The Mathematical Field
The arithmetic, algebraic and geometric applications can be seen by human beings in:
The Mathematical Field
The arithmetic, algebraic and geometric applications can be seen by human beings in:
AP Precalculus
AP Precalculus: Student Edition is a collection of lessons and activities for every topic in the AP Precalculus course that will be assessed on the AP exam. Each lesson or activity comes with a homework assignment with questions similar to those that will appear on the AP exam. A corresponding teachers' guide and solutions manual, AP Precalculus: The Teacher's Compendium, is available separately.
The Voice of Math
A journey through math.Have you always wondered about the mysteries of the universe? The patterns we see in life aren't a coincidence, and it's taken thousands of years for us to see it.Take a dive into a book where we analyze what you think you know then turn it on its head. Did we always know that the patterns we see in seashells also exist in galaxies? Did ancient societies unlock the key to coding, and can we use principles thousands of years old to create innovations that were once just science fiction?Journey into The Voice of Math, a fascinating dive into understanding numbers, where they came from, and where they can take us, not only in laboratories, but in our daily lives.
Multivariable and Vector Calculus
This book covers multivariable and vector calculus. It can be used as a textbook for a one-semester course or self-study. It includes worked-through exercises, with answers provided for many of the basic computational ones and hints for the more complex ones.. This second edition features new exercises, new sections on twist and binormal vectors for curves in space, linear approximations, and the Laplace and Poisson equations.
Secure signal transmission
Voice communication is closely linked to everyday life, such as education, e-learning, commerce, politics and the dissemination of information. To maintain security, sensitive data must be protected during transmission. Chaotic systems have become good candidates for cryptography to increase the degree of security. In this book, we focus on the design of a high-security voice communication system using two levels of encryption based on chaotic systems. The first level is chaotic masking, while the second level is scrambling. In the masking level using two methods, the first method is masking using a hybridization between chaotic frameworks (logistic map and tent map), while the second method is based on the Chua chaotic system. At the scrambling level, we use Arnold's map. At receiver level, we use Pecore and Carroll synchronization to recover the encrypted audio signal.
An Observer's Journey Into the Heart of Universes
This work is based exclusively on the observation of sacred arts: Ngombi or Ngoma (Sacred Harp), Mvet ?kang (Harp Cithare), Masque Punu, Songo (sowing game), Menorah (7-branch candlestick) and Hanoukkia (9-branch candlestick), with the current Calendar as their common point of departure. Mathematical universes are built around the recurring unity of quadrilaterals (square or rectangle) with the trilateral figure (triangle) referring to the pyramid. They are mainly characterized by the conversation of one of the quadrilateral's diagonals into a triangular base, while excluding the second, hence the term concave geometric construction. The inner side of geometric figures is the expression of a dynamism whose evolution is both ascending and descending, under a fractal grip by the action of the arithmetic triplet. Central symmetry, orthogonal symmetry, parallelism, perpendicularity, triangulation, diagonometry and more are just some of the geometric theorems to be found here. Civilizational memories are all revealed as bearing the same geometric framework.
Computational Medical Image Analysis
This Special Issue covers a variety of computational applications in medical image analysis. With a vast majority of the articles reporting on machine learning or deep learning-based methodologies, it highlights the transistion toward artificial intelligence over the past decade.
New Frontiers in Parameterized Complexity and Algorithms
The research on parameterized complexity (PC), described in these peer-reviewed chapters by esteemed researchers, provides ties to practice as well as new theoretical developments, many in the direction of AI. Applications in bioinformatics and social choice are described, as well as faster, less costly approximation methods and new techniques using machine learning to find treewidth and other metrics. Many practical problems can be solved by harnessing the power of both PC and SAT solvers or integer linear programming modeled by parameterized graph problems. The extremely rapid development and deployment of PC continues to bring fresh understanding and solutions to fundamental open questions.
