Mathematics Commons^™

Differential Graded Contact Geometry And Jacobi Structures, Rajan Amit Mehta

Mathematics Sciences: Faculty Publications

We study contact structures on nonnegatively graded manifolds equipped with homological contact vector fields. In the degree 1 case, we show that there is a one-to-one correspondence between such structures (with fixed contact form) and Jacobi manifolds. This correspondence allows us to reinterpret the Poissonization procedure, taking Jacobi manifolds to Poisson manifolds, as a supergeometric version of symplectization.

Nsf's Math-Science Partnership Projects- Measuring The Trickle-Down Effect Of American Tax Dollars, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Teacher Learning In Lesson Study, Jennifer M. Lewis, Davida Fischman, Iris Riggs, Kelli Wasserman

The Mathematics Enthusiast

This article documents teacher learning through participation in lesson study, a form of professional development that originated in Japan and is currently practiced widely in the US. Specifically, the paper shows how teachers in three different lesson study teams 1) expanded their mathematical content knowledge, 2) grew more skillful at eliciting and analyzing student thinking, 3) became more curious about mathematics and about student thinking, 4) emphasized students’ autonomous problem‐solving, and 5) increasingly used multiple representations for solving mathematics problems. These outcomes were common across three lesson study teams, despite significant differences among the teams’ composition, leadership, and content foci.

Supporting Middle School Mathematics Specialists’ Work: A Case For Learning And Changing Teachers’ Perspectives, Joy W. Whitenack, Aimee J. Ellington

The Mathematics Enthusiast

In this paper, we highlight one whole‐class discussion that took place in a middle school mathematics Rational Number and Proportional Reasoning course, one of the six mathematics courses teachers take to complete our state‐wide middle school mathematics specialist program. Statistical measures indicate that teachers made gains in their understanding of concepts and substantial gains in their views of teaching and preparedness. We provide a microanalysis of one of the lessons, to explain, in part, how they might have made this progress. To develop our argument, we coordinate a social analysis with an analysis of the types of specialized mathematical knowledge …

Feedback To Support Learning In The Leadership Institute For Teachers, Cathy Kinzer, Janice Bradley, Patrick Morandi

The Mathematics Enthusiast

Feedback is a type of formative assessment used to inform instruction and advance learning. Feedback serves as a mechanism to connect teaching and learning at the student level. Learners receive feedback, formally or informally, as they engage in learning experiences. Within the Leadership Institute for Teachers, a National Science Foundation funded research project, we are exploring feedback as a research‐informed process to support learning and improvement for individuals, teams, and university courses. There is an explicit focus on creating a culture of critical thinking and reasoning, taking ownership for learning both individually and collectively, and understanding how to improve teaching …

A Partnership's Effort To Improve The Teaching Of K-12 Mathematics In Rapid City, South Dakota, Ben Sayler, June Apaza, Vicki Kapust, Susan Roth, Becky Carroll, Pam Tambe, Mark St. John

The Mathematics Enthusiast

Over the span of ten years, a National Science Foundation‐funded partnership effort has collected and analyzed multiple forms of evidence, both direct and indirect, about improved teaching of mathematics within Rapid City Area Schools. This article describes the project's impact on K‐12 teaching and factors contributing to that impact. The authors argue that improvements in teaching are attributable largely to a robust infrastructure established to support teacher growth. Direct evidence includes classroom observations conducted by the project's external evaluation team. Indirect evidence exists in the form of data on student outcomes: achievement on the state's multiple‐choice accountability measure and achievement …

Decoupling The Stationary Navier-Stokes-Darcy System With The Beavers-Joseph-Saffman Interface Condition, Yong Cao, Yuchuan Chu, Xiaoming He, Mingzhen Wei

Mathematics and Statistics Faculty Research & Creative Works

This paper proposes a domain decomposition method for the coupled stationary Navier-Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition in order to improve the efficiency of the finite element method. The physical interface conditions are directly utilized to construct the boundary conditions on the interface and then decouple the Navier-Stokes and Darcy equations. Newton iteration will be used to deal with the nonlinear systems. Numerical results are presented to illustrate the features of the proposed method.

