319,479 research outputs found

    The Uses of Argument in Mathematics

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    Stephen Toulmin once observed that `it has never been customary for philosophers to pay much attention to the rhetoric of mathematical debate'. Might the application of Toulmin's layout of arguments to mathematics remedy this oversight? Toulmin's critics fault the layout as requiring so much abstraction as to permit incompatible reconstructions. Mathematical proofs may indeed be represented by fundamentally distinct layouts. However, cases of genuine conflict characteristically reflect an underlying disagreement about the nature of the proof in question.Comment: 10 pages, 5 figures. To be presented at the Ontario Society for the Study of Argumentation Conference, McMaster University, May 2005 and LOGICA 2005, Hejnice, Czech Republic, June 200

    Overgeneration in the Higher Infinite

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    The Overgeneration Argument is a prominent objection against the model-theoretic account of logical consequence for second-order languages. In previous work we have offered a reconstruction of this argument which locates its source in the conflict between the neutrality of second-order logic and its alleged entanglement with mathematics. Some cases of this conflict concern small large cardinals. In this article, we show that in these cases the conflict can be resolved by moving from a set-theoretic implementation of the model-theoretic account to one which uses higher-order resources

    A Simple Proof of the Alternation Theorem

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    A simple proof of the alternation theorem for minimax FIR filter design is presented in this paper. It requires no background on mathematical optimization theory, and is based on easily understood properties of filters with equiripple behavior. The method is similar to the classical counting argument used in early mathematics literature. The contribution here is a simplified presentation which directly uses filter design language

    one = zero

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    In this paper, I use Mathematics in addition to the three most pure sciences --- Physics, Chemistry, and Rap --- to prove that 1=0. The argument uses The Ideal Gas Law, Ohm\u27s Law, the Definitions of Power and Velocity in addition to indefinite integrals, simple mathematical operations, and the 99 Problems Law. The intuition-crushing result can be applied to all branches of mathematics and sciences and will likely go down as one of the greatest discoveries of all time

    The Analysis of Large Order Bessel Functions in Gravitational Wave Signals from Pulsars

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    In this work, we present the analytic treatment of the large order Bessel functions that arise in the Fourier Transform (FT) of the Gravitational Wave (GW) signal from a pulsar. We outline several strategies which employ asymptotic expansions in evaluation of such Bessel functions which also happen to have large argument. Large order Bessel functions also arise in the Peters-Mathews model of binary inspiralling stars emitting GW and several problems in potential scattering theory. Other applications also arise in a variety of problems in Applied Mathematics as well as in the Natural Sciences and present a challenge for High Performance Computing(HPC).Comment: 8 pages, Uses IEEE style files: Ieee.cls, Ieee.clo and floatsty.sty. Accepted for publication in High Performance Computing Symposium, May 15-18 (HPCS 2005) Guelph, Ontario, Canad

    Comparison of Two Approaches to Interpretive Use Arguments

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    The Standards for Educational and Psychological Testing (AERA, APA, & NCME, 2014) recommend an argument-based approach to validation that involves a clear statement of the intended interpretation and use of test scores, the identification of the underlying assumptions and inferences in that statement—termed the interpretation/use argument, and gathering of evidence to support or refute the assumptions and inferences. We present two approaches to articulating the assumptions and inferences that underlie a score interpretation and use statement, also termed the interpretation/use argument (Kane, 2016). One approach uses the five sources of validity evidence in the Standards for Educational and Psychological Testing (AERA, APA, & NCME, 2014) as a framework and the other approach uses Kane’s chain of assumptions/inferences approach (Kane, 2006, 2013a, 2016) as a framework. Through this process we identified aspects of these approaches that need to be further clarified for instrument developers to consistently implement either approach, identified important differences in the perspective each approach takes on validation, and highlight important questions for the measurement and mathematics education research fields to consider

    Arc - centre theorem

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    Student Haren Sathvik uses mathematics as a power tool to win an argument and prove his point. Exactly what the Position Paper of the National Focus Group on Mathematics says: Children use abstractions to perceive relationships, to see structure, to reason about things, to argue the truth or falsity of statements. Logical thinking is a great gift mathematics can offer us, and inculcating such habits of thought and communication in children is a principal goal of teaching mathematics. Read on to find out mor

    A Simple Proof of the Alternation Theorem

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    Abstract-A simple proof of the alternation theorem for minimax FIR filter design is presented in this paper. It requires no background on mathematical optimization theory, and is based on easily understood properties of filters with equiripple behavior. The method is similar to the classical counting argument used in early mathematics literature. The contribution here is a simplified presentation which directly uses filter design language.&apos

    Factorization in quaternion orders

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    AbstractHurwitz's proof of Lagrange's theorem that every positive integer is a sum of four squares of integers is but one of the extensive list of articles which relate quaternion arithmetics to quaternary (and ternary) quadratic forms (see [Marie-France Vignéras, Arithmétique des algèbres the quaternions, in “Lecture Notes in Mathematics,” Vol. 800, Springer-Verlag, New York, 1980] for a partial bibliography). Hurwitz's argument uses the property that a quaternion in the ring of Hurwitz quaternions with norm divisible by a prime p has a factor of norm p. The purpose of this article is to determine the connections between factorization in general quaternion orders over the integers, the ideal theory of the order and the genus structure of the corresponding quadratic lattice; and to list the positive definite quaternion orders which admit various types of factorization. Our work can be viewed as a continuation of Gordon Pall's initial investigations in [Trans. Amer. Math. Soc. 59 (1946), 503–513; Duke Math. J. 4 (1938), 696–704]

    Pengembangan Soal Berbasis Literasi Matematika dengan Menggunakan Konteks Jawa Timur

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    Abstract Mathematical literacy, the ability which describes a person’s capacity to formulate, employ, and interpret mathematics in a variety of context, mathematical literacy is very important because it can help to understand the usefulness or role of mathematics in everyday life, so that mathematical literacy become the relation of understanding in the classroom with the real world. The problems of mathematical literacy give priority to the context of real life, the context is directly related to the surround of students. This research is development research that the result is a set of problems based on mathematical literacy that using context East Java by referring to the valid, practical, and potential effects. This research uses development stages Design research type development study with detail: (1) Preliminary, (2) Self Evaluation, (3) One-to-one, (4) Expert Reviews, (5) Small Group, (6) Field Test. Validation process is done on two validator, one of Unesa’s mathematics lecturer and one teacher of mathematics subject of High School Al-Azhar Gresik. Subjects on this study were 10th grade high school students precisely at 10 INT C high school Gresik academic year 2016/2017 which amounted to 5 children in the small group stage and 5 children at field test.  The results show that the developed questions meet the valid criteria of 3.58 from a maximum score of 4.00 and meet the practical criteria of 3.12 from a maximum score of 4.00 based on the analysis results of one-to-one, expert reviews, and small groups, and the problems developed have potential effects generating basic mathematical skills such as reasoning and argument, communicating and increasing the motivation and feelings of challenged learners based on the analysis of field test results. Keywords: Development Problems, Mathematical Literacy, East Java Context
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