Perturbation Methods
"Perturbation Methods" takes readers on a captivating journey through the realms of science, unlocking the hidden wonders of complex systems through the lens of perturbation theory. This illuminating approach grants us access to the intricate tapestry of particles, forces, and interactions that shape the very fabric of the universe. Delve into the pages of this book and discover the profound impact of perturbation theory across various scientific disciplines. From unraveling the mysteries of quantum mechanics to shedding light on celestial dynamics, prepare to be awed by the immense repercussions of perturbation theory. Join us as we step into a world where even the subtlest disturbances lead to groundbreaking insights and paradigm-shifting discoveries.
Didactics of Mathematics
This book is the first part of a 3-part series on the didactics of mathematics. By the way, everyone asks the question: What is didactics in teaching?In the didactic teaching method, the teacher gives instructions to the students, and the students are mostly passive listeners. It's a teacher-centered, content-oriented teaching method. Neither the content nor the teacher's knowledge is questioned.
Journal of Applied Logics, Volume 11, number 3. Special issue
The Journal of Applied Logics - IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are free open access and available via the College Publications website. This Journal is open access, puts no limit on the number of pages in an issue and puts no limit on the number of issues per year. We insist only on a very high academic standard, and will publish issues as they come.
Mathmamiya
This is a math-mentoring book without the gory mathematical expressions. The intended purpose of this book is to allay the fear of mathematics that most people have. Math is actually a tame and fun ally in accomplishing a lot of things in life, such as investment, social networking, commerce, technology, engineering, and science. I encourage and spark the interest of young people, especially girls, to embrace Mathematics to their full potential. The inherent mathematical ability may be there, but the confidence and pathway to manifest and leverage the ability may not be known. One way to discover and elicit the underlying ability is through humor and cajoling, which is the purpose of this freeform book.
The Dependability Revolution
"The Dependability Revolution: Mathematical Tools for Building Secure, Reliable Systems" dives into the fascinating world of formal methods for ensuring the smooth operation of critical systems. Imagine a world where power grids never flicker, airplanes never experience malfunctions, and online transactions are always secure. This book explores the mathematical tools and techniques that are revolutionizing the way we design and build dependable systems. You'll delve into concepts like reliability theory, hazard analysis, and formal verification. With clear explanations, the book unveils how these tools can identify potential weaknesses in systems before they become real-world problems. "The Dependability Revolution" isn't just about complex math - it's about real-world impact. Learn how these techniques are used in fields like aerospace engineering, cybersecurity, and financial technology. This book is a must-read for anyone interested in the future of safe, secure, and reliable systems.
Building a Foundation of Trust
In the modern society of the 21st century, science and technology are becoming increasingly em-bedded in the everyday life of people all around the world. Driggers (2011) stresses the importance of science and technology by pointing to the many times in history that these components have contributed to moving our society forward and how they will keep on doing so. Similarly, Fen-ster & Gopp (2020) emphasize the important role science plays, and will continue to play, for the continued development of our society, something they claim has become even more critical and apparent in 2020 as the Covid-19 pandemic is casting its shadow over the continents of the world. The term science is very broad. Obviously, the scientific community is vast and encompasses many different fields that all play important roles in shaping the world. Even though these fields are inherently different on many levels, they all work according to some basic principles that can be applied to all disciplines and branches of the scientific community. One example of these fundamental principles is openness: At its core, science depends upon openness and the "willing-ness of individual investigators to accept constructive criticism of work that has been conducted", primarily with the purpose to promote the advancement of knowledge (Committee on Science, Engineering, and Public Policy (U.S.). Panel on Scientific Responsibility and the Conduct of Research, 1992, p. 154).
