Belal Ehsan Baaquie – författare

An introduction to how the mathematical tools from quantum field theory can be applied to economics and finance, providing a wide range of quantum mathematical techniques for designing financial instruments. The ideas of Lagrangians, Hamiltonians, state spaces, operators and Feynman path integrals are demonstrated to be the mathematical underpinning of quantum field theory, and which are employed to formulate a comprehensive mathematical theory of asset pricing as well as of interest rates, which are validated by empirical evidence. Numerical algorithms and simulations are applied to the study of asset pricing models as well as of nonlinear interest rates. A range of economic and financial topics are shown to have quantum mechanical formulations, including options, coupon bonds, nonlinear interest rates, risky bonds and the microeconomic action functional. This is an invaluable resource for experts in quantitative finance and in mathematics who have no specialist knowledge of quantum field theory.

Quantum Chromodynamics is the theory of strong interactions: a quantum field theory of colored gluons (Yang–Mills gauge fields) coupled to quarks (Dirac fermion fields). Lattice gauge theory is defined by discretizing spacetime into a four-dimensional lattice — and entails defining gauge fields and Dirac fermions on a lattice. The applications of lattice gauge theory are vast, from the study of high-energy theory and phenomenology to the numerical studies of quantum fields.Lattice Quantum Field Theory of the Dirac and Gauge Fields: Selected Topics examines the mathematical foundations of lattice gauge theory from first principles. It is indispensable for the study of Dirac and lattice gauge fields and lays the foundation for more advanced and specialized studies.

The primary aim of this book is to understand the ground-breaking paradigms and policies that have powered China's remarkable rise: from an agricultural society to an industrial powerhouse and a leading nation — and that too in a span of merely forty years from 1979 to 2019. The book covers the rise of China up to 2019 and is divided into five parts. The first part takes a strategic view of China's rise, the second part provides a quantitative assessment of China's rise using macroeconomic indicators; the third part provides a historical background of modern China, starting from the unification of China in 221 BC to the rise to power of the Communist Party of China, leading to the establishment of the People's Republic of China in 1949. The fourth part analyses China's governance as well as its economic system and lastly, part five summarizes China's rise and the paradigms that powered this rise.

Given the rapid pace of development in economics and finance, a concise and up-to-date introduction to mathematical methods has become a prerequisite for all graduate students, even those not specializing in quantitative finance. This book offers an introductory text on mathematical methods for graduate students of economics and finance–and leading to the more advanced subject of quantum mathematics. The content is divided into five major sections: mathematical methods are covered in the first four sections, and can be taught in one semester. The book begins by focusing on the core subjects of linear algebra and calculus, before moving on to the more advanced topics of probability theory and stochastic calculus. Detailed derivations of the Black-Scholes and Merton equations are provided – in order to clarify the mathematical underpinnings of stochastic calculus. Each chapter of the first four sections includes a problem set, chiefly drawn from economicsand finance.  In turn, section five addresses quantum mathematics. The mathematical topics covered in the first four sections are sufficient for the study of quantum mathematics; Black-Scholes option theory and Merton’s theory of corporate debt are among topics analyzed using quantum mathematics.

Given the rapid pace of development in economics and finance, a concise and up-to-date introduction to mathematical methods has become a prerequisite for all graduate students, even those not specializing in quantitative finance. This book offers an introductory text on mathematical methods for graduate students of economics and finance–and leading to the more advanced subject of quantum mathematics. The content is divided into five major sections: mathematical methods are covered in the first four sections, and can be taught in one semester. The book begins by focusing on the core subjects of linear algebra and calculus, before moving on to the more advanced topics of probability theory and stochastic calculus. Detailed derivations of the Black-Scholes and Merton equations are provided – in order to clarify the mathematical underpinnings of stochastic calculus. Each chapter of the first four sections includes a problem set, chiefly drawn from economicsand finance.  In turn, section five addresses quantum mathematics. The mathematical topics covered in the first four sections are sufficient for the study of quantum mathematics; Black-Scholes option theory and Merton’s theory of corporate debt are among topics analyzed using quantum mathematics.

