Multiplication in different logical view
Multiplication process is discussed differently here in the book. This logical view is different from previous and this method describes the multiplication process perfectly. The various types of multiplication is discussed here which is different than our previous knowledge and my logical view on multiplication gives the proper view of product rule of two numbers as well as two different things. Field system is discussed here which is different than our own field system of higher mathematics. Multiplication process perfectly described here with other operation and anyone who knows multiplication can read and think about my logical method. It is a new point of view for multiplication rule and it will help us to understand the view of multiplication process. Reader may read my research paper published in "International Journal of Scientific & Engineering Research" where I also wrote the method and in my book I have discussed the method perfectly to establish a new process of multiplication which is logically perfect than before.
Geometric Modeling
This book provides the fundamental knowledge and tools necessary to understand the principles and techniques in the field of geometric modeling and is an essential textbook for undergraduate and graduate students. It includes a detailed exploration of key modeling techniques, from wireframe modeling to complex fractal modeling, highlighting their various applications in different fields and industries. In this book, the basic representation of geometric 3D objects with wireframes as the backbone of more complex models is explored. The details of surface modeling with techniques such as NURBS and subdivision surfaces are discussed. Concepts of constructive solid geometry (CSG) and boundary representation (B-rep) are explained and methods of representing 3D objects with volume are presented. The beauty of fractals and their ability to simulate natural phenomena, produce complex patterns and create stunning visual designs are explained. And finally, the basic and attractive concepts of rendering and visualization have been discussed.
Challenging mathematics
This comprehensive text delves into the intricate world of higher mathematics, offering a rigorous exploration of advanced concepts crucial for today's aspiring mathematicians and scientists. From abstract algebra to complex analysis, the book covers a wide spectrum of topics, providing readers with a solid foundation for further academic pursuits and real-world problem-solving. Written for upper-level undergraduate and graduate students, this volume stands out for its clear explanations of challenging theories and its emphasis on practical applications. The authors expertly balance theoretical depth with insightful examples, making abstract ideas accessible without sacrificing mathematical rigor.By mastering the contents of this book, readers will not only enhance their mathematical prowess but also develop critical thinking skills essential for tackling complex problems in various scientific and technological fields.Whether you're aiming for a career in pure mathematics, physics, engineering, or data science, this text is an indispensable resource for pushing the boundaries of your mathematical understanding.
Mathematics for the Engineers I
Mathematics is the language of engineering and a compulsory subject in worldwide engineering education. So as engineering students, it is mandatory to study Mathematics and learn Mathematical calculations meticulously. In engineering, there are several branches such as computer engineering, electrical and electronic engineering, mechanical engineering, communication engineering and civil engineering and each branch has a different study set focused on the significance of Mathematics. Mathematics provides the analytical and problem-solving tools necessary for engineers to design, analyze and optimize systems, ensuring that they meet safety, efficiency and performance requirements. Without mathematics, engineers would struggle to design effective control systems, leading to inefficiencies and instability in processes. This book provides the easiest and comfortable techniques to the students to learn mathematical calculations effortlessly and independently at home. Moreover, the necessary formulas have been included here with the very beginning of this book so that students can get a complete idea of calculations without the help of other study materials.
Mathematics for the Engineers II
Mathematics is the language of engineering and a compulsory subject in worldwide engineering education. So as engineering students, it is mandatory to study Mathematics and learn Mathematical calculations meticulously. In engineering, there are several branches such as computer engineering, electrical and electronic engineering, mechanical engineering, communication engineering and civil engineering and each branch has a different study set focused on the significance of Mathematics. Mathematics provides the analytical and problem-solving tools necessary for engineers to design, analyze and optimize systems, ensuring that they meet safety, efficiency and performance requirements. Without mathematics, engineers would struggle to design effective control systems, leading to inefficiencies and instability in processes. This book provides the easiest and comfortable techniques to the students to learn mathematical calculations effortlessly and independently at home. Moreover, the necessary formulas have been included here with the very beginning of this book so that students can get a complete idea of calculations without the help of other study materials.
Is Math Real?
One of the world's most creative mathematicians offers a new way to look at math--focusing on questions, not answers        Winner of the Los Angeles Times Book Prize A New Scientist Best Book of the Year    "Brilliant."--Popular Science   Where do we learn math: From rules in a textbook? From logic and deduction? Not really, according to mathematician Eugenia Cheng: we learn it from human curiosity--most importantly, from asking questions. This may come as a surprise to those who think that math is about finding the one right answer, or those who were told that the "dumb" question they asked just proved they were bad at math. But Cheng shows why people who ask questions like "Why does 1 + 1 = 2?" are at the very heart of the search for mathematical truth.        Is Math Real? is a much-needed repudiation of the rigid ways we're taught to do math, and a celebration of the true, curious spirit of the discipline. Written with intelligence and passion, Is Math Real? brings us math as we've never seen it before, revealing how profound insights can emerge from seemingly unlikely sources.       