Beyond Michaelis-Menten
The Michaelis-Menten equation (MM) has been a pillar of enzyme kinetics for a century. "Beyond Michaelis-Menten: Modernizing the Equation for Enzyme Kinetics" explores the need to evolve our understanding of enzymes as research unveils their true complexity. Imagine a model that captures just a glimpse of a fascinating reality. While MM provides a valuable framework, it has limitations: - Simplified View: MM assumes a single substrate and a straightforward reaction path. Enzymes can interact with multiple substrates and exhibit intricate behaviors. - Hidden Dynamics: MM focuses on steady-state activity, neglecting the dynamic nature of enzymes within living cells. - Limited Predictive Power: Complexities like cooperativity (synergy between substrates) and allosteric regulation (indirect enzyme control) fall outside MM's scope. These limitations necessitate a more nuanced approach: - Incorporating Complexity: Modern models consider cooperativity, allosteric regulation, and other factors, providing a more accurate picture of enzyme behavior. - Capturing Dynamics: New techniques analyze enzyme activity in real-time, capturing the dynamic fluctuations that occur within cells. - Computational Approaches: Computational modeling allows scientists to simulate complex enzyme systems, leading to a deeper understanding of their functions. The benefits are far-reaching: - Drug Discovery: A more comprehensive understanding of enzyme behavior can lead to the design of more targeted and effective drugs. - Metabolic Engineering: By accurately modeling complex enzyme pathways, we can engineer them for more efficient biofuel production and other applications. - Unveiling Cellular Processes: A deeper understanding of enzyme dynamics offers insights into the intricate workings of living cells. While MM remains a valuable historical landmark, modernizing the equation is crucial for unlocking the full potential of enzyme research. By embracing complexity and dynamics, we can move beyond
Financial mathematics and the learning process
Interest rates, inflation, capitalization, discounts, compound interest, purchasing power, the constant amortization system (SAC), consumption and income are all topics that people come into constant contact with. However, there is some difficulty in understanding the subject and financial calculations. With this in mind, the aim of this paper is to address the process of learning financial mathematics in elementary school, in other words, to show how some financial mathematics topics have been approached in elementary school. To do this, we will analyze the didactic material offered by the Rio de Janeiro state school system. The research will be based on textbooks from the National Textbook Program (PNLD), the oldest of the programs aimed at distributing textbooks to students in the Brazilian public school system, according to the National Education Development Fund (FNDE). In this way, we will help to ensure that students, future citizens, make rational decisions based on an education system that uses appropriate material.
Walking the Resistance
"Walking the Resistance" isn't your typical hike through the woods. It takes you on a surprising journey that connects the seemingly unrelated worlds of random walks and electrical networks. This book explores the beautiful and powerful relationship between these two seemingly disparate concepts. Imagine a tiny particle taking random steps on a grid, like a lost hiker. "Walking the Resistance" shows how this random walk can be mapped to the flow of electricity in a network of resistors. By understanding the electrical properties of the network, we can predict the behavior of the random walk, and vice versa. This book delves into the mathematics behind this connection, but it doesn't get bogged down in technical jargon. It uses clear explanations and analogies to make the concepts accessible to a broad audience. Readers will discover how this connection has applications in various fields, from physics and computer science to finance and biology. "Walking the Resistance" is a mind-bending exploration that will change the way you see random walks and electrical networks.
The Didactic Triad in Trigonometry
The purpose of this book is to share the results obtained in the research carried out at the Faculty of Exact and Natural Sciences of the National University of Mar del Plata, regarding the knowledge and difficulties on basic aspects of Trigonometry of students taking Algebra in the first year of Bachelor's Degrees in Chemistry, Biochemistry, Physics and Mathematics, as well as on the approach to the subject of Trigonometry made by teachers of the sixth year of secondary schools in their classes during the pandemic. Likewise, a didactic sequence related to the subject is presented for the sixth year of Secondary School.On the other hand, an experience is reported on a first year class of the Faculty, using GeoGebra, whose objective is to reaffirm concepts related to the properties of the modules and arguments of Complex Numbers (a subject in which Trigonometry concepts are applied).
Mathematics for Economics and Finance
Accessible, concise, and interactive, this book introduces the mathematical methods that are indispensable in economics and finance. Fully updated to be as student friendly as possible, this edition contains extensive problems, worked examples and exercises (with full solutions at the end of the book). Two brand new chapters cover coupled systems of recurrence/differential equations, and matrix diagonalisation. All topics are motivated by problems from economics and finance, demonstrating to students how they can apply the mathematical techniques covered. For undergraduate students of economics, mathematics, or both, this book will be welcomed for its clarity and breadth and the many opportunities it provides for readers to practise and test their understanding.
