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Добірка наукової літератури з теми "Quantitative Algebra"

Автор: Grafiati
Опубліковано: 5 жовтня 2024

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Статті в журналах з теми "Quantitative Algebra"

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Perrucci, Daniel, and Marie-Françoise Roy. "Quantitative fundamental theorem of algebra." Quarterly Journal of Mathematics 70, no. 3 (May 15, 2019): 1009–37. http://dx.doi.org/10.1093/qmath/haz008.

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Abstract Using subresultants, we modify a real-algebraic proof due to Eisermann of the fundamental theorem of Algebra (FTA) to obtain the following quantitative information: in order to prove the FTA for polynomials of degree d, the intermediate value theorem (IVT) is required to hold only for real polynomials of degree at most d2. We also explain that the classical proof due to Laplace requires IVT for real polynomials of exponential degree. These quantitative results highlight the difference in nature of these two proofs.
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2

Burch, Lori, Erik S. Tillema, and Andrew M. Gatza. "“Counting” on Quantitative Reasoning for Algebra." Mathematics Teacher: Learning and Teaching PK-12 114, no. 6 (June 2021): 452–62. http://dx.doi.org/10.5951/mtlt.2020.0183.

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Use this approach to developing algebraic identities as a generalization of combinatorial and quantitative reasoning. Secondary school students reason about important ideas in the instructional sequence, and teachers consider newfound implications for and extensions of this generalization in secondary algebra curricula.
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3

McIver, A. K., C. C. Morgan, and T. Rabehaja. "Program algebra for quantitative information flow." Journal of Logical and Algebraic Methods in Programming 106 (August 2019): 55–77. http://dx.doi.org/10.1016/j.jlamp.2019.04.002.

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4

Holgate, Philip. "Biometric and chromosome algebras." Journal of Applied Probability 29, no. 2 (June 1992): 247–54. http://dx.doi.org/10.2307/3214563.

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This note continues the development of the infinite-dimensional genetic algebra approach to problems of population genetics. Two algebras are studied. One describes the familiar problem of a quantitative characteristic, and the other provides a way of treating the whole chromosome as an entity.
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Holgate, Philip. "Biometric and chromosome algebras." Journal of Applied Probability 29, no. 02 (June 1992): 247–54. http://dx.doi.org/10.1017/s0021900200043011.

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Анотація:
This note continues the development of the infinite-dimensional genetic algebra approach to problems of population genetics. Two algebras are studied. One describes the familiar problem of a quantitative characteristic, and the other provides a way of treating the whole chromosome as an entity.
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6

Sari, Puspita, and Swee Fong Ng. "Exploring quantitative relationship through area conservation activity." Journal on Mathematics Education 13, no. 1 (February 11, 2022): 31–50. http://dx.doi.org/10.22342/jme.v13i1.pp31-50.

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Algebra as a study of quantitative relationship is one of four conceptions of school algebra which serves as a foundation for the concept of function. However, there is still a lack of attention to this particular relationship, especially in early algebraic reasoning. This study aims to investigate how the aspect of quantitative relationship in early algebra can be explored through area conservation activities. Understanding area conservation is said to be fundamental in developing the concept of area measurement. In this study, a ten-year old pupil was observed during her involvement while comparing area of two polygons that can be decomposed into equivalent triangles. Data for this study include the pupil’s written artefacts, and video recordings of the activities and interviews. Findings from this study show that the area conservation activity has the potential to build the notion of quantitative relationships in early algebra. The quantitative relationship between the unit of measurement and the result of measurement of a shape can also be explored, that is, the smaller the unit of measurement, the larger the result of measurement. Hence, this study can provide a groundwork for further studies in the relation between quantitative relationship in algebra and area conservation in geometry at the elementary school level.
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7

Thompson, Robert C. "High, low, and quantitative roads in linear algebra." Linear Algebra and its Applications 162-164 (February 1992): 23–64. http://dx.doi.org/10.1016/0024-3795(92)90371-g.

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8

Arendasy, Martin, Markus Sommer, Georg Gittler, and Andreas Hergovich. "Automatic Generation of Quantitative Reasoning Items." Journal of Individual Differences 27, no. 1 (January 2006): 2–14. http://dx.doi.org/10.1027/1614-0001.27.1.2.