Topics In Electromagnetic, Acoustic, And Potential Scattering Theory, Umaporn Nuntaplook

Mathematics & Statistics Theses & Dissertations

With recent renewed interest in the classical topics of both acoustic and electromagnetic aspects for nano-technology, transformation optics, fiber optics, metamaterials with negative refractive indices, cloaking and invisibility, the topic of time-independent scattering theory in quantum mechanics is becoming a useful field to re-examine in the above contexts. One of the key areas of electromagnetic theory scattering of plane electromagnetic waves — is based on the properties of the refractive indices in the various media. It transpires that the refractive index of a medium and the potential in quantum scattering theory are intimately related. In many cases, understanding such scattering …

Bimodules Over Cartan Masas In Von Neumann Algebras, Norming Algebras, And Mercer's Theorem, Jan Cameron, David R. Pitts, Vrej Zarikian

Department of Mathematics: Faculty Publications

In a 1991 paper, R. Mercer asserted that a Cartan bimod- ule isomorphism between Cartan bimodule algebras A1 and A2 extends uniquely to a normal -isomorphism of the von Neumann algebras gener- ated by A1 and A2 (Corollary 4.3 of Mercer, 1991). Mercer's argument relied upon the Spectral Theorem for Bimodules of Muhly, Saito and Solel, 1988 (Theorem 2.5, there). Unfortunately, the arguments in the literature supporting their Theorem 2.5 contain gaps, and hence Mercer's proof is incomplete.

In this paper, we use the outline in Pitts, 2008, Remark 2.17, to give a proof of Mercer's Theorem under the additional …

Penggunaan Pita Melalui Pembelajaran Missouri Mathematics Project Untuk Memahamkan Siswa Tentang Luas Permukaan Bola, Pentri Arfia Dewi

Jurnal Pendidikan Sains

Penelitian ini akan mendeskripsikan penggunaan pita melalui pembelajaran Missouri Mathematics Project untuk memahamkan siswa tentang luas permukaan bola. Pembelajaran yang dilaksanakan berdasarkan pada tahapan pembelajaran Missouri Mathematics Project yang dipadukan dengan bahan manipulatif. Penelitian ini merupakan penelitian tindakan kelas. Setiap siklus terdiri dari tiga kali pertemuan. Dalam penelitian ini juga dilakukan kajian dari jawaban siswa. Hasil penelitian ini menunjukkan bahwa penerapan pembelajaran menggunakan bahan manipulatif bola dan pita dapat memahamkan siswa tentang luas permukaan bola.

Pembelajaran Berbantuan Multimedia Berdasarkan Teori Beban Kognitif Untuk Meningkatkan Kemampuan Menyelesaikan Masalah Program Linear Siswa X Tkr 1 Smkn 1 Doko, Fifi Damayanti

Jurnal Pendidikan Sains

Berdasarkan teori beban kognitif, pembelajaran efektif terjadi apabila beban intrinsic dikelola dengan baik, beban germane ditingkatkan, dan beban extraneous dikurangi. Penerapan multimedia merupakan salah satu upaya untuk mencapai pembelajaran yang efektif. Penelitian ini mengkaji penerapan pembelajaran matematika berbantuan multimedia dalam meningkatkan kemampuan siswa menyelesaikan masalah program linear. Penelitian ini menggunakan pendekatan penelitian tindakan kelas yang dilaksanakan dalam dua siklus. Hasil penelitian menunjukkan bahwa penggunaan multimedia dapat mengelola beban intrinsic, meningkatkan beban germane, dan mengurangi beban extraneous, sehingga kemampuan siswa dalam menyelesaikan masalah program linear meningkat.