Mathematics for Economics and Finance
Accessible, concise, and interactive, this book introduces the mathematical methods that are indispensable in economics and finance. Fully updated to be as student friendly as possible, this edition contains extensive problems, worked examples and exercises (with full solutions at the end of the book). Two brand new chapters cover coupled systems of recurrence/differential equations, and matrix diagonalisation. All topics are motivated by problems from economics and finance, demonstrating to students how they can apply the mathematical techniques covered. For undergraduate students of economics, mathematics, or both, this book will be welcomed for its clarity and breadth and the many opportunities it provides for readers to practise and test their understanding.
Mathematics for Engineers - Volume 1
The Karlsruhe University of Applied Sciences started an English-language Bachelor's program in Electrical Engineering in 2021. In order to support our international students with appropriate material, this three-volume textbook was written. Taking into account that different students will attend different mathematics courses, we decided to design three volumes of a series of mathematics books, each part for a single semester.Mathematical terms are clearly motivated, systematically equated and visualized in many animations. Mathematical proofs are almost completely renounced. Instead, a lot of applications support not only the application of mathematics but also contribute to a better understanding of mathematics.Important formulas and statements are clearly highlighted in order to increase the readability of the books. More than 300 images and sketches support the character of modern textbooks. The color-coded layout provides a clear overview of the presentation of the content, e.g. by adding new terms and definitions in light grey, important statements and sentences in grey.
Mathematics for Engineers - Volume 1
The Karlsruhe University of Applied Sciences started an English-language Bachelor's program in Electrical Engineering in 2021. In order to support our international students with appropriate material, this three-volume textbook was written. Taking into account that different students will attend different mathematics courses, we decided to design three volumes of a series of mathematics books, each part for a single semester.Mathematical terms are clearly motivated, systematically equated and visualized in many animations. Mathematical proofs are almost completely renounced. Instead, a lot of applications support not only the application of mathematics but also contribute to a better understanding of mathematics.Important formulas and statements are clearly highlighted in order to increase the readability of the books. More than 300 images and sketches support the character of modern textbooks. The color-coded layout provides a clear overview of the presentation of the content, e.g. by adding new terms and definitions in light grey, important statements and sentences in grey.
Problems and Solutions in Mathematical Olympiad (Secondary 1)
The series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 Most Influential Educational Brands in China.The series is created in line with the mathematics cognition and intellectual development levels of the students in the corresponding grades. All hot mathematics topics of the competition are included in the volumes and are organized into chapters where concepts and methods are gradually introduced to equip the students with necessary knowledge until they can finally reach the competition level.In each chapter, well-designed problems including those collected from real competitions are provided so that the students can apply the skills and strategies they have learned to solve these problems. Detailed solutions are provided selectively. As a feature of the series, we also include some solutions generously offered by the members of Chinese national team and national training team.
Problems and Solutions in Mathematical Olympiad (Secondary 1)
The series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 Most Influential Educational Brands in China.The series is created in line with the mathematics cognition and intellectual development levels of the students in the corresponding grades. All hot mathematics topics of the competition are included in the volumes and are organized into chapters where concepts and methods are gradually introduced to equip the students with necessary knowledge until they can finally reach the competition level.In each chapter, well-designed problems including those collected from real competitions are provided so that the students can apply the skills and strategies they have learned to solve these problems. Detailed solutions are provided selectively. As a feature of the series, we also include some solutions generously offered by the members of Chinese national team and national training team.
