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For almost every student of physics, the first course on quantum theory raises a lot of puzzling questions and creates a very uncertain picture of the quantum world. This book presents a clear and detailed exposition of the fundamental concepts of quantum theory: states, effects, observables, channels and instruments. It introduces several up-to-date topics, such as state discrimination, quantum tomography, measurement disturbance and entanglement distillation. A separate chapter is devoted to quantum entanglement. The theory is illustrated with numerous examples, reflecting recent developments in the field. The treatment emphasises...
Abstract. This paper collects and extends the lectures I gave at the “XXIV International Fall Workshop on Geometry and Physics” held in Zaragoza (Spain) duringSeptember 2015. Within these lectures I review the formulation of Quantum Mechanics,and quantum theories in general, from a mathematically advanced viewpoint, essentiallybased on the orthomodular lattice of elementary propositions, discussing some fundamental ideas, mathematical tools and theorems also related to the representation ofphysical symmetries. The final step consists of an elementary introduction the so-called(C*-) algebraic formulation of quantum theories...
Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this collection we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start with splitting the experiment into two parts: a preparation process and a measurement process leading to a registration of a particular outcome.
Mathematical Foundations of Quantum Theory is a collection of lecture notes. The goal is to give a mathematically clear and self-containing explanation of the main concepts of the modern language of quantum theory. The contributors present their topics from a...
How is life different from 25 or even 10 years ago? Mathematics has profoundly changed our world, from banking & computers to listening to music. This course is designed for those who haven't had college mathematics but would like to understand some of the mathematical concepts behind important modern applications.
Topics:
Cryptography
Error correction & compression
Probability & Statistics
Birth, Growth, Death & Chaos
Graph Theory
Voting & Social Choice
About the Authors
Ingrid Daubechies is a Belgian physicist and mathematician. She is best known for her work with wavelets in image...
This book is about Information Retrieval (IR), particularly Classical Information Retrieval (CIR). It looks at these topics through their mathematical roots. The mathematical bases of CIR are briefly reviewed, followed by the most important and interesting models of CIR, including Boolean, Vector Space, and Probabilistic. The primary goal of book is to create a context for understanding the principles of CIR by discussing its mathematical bases.
Mathematics is a foundation and building block of all areas of knowledge. It particularly affects disciplines concerned with information organization, storage, retrieval, and exchange...
“The presentation is clear and proofs for most of the results used are given … The book is accessible to students from a wide variety of backgrounds and has as prerequisites only basic calculus, linear algebra and ordinary differential equations.” Mathematical Reviews This book provides an introduction to those parts of analysis that are most useful in applications for graduate students. The material is selected for use in applied problems, and is presented clearly and simply but without sacrificing mathematical rigor. The text is accessible to students from a wide variety of backgrounds, including undergraduate students entering...
This textbook develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation for when, why, and how the tools of linear algebra can be used across modern applied mathematics.
Providing an extensive treatment of essential topics such as Gaussian elimination, inner products and norms, and eigenvalues and singular values, this text can be used for an in-depth...
The present text book contains a collection of six high-quality articles. In particular, this book is devoted to Linear Mathematics by presenting problems in Applied Linear Algebra of general or special interest.
In order not to intimidate students by a too abstract approach, this textbook on linear algebra is written to be easy to digest by non-mathematicians. It introduces the concepts of vector spaces and mappings between them without dwelling on statements such as theorems and proofs too much. It is also designed to be self-contained, so no other material is required for an understanding of the topics covered.
As the basis for courses on space and atmospheric science, remote sensing, geographic information systems, meteorology, climate and satellite communications at UN-affiliated regional centers, various applications of the formal...
This textbook on the basics of option pricing is accessible to readers with limited mathematical training. It is for both professional traders and undergraduates studying the basics of finance. Assuming no prior knowledge of probability.
Applied Finite Mathematics covers topics including linear equations, matrices, linear programming, the mathematics of finance, sets and counting, probability, Markov chains, and game theory. Finite Math covers a variety of topics united by their focus on mathematical techniques used in business applications. The growing field of “business analytics” encompasses many types of applications; the topics we learn give insight to some methods used in industry, although we will explore them on a smaller scale. Topics include linear models and optimization, probability and related models, exponential models and financial...
Applied Finite Mathematics covers topics including linear equations, matrices, linear programming (geometrical approach and simplex method), the mathematics of finance, sets and counting, probability, Markov chains, and game theory.
Having the right answer doesn't guarantee understanding. This book helps physics students learn to take an informed and intuitive approach to solving problems. It assists undergraduates in developing their skills and provides them with grounding in important mathematical methods.
Starting with a review of basic mathematics, the author presents a thorough analysis of infinite series, complex algebra, differential equations, and Fourier series. Succeeding chapters explore vector spaces, operators and matrices, multivariable and vector calculus, partial differential equations, numerical and complex analysis, and tensors. Additional...
This book offers advanced undergraduates and graduate students in physics, engineering, and other natural sciences a solid foundation in several fields of mathematics. Clear and well-written, it assumes a previous knowledge of the theory of functions of real and complex variables, and is ideal for classroom use, self-study, or as a supplementary text.
Starting with vector spaces and matrices, the text proceeds to orthogonal functions; the roots of polynomial equations; asymptotic expansions; ordinary differential equations; conformal mapping; and extremum problems. Each chapter goes straight to the heart of the matter, developing...
This book is written for engineers and students and covers a range of mathematics from school to university. The first chapter is a summary so students can quickly see where further study is needed.
This book explains mathematical jargon and develops the formulae used by engineers from first principles. The first chapter is a summary so the reader can quickly see where further study is needed. The book is in two parts, pure and applied.
The principal goal of this book is to provide the reader with a comprehensive knowledge of fundamental concepts and methods of applied mathematics used in different engineering disciplines. Each topic is covered in great detail, followed by several meticulously worked-out examples, as well as a problem set containing a large number of additional related exercises.
This textbook covers topics such as functions, single variable calculus, multivariate calculus, differential equations and complex functions. The necessary linear algebra for multivariate calculus is also outlined. More advanced topics which have been omitted, but which you will certainly come across, are partial differential equations, Fourier transforms and Laplace transforms.
This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.
This text serves as an introduction to discrete mathematics, probability, and mathematical thinking for computer scientists. This subject offers an interactive introduction to discrete mathematics oriented toward computer science and engineering. The subject coverage divides roughly into thirds:
Fundamental concepts of mathematics: Definitions, proofs, sets, functions, relations.
Discrete structures: graphs, state machines, modular arithmetic, counting.
Discrete probability theory.
Students will be able to explain and apply the basic methods of discrete (noncontinuous) mathematics in computer science. They will be...
Intended audience: Sophomores. This is the second quarter of a 2 quarter sequence; however, there is some overlap since not all students have had the first course. Background: Some familiarity with calculus is assumed but is not essential.
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