The Cognitive Dimension of Social Argumentation Proceedings of the 4th European Conference on Argumentation Volume III
This is Volume III of the proceedings of the 4th European Conference on Argumentation, "The cognitive dimension of social argumentation", held at the University of Roma Tre in September 2022. The European Conference on Argumentation (ECA) is an international initiative aiming to consolidate and advance various strands of research on argumentation and reasoning by gathering scholars from a range of disciplines such as philosophy, communication, linguistics, computer science, cognitive science, discourse analysis, and more. The 2022 Rome edition focused on the sociocognitive factors that affect argumentation, both in terms of dynamics and outcomes. Taken together, the contributions collected in these three volumes of the ECA 2022 proceedings provide a faithful approximation of the breadth and depth of ongoing discussions in argumentation scholarship. They also attest how the markedly interdisciplinary character of this field has been evolving in recent years: whereas philosophy and linguistics were always partners in the study of argument, nowadays they are supported also by computer science and experimental psychology, as well as communication and media studies in a broader sense - all of which are well represented in this volume.
The Cognitive Dimension of Social Argumentation Proceedings of the 4th European Conference on Argumentation Volume II
This is Volume II of the proceedings of the 4th European Conference on Argumentation, "The cognitive dimension of social argumentation", held at the University of Roma Tre in September 2022. The European Conference on Argumentation (ECA) is an international initiative aiming to consolidate and advance various strands of research on argumentation and reasoning by gathering scholars from a range of disciplines such as philosophy, communication, linguistics, computer science, cognitive science, discourse analysis, and more. The 2022 Rome edition focused on the sociocognitive factors that affect argumentation, both in terms of dynamics and outcomes. Taken together, the contributions collected in these three volumes of the ECA 2022 proceedings provide a faithful approximation of the breadth and depth of ongoing discussions in argumentation scholarship. They also attest how the markedly interdisciplinary character of this field has been evolving in recent years: whereas philosophy and linguistics were always partners in the study of argument, nowadays they are supported also by computer science and experimental psychology, as well as communication and media studies in a broader sense - all of which are well represented in this volume.
The Cognitive Dimension of Social Argumentation Proceedings of the 4th European Conference on Argumentation Volume I
This is Volume I of the proceedings of the 4th European Conference on Argumentation, "The cognitive dimension of social argumentation", held at the University of Roma Tre in September 2022. The European Conference on Argumentation (ECA) is an international initiative aiming to consolidate and advance various strands of research on argumentation and reasoning by gathering scholars from a range of disciplines such as philosophy, communication, linguistics, computer science, cognitive science, discourse analysis, and more. The 2022 Rome edition focused on the sociocognitive factors that affect argumentation, both in terms of dynamics and outcomes. Taken together, the contributions collected in these three volumes of the ECA 2022 proceedings provide a faithful approximation of the breadth and depth of ongoing discussions in argumentation scholarship. They also attest how the markedly interdisciplinary character of this fi eld has been evolving in recent years: whereas philosophy and linguistics were always partners in the study of argument, nowadays they are supported also by computer science and experimental psychology, as well as communication and media studies in a broader sense - all of which are well represented in this volume.
Mathematics of Business
Businesses are always indispensable entity in any society. Money may be given to loaf without being useful to anyone. The major and the fundamental principles of any form of banking is that every idle money usually yields in most cases no increase. Thus, any individual who possesses certain amount of money than is needed for day to day activities as well as the necessities for living may not just put them away in safe places. Financial Mathematics plays a vital role in Economics and Commerce. Certain Economic terminologies with usual notations are necessary and imperative tools for any form of demonstrations of the applications of the financial Mathematics.
Contributions to the Theory of Partitions and Their Applications
The theory of partitions, which studies the ways in which integers can be expressed as sums of other integers, has profound implications in various fields of mathematics. Significant contributions by mathematicians such as Euler and Hardy have paved the way for a deeper understanding of partition functions and their properties. Recent advancements have explored partitions in combinatorial contexts, offering insights into generating functions and generalized partition functions, including k-color overpartitions, Andrews' singular overpartitions, designated summands, l-regular cubic partition pairs, (l; m)-regular bipartition triples, and partition quadruples with t-cores.