The Mystery of Space; A Study of the Hyperspace Movement in the Light of the Evolution of New Psychic Faculties and an Inquiry into the Genesis and Essential Nature of Space
The Mystery of Space; A Study of the Hyperspace Movement in the Light of the Evolution of New Psychic Faculties and an Inquiry into the Genesis and Essential Nature of Space, a classical book, was published more than a century ago and has been considered important throughout the human history, and so that this work is never forgotten we at Alpha Editions have made efforts in its preservation by republishing this book in a modern format for present and future generations. This whole book has been reformatted, retyped and designed. These books are not made of scanned copies of their original work and hence the text is clear and readable.
New Advances in Audio Signal Processing
In the era of digitalization, audio signal processing is gaining peculiar relevance as an automation and remote analysis means, also considering its enhancement by novel artificial intelligence (AI) techniques.This Reprint aims to offer an overview of the current developments in all fields that revolve around audio processing: from advancements in the acoustic domain to deep learning architectures for the audio-based analysis of real-world problems such as pitch detection or pathology identification.
Advances in Radar Systems for Target Detection and Tracking
Radar systems can provide the all-weather and all-time detection and tracking of targets of interest, and they have been extensively applied by the remote sensing community, in applications such as geological exploration, disaster forecasting, traffic monitoring, urban planning, environmental sciences, hydrology, littoral zones, oceans, etc. This reprint contains the several advance research studies on radar systems for target detection and tracking. It includes multipath ghost suppression, maneuvering target tracking, target detection, and other topics.
Applied Statistical Modeling and Data Mining
This reprint comprises a compilation of 15 insightful research papers published in the Special Issue "Applied Statistical Modeling and Data Mining" within the Mathematics journal. Spanning multiple domains at the intersection of statistics, machine learning, and real-world applications, the collection presents diverse perspectives and innovative approaches in the field of applied statistical modeling and data mining. These selected papers explore diverse and important topics, including predictive modeling in healthcare, cybersecurity in transportation systems, data quality assessment, emergency call modeling, and innovative crime prevention strategies, among others. By covering a wide spectrum of subjects, this reprint serves as a valuable resource for researchers, academics, and practitioners interested in addressing contemporary challenges across diverse domains through statistical modeling, data mining, and machine learning applications.
Solving Spatial Metric Geometry Problems
The aim of this work is to propose an activity aimed at second-year high school students, with the aim of teaching some concepts of Spatial Metric Geometry, specifically calculating the areas and volumes of geometric solids such as cones, cylinders, spheres, pyramids and prisms, with the help of technology, using the GeoGebra software. In order to develop this activity, we looked at some trends in teaching and learning mathematics, focusing mainly on Problem Solving and Information and Communication Technology.
Real Analysis
This is a classical Real Analysis/Calculus problem book. This volume contains a huge number of engaging problems and solutions, as well as detailed explanations of how to achieve these solutions. This latter quality is something that many problem books lack, and it is hoped that this feature will be useful to students and instructors alike.
Numerical Approaches to Optimal Control
Optimal control has been widely applied to modern control systems design and has drawn great attention for decades. In the optimal control theory, the control problem is formulated as an optimization problem, and the control law is calculated by solv-ing the optimal control problem (OCP). Comparing with traditional control methods like PID control, optimal control is capable of providing an optimal control law in a systematic way. However, optimal control can achieve an analytic expression of the optimal control law only for some relatively simpler cases, for instance, unconstrained linear systems. Specifically, the optimal feedback control law for unconstrained linear systems with a quadratic cost function is in a simple linear form, and the optimal control gain is obtained by solving a Riccati equation. In practical systems, most of the physical plants are essentially nonlinear systems subject to physical constraints. For these cases, it is difficult to obtain an analytical solution to the optimal control problems. In order to find the optimum to an intractable optimization problem, ap-proximate solutions have to be taken into account.