Given the rapid pace of development in economics and finance, a concise and up-to-date introduction to mathematical methods has become a prerequisite for all graduate students, even those not specializing in quantitative finance. This book offers an introductory text on mathematical methods for graduate students of economics and finance–and leading to the more advanced subject of quantum mathematics. The content is divided into five major sections: mathematical methods are covered in the first four sections, and can be taught in one semester. The book begins by focusing on the core subjects of linear algebra and calculus, before moving on to the more advanced topics of probability theory and stochastic calculus. Detailed derivations of the Black-Scholes and Merton equations are provided – in order to clarify the mathematical underpinnings of stochastic calculus. Each chapter of the first four sections includes a problem set, chiefly drawn from economicsand finance.  In turn, section five addresses quantum mathematics. The mathematical topics covered in the first four sections are sufficient for the study of quantum mathematics; Black-Scholes option theory and Merton’s theory of corporate debt are among topics analyzed using quantum mathematics.

This book presents various theories and algorithms to create a quantum computer. The concept of the classical and quantum computers, and the concept of circuits and gates are reviewed. The example of the Deutsch and the Deutsch-Josca algorithm is discussed to illustrate some key features of quantum computing. The Grover algorithm, considered to be of major milestone of the subject, is discussed in detail to exemplify the techniques used in computer algorithms. The role of quantum superposition (also called quantum parallelism) and of quantum entanglement is discussed in order to understand the key advantages of a quantum over a classical computer.

This book presents various theories and algorithms to create a quantum computer. The concept of the classical and quantum computers, and the concept of circuits and gates are reviewed. The example of the Deutsch and the Deutsch-Josca algorithm is discussed to illustrate some key features of quantum computing. The Grover algorithm, considered to be of major milestone of the subject, is discussed in detail to exemplify the techniques used in computer algorithms. The role of quantum superposition (also called quantum parallelism) and of quantum entanglement is discussed in order to understand the key advantages of a quantum over a classical computer.

This book presents various theories and algorithms to create a quantum computer. The concept of the classical and quantum computers, and the concept of circuits and gates are reviewed. The example of the Deutsch and the Deutsch-Josca algorithm is discussed to illustrate some key features of quantum computing. The Grover algorithm, considered to be of major milestone of the subject, is discussed in detail to exemplify the techniques used in computer algorithms. The role of quantum superposition (also called quantum parallelism) and of quantum entanglement is discussed in order to understand the key advantages of a quantum over a classical computer.

This book is a comprehensive presentation of an amazing variety of metaphors and metonyms in physics, chemistry and biology. Their crucial role in many disciplines has come to light only over the last few decades.This verbal symbolic reasoning can be considered as a framework of the scientific language of the 21st century. The unique role of metaphors as a “bridge” between different levels of realities — micro-, meso-, and macro-realities — is explained in detail. Special attention is paid to the “magic triad” of fundamental metaphors (atom, molecule, gene) as well as metaphors of the “machine” and “book/text”.Generously illustrated by a collection of scientific legends and myths, such as Plato's cave and Occam's razor, the book also analyzes special relationships between verbal symbolic reasoning (particularly metaphoric reasoning) and scientific motivation and humor.

This book emerged from a simple observation: while Large Language Models (LLMs) have become ubiquitous, their mathematical foundations remain opaque to many practitioners, students, and enthusiasts. This book bridges that gap by presenting LLMs from first principles – not as a black box, but as an elegant mathematical construction. The journey begins with the simplest language models – bigrams and n-grams – and progressively builds toward the transformer architecture that powers modern LLMs. The emphasize is on clarity over completeness, intuition over implementation details, and mathematical rigor over hand-waving explanations. This book is self-contained and only assumes familiarity with undergraduate-level linear algebra, probability, and calculus. Wherever possible, the abstract concepts are connected to concrete examples, often using minimal two word vocabularies to illuminate general principles. The hope is that this primer serves as both an introduction for newcomers and a reference for practitioners seeking deeper understanding of the mathematical machinery underlying today’s most influential AI systems.

This proceedings covers topics on high Tc superconducting materials, their structure and properties, the devices and their applications. It also covers the theoretical studies as well as state-of-the-art developments in high Tc superconductivity.