The Experts below are selected from a list of 3954 Experts worldwide ranked by ideXlab platform
Yuri Velinov - One of the best experts on this subject based on the ideXlab platform.
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Workshop on Implementing Automata - Teaching Theory of Computation with Tape Machines
Lecture Notes in Computer Science, 1998Co-Authors: Yuri VelinovAbstract:The purpose of this paper is to outline an approach for the development of the Tape Machine model in Theory of Computation which is linked more closely to the real computer world. The approach is based on a developed software package consisting of a Tape Machine Simulator, a Tape Machine Assembler and a Register Machine Simulator. Using the software and the ideas underlying it the aims of the theory can be achieved without any loss of Mathematical Rigor but in a more natural, useful and attractive manner.
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Teaching Theory of Computation with Tape Machines
Lecture Notes in Computer Science, 1998Co-Authors: Yuri VelinovAbstract:The purpose of this paper is to outline an approach for the development of the Tape Machine model in Theory of Computation which is linked more closely to the real computer world. The approach is based on a developed software package consisting of a Tape Machine Simulator, a Tape Machine Assembler and a Register Machine Simulator. Using the software and the ideas underlying it the aims of the theory can be achieved without any loss of Mathematical Rigor but in a more natural, useful and attractive manner.
Yong Hah Lee - One of the best experts on this subject based on the ideXlab platform.
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Designing Tasks of Introductory Real Analysis to Bridge a Gap Between Students’ Intuition and Mathematical Rigor: the Case of the Convergence of a Sequence
International Journal of Research in Undergraduate Mathematics Education, 2017Co-Authors: Kyeong Hah Roh, Yong Hah LeeAbstract:The purpose of this study is to explore how an introductory real analysis (IRA) course can be designed to bridge a gap between students’ intuition and Mathematical Rigor. In particular, we focus on a task, called the ε -strip activity, designed for the convergence of a sequence. Data were collected from a larger study conducted as a classroom teaching experiment for a semester-long IRA course. Fischbein’s notion of secondary intuition was employed to elucidate the development of student intuition throughout the ε -strip activity. We discuss how the ε -strip activity played a role in developing students’ intuition and how it impacted students’ learning of the subsequent topics in the course, including definitions and theorems about convergence.
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Designing Tasks of Introductory Real Analysis to Bridge a Gap between Students' Intuition and Mathematical Rigor: The Case of The Convergence of a Sequence.
International Journal of Research in Undergraduate Mathematics Education, 2016Co-Authors: Kyeong Hah Roh, Yong Hah LeeAbstract:The purpose of this study is to explore how an introductory real analysis (IRA) course can be designed to bridge a gap between students’ intuition and Mathematical Rigor. In particular, we focus on a task, called the e-strip activity, designed for the convergence of a sequence. Data were collected from a larger study conducted as a classroom teaching experiment for a semester-long IRA course. Fischbein’s notion of secondary intuition was employed to elucidate the development of student intuition throughout the e-strip activity. We discuss how the e-strip activity played a role in developing students’ intuition and how it impacted students’ learning of the subsequent topics in the course, including definitions and theorems about convergence.
Yacin Hamami - One of the best experts on this subject based on the ideXlab platform.
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Mathematical Rigor AND PROOF
The Review of Symbolic Logic, 2019Co-Authors: Yacin HamamiAbstract:Abstract Mathematical proof is the primary form of justification for Mathematical knowledge, but in order to count as a proper justification for a piece of Mathematical knowledge, a Mathematical proof must be Rigorous. What does it mean then for a Mathematical proof to be Rigorous? According to what I shall call the standard view, a Mathematical proof is Rigorous if and only if it can be routinely translated into a formal proof. The standard view is almost an orthodoxy among contemporary mathematicians, and is endorsed by many logicians and philosophers, but it has also been heavily criticized in the philosophy of mathematics literature. Progress on the debate between the proponents and opponents of the standard view is, however, currently blocked by a major obstacle, namely, the absence of a precise formulation of it. To remedy this deficiency, I undertake in this paper to provide a precise formulation and a thorough evaluation of the standard view of Mathematical Rigor. The upshot of this study is that the standard view is more robust to criticisms than it transpires from the various arguments advanced against it, but that it also requires a certain conception of how Mathematical proofs are judged to be Rigorous in Mathematical practice, a conception that can be challenged on empirical grounds by exhibiting Rigor judgments of Mathematical proofs in Mathematical practice conflicting with it.