Kajian Morfologi, Anatomi, Dan Agronomi Antara Kedelai Sehat Dengan Kedelai Terserang Cowpea Mild Mottle Virus Serta Pemanfaatannya Sebagai Bahan Ajar Di Sekolah Menengah Kejuruan, As’Ad Syamsul Arifin

Jurnal Pendidikan Sains

Salah satu penyebab rendahnya produktivitas kedelai di Indonesia adalah serangan virus belang samar kacang tunggak, Cowpea mild mottle virus (CPMMV). Penelitian ini merupakan penelitian survei yang bertujuan untuk menggambarkan dan mengumpulkan informasi mengenai kajian morfologi, anatomi, dan agronomi terhadap infeksi CPMMV pada varietas yang terinfeksi dan yang tidak terinfeksi. Data dianalisis secara deskriptif dan inferensial menggunakan ANAVA melalui program SPSS for Windows versi 16. Hasil penelitian menunjukkan bahwa varietas Gumitir sehat, Anjosmoro sehat, Mahameru sehat, MLGG 0021, dan MLGG 0268 memiliki ukuran daun, panjang petiol, serta nisbah daun (L/W dan L/PL) lebih besar dibandingkan varietas yang sakit. Varietas Argopuro sakit …

Pengaruh Model Siklus Belajar Berbantuan Mind Map Terhadap Prestasi Belajar Fisika Ditinjau Dari Kinerja Laboratorium Siswa Kelas Viii Smpn 1 Rejoso Kabupaten Pasuruan, Ary Analisa Rahma

Jurnal Pendidikan Sains

Penelitian ini bertujuan untuk menguji pengaruh model siklus belajar berbantuan mind map terhadap prestasi belajar fisika ditinjau dari kinerja laboratorium siswa kelas VIII pada materi cahaya di SMP Negeri 1 Rejoso, Kabupaten Pasuruan. Penelitian ini merupakan penelitian eksperimen semu dengan rancangan faktorial 2 × 2. Subjek penelitian berjumlah 204 siswa. Instrumen penelitian terdiri atas instrumen perlakuan yang meliputi silabus, RPP, dan LKS, serta instrumen pengukuran berupa instrumen kinerja laboratorium dan tes prestasi belajar fisika. Hasil penelitian menunjukkan bahwa prestasi belajar fisika siswa yang belajar menggunakan model siklus belajar berbantuan mind map lebih tinggi dibandingkan dengan siswa yang belajar melalui pembelajaran …

Pengembangan Profesionalitas Berkelanjutan/Continuing Professional Development (Cpd) Guru Bersertifikat Pendidik Di Smk Rumpun Teknologi Se-Malang Raya, Sujianto Sujianto

Jurnal Pendidikan Sains

Penelitian ini bertujuan untuk mendeskripsikan pengembangan profesionalitas berkelanjutan guru bersertifikat pendidik melalui investasi pengembangan diri, publikasi ilmiah, dan karya inovatif, baik secara mandiri, berkelompok, maupun melembaga. Penelitian menggunakan rancangan deskriptif kuantitatif dengan subjek guru kejuruan bersertifikat pendidik di wilayah Malang Raya. Instrumen penelitian meliputi kuesioner (angket) dan pedoman wawancara. Hasil penelitian menunjukkan bahwa pemberlakuan Undang-Undang Guru dan Dosen (UU Nomor 14 Tahun 2005) yang disertai pemberian tunjangan profesi sejatinya memberikan harapan besar dalam mendorong minat guru untuk terus mengembangkan profesionalitasnya. Namun, temuan penelitian menunjukkan kondisi yang berbeda. Tingkat pengembangan profesionalitas berkelanjutan guru bersertifikat pendidik di SMK rumpun teknologi se-Malang Raya …

Analisis Variasi Genetik Varian Jati Arboretum Dengan Penanda Mikrosatelit, Imas Cintamulya

Jurnal Pendidikan Sains

Seleksi tanaman jati untuk memperoleh sifat unggul tidak cukup hanya melalui penanda morfologi, tetapi juga perlu menggunakan penanda molekuler berdasarkan polimorfisme DNA. Oleh karena itu, perlu dilakukan kajian tanaman jati dari segi genetik pada level DNA untuk melihat variasi genetik. Informasi tentang variasi genetik jati diperlukan dalam pengadaan bibit untuk pembangunan hutan tanaman industri, dengan tujuan mencegah inbreeding dan mendukung upaya konservasi. Penelitian ini bertujuan untuk menganalisis variasi genetik varian jati arboretum menggunakan penanda molekuler mikrosatelit serta menyusun buku pengayaan kajian dasar-dasar molekuler tumbuhan, khususnya penanda mikrosatelit, dalam menganalisis variasi genetik varian jati arboretum yang berkualitas. Langkah-langkah penelitian meliputi isolasi …

