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Showing 1 to 6 of 6 for “"mathematical induction"”.
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Interactive Online System for Mathematical Induction
Mathematical Induction is a foundational proof technique in discrete mathematics, whereas many students struggle to cover the gap from procedural to abstract reasoning. This project is based on the interactive online system for mathematical induction, developed to teach mathematical induction with …
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The theory and some applications of Pták's method of non-discrete mathematical induction
… Contraction Principle; (ii) by connecting the Induction Theorem to Baire's Category Theorem and Cantor's Intersection Theorem. Throughout the exposition the editorial "we" is to be understood in the sense of Halmos [ 18]; "we" means "the author and the reader".
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The Infinite Ladder in Mathematics: Transfinite Induction
This project explores the mathematical proof method of transfinite induction. Transfinite induction is mathematical induction beyond the natural numbers. These numbers are called ordinals, denoted by Greek letters. This thesis will introduce fundamental concepts of set theory, starting from the …
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Emergency Evacuation Modeling with Consideration of Fairness
… algorithms, numerical optimization, mathematical induction and algebra, and computer programming, are used in the thesis.
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Errors in South African secondary school mathematics textbooks
… topics were characterised by an emphasis on mathematical structure (set theory, groups, rings and fields, the construction of the real number system, relations and functions, vectors and mathematical induction). Textbooks that were published in South Africa during this time have been found to …
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Frequency Dependent Mechanical Properties of Elastic Metamaterials with Locally Resonant Microstructures
… with decreasing density was obtained using Mathematical Induction method. Making use of the frequency dependent properties, the elastic phase-controlling metalayer was also analyzed. It was analytically and numerically demonstrated that, whether a normal incident longitudinal wave can …