The Symbolic and Mathematical Influence of Diophantus\u27s Arithmetica

Though it was written in Greek in a center of ancient Greek learning, Diophantus\u27s Arithmetica is a curious synthesis of Greek, Egyptian, and Mesopotamian mathematics. It was not only one of the first purely number-theoretic and algebraic texts, but the first to use the blend of rhetorical and symbolic exposition known as syncopated mathematics. The text was influential in the development of Arabic algebra and European number theory and notation, and its development of the theory of indeterminate, or Diophantine, equations inspired modern work in both abstract algebra and computer science. We present, in this article, a selection of problems from the Arithmetica, which have been rewritten for ease of reading, and consider Diophantus\u27s advancements in mathematics and mathematical notation in the context of ancient Greek mathematics. In particular, we examine Diophantus\u27s use of syncopated mathematics, most notably his use of generic solutions that present an algorithm for solving an entire class of equations through the application of that algorithm to a single representational example, and how these techniques suggest a more extensive use of concrete examples when approaching modern mathematics

INTEGRATING MATHEMATICAL AND SYMBOLIC MODELS THROUGH AESOP: AN EXPERT FOR STOCK OPTIONS PRICING

This paper reports on an effort to integrate symbolic and mathematical models to tailor the optimal output of an operations research model to the particular domain of a decision maker. AESOP combines the Black-Scholes model of stock options pricing with an expert system; the integrated model is designed for use by an options specialist on the American Stock Exchange. The specialist makes a number of adjustments to the output of the mathematical model; the purpose of the symbolic model is to make as many of these modifications as possible automatically. The paper reports on the development and structure of AESOP and presents data on its use.Information Systems Working Papers Serie

Architecture and Design of Medical Processor Units for Medical Networks

This paper introduces analogical and deductive methodologies for the design medical processor units (MPUs). From the study of evolution of numerous earlier processors, we derive the basis for the architecture of MPUs. These specialized processors perform unique medical functions encoded as medical operational codes (mopcs). From a pragmatic perspective, MPUs function very close to CPUs. Both processors have unique operation codes that command the hardware to perform a distinct chain of subprocesses upon operands and generate a specific result unique to the opcode and the operand(s). In medical environments, MPU decodes the mopcs and executes a series of medical sub-processes and sends out secondary commands to the medical machine. Whereas operands in a typical computer system are numerical and logical entities, the operands in medical machine are objects such as such as patients, blood samples, tissues, operating rooms, medical staff, medical bills, patient payments, etc. We follow the functional overlap between the two processes and evolve the design of medical computer systems and networks.Comment: 17 page

Teachers' Perceptions of Physics Scientific Argumentation Test Instruments Based on Modern Test Theory Using Question Modeling Through E-Learning Edpuzzle LMS

The study aims to understand teachers' perceptions of scientific argumentation test instruments in physics based on modern test theory using question modelling through Edpuzzle LMS e-learning. It employed a mixed method with a Sequential Explanatory Design. Data were collected through questionnaires and analyzed descriptively. Initially, it was found that 75% of teachers had not developed assessment instruments capable of optimally training students, resulting in 68% of students struggling to understand physics learning. Additionally, 54% of students reported having identified and solved complex physics problems using scientific argumentation, while 46% had not. Based on survey results, 95% of students and teachers agreed that assessment activities encourage scientific argumentation, indicated by identifying scientific issues and explaining scientific phenomena. Hence, there is a need for a physics scientific argumentation test model based on modern test theory. For future research, it is suggested to explore how integrating this test model in different educational settings impacts students' scientific argumentation skills and understanding of physics concepts

Learning mathematical symbolization: conceptual challenges and instructional strategies in secondary schools

This paper investigates South African 12th Grade students’ conceptual challenges with mathematical symbolization and instructional strategies that teachers use to mitigate mathematical symbolization. The study is motivated by the students’ failure to connect representations between symbolic and mathematical ideas to understand concepts and procedures. The study attempts to gain insight into mathematical symbols as potential barriers to students’ understanding of mathematical concepts and processes. The study consists of 120 randomly selected 12th Grade students and 15 purposefully selected mathematics teachers from Sekhukhune district of Limpopo Province, South Africa. Data was collected through questionnaires and focus group interviews. A mixed-method sequential explanatory design was employed. An SPSS cluster analysis of data produced three (3) clusters consisting of 50 (41.6%), 47 (39.3%) and 23 (19.1%) students with severe, mild, and minor challenges with mathematical symbols. Two themes emerged from the students’ difficulties with mathematical symbols. Firstly, students lack symbol sense for mathematical concepts and algebraic insight for problem-solving. Secondly, students disregard conceptual and contextual uses of symbols. The study therefore suggests that students’ negotiation of discourse between the mathematical symbol and the mathematical concept or procedure is crucial developing symbolic meaning. Therefore, teachers need to use appropriate strategies to engage students in processes that allow them to make meanings of mathematical symbols. The study recommends that concepts should be understood before symbolised

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INTEGRATING MATHEMATICAL AND SYMBOLIC MODELS THROUGH AESOP: AN EXPERT FOR STOCK OPTIONS PRICING

This paper reports on an effort to integrate symbolic and mathematical models to tailor the optimal output of an operations research model to the particular domain of a decision maker. AESOP combines the Black-Scholes model of stock options pricing with an expert system; the integrated model is designed for use by an options specialist on the American Stock Exchange. The specialist makes a number of adjustments to the output of the mathematical model; the purpose of the symbolic model is to make as many of these modifications as possible automatically. The paper reports on the development and structure of AESOP and presents data on its use.Information Systems Working Papers Serie