Make: Math Teacher's Supplement
Make: Math Teacher's Supplement is the essential guide for teachers, parents, and other educators wanting to supplement their curriculum with Joan Horvath and Rich Cameron's Make: Geometry, Make: Trigonometry, and Make: Calculus books. This book is a companion to the three math books, and does not duplicate the content in them. Drawing on the authors' experience guiding both students and teachers, it covers: The philosophy behind the Make: math book series, including the key inclusion of universal design principles to make the material accessible to those who learn differently A list of topics, projects, and needed maker skills, tied to the math book chapters Key learning objectives and associated assessment ideas A practical primer on 3D printing in an educational environment Helpful tips to manage student 3D printed workflow Five specific examples of ways to use content from the math books, including studying geometry with castles and using LEGO bricks to demonstrate calculus concepts Packed with tips and links to online resources, Make: Math Teacher's Supplement will let you see how to build math intuition to create a solid base for your learner's future.
Optimization Problems in Transportation and Logistics
This educational guide will help students and practitioners seeking to understand the fundamentals and practice of linear programming. The exercises contained within demonstrate how to solve classical optimization problems with an emphasis on spatial analysis in supply chain management and transport logistics. All exercises describe the Python programs and optimization libraries that can be used to solve them. The first chapter introduces key concepts in linear programming and establishes a new cognitive framework to help students and practitioners set up each optimization problem. This cognitive framework organizes the decision variables, constraints, objective function, and variable bounds in a format that allows for direct application to optimization software. The second chapter introduces two types of mobility optimization problems (shortest path in a network and minimum cost tour) in the context of delivery and service planning logistics. The third chapter introduces four types of spatial optimization problems (neighborhood coverage, flow capturing, zone heterogeneity, service coverage) and provides a workflow for visualizing the optimized solutions in maps. The workflow creates decision variables from maps by using the free geographic information systems (GIS) programs QGIS and GeoDA. The fourth chapter introduces three types of spatial logisticsproblems (spatial distribution, flow maximization, warehouse location optimization) and demonstrates how to scale the cognitive framework in software to reach solutions. The final chapter summarizes lessons learned and provides insights about how students and practitioners can modify the Python programs and GIS workflows to solve their own optimization problem andvisualize the results.
Computational Methods for Coupled Problems in Science and Engineering
The ninth edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2021) was organized to take place on 13-16 June 2021. Due to the pandemic, COUPLED 2021 was a fully online and completely synchronous conference. The previous eight editions of this conference were held on the islands of Santorini (Greece) on 25-28 May 2005; Ibiza (Spain) on 21-23 May 2007; Ischia (Italy) on 8-11 June 2009; Kos (Greece) on 20-22 June 2011; Ibiza (Spain) on 17-19 June 2013; San Servolo, Venice (Italy), on 18-20 May 2015; Rhodes Island (Greece) on 12-14 June 2017; and Sitges (Spain) on 3-5 June 2019. The objectives of COUPLED PROBLEMS 2021 were to present and discuss the state of the art in mathematical models, numerical methods and computational techniques for solving coupling problems of a multidisciplinary character in science and engineering. The conference's goal was to make advances in the formulation and solution of real-life problems with a multidisciplinary perspective, accounting for all the complex couplings involved in the physical description of the problem. The conference was one of the Thematic Conferences of the European Community on Computational Methods in Applied Sciences (ECCOMAS) and a Special Interest Conference of the International Association for Computational Mechanics (IACM). It was also supported by other scientific organizations in Europe and across the globe.
Risk Revealed
Explore the concept of risk through numerous examples and their statistical modeling, traveling from a historical perspective all the way to an up-to-date technical analysis. Written with a wide readership in mind, this book begins with accounts of a selection of major historical disasters, such as the North Sea flood of 1953 and the L'Aquila earthquake. These tales serve to set the scene and to motivate the second part of the book, which describes the mathematical tools required to analyze these events, and how to use them. The focus is on the basic understanding of the mathematical modeling of risk and what types of questions the methods allow one to answer. The text offers a bridge between the world of science and that of everyday experience. It is written to be accessible to readers with only a basic background in mathematics and statistics. Even the more technical discussions are interspersed with historical comments and plentiful examples.