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This paper deals with three studies on the computer-based, automatic generation of algebra word problems. The cognitive psychology based generative/quality control frameworks of the item generator are presented. In Study I the quality control framework is empirically tested using a first set of automatically generated items. Study II replicates the findings of Study I using a larger set of automatically generated algebra word problems. Study III deals with the generative framework of the item generator by testing construct validity aspects of the item generator produced items. Using nine Rasch-homogeneous subscales of the new intelligence structure battery (INSBAT, Hornke et al., 2004 ), a hierarchical confirmatory factor analysis is reported, which provides first evidence of convergent as well as divergent validity of the automatically generated items. The end of the paper discusses possible advantages of automatic item generation in general ranging from test security issues and the possibility of a more precise psychological assessment to mass testing and economical questions of test construction.
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MCIVER, ANNABELLE, LARISSA MEINICKE, and CARROLL MORGAN. "Hidden-Markov program algebra with iteration." Mathematical Structures in Computer Science 25, no. 2 (November 10, 2014): 320–60. http://dx.doi.org/10.1017/s0960129513000625.

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We use hidden Markov models to motivate a quantitative compositional semantics for noninterference-based security with iteration, including a refinement- or ‘implements’ relation that compares two programs with respect to their information leakage; and we propose a program algebra for source-level reasoning about such programs, in particular as a means of establishing that an ‘implementation’ program leaks no more than its ‘specification’ program.This joins two themes: we extend our earlier work, having iteration but only qualitative (Morgan 2009), by making it quantitative; and we extend our earlier quantitative work (McIver et al. 2010) by including iteration.We advocate stepwise refinement and source-level program algebra – both as conceptual reasoning tools and as targets for automated assistance. A selection of algebraic laws is given to support this view in the case of quantitative noninterference; and it is demonstrated on a simple iterated password-guessing attack.
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Wang, Yingxu, Mehrdad Valipour, and Omar A. Zatarain. "Quantitative Semantic Analysis and Comprehension by Cognitive Machine Learning." International Journal of Cognitive Informatics and Natural Intelligence 10, no. 3 (July 2016): 13–28. http://dx.doi.org/10.4018/ijcini.2016070102.

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Анотація:
Knowledge learning is the sixth and the most fundamental category of machine learning mimicking the brain. It is recognized that the semantic space of machine knowledge is a hierarchical concept network (HCN), which can be rigorously represented by formal concepts in concept algebra and semantic algebra. This paper presents theories and algorithms of hierarchical concept classification by quantitative semantic analysis based on machine learning. Semantic equivalence between formal concepts is rigorously measured by an Algorithm of Concept Equivalence Analysis (ACEA). The semantic hierarchy among formal concepts is quantitatively determined by an Algorithm of Relational Semantic Classification (ARSC). Experiments applying Algorithms ACEA and ARSC on a set of formal concepts have been successfully conducted, which demonstrate a deep machine understanding of formal concepts and quantitative relations in the hierarchical semantic space by machine learning beyond human empirical perspectives.
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Дисертації з теми "Quantitative Algebra"

1

Perkins, Jonathan Hale. "Some applications of linear algebra to quantitative spectroscopy /." Thesis, Connect to this title online; UW restricted, 1988. http://hdl.handle.net/1773/11534.

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2

Sarkis, Ralph. "Lifting Algebraic Reasoning to Generalized Metric Spaces." Electronic Thesis or Diss., Lyon, École normale supérieure, 2024. http://www.theses.fr/2024ENSL0025.

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On retrouve le raisonnement algébrique partout en mathématique et en informatique, et il a déjà été généralisé à pleins de contextes différents. En 2016, Mardare, Panangaden et Plotkin ont introduit les algèbres quantitatives, c'est-à-dire, des espaces métriques équipés d'opérations 1-lipschitzienne relativement à la métrique. Ils ont prouvées des homologues à des résultats importants en algèbre universelle, et en particulier ils ont donné un système de déduction correct et complet qui généralise la logique équationnelle de Birkhoff en remplaçant l'égalité par l'égalité à \varepsilon près. Ça leur a permis de donner une axiomatisation algébrique pour quelques métriques importantes comme la distance de Hausdorff et celle de Kantorovich.Dans cette thèse, on modifie deux aspects du cadre de Mardare et al. Premièrement, on remplace les métriques par une notion plus générale qui englobe les pseudométriques, les ordres partiels, les métriques probabilistes, entre autres. Deuxièmement, on n'exige pas que les operations de nos algèbres quantitatives soient lipschitzienne. On donne un système de déduction correct et complet, on construit les algèbres quantitatives libres, et on démontre la valeur de notre généralisation en prouvant que toute monade sur les espaces métriques généralisés qui est le relèvement d'une monade finitaire sur les ensembles peut être présentée par une théorie algébrique quantitative. On applique ce dernier résultat pour obtenir une axiomatisation de la distance de \L ukaszyk--Karmowski
Algebraic reasoning is ubiquitous in mathematics and computer science, and it has been generalized to many different settings. In 2016, Mardare, Panangaden, and Plotkin introduced quantitative algebras, that is, metric spaces equipped with operations that are nonexpansive relative to the metric. They proved counterparts to important results in universal algebra, and in particular they provided a sound and complete deduction system generalizing Birkhoff's equational logic by replacing equality with equality up to \varepsilon. This allowed them to give algebraic axiomatizations for several important metrics like the Hausdorff and Kantorovich distances.In this thesis, we make two modifications to Mardare et al.'s framework. First, we replace metrics with a more general notion that captures pseudometrics, partial orders, probabilistic metrics, and more. Second, we do not require the operations in a quantitative algebra to be nonexpansive. We provide a sound and complete deduction system, we construct free quantitative algebras, and we demonstrate the value of our generalization by proving that any monad on generalized metric spaces that lifts a monad on sets can be presented with a quantitative algebraic theory. We apply this last result to obtain an axiomatization for the \L ukaszyk--Karmowski distance
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3

