Proof by mathematical induction: Professional practice for secondary teachers

Mathematical induction is a proof technique that can be applied to establish the veracity of mathematical statements. This professional practice paper offers insight into mathematical induction as it pertains to the Australian Curriculum: Mathematics (ACMSM065, ACMSM066) and implications for how secondary teachers might approach this technique with students. In particular, literature on proof—and specifically, mathematical induction—will be presented, and several worked examples will outline the key steps involved in solving problems. After various teaching and learning caveats have been explored, the paper will conclude with some mathematical induction example problems that can be used in the secondary classroom

Induction motor controller using fuzzy logic

Induction Motor is widely used in general industry applications focusing on production area. Induction motor speed control is becoming very important due to increase the profit to the industries with increase efficiency, reliability and performance of induction motor. Due to the problem facing in induction motor that require complex mathematical model and varying parameters, Fuzzy Logic Controller (FLC) is applied to overcome this problem. The FLC based on the concepts of an artificial intelligence and attractive alternatives method to tackle the problem of controller design for complex mathematical model of system. This project used FLC Sugeno types. The purpose used FLC is to control speed and increase the efficiency of IM. While, the conventional controller only works well for linear system and their performances will decrease for nonlinear system. To make an induction motor operates such as Direct Current (DC) motor, Field Oriented Control (FOC) drives is applied for Induction Motor drive. FOC also offering a fast dynamic response and a high precision ability for IM drive. This project is implemented using Simulink Matlab. Based on the test results show the response of the speed curve takes less time to settle and reach the desired value

Higher order reasoning produced in proof construction: how well do secondary school students explain and write mathematical proofs?

The culture of mathematical explanations and writings based on conceptual understanding in proof construction is on the focus of the paper. We explore students’ attempts to explain construction of mathematical proofs after reading them and write mathematical proofs after working out their own constructions. Two examples of proofs, by induction and by contradiction, are discussed in detail to highlight students’ difficulties in proving and possible ways for their resolving

Linear Model Predictive Control of Induction Machine

This article presents new control algorithm for induction machine based on linear model predictive control (MPC). Controller works in similar manners as field oriented control (FOC), but control is performed in stator coordinates. This reduces computational demands as Park’s transformation is absent and induction machine mathematical model in stator coordinates contains less nonlinear elements. Another aim of proposed controller was to achieve fast torque response

Rejecting Mathematical Realism while Accepting Interactive Realism

Indispensablists contend that accepting scientific realism while rejecting mathematical realism involves a double standard. I refute this contention by developing an enhanced version of scientific realism, which I call interactive realism. It holds that interactively successful theories are typically approximately true, and that the interactive unobservable entities posited by them are likely to exist. It is immune to the pessimistic induction while mathematical realism is susceptible to it

The Profile of Students’ Thinking in Solving the Tasks of Mathematical Induction Seen from Mathematical Ability

Abstract Every individual thinks in his life, especially when get a difficulties. Mathematics has an abstract mathematical object. This makes students have difficulty in solving math tasks. So, students will think in solving math tasks. One of the mathematical material that requires students to think is mathematical induction. Students are required to prove the truth of mathematical statements related to natural numbers using the principle of mathematical induction. Students mathematical abilities have an influence when students solve math induction tasks. Thus, differences in mathematical abilities in solving tasks will lead to differences in students thinking. This study aims to describe the profile of students thinking in solving the tasks of mathematical induction seen from mathemtical abilities. Thinking in this study refers to information processing model of Slavin, which is receiving information, processing the information, storing information, and recalling iformation. This study is a qualitative descriptive study. The subjects of this study is three senior high school students in 11st grade, among them one student with high mathematical ability, one student with average mathematical ability, and one student with low mathematical ability. The technique of data collection was done by giving tests related to the mathematical ability test, task solving test of mathematical induction and interviews.The results confirm that the differences in mathematical abilities have affect when the students thinking to solving mathematical induction tasks. Keyword: thinking, mathematical induction, and mathematical abilit

Localized induction equation and pseudospherical surfaces

We describe a close connection between the localized induction equation hierarchy of integrable evolution equations on space curves, and surfaces of constant negative Gauss curvature.Comment: 21 pages, AMSTeX file. To appear in Journal of Physics A: Mathematical and Genera