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Englert B: Lectures On Quantum State
Estimation

Lectures On Quantum State Estimation

Simons Symposia

This book is a tribute to the memory of Yuri Ivanovich Manin, who passed away on January 7, 2023. Manin was one of the giants of modern mathematics. His work covered a wide range of fields, including logic, number theory, geometry, mathematical physics, theoretical computer science, and linguistics. The contributions collected here are on topics close to his life-long passion: arithmetic and algebraic geometry.

A Mathematical Tribute to Yuri Manin

Arithmetic and Algebraic Geometry

Selected Topics

Quantum Modelling of Economic and Financial Systems

A Brief History of the Universe (and our place in it)

Gibbs Measures In Machine Learning

Radon Series on Computational and Applied Mathematics

Hilbert Space Methods for the Theory of Electromagnetism

Maxwell’s Equations

Surveys and Tutorials in the Applied Mathematical Sciences

Mechanics is one of the oldest and most foundational subjects in undergraduate curricula for mathematicians, physicists, and engineers. Traditionally taught through a classical, or "analytical," approach, modern advancements have introduced a "geometric" perspective that has found applications in diverse fields such as machine learning, climate research, satellite navigation, and more.This book bridges the gap between classical mechanics and its modern, geometric counterpart. Designed for students and educators, it presents the essential topics typically required in mechanics courses while integrating a geometric approach to deepen understanding.Key features include:*Clear explanations of core concepts, including Lagrangian mechanics, variational methods, canonical transformations, and systems with constraints.*Numerous solved problems and real-world examples to solidify understanding.*Sample midterms and final exams to help students prepare for coursework and assessments.*Every chapter includes a ‘looking forward’ section outlining modern applications of the materialThe book minimizes mathematical abstraction, introducing only the necessary concepts to make the material accessible and practical. Whether you're a student looking to master the essentials or an instructor seeking a fresh perspective, this book provides a comprehensive, approachable, and modern exploration of mechanics.

Mechanics is one of the oldest and most foundational subjects in undergraduate curricula for mathematicians, physicists, and engineers. Traditionally taught through a classical, or "analytical," approach, modern advancements have introduced a "geometric" perspective that has found applications in diverse fields such as machine learning, climate research, satellite navigation, and more.This book bridges the gap between classical mechanics and its modern, geometric counterpart. Designed for students and educators, it presents the essential topics typically required in mechanics courses while integrating a geometric approach to deepen understanding.Key features include:*Clear explanations of core concepts, including Lagrangian mechanics, variational methods, canonical transformations, and systems with constraints.*Numerous solved problems and real-world examples to solidify understanding.*Sample midterms and final exams to help students prepare for coursework and assessments.*Every chapter includes a ‘looking forward’ section outlining modern applications of the material.The book minimizes mathematical abstraction, introducing only the necessary concepts to make the material accessible and practical. Whether you're a student looking to master the essentials or an instructor seeking a fresh perspective, this book provides a comprehensive, approachable, and modern exploration of mechanics.

A Concise Introduction to Classical Mechanics

"The quantum Hall effect (QHE) is a fundamental phenomenon that occurs in a two-dimensional electron gas (2DEG) at low temperature and in the presence of a strong magnetic field. It has various applications in the fields like metrology and topological quantum computers. It also provides an extremely precise and independent determination of the fine-structure constant-a quantity of fundamental importance in quantum electrodynamics. This book attempts to present concepts of QHE to undergraduate and graduate students, post-doctoral researchers, and teachers taking advanced courses on condensed matter physics. The author has tried to integrate all the important concepts of QHE like graphene, the connection between topology and condensed matter physics, the prospects of next-generation storage devices based on the manipulation of spins (spintronic) and present them in a lucid manner. It offers the advantage of providing a pedagogical presentation to help students with some intermediate steps in derivation. The book starts with an introduction to the experimental discovery of the QHE that segues into the basics of 2DEG in a magnetic field. The physics of the Landau levels, their properties, and their relevance to the integer QHE are discussed. The importance of conduction and its connection to topological insulators is also emphasised. At a pedagogical level, concepts like linear response theory, Kubo formula, and topological invariance are explained and their relations to the understanding of QHE, graphene, its symmetries and its relevance as a quantum Hall insulator are also covered. It ends with an explanation of the role of interparticle interactions to explain fractional QHE with the help of topics such as the Laughlin wave function, fractional charge and statistics, and non-abelian anyons"--

This book deals with the discovery and explanation of the quantum Hall effect and its fundamental principles. It is meant for undergraduate and graduate students of physics, engineering and applied sciences studying condensed matter physics. Doctoral students and researchers of this subject will also find it equally useful.

Lectures On Quantum State Estimation

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