Feng, Cheng. "Process algebra for located Markovian agents and scalable analysis techniques for the modelling of Collective Adaptive Systems." Thesis, University of Edinburgh, 2017. http://hdl.handle.net/1842/22070.

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Recent advances in information and communications technology have led to a surge in the popularity of artificial Collective Adaptive Systems (CAS). Such systems, comprised by many spatially distributed autonomous entities with decentralised control, can often achieve discernible characteristics at the global level; a phenomenon sometimes termed emergence. Examples include smart transport systems, smart electricity power grids, robot swarms, etc. The design and operational management of CAS are of vital importance because different configurations of CAS may exhibit very large variability in their performance and the quality of services they offer. However, due to their complexity caused by varying degrees of behaviour, large system scale and highly distributed nature, it is often very difficult to understand and predict the behaviour of CAS under different situations. Novel modelling and quantitative analysis methodologies are therefore required to address the challenges posed by the complexity of such systems. In this thesis, we develop a process algebraic modelling formalism that can be used to express complex dynamic behaviour of CAS and provide fast and scalable analysis techniques to investigate the dynamic behaviour and support the design and operational management of such systems. The major contributions of this thesis are: (i) development of a novel high-level formalism, PALOMA, the Process Algebra for Located Markovian Agents for the modelling of CAS. CAS specified in PALOMA can be automatically translated to their underlying mathematical models called Population Continuous-Time Markov Chains (PCTMCs). (ii) development of an automatic moment-closure approximation method which can provide rapid Ordinary Differential Equation-based analysis of PALOMA models. (iii) development of an automatic model reduction algorithm for the speed up of stochastic simulation of PALOMA/PCTMC models. (iv) presenting a case study, predicting bike availability in stations of Santander Cycles, the public bike-sharing system in London, to show that our techniques are well-suited for analysing real CAS.
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4

Murray, Gregory V. "Relationships Between Classroom Schedule Types and Performance on the Algebra I Criterion-Referenced Test." DigitalCommons@USU, 2012. https://digitalcommons.usu.edu/etd/1403.

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Public education has options with regard to educational settings and structures. States and school districts may select varying lengths for the school year, lengths for the school day, and lengths for individual class periods. In Utah, one measure of students' achievement is scores on the State's end-of-level criterion-referenced test (CRT) for Algebra I. Additionally, an option regarding educational structures is the schedule type used to deliver Algebra I classes. This study examined the relationship between student achievement as measured by Algebra I CRT scores, and the schedule type used to deliver Algebra I classes. The schedule types compared were the traditional daily schedule, trimester 3/3 schedule, trimester 2/3 schedule, and the block A/B schedule. This study sought to answer two research questions: (1) What is the relationship between mathematics instructional schedule type and student scores on Utah's CRT for Algebra I, for all students? and (2) What is the relationship between mathematics instructional schedule type and student scores on Utah's CRT for Algebra I, by individual grade levels? Data were obtained from the Utah State Office of Education and included the scores for 50,000 Utah students, from over 300 different schools, who took the identical Algebra I CRT at the end of the 2010-2011 school year. Data were also obtained from each school district to determine the schedule type of each participating student. Both a multinomial logistic regression analysis and a t-test analysis were conducted to determine relationships between Algebra I CRT scores and schedule types. The results indicated significant differences in student achievement based on the schedule type overall and for individual grade levels. Generally, the earlier the grade level the higher the CRT score. Within individual grade levels, there were both statistically significant and nonsignificant differences. The schedule types that generally score the highest (trimester 3/3 and traditional) had more time in the mathematics classroom and the students' mathematics class met daily. The results suggest the value of daily time spent in the mathematics classroom and may assist educators when considering options available to foster student achievement.
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5

Gallina, Lucia <1984&gt. "Formal models for qualitative and quantitative analysis of mobile ad hoc and sensor networks." Doctoral thesis, Università Ca' Foscari Venezia, 2013. http://hdl.handle.net/10579/3045.

