scholarly journals Mathematical proof analysis using mathematical induction of grade XI students

2020 ◽  
Vol 1480 ◽  
pp. 012044
Author(s):  
G Emeira ◽  
Hapizah ◽  
Scristia
Keyword(s):  
Mathematical Proof ◽  
Mathematical Induction ◽  
Proof Analysis

scholarly journals Kemampuan Pembuktian Matematis Mahasiswa Menggunakan Induksi Matematika

2019 ◽  
Vol 3 (1) ◽  
pp. 1
Author(s):  
Siska Firmasari ◽  
Herri Sulaiman
Keyword(s):  
Cognitive Ability ◽  
Mathematical Proof ◽  
Third Graders ◽  
Mathematical Induction ◽  
Induction Step ◽  
Study Program ◽  
Descriptive Research ◽  
Distributive Property ◽  
Appropriate Treatment ◽  
High Cognitive Ability

Kemampuan mahasiswa dalam melakukan pembuktian matematis tidak sama bergantung dari kategori kognitifnya. Salah satu metode pembuktian matematika adalah induksi matematika yang memerlukan pemahaman konsep secara sistematis. Tujuan penelitian adalah untuk mengetahui kemampuan pembuktian matematis mahasiswa yang memiliki kategori kognitif tinggi dan rendah menggunakan induksi matematika. Subjek penelitian ini adalah empat orang mahasiswa tingkat tiga Program Studi Pendidikan Matematika dengan klasifikasi dua orang mahasiswa memiliki kemampuan kognitif tinggi dan dua mahasiswa berkemampuan rendah. Instrumen penelitian yang digunakan adalah lembar tes materi induksi matematika dan pedoman wawancara. Penelitian ini merupakan penelitian deskriptif yang mendeskripsikan kemampuan pembuktian matematis mahasiswa dalam menyelesaikan soal terkait induksi matematika disesuaikan dengan kemampuan kognitif tinggi dan rendah. Hasil penelitian menunjukkan bahwa mahasiswa dengan kategori kognitif tinggi mampu menyelesaikan setiap langkah pembuktian secara benar namun belum sistematis, sedangkan yang berkemampuan kognitif rendah tidak memahami alur pembuktian pada langkah induksi, kekeliruan memahami sifat distributif, dan ketidakteraturan menghubungkan setiap langkah pembuktian. Melalui artikel ini, peneliti berharap dapat menganalisis perlakuan yang tepat pada mahasiswa saat mengajar berbagai materi matematika yang menggunakan prasyarat induksi matematika. Kata kunci: pembuktian matematis, induksi matematika, kemampuan kognitif.   ABSTRACT The students’ ability to perform mathematical proof is different depending on their cognitive category. One of mathematical proofing is mathematical induction which requires concepts understanding systematically. The purpose of this research is to know the ability of mathematical proof using mathematical induction of high and low cognitive category students. The subjects of this study are four third graders of Mathematics Education Study Program. Two students have high cognitive ability and the others have low cognitive ability. The mathematical induction material test sheet and interview guideline are used as research instruments. This is a descriptive research which describes the mathematical proof ability of students in solving problems related to mathematical induction adjusted with high and low cognitive ability. The results show that students with high cognitive category are able to complete each step of proof correctly but not systematically. At the same time, the students with low cognitive ability are not understand the proof steps at the induction step, the misunderstood the distributive property, and the irregularity connect the proof steps. The researcher expects to analyze the appropriate treatment to the students while teaching mathematical materials using mathematical induction prerequisites. Keywords: mathematical proof, mathematical induction, cognitive ability.

scholarly journals Understanding Mathematical Induction by Writing Analogies

2019 ◽  
Vol 3 (2) ◽  
Author(s):  
Andrew A. Cooper
Keyword(s):  
Peer Review ◽  
Lived Experiences ◽  
Mathematical Proof ◽  
Mathematical Induction ◽  
Proof Technique ◽  
Inductive Proof ◽  
Writing Assignment ◽  
Beginning Students

Mathematical induction has some notoriety as a difficult mathematical proof technique, especially for beginning students. In this note, I describe a writing assignment in which students are asked to develop, describe in detail, critique, defend, and finally extend their own analogies for mathematical induction. By putting the work of explanation into the students' hands, this assignment requires them to engage in detail with the necessary parts of an inductive proof. Students select their subject for the analogy, allowing them to connect abstract mathematics to their lived experiences. The process of peer review helps students recognize and remedy several of the most common errors in writing an inductive proof. All of this takes place in the context of a creative assignment, outside the work of writing formal inductive proofs.

scholarly journals Kesalahan Mahasiswa dalam Pembuktian Matematik

2019 ◽  
Vol 6 (1) ◽  
pp. 54-68
Author(s):  
Rezky Agung Herutomo
Keyword(s):  
Mathematical Proof ◽  
Mathematics Learning ◽  
Algebraic Manipulation ◽  
Mathematical Induction ◽  
Education Department ◽  
Mathematical Proofs ◽  
Proof Techniques ◽  
Reasoning Errors ◽  
And Mathematics ◽  
Academic Year