The families of prime numbers
The book introduces innovative approaches to conjectures and established knowledge in the realm of prime numbers. It explores how famous mathematicians like Sophie Germain and Mersenne, among others, conceptualized prime numbers Not only does the text clarify Fermat's Little Theorem, but it also offers an explanation for the existence of pseudoprimes. Furthermore, it sheds light on the effectiveness of the Lucas-Lehmer algorithm in discovering Mersenne Primes. By elucidating fundamental concepts, the book provides fresh insights into the study of prime numbers within Number Theory. While its primary audience consists of enthusiasts and mathematicians in search of new patterns and analytical methodologies for prime numbers, the book is designed to be accessible to a broader audience. With over 70 explanatory figures and clear prose, it appeals to anyone intrigued by the intricate world of prime numbers.
Tangles
Tangles offer a precise way to identify structure in imprecise data. By grouping qualities that often occur together, they not only reveal clusters of things but also types of their qualities: types of political views, of texts, of health conditions, or of proteins. Tangles offer a new, structural, approach to artificial intelligence that can help us understand, classify, and predict complex phenomena. This has become possible by the recent axiomatization of the mathematical theory of tangles, which has made it applicable far beyond its origin in graph theory: from clustering in data science and machine learning to predicting customer behaviour in economics; from DNA sequencing and drug development to text and image analysis. Such applications are explored here for the first time. Assuming only basic undergraduate mathematics, the theory of tangles and its potential implications are made accessible to scientists, computer scientists, and social scientists.
Higher Special Functions
Higher special functions emerge from boundary eigenvalue problems of Fuchsian differential equations with more than three singularities. This detailed reference provides solutions for singular boundary eigenvalue problems of linear ordinary differential equations of second order, exploring previously unknown methods for finding higher special functions. Starting from the fact that it is the singularities of a differential equation that determine the local, as well as the global, behaviour of its solutions, the author develops methods that are both new and efficient and lead to functional relationships that were previously unknown. All the developments discussed are placed within their historical context, allowing the reader to trace the roots of the theory back through the work of many generations of great mathematicians. Particular attention is given to the work of George Cecil Jaff矇, who laid the foundation with the calculation of the quantum mechanical energy levels of the hydrogen molecule ion.
Linear Partial Differential and Difference Equations and Simultaneous Systems with Constant or Homogeneous Coefficients
Linear Partial Differential and Difference Equations and Simultaneous Systems: With Constant or Homogeneous Coefficients is part of the series "Mathematics and Physics for Science and Technology," which combines rigorous mathematics with general physical principles to model practical engineering systems with a detailed derivation and interpretation of results. Volume V presents the mathematical theory of partial differential equations and methods of solution satisfying initial and boundary conditions, and includes applications to: acoustic, elastic, water, electromagnetic and other waves; the diffusion of heat, mass, and electricity; and their interactions. This is the third book of the volume.The book starts with six different methods of solution of linear partial differential equations (p.d.e.) with constant coefficients. One of the methods, namely characteristic polynomial, is then extended to a further five classes, including linear p.d.e. with homogeneous power coefficients and finite difference equations and simultaneous systems of both (simultaneous partial differential equations [s.p.d.e.] and simultaneous finite difference equations [s.f.d.e.]). The applications include detailed solutions of the most important p.d.e. in physics and engineering, including the Laplace, heat, diffusion, telegraph, bar, and beam equations. The free and forced solutions are considered together with boundary, initial, asymptotic, starting, and other conditions.The book is intended for graduate students and engineers working with mathematical models and can be applied to problems in mechanical, aerospace, electrical, and other branches of engineering dealing with advanced technology, and also in the physical sciences and applied mathematics.
Vector Calculus
A calculus book must tell the truth. This book is carefully written in the accepted language of mathematics in a readable exposition. It includes useful and fascinating applications, acquaints students with the history of the subject and offers a sense of what mathematics is all about.