Pembelajaran Kooperatif Tai Dan Game Puzzle Dalam Meningkatkan Motivasi Belajar Dan Pemahaman Konsep Matematika, Any Herawati

Jurnal Pendidikan Sains

Penelitian ini mendeskripsikan rancangan dan pelaksanaan pembelajaran kooperatif Team Assisted Individualized (TAI) dan game puzzle dalam meningkatkan motivasi belajar serta pemahaman konsep fungsi komposisi dan fungsi invers di SMA Negeri 3 Malang. Penelitian ini merupakan penelitian tindakan kelas dengan pendekatan mix research, yang dilaksanakan dalam tiga siklus. Subjek penelitian adalah siswa kelas XI IPA 1 semester genap tahun pelajaran 2011/2012 sebanyak 33 siswa, terdiri atas 13 siswa laki-laki dan 20 siswa perempuan. Data yang dikumpulkan meliputi motivasi belajar dan pemahaman konsep matematika siswa. Hasil penelitian menunjukkan bahwa pembelajaran kooperatif TAI dan game puzzle mampu meningkatkan motivasi belajar dan pemahaman konsep. …

Persepsi Pengelola Terhadap Peran Sistem Informasi Manajemen (Sim) Berbasis Teknologi Informasi (Ti) Dalam Pengelolaan Administrasi Sekolah Menengah Kejuruan Kota Mojokerto, Tri Wahjoedi Hidajat

Jurnal Pendidikan Sains

Peran sistem informasi manajemen (SIM) berbasis teknologi informasi sangat penting dalam pengelolaan sekolah untuk meningkatkan kualitas pelayanan, proses, dan prestasi belajar siswa. Oleh karena itu, penelitian ini bertujuan untuk mengungkap dan mendeskripsikan persepsi pengelola terhadap peran SIM berbasis TI dalam pengelolaan administrasi SMK di Kota Mojokerto. Penelitian ini menggunakan rancangan deskriptif kuantitatif dan dilaksanakan pada sembilan SMK di Kota Mojokerto dengan 45 pengelola administrasi akademik sebagai populasi. Teknik pengambilan sampel yang digunakan adalah sampel jenuh, yaitu seluruh populasi dijadikan sampel. Hasil penelitian menunjukkan bahwa: (1) secara umum, persepsi pengelola terhadap peran SIM berbasis TI dalam pengelolaan administrasi SMK tergolong penting, …

Integrasi Pendidikan Karakter Melalui Inkuiri Dengan Lesson Study Dalam Pembelajaran Biologi Untuk Meningkatkan Sikap Ilmiah Dan Hasil Belajar Kognitif Siswa Kelas Vii Smpn I Singosari, Elly Lailatul Budur

Jurnal Pendidikan Sains

Pembelajaran inkuiri memungkinkan siswa terlibat secara aktif dalam proses berpikir dan menemukan konsep yang dipelajarinya. Pengetahuan dan keterampilan yang diperoleh siswa diharapkan bukan sekadar hasil menghafal fakta, melainkan hasil dari proses penemuan secara mandiri. Hasil pengamatan awal menunjukkan bahwa siswa SMP Negeri 1 Singosari masih cenderung menghafal materi pembelajaran sehingga keterampilan proses dan sikap ilmiah belum berkembang secara optimal. Selain itu, karakter siswa sebagaimana diamanatkan dalam tujuan pendidikan nasional belum sepenuhnya tercapai. Penelitian ini bertujuan untuk meningkatkan sikap ilmiah dan hasil belajar kognitif siswa melalui integrasi pendidikan karakter dengan metode inkuiri terbimbing berbasis lesson study pada siswa kelas VII SMP …

