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Problems and Proofs in Numbers and Algebra
by Richard S. Millman Peter J. Shiue Eric Brendan KahnFocusing on an approach of solving rigorous problems and learning how to prove, this volume is concentrated on two specific content themes, elementary number theory and algebraic polynomials. The benefit to readers who are moving from calculus to more abstract mathematics is to acquire the ability to understand proofs through use of the book and the multitude of proofs and problems that will be covered throughout. This book is meant to be a transitional precursor to more complex topics in analysis, advanced number theory, and abstract algebra. To achieve the goal of conceptual understanding, a large number of problems and examples will be interspersed through every chapter. The problems are always presented in a multi-step and often very challenging, requiring the reader to think about proofs, counter-examples, and conjectures. Beyond the undergraduate mathematics student audience, the text can also offer a rigorous treatment of mathematics content (numbers and algebra) for high-achieving high school students. Furthermore, prospective teachers will add to the breadth of the audience as math education majors, will understand more thoroughly methods of proof, and will add to the depth of their mathematical knowledge. In the past, PNA has been taught in a "problem solving in middle school" course (twice), to a quite advanced high school students course (three semesters), and three times as a secondary resource for a course for future high school teachers. PNA is suitable for secondary math teachers who look for material to encourage and motivate more high achieving students.
Problems and Solutions in Many-Body Quantum Theory: Sailing the Fermi Sea
by Bruno Julia-Diaz Arnau Rios Huguet Héctor Briongos Merino Javier Rozalén SarmientoThis practical guidebook provides a comprehensive set of exercises which illustrate the most relevant concepts in a first course on quantum many-body theory either as part of advanced undergraduate or graduate courses. The problems come with detailed solutions which can easily be followed either by both professors and students. Quantum many-body theory is relevant in a number of fields, from condensed matter to astrophysics. The problems proposed in this book cover this variety of topics and are illustrated whenever possible with state-of-the-art-examples.Key Features: Provides a problems-based approach to quantum many-body theory, unlike existing textbooks. In-depth solutions to problems are presented, with the aim to maximize understanding and improve the teaching experience of the subject. The multidisciplinary nature of quantum many-body theory is explored in problems that deal with nuclear physics to ultracold atoms and astrophysics.
Problems and Solutions on Vector Spaces for Physicists: From Part I in Mathematical Physics—A Modern Introduction to Its Foundations
by Robert B. ScottThis book offers supporting material for the comprehensive textbook Mathematical Physics—A Modern Introduction to Its Foundations authored by Sadri Hassani. The book covers mathematical preliminaries and all of Part I in Hassani’s textbook. The subjects covered here include the key topics necessary for physicists to form a solid mathematical foundation: vectors and linear maps, algebras, operators, matrices, and spectral decomposition. In particular, the vector space concept is a central unifying theme in later chapters of Hassani’s textbook. Detailed solutions are provided to one third of the end-of-chapter exercises in the first six chapters of his text. The present volume helps upper-undergraduate and early postgraduate physics students deepen their understanding of the mathematics that they encounter in physics, learn physics more efficiently, and use mathematics with more confidence and creativity. The content is thus presented rigorously but remains accessible to physics students. New exercises are also proposed, some with solutions, some without, so that the total number of unsolved exercises remains unchanged. They are chosen to help explain difficult concepts, amplify key points in Hassani's textbook, or make further connections with applications in physics. Taken together with Hassani's work, the two form a self-contained set and the solutions make detailed reference to Hassani's text. The solutions also refer to other mathematics and physics textbooks, providing entry points to further literature that finds a useful place in the physicist's personal library.
Problems and Worked Solutions in Vector Analysis (Dover Books on Mathematics)
by L. R. Shorter"A handy book like this," noted The Mathematical Gazette, "will fill a great want." Devoted to fully worked out examples, this unique text constitutes a self-contained introductory course in vector analysis for undergraduate and graduate students of applied mathematics.Opening chapters define vector addition and subtraction, show how to resolve and determine the direction of two or more vectors, and explain systems of coordinates, vector equations of a plane and straight line, relative velocity and acceleration, and infinitely small vectors. The following chapters deal with scalar and vector multiplication, axial and polar vectors, areas, differentiation of vector functions, gradient, curl, divergence, and analytical properties of the position vector. Applications of vector analysis to dynamics and physics are the focus of the final chapter, including such topics as moving rigid bodies, energy of a moving rigid system, central forces, equipotential surfaces, Gauss's theorem, and vector flow.