Fundamentals of Multivariable Calculus
This textbook is carefully designed as an early undergraduate introduction to the calculus of several real variables. The balanced coverage is devoted to limits, continuity, partial derivatives, extrema, the nabla operator, multiple integrals, line integrals, surface integrals, and the fundamental theorems of vector calculus.Engaging and accessible with detailed diagrams and copious worked examples, the presentation is well suited to students pursuing applied fields such as engineering. Multiple integration is motivated intuitively through the calculation of mass. The chapter-end problems provide both drill and challenge.Overall, the book should equip students with the knowledge and confidence needed for subsequent courses.An appendix on hints renders the book suitable for self-study. Prerequisites are limited to single-variable calculus, linear algebra, and analytic geometry.
Advanced Fractal Graph Theory and Applications
This book explores the dynamic interplay between fractals and graph theory, two powerful mathematical tools with vast applications. It presents a strategic combination and the synergistic use of these disciplines to address real-world problems and challenges.
Deep Learning Technology and Image Sensing
In this Special Issue, we explore the transformative power of deep learning-based computing technologies in improving the accuracy and reliability of image recognition systems. From advancing autonomous driving to enhancing object detection, deep learning continues to push the boundaries of what is achievable. Additionally, cutting-edge computer vision technologies enable precise medical imaging segmentation and improve image quality in challenging conditions, such as low-light environments and astronomical observations. Leading experts in the field present their latest research and innovations, offering a comprehensive view of the applications and future potential of deep learning in image and video sensing technologies. Together, we envision a future where artificial intelligence not only enhances our everyday devices but also redefines how we interact with technology and the world around us.
The Making, The Rise, And the Future of The Speaking Man - Fifth Edition
The making, rise, and future of the speaking man encapsulates not just the biological and cognitive evolution of Homo sapiens but also the dynamic relationship between culture, technology, and society. From the early developments of vocal communication to the creation of language-based civilizations and the potential of futuristic technologies, human speech is at the core of how we define ourselves as a species. Looking ahead, the speaking man will continue to evolve, shaped by forces both biological and technological, creating new possibilities for how we communicate and connect with each other-and with the world around us.
An Orthogonal Projection Algorithm for Solving Quadratic Program
This book deals with the construction of an orthogonal projection algorithm for solutions of quadratic programming problems. The algorithm starts by finding the unconstrained optimum using the classical theory of differentiation and then tests the solution for feasibility in the constrained problem. If the unconstrained optimum is infeasible in the constrained problem, then the algorithm makes a move to search for the optimum solution which in most situations is achievable in only one step. The work-ability of the algorithm is shown by applying it in solving several quadratic programming problems. The solutions obtained by using the Projection Algorithm are compared with those obtained by using OPTIMIZER software. The projection algorithm is found to give the same or better optimal solutions than the OPTIMIZER.
Geometry learning mediated by Cabri-G矇om癡tre software
This study is the result of research that culminated in our master's dissertation, which looked at the various phases of learning in the light of Guy Brousseau's theory of didactic situations. It was developed from a qualitative perspective, prioritizing the context of the relationships and interactions that took place in a learning environment, supported by dynamic geometry software, with the involvement of 37 students from a school in Curitiba. There were six sessions of observation of mathematics classes that dealt with the teaching of quadrilaterals. The analysis showed that the students who already had a command of the computer and did so with skill, had difficulties when dealing with the software. This suggests a "student-machine" paradox, that is, even though they have the skills to deal with the computer, the student is challenged with the minimum skills required to deal with the software. Faced with this situation, new didactic contracts emerge to replace the previous ones. The study shows that the didactic contracts established between student, teacher and knowledge, when broken, open up as an opportunity to take new paths towards full learning.
Mathematical Data Science with Applications in Business, Industry, and Medicine
Mathematical data science is a field that combines mathematical techniques with data science methods to extract insights and knowledge from data. It involves working with data at all stages of the data lifecycle, from collection and storage to cleansing and processing, the analysis and visualization of data, and the communication of the results and findings. Data scientists use a variety of tools and techniques to analyze data, including mathematical concepts and models, artificial intelligence techniques, machine learning algorithms, statistical analysis, and data visualization. Furthermore, data science can be used to make predictions, identify patterns, and draw conclusions from data, and it is applied in a variety of areas, including business, industry, and medicine. It is a rapidly evolving field, and data scientists are expected to stay up to date with new tools, techniques, and technologies. This Reprint is a collection of articles on a wide range of topics in the field of mathematical data science, with applications in business, industry, and medicine. The proposed methods and concepts are discussed in detail and illustrated with several real-life data examples.