Penerapan Pembelajaran Inkuiri Terbimbing Berbasis Laboratorium Untuk Meningkatkan Keterampilan Proses Dan Hasil Belajar Ipa Siswa Kelas Viii-4 Di Smpn 1 Probolinggo, Karyatin Karyatin

Jurnal Pendidikan Sains

Penelitian ini bertujuan untuk mendeskripsikan keterlaksanaan pembelajaran inkuiri terbimbing berbasis kegiatan laboratorium dalam meningkatkan keterampilan proses sains dan hasil belajar kognitif IPA (biologi) siswa. Deskripsi keterlaksanaan pembelajaran diperoleh melalui identifikasi permasalahan yang muncul selama proses pembelajaran di kelas, yang selanjutnya dianalisis untuk menemukan solusi berdasarkan data empiris di lapangan. Penelitian ini juga berupaya mengungkap permasalahan pembelajaran secara menyeluruh dan kontekstual dengan menempatkan peneliti sebagai instrumen kunci. Pendekatan yang digunakan adalah kualitatif dengan jenis penelitian tindakan kelas (PTK) yang dilaksanakan dalam dua siklus. Setiap siklus terdiri atas empat pertemuan dengan alokasi waktu 2 × 40 menit per pertemuan. Teknik pengumpulan data …

The Frobenius Manifold Structure Of The Landau-Ginzburg A-Model For Sums Of An And Dn Singularities, Rachel Megan Webb

Theses and Dissertations

In this thesis we compute the Frobenius manifold of the Landau-Ginzburg A-model (FJRW theory) for certain polynomials. Specifically, our computations apply to polynomials that are sums of An and Dn singularities, paired with the corresponding maximal symmetry group. In particular this computation applies to several K3 surfaces. We compute the necessary correlators using reconstruction, the concavity axiom, and new techniques. We also compute the Frobenius manifold of the D3 singularity.

Market Dynamics With Non-Homogeneous Poisson Processes, Preston T. Redd

Theses and Dissertations

The Bertrand Duopoly model for demand in economics is a well-used model. Although this model has important insights towards pricing strategy, it does not accurately depict true market behaviors. In this paper, we will examine the advantages and disadvantages of the current model and its assumptions.We then take a whole new approach towards modeling this phenomena, using Poisson processes to model the demand of goods. We will discuss why this is a better approach and explain how we can extend this to better understand pricing strategies and market dynamics. We then apply our findings to the newsvendor problem, a commonly …

Identification Of Beryllium-Dependent Peptides Recognized By Cd4+ T Cells In Chronic Beryllium Disease, Michael T. Falta, Clemencia Pinilla, Douglas G. Mack, Alex N. Tinega, Francis Crawford, Marc Giulianotti, Radleigh Santos, Gina M. Clayton, Yuxiao Wang, Xuewu Zhang, Lisa A. Maier, Philippa Marrack, John W. Kappler, Andrew P. Fontenot

Mathematics Faculty Articles

Chronic beryllium disease (CBD) is a granulomatous disorder characterized by an influx of beryllium (Be)-specific CD4+ T cells into the lung. The vast majority of these T cells recognize Be in an HLA-DP–restricted manner, and peptide is required for T cell recognition. However, the peptides that stimulate Be-specific T cells are unknown. Using positional scanning libraries and fibroblasts expressing HLA-DP2, the most prevalent HLA-DP molecule linked to disease, we identified mimotopes and endogenous self-peptides that bind to MHCII and Be, forming a complex recognized by pathogenic CD4+ T cells in CBD. These peptides possess aspartic and glutamic acid residues at …

Modelling Infertility With Markov Chains, Rebecca Dorff

Theses and Dissertations

Infertility affects approximately 15% of couples. Testing and interventions are costly, in time, money, and emotional energy. This paper will discuss using Markov decision and multi-armed bandit processes to identify a systematic approach of interventions that will lead to the desired baby while minimizing costs.

Investment-Consumption With A Randomly Terminating Income, James Benjamin Taylor Jr.

