk dalam kategori Multi Travelling Salesman Problem (MTSP). Algoritma genetika yang mengadopsi proses evolusi makhluk hidup, pada penerapannya mengikuti langkah pembentukan populasi, menentukan nilai fitness, melakukan proses seleksi, melakukan pindah silang dan mutasi, dan membentuk individu baru. Algoritma genetika dapat digunakan untuk menentukan rute optimum perjalanan beberapa loper koran di suatu agen surat kabar. Penentuan rute perjalanan beberapa …

Software Requirements Specification Sinapra Berbasis Sistem Informasi, Nur Hadi Waryanto

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Sistem Informasi Sarana dan Prasarana (SINAPRA) merupakan bagian dari beberapa sistem informasi yang dipakai oleh Univeristas Negeri Yogyakarta. SINAPRA merupakan salah satu sistem yang akan dikembangkan dalam Sistem Informasi Terpadu (SIPADU).

Software Requirements Specification SINAPRA merupakan acuan teknis developer dalam mengembangkan sistem untuk tahap selanjutnya. Software Requirements Specification SINAPRA dikembangkan menggunakan model WSU-TC CptS 322 dengan berbasis sistem informasi terpadu UNY Kata Kunci : Software Requirements Specification, WSU-TC CptS 322, SINAPRA

Permanen Dan Dominan Suatu Matriks Atas Aljabar Max-Plus Interval, Siswanto Siswanto

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Misalkan himpunan bilangan real. Aljabar Max-Plus adalah himpunan dilengkapi dengan operasi maksimum dan penjumlahan ( . Setiap matriks persegi atas aljabar Max-Plus dapat dikaitkan dengan perrmanen dan dominan. Dari aljabar Max-Plus dapat dibentuk aljabar Max-Plus interval yaitu himpunan yang anggotanya merupakan interval-interval tertutup dalam atau dilengkapi dengan operasi maksimum dan penjumlahan . Dapat dibentuk himpunan matriks persegi atas aljabar Max-Plus interval. Dalam penelitian ini, akan dikaji tentang permanen dan dominan matriks atas aljabar Max-Plus interval, hubungan antara permanen dan dominan, serta bideterminan matriks atas aljabar Max-Plus interval. Dari hasil penelitian diperoleh formula permanen dan dominan, dominan selalu lebih kecil atau …

Kestabilan Global Bebas Penyakitflu Singapura (Hand, Foot And Mouth Disease)Berdasarkan Model Seirs, Eminugroho Ratna Sari

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

AbstrakPenelitian mengenai penyebaran HFMD pertama dilakukan menggunakan model SIR. Pada model ini,populasi individu yang sebenarnya telah terinfeksi tetapi belum menunjukkan gejala-gejala penyakit tidakdijelaskan. Dalam paper ini akan dibahas mengenai pembentukan model matematika dari penyebaranpenyakit HFMD menggunakan model SEIRS. Adanya penambahan kelas populasi E (Exposed) untukmelengkapi kekurangan pada model sebelumnya. Berdasarkan model, diperoleh titik ekuilibrium bebaspenyakit dan endemik. HFMD tidak akan mewabah jika R0 ï"¼1. Selanjutnya dilakukan simulasimenggunakan MAPLE 13.