Proofs are the key component in mathematics and mathematics learning. But in reality, there are still many students who make errors when constructing mathematical proofs. Therefore this study aimed to identify common errors when the students are constructing mathematical proofs. The participant  of this study was 51 of 3rd year students of Mathematics Education Department  who enrolled in Real Analysis course in the second semester of the 2017/2018 academic year. The data of the study were obtained by conducting a test consisting of five questions and interview guidelines. The errors identified in this study were (1) proving general statements using specific examples, (2) inappropriate algebraic manipulation in mathematical induction, (3) incorrect reasoning and assumptions in proving with contradictions, and (4) reasoning errors involving natural numbers in mathematical induction. Hence, further study can be developed learning models that promote the conceptual understanding, logical reasoning, and mastery of mathematical proof techniques.

Mathematical proof that rocked number theory will be published

Nature ◽  
2020 ◽  
Vol 580 (7802) ◽  
pp. 177-177
Author(s):  
Davide Castelvecchi
Keyword(s):  
Number Theory ◽  
Mathematical Proof

Sourcebook in the Mathematics of Medieval Europe and North Africa

2016 ◽  
Keyword(s):  
North Africa ◽  
Cultural Influences ◽  
Mathematical Induction ◽  
Cross Cultural ◽  
General Introduction ◽  
Extensive Survey ◽  
Medieval Europe ◽  
Ceva’S Theorem ◽  
Arabic Speaking ◽  
First Time

Medieval Europe was a meeting place for the Christian, Jewish, and Islamic civilizations, and the fertile intellectual exchange of these cultures can be seen in the mathematical developments of the time. This book presents original Latin, Hebrew, and Arabic sources of medieval mathematics, and shows their cross-cultural influences. Most of the Hebrew and Arabic sources appear here in translation for the first time. Readers will discover key mathematical revelations, foundational texts, and sophisticated writings by Latin, Hebrew, and Arabic-speaking mathematicians, including Abner of Burgos's elegant arguments proving results on the conchoid—a curve previously unknown in medieval Europe; Levi ben Gershon's use of mathematical induction in combinatorial proofs; Al-Muʾtaman Ibn Hūd's extensive survey of mathematics, which included proofs of Heron's Theorem and Ceva's Theorem; and Muhyī al-Dīn al-Maghribī's interesting proof of Euclid's parallel postulate. The book includes a general introduction, section introductions, footnotes, and references.

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

How is science to be carried forward, and its conclusions reported?

2018 ◽  
Author(s):  
Andrew Briggs ◽  
Hans Halvorson ◽  
Andrew Steane
Keyword(s):  
Mathematical Proof ◽  
Good Practice ◽  
Natural World ◽  
Component Part ◽  
Journal Articles ◽  
Scientific Publications ◽  
Direct Role ◽  
Intellectual Activity ◽  
Self Identity ◽  
The World

The chapter appraises science as an intellectual activity that is appropriately carried out on its own terms. Consequently, it is not appropriate to introduce references to God as a component part of a mathematical proof, nor of a system of forces in the natural world, nor of a sequence of impersonal processes in the biosphere. This does not mean that it is inappropriate to be thankful to God and to celebrate all these aspects of the world as gifts. They can be employed as opportunities to express appreciation through studying and understanding them better in their own right. Nevertheless, there may be processes, such as those which shape a person’s self-identity, in which it is appropriate to recognize God’s more direct role. Good practice concerning acknowledgements sections in scientific publications such as doctoral theses and journal articles is then discussed.

scholarly journals Nonlinear stability of two-layer shallow water flows with a free surface

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190594
Author(s):  
Francisco de Melo Viríssimo ◽  
Paul A. Milewski
Keyword(s):  
Free Surface ◽  
Initial Data ◽  
Nonlinear Stability ◽  
Mathematical Proof ◽  
Passive Layer ◽  
Physical Parameters ◽  
Immiscible Fluid ◽  
Dimensional System ◽  
The Cauchy Problem ◽  
The Difference

The problem of two layers of immiscible fluid, bordered above by an unbounded layer of passive fluid and below by a flat bed, is formulated and discussed. The resulting equations are given by a first-order, four-dimensional system of PDEs of mixed-type. The relevant physical parameters in the problem are presented and used to write the equations in a non-dimensional form. The conservation laws for the problem, which are known to be only six, are explicitly written and discussed in both non-Boussinesq and Boussinesq cases. Both dynamics and nonlinear stability of the Cauchy problem are discussed, with focus on the case where the upper unbounded passive layer has zero density, also called the free surface case. We prove that the stability of a solution depends only on two ‘baroclinic’ parameters (the shear and the difference of layer thickness, the former being the most important one) and give a precise criterion for the system to be well-posed. It is also numerically shown that the system is nonlinearly unstable, as hyperbolic initial data evolves into the elliptic region before the formation of shocks. We also discuss the use of simple waves as a tool to bound solutions and preventing a hyperbolic initial data to become elliptic and use this idea to give a mathematical proof for the nonlinear instability.

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