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Mathematical Rigor, Proof Gap and the Validity of Mathematical Inference
2014Co-Authors: Yacin HamamiAbstract:Mathematical Rigor is commonly formulated by mathematicians and philosophers using the notion of proof gap: a Mathematical proof is Rigorous when there is no gap in the Mathematical reasoning of the proof. Any philosophical approach to Mathematical Rigor along this line requires then an account of what a proof gap is. However, the notion of proof gap makes sense only relatively to a given conception of valid Mathematical reasoning, i.e., to a given conception of the validity of Mathematical inference. A proof gap can in particular be conceived as a failure in drawing a valid Mathematical inference. The aim of this paper is to discuss two possible views of the validity of mathematical inference with respect to their capacity to yield a plausible account of the intuitive notion(s) of proof gap present in Mathematical practice. The first view is the one provided by the contemporary standards of Mathematical Rigor: a Mathematical inference is valid if and only if its conclusion can be formally derived from its premises. We will argue that this conception does not lead to a plausible account of the intuitive notion(s) of proof gap. The second view is based on a new account of the validity of inference proposed by Prawitz: an inference is valid if and only if it consists in an operation that provides a ground for its conclusion given (previously obtained) grounds for its premises. We will first specify Prawitz's account to Mathematical inference and we will then argue that the resulting ground-based account is able to capture various intuitive notions of proof gap as different types of failure in drawing valid Mathematical inferences. We conclude that the ground-based account appears of particular interest for the philosophy of Mathematical practice, and we finally raise several challenges facing a full development of a ground-based account of the notions of Mathematical Rigor, proof gap and the validity of Mathematical inference.
O.m. Nielsen - One of the best experts on this subject based on the ideXlab platform.
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Wavelet analysis for power system transients
IEEE Computer Applications in Power, 1999Co-Authors: A.w. Galli, O.m. NielsenAbstract:The purpose of this tutorial is to introduce the basics of wavelet analysis and propose how this new Mathematical tool may be applied in power engineering. Frequently, newcomers to wavelet analysis become discouraged due to the oftentimes elusive Mathematical Rigor of the subject and the variety of nomenclatures that are used in various arenas. This tutorial presents wavelet analysis in such a way that the reader can easily grasp the rudiments and begin investigating the use of this powerful tool in a variety of applications related to power engineering.
Kyeong Hah Roh - One of the best experts on this subject based on the ideXlab platform.
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Designing Tasks of Introductory Real Analysis to Bridge a Gap Between Students’ Intuition and Mathematical Rigor: the Case of the Convergence of a Sequence
International Journal of Research in Undergraduate Mathematics Education, 2017Co-Authors: Kyeong Hah Roh, Yong Hah LeeAbstract:The purpose of this study is to explore how an introductory real analysis (IRA) course can be designed to bridge a gap between students’ intuition and Mathematical Rigor. In particular, we focus on a task, called the ε -strip activity, designed for the convergence of a sequence. Data were collected from a larger study conducted as a classroom teaching experiment for a semester-long IRA course. Fischbein’s notion of secondary intuition was employed to elucidate the development of student intuition throughout the ε -strip activity. We discuss how the ε -strip activity played a role in developing students’ intuition and how it impacted students’ learning of the subsequent topics in the course, including definitions and theorems about convergence.
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Designing Tasks of Introductory Real Analysis to Bridge a Gap between Students' Intuition and Mathematical Rigor: The Case of The Convergence of a Sequence.
International Journal of Research in Undergraduate Mathematics Education, 2016Co-Authors: Kyeong Hah Roh, Yong Hah LeeAbstract:The purpose of this study is to explore how an introductory real analysis (IRA) course can be designed to bridge a gap between students’ intuition and Mathematical Rigor. In particular, we focus on a task, called the e-strip activity, designed for the convergence of a sequence. Data were collected from a larger study conducted as a classroom teaching experiment for a semester-long IRA course. Fischbein’s notion of secondary intuition was employed to elucidate the development of student intuition throughout the e-strip activity. We discuss how the e-strip activity played a role in developing students’ intuition and how it impacted students’ learning of the subsequent topics in the course, including definitions and theorems about convergence.