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Mobile ad-hoc networks (MANETs) are systems of mobile devices communicating with each other through wireless links without a pre-established networking infrastructure. The absence of a central infrastructure, together with the heterogeneous nature of the devices, make this kind of networks particularly fit to face critical situations, such as natural disasters or battlefield environments. Connectivity, energy consumption and communication interference are key aspects in mobile ad-hoc networks, due to the dynamic characteristics of the devices. In this thesis we propose a broadcast process algebraic model for the analysis of such aspects of MANETs. In particular we first introduce a non-deterministic calculus, which enables us to define and prove some important connectivity properties of ad hoc networks, and then we introduce two different probabilistic extensions of such calculus, with the aim of providing both a qualitative and quantitative analysis of ad hoc networks. In particular, we concentrate on the energy consumption and the level of interference. Using the model checking technique, we finally provide a framework for automatically evaluate the performances of ad hoc networks, with respects to the metrics previously defined.
Le reti ad hoc (MANETs) sono sistemi di dispositivi mobili che comunicano tra loro usando collegamenti wireless, senza alcuna infrastruttura prestabilita. L’assenza di una infrastruttura centrale e la natura eterogenea dei dispositivi rendono questa rete particolarmente adatta a gestire situazioni critiche, come ad esempio le comunicazioni in caso di disastri naturali, o nei campi di battaglia. La connettivit`a, il consumo energetico e l’interferenza nelle comunicazioni sono aspetti chiave nella gestione delle reti ad hoc, date le caratteristiche dinamiche dei dispositivi che le costituiscono. In questa tesi proponiamo un modello formale per l’analisi di queste problematiche. In particolare introduciamo un modello non deterministico che ci permette di definire e provare alcune importanti propriet`a legate alla connettivit`a delle reti. Proponiamo poi due differenti estensioni probabilistiche del calcolo introdotto, volte ad un’analisi sia qualitativa che quantitativa delle reti ad hoc. In particolare questa tesi si concentra sullo studio del consumo energetico e del livello di interferenza. Infine, grazie alla tecnica del model checking, viene fornito uno strumento per valutare in modo automatico le prestazioni delle reti ad hoc rispetto alle metriche proposte.
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6

Fiermonte, Karen Juliet Grysko. "A Quantitative Analysis of Algebra I in Grade Eight and the Impact on Academic Performance in a Large, Urban, New Jersey Public School District." Thesis, Saint Peter's University, 2019. http://pqdtopen.proquest.com/#viewpdf?dispub=10978505.

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Анотація:

For most American High School students, taking algebra in high school has always been a rite of passage. Traditionally, Algebra I has long been a ninth-grade student's first experience with higher-level mathematics. To maintain a competitive edge in a global economy, numerous school districts in the United States have rearranged mathematics curricula to relocate algebra down to the middle school. Placement in eighth grade algebra provides students with an opportunity for rigor and higher levels of attainment in mathematics coursework by the completion of grade twelve. The effectiveness of moving algebra from grade nine to grade eight has become a highly debated topic amongst educators and lawmakers. Policymakers and administrators that favor moving Algebra I into the eighth grade believe doing so will assist in closing the achievement gap currently in existence for gender, race and socioeconomic status. To achieve this, substantial sums of money must be invested in the implementation of algebra programs in middle school. Proponents of grade eight algebra strongly advocate for algebra placement prior to high school as an intervention to reduce the gap between American students and their global counterparts. "The U.S. also needs to do a better job of identifying and nurturing its mathematically talented youth, regardless of their gender, race, or national origin. Doing so is vital to the future of the U.S. Economy" (Hyde, Mertz, & Scheckman, 2009). In contrast, researchers such as Nomi (2012) have argued that early algebra placement is not beneficial for every child. Researchers such as Levy (2012) and Shearing (2016) agree that Black and Hispanic students, particularly of low socioeconomic status are victims of an achievement gap. "Students who are eligible for free and reduced lunch tend to be approximately two years behind that of students of the "average better-off student of the same age" (McKinsey & Company, 2009, p. 6). While there has been agreement among the experts regarding the existence of the gap, their suggested solutions conflict.

The research conducted by this researcher will contribute to the existing literature on Algebra I placement. The purpose of this study was to examine both the proportionality of student placement in grade eight Algebra I by gender, ethnicity and socioeconomic status, and the impact of grade eight Algebra I participation on academic performance on mathematics in a large, urban, New Jersey Public School District. This impact was measured based on the outcomes of Algebra I and Geometry final grades, Algebra I and Geometry PARCC scores, and tenth-grade mathematics PSAT/NMSQT scores. This study examined the relationships between academic outcomes for eighth-grade Algebra exposure and academic outcomes as described.

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Roberts, Robert E. "A study of the cognitive and affective characteristics of high and low achievers in Year 10 algebra." Thesis, Queensland University of Technology, 2003. https://eprints.qut.edu.au/36679/1/36679_Digitised%20Thesis.pdf.