Problems in Differential Equations (Dover Books on Mathematics)
by J. L. BrennerA supplement for elementary and intermediate courses in differential equations, this text features more than 900 problems and answers. Suitable for undergraduate students of mathematics, engineering, and physics, this volume also represents a helpful tool for professionals wishing to brush up on their problem-solving skills.The book is divided into twenty sections, each preceded by a clear and logical explanation of the basic ideas needed for solving the problems within the section. Many fully explained illustrative problems appear throughout the text. Subjects include applied routine and nonroutine problems in vibrations, electrical engineering, mechanics, and physics. Stars indicate advanced problems. Short mathematical and numerical tables are provided at the end of the book.
Problems in Finite Element Methods: Aubin Nitsche’s Duality Process, Nodal Methods and Friedrichs Systems (Infosys Science Foundation Series)
by Aref JeribiThis book discusses major topics and problems in finite element methods. It is targeted to graduate students and researchers in applied mathematics, physics, and engineering, wishing to learn and familiarize themselves with finite element theory. The book describes the nodal method for squares or rectangles and triangles, as well as an increase of the error between exact solution and approximate solution. It discusses an approximation of positive symmetric first-order systems in the Friedrichs sense by finite element methods. In addition, the book also explains the continuous and discontinuous approximation methods, adapted to the structure of the transport equation, leading to linear systems of quasi-explicit resolution, and therefore commonly used in practice.
Problems in Mathematical Analysis (Pure and Applied Mathematics #132)
by Piotr Biler Alfred WitkowskiChapter 1 poses 134 problems concerning real and complex numbers, chapter 2 poses 123 problems concerning sequences, and so it goes, until in chapter 9 one encounters 201 problems concerning functional analysis. The remainder of the book is given over to the presentation of hints, answers or referen
Problems in Mathematical Biophysics: A Volume in Memory of Alberto Gandolfi (SEMA SIMAI Springer Series #38)
by Antonio Fasano Alberto D’Onofrio Federico Papa Carmela SinisgalliThe book "Problems in Mathematical Biophysics - a volume in memory of Alberto Gandolfi" aims at reviewing the current state of the art of the mathematical approach to various areas of theoretical biophysics. Leading authors in the field have been invited to contribute, having a strong appreciation of Alberto Gandolfi as a scientist and as a man and sharing his same passion for biology and medicine, as well as his style of investigation. Encompassing both theoretical and practical aspects of Mathematical Biophysics, the topics covered in this book span a spectrum of different problems, in biology, and medicine, including population dynamics, tumor growth and control, immunology, epidemiology, ecology, and others. As a result, the book offers a comprehensive and current overview of compelling subjects and challenges within the realm of mathematical biophysics. In their contributions, the authors have effectively conveyed not only their research findings but also their peculiar perspective and approach to problem-solving, dealing with oncology, epidemiology, neuro-sciences, and biochemistry. The chapters pertain to a wide array of mathematical areas such as continuous Markov chains, partial differential equations, kinetic theory, applied statistical mechanics, noise-induced transitions, and many others.
Problems in Probability
by Albert N. Shiryaev Andrew LyasoffFor the first two editions of the book Probability (GTM 95), each chapter included a comprehensive and diverse set of relevant exercises. While the work on the third edition was still in progress, it was decided that it would be more appropriate to publish a separate book that would comprise all of the exercises from previous editions, in addition to many new exercises. Most of the material in this book consists of exercises created by Shiryaev, collected and compiled over the course of many years while working on many interesting topics. Many of the exercises resulted from discussions that took place during special seminars for graduate and undergraduate students. Many of the exercises included in the book contain helpful hints and other relevant information. Lastly, the author has included an appendix at the end of the book that contains a summary of the main results, notation and terminology from Probability Theory that are used throughout the present book. This Appendix also contains additional material from Combinatorics, Potential Theory and Markov Chains, which is not covered in the book, but is nevertheless needed for many of the exercises included here.