Current topics in Logic and the Philosophy of Science. Papers from SILFS 2022 postgraduate conference
Logic and the Philosophy of Science are disciplines that avoid stopping and wandering around in circles on the same topics. Their role in dedicating themselves to scientific and applicative subjects always makes them extraordinarily fruitful and productive, in step with the developments of scientific and technological knowledge. The writings contained in this volume are proof of this. The set of research selected for this publication, starting from the 2022 Postgraduate Conference of SILFS (the Italian Society for Logic and the Philosophy of Science), testifies to a lively and rich knowledge widespread among young scholars of this area who combine pure logic and philosophy to the analysis of cutting-edge knowledge produced by current scientific and technological disciplines. The result is a kaleidoscope of research on updated logical and philosophical-scientific topics, which gives rise to promising developments on the part of young scholars who are contributing today to the logic and philosophy of science to create further perspectives in the future.
The Code of Mathematics
Inspired by recent developments in dependent type theory and infinity categories, this book presents a history of ideas around the topics of truth, proof, equality and equivalence. Besides selected ideas of Platon, Aristoteles, Leibniz, Kant, Frege and others, the results of G繹del and Tarski on incompleteness, undecidability and truth in deductive systems and their semantic models are covered. The main focus of this textbook is on dependent type theory and its recent variant homotopy type theory. Such theories contain identity types, which give a new understanding of equality, symmetry, equivalence and isomorphism in a conceptual way. The interaction of type theory and infinity category theory yields a new paradigm for a structural view on mathematics. This supports the tendencies towards formalising mathematics with the help of proof assistants. This book was first published in German. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.
Bridging Gaps In Elementary Mathematics
Bridging Gaps in Elementary Mathematics is a Mathematics study supplement created to improve upon the appreciation and fundamental understanding of Mathematics by employing the "why" of Mathematics approach. It was also created to ensure that those who did not have an opportunity in their earlier years to study Mathematics, or those who did but need better understanding, would be able to "bridge" the gaps formed in their education. The material covers topics found in the curriculum at the Primary to the pre-Junior High School level. It is not intended to substitute for formally prescribed schooling study materials and textbooks. Still, it is a supplement that provides a more profound understanding, real-life applications and different perspectives of the universal elements of the Mathematics curriculum. It effectively approaches the subject from the root to help make it less abstract.
Inverse Gravity Cosmology
The book is about the inverse gravity cosmology hypothesis which is based on three of the author's published papers which past peer review. Hence, the book presents the inverse gravity concept, its mathematical structure, and its incorporation to established and proven aspects of physics. New developments and mathematics of the theoretical concept are expressed. Moreover, the book cites mistakes/deficiencies and omissions in previous publications. Lastly, the book's introduction includes information about the author's background that inspired the inception of the theoretical concept.
Partitions, Objective Indefiniteness, and Quantum Reality
This book presents a new 'partitional' approach to understanding or interpreting the math of standard quantum mechanics (QM). The thesis is that the mathematics (not the physics) of QM is the Hilbert space version of the math of partitions on a set and, conversely, the math of partitions is a skeletonized set level version of the math of QM. Since at the set level, partitions are the mathematical tool to represent distinctions and indistinctions (or definiteness and indefiniteness), this approach shows how to interpret the key non-classical QM notion of superposition in terms of (objective) indefiniteness between definite alternatives (as opposed to seeing it as the sum of 'waves'). Thus, the book develops a new mathematical, or indeed, logical, approach to the century-old problem of interpreting quantum mechanics, ensure it is of interest to philosophers of science as well as mathematicians and physicists.
Risk Revealed
Explore the concept of risk through numerous examples and their statistical modeling, traveling from a historical perspective all the way to an up-to-date technical analysis. Written with a wide readership in mind, this book begins with accounts of a selection of major historical disasters, such as the North Sea flood of 1953 and the L'Aquila earthquake. These tales serve to set the scene and to motivate the second part of the book, which describes the mathematical tools required to analyze these events, and how to use them. The focus is on the basic understanding of the mathematical modeling of risk and what types of questions the methods allow one to answer. The text offers a bridge between the world of science and that of everyday experience. It is written to be accessible to readers with only a basic background in mathematics and statistics. Even the more technical discussions are interspersed with historical comments and plentiful examples.