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This study focused on successful performance in school algebra. It sought to determine what high achievers in Year 10 algebra knew and felt about algebra that enabled them to succeed while their peers were less successful. The study aimed to identify essential cognitive and affective variables which associate significantly with successful performance in algebra and to develop a model to explain how these variables interact to facilitate that success. Implications for instruction were then drawn and recommendations made relating to curriculum design, teacher education and further associated research. The literature study indicated that three basic concepts, which are representation, generalisation, and functionality, appear to underlie algebraic thinking. A conceptual understanding of a subject together with a range of problem solving abilities distinguish expert from novice intellectual behaviour generally. In addition a range of affective variables including belief in the value of the task, self-concept and self-efficacy beliefs, together with attitudinal variables, impact significantly on successful performance generally. A two-stage research design was chosen for the study, involving a gender-balanced sample of 54 Year 10 extension (top stream) mathematics students - approximately half from a state school, and the remainder from a private school - from a semi-rural area of Australia. In Stage One all subjects were given a written test of algebra attainment and a series of written tests of the identified basic concepts, that is representation, generalisation and functionality. A questionnaire survey was conducted to determine their beliefs about and attitudes towards, themselves, algebra and mathematics in general. The questionnaire also asked about classroom experiences, perceived scholastic abilities, parental, and perceived teacher and peer group influences on the subjects' learning of algebra. The data were analysed quantitatively and qualitatively and comparisons made between the responses of a group of ten high and a group of ten low achievers in algebra. In Stage Two gender and school-balanced sub-samples from the high and low achievers groups of Stage One were selected for interview. These groups participated one-on-one in a one hour audio/video recorded think-aloud mode algebra problem solving interview conducted by the researcher. The subjects articulated theirthinking procedures and feelings as they solved a range of routine to novel algebra problems. The data gathered from this interview were analysed using both quantitative and qualitative techniques and triangulated with that of Stage One. The Stage One findings confirmed that high achievers had a significant command of the concepts identified as basic to algebraic thinking. The questionnaire data showed high achievers held positive beliefs and attitudes about algebra and about their own capabilities. These beliefs and attitudes were significantly different from those of their less successful peers. High achievers were generally positive and confident about algebra. They valued the subject for aesthetic and practical reasons. They reported enjoying algebra and believed it enhanced their general thinking and problem solving capabilities. High achievers were self-aware and held strong self-efficacy beliefs. They knew they worked hard and were respected by their teachers and peers and were supported by their parents. Subjects who were less successful in algebra also reported parental support and generally good teacher relations, but reported not being inspired by algebra and not being confident that they could succeed in the subject. No gender or school effects (private or state) were found. The data gathered from algebra problem solving interviews conducted in Stage Two confirmed the high and low achiever ratings on the identified basic algebra concepts. This was particularly evident with generalisation and with functionality. Noticeably, however, even high achievers at this Year 10 level had difficulties with the function concept. The qualitative data analysis of the interview transcripts was aided by a grounded theory methodology which identified three stages in the algebra problem solving process, these are, information gathering, information processing and information reporting. The analysis identified eight cognitive and eight affective variables which associated significantly with successful performance in Year 10 algebra. Based on these findings an algebra learning success model was developed. The model postulates that success in algebra results from the reciprocal interaction of positive beliefs and attitudes towards algebra, a sound knowledge of the identified basic concepts of representation, generalisation, and functionality from and the application of a range of problem solving abilities. These abilities are developed, it is postulated, through the confidence building and optimistic experiences gained from early and sustained comprehension of and success with algebra. Implications for curriculum design and teacher education have been identified, presented and discussed, together with suggestions for further research relating to the algebra learning success model.
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Christo, Danilo dos Santos. "Introdução da noção de variável em expressões algébricas por meio da resolução de problemas: Uma abordagem dinâmica." Pontifícia Universidade Católica de São Paulo, 2006. https://tede2.pucsp.br/handle/handle/11080.