Theses and Dissertations

We develop a stochastic control model for an investor's optimal investment and consumption over an uncertain planning horizon when the investor is endowed with a defaultable income stream. The distributions of the random time of default and the random terminal time are prescribed by deterministic hazard rates, and the investor makes investments in a standard financial market with a bond and a stock, modeled by geometric Brownian motion. In addition, the investor purchases insurance against both default and the terminal date, the default insurance serving as a proxy for the investor's disutility for default. We approximate the original continuous-time problem …

Quadratic Fields With 2-Skylow Class Group Isomorphic To C2kc2, Adele Lopez, Dr. Paul Jenkins

Journal of Undergraduate Research

We prove that there are infinitely many imaginary quadratic fields with 2-class group isomorphic to C2kC2 for any given positive integer k. This work is based on a related result for cyclic 2-class groups by Dominguez, Miller and Wong, and our proof proceeds similarly. However, we make some improvements in some of the techniques used. In particular, we provide a more general way of introducing congruence conditions into Perelli’s version of the Goldbach conjecture for polynomials.

Moral Hazard In Hedge Funds: An Approach Using Stochastic Differential Games, Jeremiah Bejarano, Dr. Jeffrey Humpherys

Journal of Undergraduate Research

This project is a continuation of a line of research that I have been working on over the last two years, with the object of analyzing the relationship incentive structure present in the hedge fund industry and identifying any potential for moral hazard. In economics theory, “moral hazard” is a situation in which one party is more willing to take on a risk due to the fact that he or she knows that the potential costs or burden of that risk will be borne, in part or in whole, by others. In this project, my goal was to develop a …

The Planar Equitent Conjecture: Combining Isoperimetry And Minimal Surfaces, Abraham Frandsen, Dr. Michael Dorff

Journal of Undergraduate Research

The goal of this project was to explore a new problem in geometric optimization: isoperimetric surfaces with both boundary and volume constraints. The idea behind the problem is the following: what is the optimal way to enclose a given volume with a surface that must also span a given boundary? In this case, optimal means least possible surface area. If we were to consider only the volume constraint, we would have the classical isoperimetric problem—and by now it is well-known and mathematically proven that the best way to enclose a given volume is with a sphere. On the other hand, …

An Explanation Of Strange Duality In Terms Of Landau-Ginzburg Mirror Symmetry, Rachel Suggs, Dr. Tyler Jarvis

Journal of Undergraduate Research

Suppose you have a physical system that can jump suddenly between two stable states. Then a function modeling the system will have a singularity at the jump. Our singularities will all be defined by polynomials, such as x3y + y5 + z2. Mathematician V.I. Arnol’d studied such singularities in an abstract setting, and he noticed that a certain 14 singularities came in pairs: numbers describing two di erent aspects of these singularities matched each singularity with its \dual” partner, which had the same numbers but with reversed roles (see Table 1). Arnol’d found no mathematical or physical reason why these …

Rock-Paper-Scissors In The Chemostat, James P. Braselton, Martha L. Abell, Lorraine Braselton

Mathematical Sciences: Faculty Publications

Rock-Paper-Scissors is a game played by two players to determine a single winner. Biological relationships of Rock-Paper-Scissors are documented. In this paper, we form a continuous model of Rock-Papers-Scissors in the chemostat that coincides with the biology of such relationships. The basic models that we develop coincide with the observed phenomena. Because the model involves a system of seven nonlinear differential equations, global results are difficult to obtain. We present several numerical studies that are the result of a substantial number of numerical trials to illustrate the various possibilities that might occur in the context of the problem discussed here.

Super-Resolution Via Superset Selection And Pruning, Laurent Demanet, Deanna Needell, Nam Nguyen

CMC Faculty Publications and Research

We present a pursuit-like algorithm that we call the "superset method" for recovery of sparse vectors from consecutive Fourier measurements in the super-resolution regime. The algorithm has a subspace identification step that hinges on the translation invariance of the Fourier transform, followed by a removal step to estimate the solution's support. The superset method is always successful in the noiseless regime (unlike L1-minimization) and generalizes to higher dimensions (unlike the matrix pencil method). Relative robustness to noise is demonstrated numerically.