Problems in Probability Theory, Mathematical Statistics and Theory of Random Functions
by A. A. SveshnikovProblem solving is the main thrust of this excellent, well-organized workbook. Suitable for students at all levels in probability theory and statistics, the book presents over 1,000 problems and their solutions, illustrating fundamental theory and representative applications in the following fields: Random Events; Distribution Laws; Correlation Theory; Random Variables; Entropy & Information; Markov Processes; Systems of Random Variables; Limit Theorems; Data Processing; and more.The coverage of topics is both broad and deep, ranging from the most elementary combinatorial problems through limit theorems and information theory. Each chapter introduction sets forth the basic formulas and a general outline of the theory necessary for the problems that follow. Next comes a group of sample problems and their solutions, worked out in detail, which serve as effective orientation for the exercises to come.The emphasis on problem solving and the multitude of problems presented make this book, translated from the Russian, a valuable reference manual for scientists, engineers, and computer specialists, as well as a comprehensive workbook for undergraduates in these fields.
Problems in Quantum Mechanics and Field Theory with Mathematical Modelling
by Aleksander V. Chichurin Elena M. Ovsiyuk Viktor M. Red’kovIn Problems in Quantum Mechanics and Field Theory with Mathematical Modelling, a number of exactly solvable problems in electrodynamics and in quantum-mechanics of particles with different spins are presented.The main topics covered include: the Cox scalar particle with intrinsic structure in presence of the magnetic field in the spaces of constant curvature, Euclid, Riemann, and Lobachevsky; Cox particle in the Coulomb field; tunneling effect through Schwarzschild barrier for a spin 1/2 particle; electromagnetic field in Schwarzschild space-time, the Majorana - Oppenheimer approach in electrodynamics; scalar particle with polarizability in the Coulomb field; Dirac particle in the Coulomb field on the background of hyperbolic Lobachevsky and spherical Riemann models; particle with spin 1 in the Coulomb field; geometrical modeling of the media in Maxwell electrodynamics; P-asymmetric equation for a spin 1/2 particle; fermion with two mass parameters in the Coulomb field; helicity operator for a spin 2 particle in presence of the magnetic field.The book will be of interest to researchers, and is accessible enough to serve as a self-study resources for courses at undergraduate and graduate levels.
Problems in Thermodynamics and Statistical Physics (Dover Books on Physics)
by Peter T. LandsbergWell respected and widely used, this volume presents problems and full solutions related to a wide range of topics in thermodynamics, statistical physics, and statistical mechanics. The text is intended for instructors, undergraduates, and graduate students of mathematics, physics, chemistry, and engineering. Twenty-eight chapters, each prepared by an expert, proceed from simpler to more difficult subjects. Similarly, the early chapters are easier than the later ones, making the book ideal for independent study.Subjects begin with the laws of thermodynamics and statistical theory of information and of ensembles, advancing to the ideal classical gases of polyatomic molecules, non-electrolyte liquids and solutions, and surfaces. Subsequent chapters explore imperfect classical and quantum gas, phase transitions, cooperative phenomena, Green function methods, the plasma, transport in gases and metals, Nyquist's theorem and its generalizations, stochastic methods, and many other topics.
Problems of High Frequency Diffraction by Elongated Bodies (Springer Series in Optical Sciences #243)
by Ivan AndronovClassical asymptotic expansions, while producing a good approximation for the diffracted fields in general, appear hardly applicable in the case of extremely elongated bodies. Thus, there are problems that are on the one hand too difficult for numerical solvers due to large system size, and on the other hand make the description with classical asymptotic methods hard. The book explains why this happens and suggests the way out. By defining the characteristics of a strongly elongated body it introduces a special class of asymptotic approximations, which are in some sense uniform with respect to the rate of body elongation. Chapter 1 briefly describes the results of V. A. Fock and further developments of his approach towards the problems of diffraction by elongated obstacles. It formulates the cases of moderately and strongly elongated bodies. The rest of the book describes the approach of special parabolic equations, which lead to new asymptotic approximations for the diffracted fields. Chapters 2, 3 and 4 discuss diffraction by bodies of elliptical shape: The elliptic cylinder with a strongly elongated cross section and prolate spheroid with a high aspect ratio. Chapter 5 generalizes the approach to some other shapes such as narrow cones and narrow hyperboloids. Mathematical formulas for the Whittaker functions widely used in the book are collected in the Appendix. The concise derivations are supplied with numerous test examples that compare asymptotic approximations with numerically computed fields and clarify the specifics of high frequency diffraction by strongly elongated bodies. The reference solutions presented in the book enable one to validate the newly developed numerical solvers.