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Made available in DSpace on 2016-04-27T16:57:46Z (GMT). No. of bitstreams: 1 EDM - Danilo S Christo.pdf: 629300 bytes, checksum: 0ef0463bceff1c7bfe0b4f7fdda99796 (MD5) Previous issue date: 2006-10-31
Students difficulties in writing and interpreting algebraic language, particularly in comprehending the meaning of variable have been discussed by such researchers as Kieran, Küchemann, Arcavi and others. In this research, we evaluate a teaching proposal in which it is aimed at explaining established relations between elements of circumstances of proportionality and generalizable arithmetic expressions. This analysis of regularity eases the algebraic language teaching through a dynamic approach in which the notion of dependence among the circumstantial variables is emphasized. This proposal was applied to a sixth grade group of a public primary school in São Paulo city. The analysis of the obtained results allows us to verify the teaching proposal s efficiency for attaining the objectives of this research and provides tools for training teachers
Dificuldades dos alunos na escrita e interpretação da linguagem algébrica e, em particular, na compreensão do significado de variável, têm sido discutidas por pesquisadores como Kieran, Küchemann, Arcavi, entre outros. Nesta pesquisa, avaliamos uma proposta de ensino na qual busca-se descrever as relações estabelecidas entre os elementos de situações de proporcionalidade com as expressões aritméticas generalizáveis. A análise dessas regularidades favorece o ensino da linguagem algébrica, em uma abordagem dinâmica em que se enfatiza a noção de dependência entre as variáveis envolvidas na situação. A proposta foi desenvolvida em uma sexta série do ensino fundamental de uma escola municipal da cidade de São Paulo. A análise dos resultados obtidos permite-nos constatar a eficiência da proposta de ensino para a consecução dos objetivos visados nesta investigação e fornece subsídios para a formação de professores
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Chandavarkar, Rohan Vivek. "Eco-inspired Robust Control Design for Linear Time-Invariant systems with Real Parameter Uncertainty." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1373467190.

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10

Narváez, Clauss Marta. "Quantitative equidistribution of Galois orbits of points of small height on the algebraic torus." Doctoral thesis, Universitat de Barcelona, 2016. http://hdl.handle.net/10803/403982.

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Анотація:
El teorema de equidistribución de Bilu establece que, dada una sucesión estricta de puntos en el toro algebraico N-dimensional cuya altura de Weil tiende a cero, las órbitas de Galois de los puntos se equidistribuyen con respecto a la medida de Haar de probabilidad del policírculo unidad. Para el caso unidimensional, versiones cuantitativas de este resultado fueron obtenidas independientemente por Petsche y por Favre y Rivera-Letelier. Se presenta en esta tesis una versión cuantitativa del resultado de Bilu para el caso de dimensión cualquiera. Dado un punto en el toro algebraico de dimensión N de altura de Weil menor que 1, se proporciona una cota para la integral de una determinada función test en P1(C)N con respecto a la medida signada definida como la diferencia de la medida discreta de probabilidad asociada a la órbita de Galois del punto y la medida de probabilidad soportada en el policírculo unidad, donde coincide con la medida de Haar normalizada. Esta cota está dada en términos de una constante que depende únicamente de la función test, de la altura de Weil del punto, y de una noción que generaliza a dimensión superior el grado de un número algebraico. Para la demostración de este resultado se utiliza el análisis de Fourier para la descomposición del problema y, a través de proyecciones, se reduce al caso unidimensional donde aplicamos la versión cuantitativa de Favre y Rivera-Letelier.
El teorema d’equidistribució de Bilu estableix que, donat una successió de punts en el tor algebraic N-dimensional amb altura de Weil que tendeix cap a zero, les òrbites de Galois dels punts es equidistribueixen respecte de la mesura de Haar de probabilitat del policercle unitat. Per al cas unidimensional, versions quantitatives d’aquest resultat van ser obtingudes independentment per Petsche, i per Favre I Rivera-Letelier. Es presenta en aquesta tesi una versió quantitativa del resultat de Bilu per al cas de dimensió qualsevol. Donat un punt en el tor algebraic de dimensió N d’altura de Weil més petita que 1, es proporciona una fita per a l’integral d’una determinada funció test en P1(C)N respecte de la mesura signada definida com la diferència de la mesura discreta de probabilitat associada a l’òrbita de Galois del punt i la mesura de probabilitat suportada en el policercle unitat, on coincideix amb la mesura de Haar normalitzada. Aquesta fita ve donada en termes d’una constant que depèn únicament de la funció test, de l’altura de Weil del punt, i d’una noció que generalitza a dimensió superior el grau d’un nombre algebraic. Per a la demostració d’aquest resultat s’utilitza l’anàlisi de Fourier per la descomposició del problema i, mitjançant projeccions, es redueix al cas unidimensional on apliquem la versió quantitativa de Favre i Rivera-Letelier.
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Книги з теми "Quantitative Algebra"

1

1968-, Basu Saugata, and González-Vega Laureano, eds. Algorithmic and quantitative real algebraic geometry: DIMACS workshop, Algorithmic and quantitative aspects of real algebraic, geometry in mathematics and computer science, March 12-16, 2001, DIMACS Center. Providence, RI: American Mathematical Society, 2003.

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2

Quantitative Literacy Through Algebra. Carnegie Learning, 2003.

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3

Quantitative Analysis Algebra with a Business Perspective. Bookboon.com, 2013.

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Quantitative Analysis Algebra with a Business Perspective. Bookboon, 2013.

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5

Quantitative Analysis Algebra with a Business Perspective. Bookboon, 2013.

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6

Quantitative Analysis Algebra with a Business Perspective. Bookboon.com, 2013.

