The development of mathematical understanding and its application to Libyan secondary school mathematics

It is unfortunate that many students in Libyan schools and elsewhere dislike mathematics and are even afraid of studying it. This is partially related to the fact that mathematics is presented in an extensive fashion in both scope and depth of content and does not provide opportunities for the student population to understand it. The primary purpose of this study was to examine the problems of the method of presenting mathematics in Libyan secondary schools and to develop principles for understanding mathematics. There were four subordinate problems inherent in the main problems: 1) to study and analyze the characteristics of the new mathematics program in terms of content and method of presentation; 2) to study the problems of Libyan secondary school mathematics, specifically to determine weaknesses in the content and method of presentation; 3) to explore and develop criteria for understanding mathematics; and 4) to evaluate method of presenting mathematics in Libyan secondary schools in terms of the developed criteria

Asymptotics of wavelets and filters

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1998.Includes bibliographical references (p. 126-131).by Jianhong (Jackie) Shen.Ph.D

Network analysis of complex biological systems : boundedness of weakly reversible chemical reaction networks and conditions for synchronisation of coupled oscillators

Imperial Users onl

Quantum computation beyond the circuit model

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2008.Includes bibliographical references (p. 133-144).The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other models of quantum computation exist which provide useful alternative frameworks for both discovering new quantum algorithms and devising new physical implementations of quantum computers. In this thesis, I first present necessary background material for a general physics audience and discuss existing models of quantum computation. Then, I present three new results relating to various models of quantum computation: a scheme for improving the intrinsic fault tolerance of adiabatic quantum computers using quantum error detecting codes, a proof that a certain problem of estimating Jones polynomials is complete for the one clean qubit complexity class, and a generalization of perturbative gadgets which allows k-body interactions to be directly simulated using 2-body interactions. Lastly, I discuss general principles regarding quantum computation that I learned in the course of my research, and using these principles I propose directions for future research.by Stephen Paul Jordan.Ph.D

Theoretical Concepts of Quantum Mechanics

Quantum theory as a scientific revolution profoundly influenced human thought about the universe and governed forces of nature. Perhaps the historical development of quantum mechanics mimics the history of human scientific struggles from their beginning. This book, which brought together an international community of invited authors, represents a rich account of foundation, scientific history of quantum mechanics, relativistic quantum mechanics and field theory, and different methods to solve the Schrodinger equation. We wish for this collected volume to become an important reference for students and researchers

Physics 131: Forces, Energy and Entropy

An openly licensed physics textbook localized for use in Physics 131: Forces, Energy, and Entropy at the University of Massachusetts Amherst. This book is adapted from the OpenStax College Physics textbook, the University of Maryland NEXUS Physics wikibook, the OpenStax Chemistry textbook and the statistics work of John S. Denker.https://scholarworks.umass.edu/physics_ed_materials/1000/thumbnail.jp