Problems of Locus Solved by Mechanisms Theory (Springer Tracts in Mechanical Engineering)
by Iulian Popescu Xenia Calbureanu Alina DutaThis book reports on an original approach to problems of loci. It shows how the theory of mechanisms can be used to address the locus problem. It describes the study of different loci, with an emphasis on those of triangle and quadrilateral, but not limited to them. Thanks to a number of original drawings, the book helps to visualize different type of loci, which can be treated as curves, and shows how to create new ones, including some aesthetic ones, by changing some parameters of the equivalent mechanisms. Further, the book includes a theoretical discussion on the synthesis of mechanisms, giving some important insights into the correlation between the generation of trajectories by mechanisms and the synthesis of those mechanisms when the trajectory is given, and presenting approximate solutions to this problem. Based on the authors’ many years of research and on their extensive knowledge concerning the theory of mechanisms, and bridging between geometry and mechanics, this book offers a unique guide to mechanical engineers and engineering designers, mathematicians, as well as industrial and graphic designers, and students in the above-mentioned fields alike.
Problems on Partial Differential Equations (Problem Books in Mathematics)
by Maciej Borodzik Paweł Goldstein Piotr Rybka Anna Zatorska-GoldsteinThis book covers a diverse range of topics in Mathematical Physics, linear and nonlinear PDEs. Though the text reflects the classical theory, the main emphasis is on introducing readers to the latest developments based on the notions of weak solutions and Sobolev spaces. In numerous problems, the student is asked to prove a given statement, e.g. to show the existence of a solution to a certain PDE. Usually there is no closed-formula answer available, which is why there is no answer section, although helpful hints are often provided. This textbook offers a valuable asset for students and educators alike. As it adopts a perspective on PDEs that is neither too theoretical nor too practical, it represents the perfect companion to a broad spectrum of courses.
Problems, Methods and Tools in Experimental and Behavioral Economics: Computational Methods in Experimental Economics (CMEE) 2017 Conference (Springer Proceedings in Business and Economics)
by Kesra Nermend Małgorzata ŁatuszyńskaThese proceedings highlight research on the latest trends and methods in experimental and behavioral economics. Featuring contributions presented at the 2017 Computational Methods in Experimental Economics (CMEE) conference, which was held in Lublin, Poland, it merges findings from various domains to present deep insights into topics such as game theory, decision theory, cognitive neuroscience and artificial intelligence. The fields of experimental economics and behavioral economics are rapidly evolving. Modern applications of experimental economics require the integration of know-how from disciplines including economics, computer science, psychology and neuroscience. The use of computer technology enhances researchers’ ability to generate and analyze large amounts of data, allowing them to use non-standard methods of data logging for experiments such as cognitive neuronal methods. Experiments are currently being conducted with software that, on the one hand, provides interaction with the people involved in experiments, and on the other helps to accurately record their responses. The goal of the CMEE conference and the papers presented here is to provide the scientific community with essential research on and applications of computer methods in experimental economics. Combining theories, methods and regional case studies, the book offers a valuable resource for all researchers, scholars and policymakers in the areas of experimental and behavioral economics.
Procedural Content Generation via Machine Learning: An Overview (Synthesis Lectures on Games and Computational Intelligence)
by Matthew Guzdial Sam Snodgrass Adam SummervilleThis second edition updates and expands upon the first beginner-focused guide to Procedural Content Generation via Machine Learning (PCGML), which is the use of computers to generate new types of content for video games (game levels, quests, characters, etc.) by learning from existing content. The authors survey current and future approaches to generating video game content and illustrate the major impact that PCGML has had on video games industry. In order to provide the most up-to-date information, this new edition incorporates the last two years of research and advancements in this rapidly developing area. The book guides readers on how best to set up a PCGML project and identify open problems appropriate for a research project or thesis. The authors discuss the practical and ethical considerations for PCGML projects and demonstrate how to avoid the common pitfalls. This second edition also introduces a new chapter on Generative AI, which covers the benefits, risks, and methods for applying pre-trained transformers to PCG problems.