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7

Ragin, Charles C. Comparative Method: Moving Beyond Qualitative and Quantitative Strategies. University of California Press, 1989.

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8

Ragin, Charles C. Comparative Method: Moving Beyond Qualitative and Quantitative Strategies. University of California Press, 2014.

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9

Ragin, Charles C. Comparative Method: Moving Beyond Qualitative and Quantitative Strategies. University of California Press, 1989.

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10

Krise, Scott. Cornerstones of Algebra: Problem Solving Quantitative Reasoning and Critical Thinking. Kendall Hunt Publishing Company, 2012.

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Частини книг з теми "Quantitative Algebra"

1

Georgoulas, Anastasis, Jane Hillston, Dimitrios Milios, and Guido Sanguinetti. "Probabilistic Programming Process Algebra." In Quantitative Evaluation of Systems, 249–64. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10696-0_21.

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2

Betti, Matthew. "Linear Algebra." In Mathematics and Statistics for the Quantitative Sciences, 119–60. Boca Raton: Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003265405-3.

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3

McIver, A. K., C. C. Morgan, and T. Rabehaja. "Algebra for Quantitative Information Flow." In Relational and Algebraic Methods in Computer Science, 3–23. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57418-9_1.

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4

Alvim, Mário S., Konstantinos Chatzikokolakis, Annabelle McIver, Carroll Morgan, Catuscia Palamidessi, and Geoffrey Smith. "Program algebra for QIF." In The Science of Quantitative Information Flow, 283–305. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-319-96131-6_15.

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5

Feng, Cheng, and Jane Hillston. "PALOMA: A Process Algebra for Located Markovian Agents." In Quantitative Evaluation of Systems, 265–80. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10696-0_22.

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6

Harrison, P. G., and B. Strulo. "Stochastic Process Algebra for Discrete Event Simulation." In Quantitative Methods in Parallel Systems, 18–37. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-79917-4_2.

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7

Marin, Andrea, Carla Piazza, and Sabina Rossi. "A Process Algebra for (Delimited) Persistent Stochastic Non-Interference." In Quantitative Evaluation of Systems, 222–38. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-30281-8_13.

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8

Siegle, Markus, and Amin Soltanieh. "Rate Lifting for Stochastic Process Algebra – Exploiting Structural Properties –." In Quantitative Evaluation of Systems, 67–84. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-16336-4_4.

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9

Benzekri, Abdelmalek. "Qualitative and Quantitative Evaluation using Process Algebra." In Proceedings of The 17th International Symposium on Computer and Information Sciences, 415–18. Boca Raton: CRC Press, 2022. http://dx.doi.org/10.1201/9780429332821-94.

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10

Baccelli, F., B. Gaujal, A. Jean-Marie, and J. Mairesse. "Analysis of Parallel Processing Systems via the (max,+) Algebra." In Quantitative Methods in Parallel Systems, 69–98. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-79917-4_5.

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Тези доповідей конференцій з теми "Quantitative Algebra"

1

Cardelli, Luca. "Invited Talk: A Process Algebra Master Equation." In Fourth International Conference on the Quantitative Evaluation of Systems (QEST 2007). IEEE, 2007. http://dx.doi.org/10.1109/qest.2007.26.

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2

Riedl, Martin, Johann Schuster, and Markus Siegle. "Recent Extensions to the Stochastic Process Algebra Tool CASPA." In 2008 Fifth International Conference on Quantitative Evaluation of Systems. IEEE, 2008. http://dx.doi.org/10.1109/qest.2008.13.

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3

Tribastone, Mirco. "Scalable Differential Analysis of Large Process Algebra Models." In 2010 Seventh International Conference on the Quantitative Evaluation of Systems (QEST). IEEE, 2010. http://dx.doi.org/10.1109/qest.2010.45.

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4

Zimmerman, Charlotte, Andrew McCarty, Suzanne White Brahmia, Alexis Olsho, Mieke De Cock, Andrew Boudreaux, Trevor I. Smith, and Philip Eaton. "Assessing physics quantitative literacy in algebra-based physics: lessons learned." In 2022 Physics Education Research Conference. American Association of Physics Teachers, 2022. http://dx.doi.org/10.1119/perc.2022.pr.zimmerman.

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5

Cardenas Escobar, Alba Zulay, Armando Antonio Diaz Mendoza, Fabian Alfonso Gazabón Arrieta, and Holmán Ospina Mateus. "Impact of Knowledge in Linear Algebra on Academic Performance in Quantitative Optimization Methods: A Data Analytical Approach." In 22nd LACCEI International Multi-Conference for Engineering, Education and Technology (LACCEI 2024): “Sustainable Engineering for a Diverse, Equitable, and Inclusive Future at the Service of Education, Research, and Industry for a Society 5.0.”. Latin American and Caribbean Consortium of Engineering Institutions, 2024. http://dx.doi.org/10.18687/laccei2024.1.1.1831.

