Real analysis, quantitative topology, and geometric complexity

2019 ◽

Vol 2 (2) ◽

Author(s):

Hanifah Nurus Sopiany

Keyword(s):

High School Students ◽

Secondary School ◽

Mathematical Reasoning ◽

Mathematics Learning ◽

Good Reason ◽

School Level ◽

Real Analysis ◽

Reasoning Ability ◽

School Students ◽

Secondary School Level

Penalaran matematis menggunakan pola pikir logis dalam menganalisa suatu masalah yang nanti pada akhirnya akan ditandai dengan aktivitas menyimpulkan atas masalah tersebut. Seseorang yang memiliki penalaran yang baik, tentunya akan berhati-hati dalam bertindak dan memutuskan sesuatu. Materi-materi pada kalkulus merupakan materi yang ada pada tingkat sekolah menengah yang nantinya menjadi lahan mengajar mahasiswa calon guru matematika S-1. Kemampuan penalaran yang dikaji mempengaruhi pembelajaran mahasiswa kedepannya karena berlaku pada matakuliah lanjut, contohnya pada kemampuan pembuktian akan selalu digunakan pada matakuliah persamaan diferensial, struktur aljabar, analisis vektor, analisis real, dll. Sedangkan sebagai calon guru yang nantinya mengajar pada tingkat sekolah menengah, maka kemampuan penalaran ini menjadi salah satu capaian pembelajaran matematika bagi siswa sekolah menengah, maka oleh karena itu guru yang mengajarnya haruslah memiliki kemampuan penalaran yang baik. Analisis kesalahan sangat penting untuk melakukan evaluasi dan refleksi pada struktur soal maupun pada perlakuan dalam pembelajaran dalam upaya memperbaiki kemampuan penalarannya. Mathematical reasoning uses a logical mindset in analyzing a problem that will eventually be marked by concluding activity on the problem. Someone who has good reason, will certainly be careful in acting and deciding something. The material content on the calculus is the material that exists at the secondary school level which will become the field of teaching the prospective master of math teacher bachelor. The reasoning ability studied influences student learning in the future as it applies to advanced courses, for example in the ability of proof will always be used in the course of differential equations, algebraic structure, vector analysis, real analysis, etc. While as a teacher candidate who will teach at the secondary school level, then this reasoning ability becomes one of the achievements of mathematics learning for high school students, therefore teachers who teach it must have good reasoning ability. Error analysis is very important to evaluate and reflect on the problem structure as well as on the treatment in learning in order to improve the reasoning ability.

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Failure Analysis Enhancement by Incorporating a Compact Scan Diagnosis System

ISTFA 2014: Conference Proceedings from the 40th International Symposium for Testing and Failure Analysis ◽

10.31399/asm.cp.istfa2014p0436 ◽

2014 ◽

Author(s):

Rommel Estores ◽

Pascal Vercruysse ◽

Karl Villareal ◽

Eric Barbian ◽

Ralph Sanchez ◽

...

Keyword(s):

Data Analysis ◽

Failure Analysis ◽

Real Analysis ◽

Failure Data ◽

Analysis Methodology ◽

Efficiency And Effectiveness ◽

Scan Chain ◽

On Chip ◽

Analysis Environment ◽

Selection Of

Abstract The failure analysis community working on highly integrated mixed signal circuitry is entering an era where simultaneously System-On-Chip technologies, denser metallization schemes, on-chip dissipation techniques and intelligent packages are being introduced. These innovations bring a great deal of defect accessibility challenges to the failure analyst. To contend in this era while aiming for higher efficiency and effectiveness, the failure analysis environment must undergo a disruptive evolution. The success or failure of an analysis will be determined by the careful selection of tools, data and techniques in the applied analysis flow. A comprehensive approach is required where hardware, software, data analysis, traditional FA techniques and expertise are complementary combined [1]. This document demonstrates this through the incorporation of advanced scan diagnosis methods in the overall analysis flow for digital functionality failures and supporting the enhanced failure analysis methodology. For the testing and diagnosis of the presented cases, compact but powerful scan test FA Lab hardware with its diagnosis software was used [2]. It can therefore easily be combined with the traditional FA techniques to provide stimulus for dynamic fault localizations [3]. The system combines scan chain information, failure data and layout information into one viewing environment which provides real analysis power for the failure analyst. Comprehensive data analysis is performed to identify failing cells/nets, provide a better overview of the failure and the interactions to isolate the fault further to a smaller area, or to analyze subtle behavior patterns to find and rationalize possible faults that are otherwise not detected. Three sample cases will be discussed in this document to demonstrate specific strengths and advantages of this enhanced FA methodology.

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