Proceeding of International Conference on Computational Science and Applications: ICCSA 2019 (Algorithms for Intelligent Systems)
by Subhash Bhalla Peter Kwan Mangesh Bedekar Rashmi Phalnikar Sumedha SirsikarThe book consists of high-quality papers presented at the International Conference on Computational Science and Applications (ICCSA 2019), held at Maharashtra Institute of Technology World Peace University, Pune, India, from 7 to 9 August 2019. It covers the latest innovations and developments in information and communication technology, discussing topics such as soft computing and intelligent systems, web of sensor networks, drone operating systems, web of sensor networks, wearable smart sensors, automated guided vehicles and many more.
Proceeding of International Conference on Computational Science and Applications: ICCSA 2021 (Algorithms for Intelligent Systems)
by Subhash Bhalla Mangesh Bedekar Rashmi Phalnikar Sumedha SirsikarThis book consists of high-quality papers presented at the International Conference on Computational Science and Applications (ICCSA 2021), held at Maharashtra Institute of Technology World Peace University, Pune, India, from 10 – 11 December 2021. It covers the latest innovations and developments in information and communication technology, discussing topics such as algorithms, data structures and applications; wireless and mobile networks; computer networks and communications; natural language processing and information theory; cryptography and information security.
Proceeding of the 2nd International Conference on Machine Intelligence and Emerging Technologies: MIET 2024 (Lecture Notes in Networks and Systems #1235)
by M. Shamim Kaiser Mohammad Shamsul Arefin Md. Shahriare Satu Pietro Lio'This book is a collection of high-quality research papers presented at the Second International Conference on Machine Intelligence and Emerging Technologies, MIET 2024, hosted by Noakhali Science and Technology University, Noakhali, Bangladesh, during 8-9 November 2024. This book focuses on theoretical, practical, state-of-art applications, and research challenges in the field of artificial intelligence and emerging technologies. It is helpful for active researchers and practitioners in this field.
Proceeding of the International Conference on Connected Objects and Artificial Intelligence: Connected Objects, Artificial Intelligence, Telecommunications and Electronics Engineering (Lecture Notes in Networks and Systems #1123)
by Youssef Mejdoub Abdelkebir Elamri’This book presents recent advances on Connected Objects, Systems, Telecommunications, Artificial Intelligence, and Electronic Engineering. On the connected objects side, the proceedings covered advancements in areas like sensor miniaturization, and networking to enable ever-more ubiquitous and autonomous IoT deployments. The AI-focused contributions explored novel machine learning architectures and training techniques tailored for resource-constrained edge devices. Key breakthroughs included federated learning models. In the telecommunications realm, the proceedings examined the critical role of 5G, 6G, and satellite communications in providing the high-bandwidth, low-latency connectivity required to unlock the full potential of AI-powered connected systems. This book is a collection of high-quality research papers presented at the 2nd International Conference on Connected Objects and Artificial Intelligence (COCIA'2024), held at High School of Technology, Hassan II University, Casablanca, Morocco, during 08–10 May 2024. This book features cutting-edge research and insights at the intersection of the important technology domains, Connected Objects, Systems, Telecommunications, Artificial Intelligence, and Electronic Engineering. It is designed for researchers, academicians, professionals, and graduates seeking to deepen their understanding and expertise at the intersection of IoT, AI, Telecommunications, and Electronic Engineering. This book includes: In-depth exploration of the latest advancements in connected objects and systems to enable autonomous IoT deployments. Detailed examinations of cutting-edge AI techniques optimized for edge computing environments, including federated learning and IA model compression. Insights into the critical role of 5G, 6G, and satellite communications in providing the high-performance connectivity required to unlock the full potential of intelligent, AI-powered IoT applications. With contributions from leading experts across academia and industry, this book equips readers with the knowledge and tools to drive innovation at the forefront of the connected intelligence revolution. It is an essential resource for anyone seeking to advance the state of the art in this rapidly evolving field.