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6

Dongxu, Liu, Xu Dongling, Zhang Shuhui, and Hu Xiaoying. "A Quantitative Approach for Reliability Evaluation of Safety I&C Systems in Nuclear Power Plants." In 2017 25th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/icone25-66483.

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Анотація:
The probability that the safety I&C system fails to actuate or advertently actuates RT or ESF functions, in part, essentially determines whether a nuclear power plant could operate safely and efficiently. Since more conservative assumptions and simplifications are introduced during the analysis, this paper achieves solid results by performing the modeling and calculation based on a relatively simple approach, the reliability block diagram (RBD) method. A typical safety I&C platform structure is involved in the model presented in this paper. From the perspective of conservation and simplicity, some assumptions are adopted in this paper. A group of formulas is derived in this paper based on Boolean algebra, probability theory, basic reliability concepts and equations, to facilitate the calculations of probabilities that the safety I&C system fails to actuate or advertently actuates RT or ESF functions. All the inputs of the analysis and calculation in this paper, which includes the I&C platform structure, the constitution of the hardware modules, and reliability data, are referenced to the nuclear power plant universal database where applicable. Although the conclusion drawn in the paper doesn’t apply to the I&C platform assessment for a specific plant, the method of modeling and process of analysis provides an illustration of an alternative quantitative reliability assessment approach for a typical safety I&C system installed in the nuclear power plant.
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7

Mardare, Radu, Prakash Panangaden, and Gordon Plotkin. "Quantitative Algebraic Reasoning." In LICS '16: 31st Annual ACM/IEEE Symposium on Logic in Computer Science. New York, NY, USA: ACM, 2016. http://dx.doi.org/10.1145/2933575.2934518.

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Mardare, Radu, Prakash Panangaden, and Gordon Plotkin. "On the axiomatizability of quantitative algebras." In 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). IEEE, 2017. http://dx.doi.org/10.1109/lics.2017.8005102.

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9

Adamek, Jiri. "Varieties of Quantitative Algebras and Their Monads." In LICS '22: 37th Annual ACM/IEEE Symposium on Logic in Computer Science. New York, NY, USA: ACM, 2022. http://dx.doi.org/10.1145/3531130.3532405.

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10

Sarkar, Somwrita, and Andy Dong. "Characterizing Modularity, Hierarchy and Module Interfacing in Complex Design Systems." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47992.

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Modular engineering systems have multiple benefits over their more integral counterparts. Despite the importance of modularity, metrics and methods for a precise quantitative characterization of modularity, hierarchy and module interfacing remain relatively ambiguous. In this paper, using graph theory and linear algebra, we develop a spectral approach to establish: (1) a metric to characterize modularity, hierarchy and module interfacing in complex engineering systems; and, (2) a method for module identification and system decomposition that addresses hierarchical and overlapping organization of modularity in a complex system. The Singular Values (SV) signatures of random, regular, modular and hierarchically modular benchmark graph models are used to establish the metric. Then, the method is applied to a real design model and its modularity signature is assessed. The modularity signature of a real world system is shown to sit in the continuum established by the extremes of random, regular and modular and hierarchically modular graph models. The main contribution of the work is that it proposes that modularity is an aggregate concept that is measured in terms of multiple concepts expressed as graph properties. An ideal numeric modularity measurement index would have to incorporate these multiple criteria that affect modularity. The method can be used in the conceptual and detailed design stages for purposes of redesigning a product based on the degree of desired modularity.
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Звіти організацій з теми "Quantitative Algebra"

1

Hernández Agramonte, Juan Manuel, Caitlin Ludlow, Emma Näslund-Hadley, and Ernesto Martínez. IDB Briefly Noted: No. 20 : September, 2012: The Making of Little Mathematicians: Fostering Early Math Understanding in Paraguay. Inter-American Development Bank, September 2012. http://dx.doi.org/10.18235/0008199.

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That four- and five-year-olds can do algebra, arithmetic, and geometry may be hard to believe. But if you visit a preschool classroom in the Cordillera region of Paraguay, you will see children who learn factoring by organizing balls and sticks into groups, and who work together to form pentagons and hexagons with their bodies. These children are participating in a project called "Tikichuela, Mathematics in My School", the result of a partnership between the Japanese and Paraguayan governments, the Organization of Ibero-American States (OEI), and the Inter-American Development Bank (IDB). The idea behind the curriculum is that preschool children need to learn premath skills to build a foundation for primary- and secondary-level mathematics. Assessed after five months, the math skills of children in the program had increased significantly compared with those of a group of children not in the program. This brief describes the implementation of the pilot program and its qualitative and quantitative findings.
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