Proceedings from the International Conference on Hydro and Renewable Energy: Net-Zero Carbon Energy Systems (Lecture Notes in Civil Engineering #391)
by Bri-Mathias Hodge Sanjeev Kumar PrajapatiThis book comprises the select peer-reviewed proceedings of the International Conference on Hydro and Renewable Energy (ICHRE 2022). It aims to provide a comprehensive and broad-spectrum picture of the state-of-the-art research and development in the area of renewable energy technologies, grid integration challenges and opportunities, negative emission technologies, role of distributed energy resources in net zero energy carbon systems, role of hydro energy and pumped storage hydro in power sector decarbonization, policies, and regulations in achieving net zero carbon energy systems, among others. This book provides a valuable resource for those in academia and industry working in the fields of renewable energy, civil engineering, mechanical engineering, among others.
Proceedings of 17th International Conference on Machine Learning and Computing: ICMLC2025, Volume 1 (Lecture Notes in Networks and Systems #1475)
by Lin Huang David GreenhalghThis book comprises original and peer reviewed research papers presented at 2025 17th International Conference on Machine Learning and Computing that was held in Guangzhou, China, from February 14 to 17, 2025. The focus of the conference is to establish an effective platform for institutions and industries to share ideas and to present the works of scientists, engineers, educators and students from all over the world. Topics discussed in this volume include Machine Learning Theory and Algorithms, High-performance Computing Models and Data Processing, Large-scale Language Models and Natural Language Processing, Data-oriented Information System Optimization and Intelligent Computing, AI-based Intelligent Control Systems and System Security, etc. The book will become a valuable resource for academics, industry professionals, and engineers working in the related fields of machine learning and computing.
Proceedings of 17th International Conference on Machine Learning and Computing: ICMLC2025, Volume 2 (Lecture Notes in Networks and Systems #1476)
by Lin Huang David GreenhalghThis book comprises original and peer reviewed research papers presented at 2025 17th International Conference on Machine Learning and Computing that was held in Guangzhou, China, from February 14 to 17, 2025. The focus of the conference is to establish an effective platform for institutions and industries to share ideas and to present the works of scientists, engineers, educators and students from all over the world. Topics discussed in this volume include Machine Learning Theory and Algorithms, High-performance Computing Models and Data Processing, Large-scale Language Models and Natural Language Processing, Data-oriented Information System Optimization and Intelligent Computing, AI-based Intelligent Control Systems and System Security, etc. The book will become a valuable resource for academics, industry professionals, and engineers working in the related fields of machine learning and computing.
Proceedings of 1st GENZERO Workshop: Revolutionizing Autonomous Systems Security with Generative AI, and Large Language Models for Zero Trust Architecture
by Martin Andreoni Shreekant ThakkarThis Open Access volume compiles peer-reviewed research at the GENZERO Workshop on Security and Autonomous Systems, hosted by the Technology Innovation Institute in Abu Dhabi in November 2024. As a leading event in the fields of security of autonomous systems and generative AI, the workshop emphasizes the expansion of Zero Trust architecture across a variety of autonomous platforms. It highlights the critical importance of protecting Physical AI systems—such as drones, unmanned ground vehicles (UGVs), and humanoid robots—from cyberattacks, which have the potential to cause significant harm. The proceedings feature theoretical models, practical frameworks, and real-world applications of large language models and other generative AI techniques aimed at enhancing security, resilience, and intelligence in UAV collectives, robotics, and other autonomous systems. Ensuring security has become a paramount challenge as these systems become increasingly complex and self-directed. The studies presented here focus on breakthroughs in distributed intelligence, secure communications, and real-time anomaly detection, offering actionable strategies for aerospace, defense, and critical infrastructure industries. Forward-looking discussions also explore how machine learning and AI-driven approaches could redefine safety and security standards, particularly in autonomous decision-making and continuous operations. Collectively, this volume provides invaluable insights for researchers, practitioners, and policymakers working toward robust and trustworthy autonomous solutions while also addressing pressing challenges and emerging opportunities in this rapidly evolving field.