Machine Learning for Cybersecurity
"Machine Learning for Cybersecurity: Threat Detection and Mitigation" delves into the transformative role of machine learning in addressing contemporary cybersecurity challenges. This reprint provides an in-depth exploration of how advanced techniques such as deep learning, natural language processing, and explainable AI are revolutionizing intrusion detection, anomaly detection, and threat intelligence. With a focus on practical applications, it covers critical topics such as malware analysis, IoT and cloud security, blockchain security, adversarial attacks, and secure data sharing. Through this reprint, readers will gain insights into cutting-edge approaches for vulnerability assessments, authentication, and privacy preservation while exploring frameworks for implementing security-aware AI systems.This comprehensive resource is essential for researchers, practitioners, and policymakers striving to strengthen digital ecosystems. It offers both theoretical insights and actionable solutions, paving the way for innovative cybersecurity strategies to combat an ever-evolving threat landscape.
Mathematical Optimizations
Mathematical optimization is a crucial field that focuses on finding the best possible solutions from a range of options. At its essence, optimization involves maximizing or minimizing a specific goal while considering various constraints or limitations. This process is widely applicable across many areas, including business, engineering, healthcare, and logistics. The optimization process starts by defining the problem clearly, identifying the key variables involved, and understanding the constraints that may impact the potential. One of the most common methods used in this field is linear programming, which involves problems where both the goals and constraints are expressed as linear relationships. This approach is particularly useful for tasks like resource allocation, where the objective is to use limited resources in the most efficient way. In contrast, nonlinear programming deals with problems that involve complex relationships between variables, allowing for a wider range of potential solutions.
Production scheduling for parallel machines
This book presents a comparison of hybrid solution methods for integrated multi-machine production sizing and scheduling problems with sequence-dependent setups. The proposed methods are based on the decomposition of the problem into 2 levels: In the first level, the assignment of jobs to machines and their sequencing is performed via genetic algorithms, the solution obtained at this level is used to determine the sizing of batches and inventories in the second level in an exact way using the branch and cut method.The results showed the variant based on the Teaching-learning based optimization (TLBO) algorithm as the best in performance with a good solution quality in a reasonable computation time.
Difference Equations and Applications
Difference Equations and Applications provides unique coverage of high-level topics in the application of difference equations and dynamical systems. The book begins with extensive coverage of the calculus of difference equations, including contemporary topics on l_p stability, exponential stability, and parameters that can be used to qualitatively study solutions to non-linear difference equations, including variations of parameters and equations with constant coefficients, before moving on to the Z-Transform and its various functions, scalings, and applications. It covers systems, Lyapunov functions, and stability, a subject rarely covered in competitor titles, before concluding with a comprehensive section on new variations of parameters. Exercises are provided after each section, ranging from an easy to medium level of difficulty. When finished, students are set up to conduct meaningful research in discrete dynamical systems. In summary, this book is a comprehensive resource that delves into the mathematical theory of difference equations while highlighting their practical applications in various dynamic systems. It is highly likely to be of interest to students, researchers, and professionals in fields where discrete modeling and analysis are essential.
Stieltjes Differential Calculus with Applications
The Stieltjes derivative is a modification of the usual derivative through a nondecreasing and left-continuous map. This change in the definition allows us to study several differential problems under the same framework.This monograph is the first published book that offers a comprehensive view of the fundamentals of Stieltjes calculus and its applications, making it approachable to newcomers and experts. It aims to provide an integrated approach to the foundations and recent developments in the area of the Stieltjes derivatives and the qualitative theory of the Stieltjes differential equations. Through 10 pedagogically organized chapters, the authors examine a wide scope of the concept of the Stieltjes derivative and its applications. Each chapter focuses on theory, and proofs, and contains sufficient examples to enrich the reader's understanding.The Stieltjes derivative contains the Hilger delta derivative on time scales. Thus, offering a new unification and extension of continuous and discrete calculus. Further, a study of differential equations in the sense of the Stieltjes derivative allows the study of many classical problems in a unique framework. This theory has the advantage that ordinary differential equations, ordinary difference equations, quantum difference equations, impulsive differential equations, dynamic equations on time scales, and generalized differential equations can be treated as particular instances of the Stieltjes differential equations. Hence, this book serves as a basic reference for researchers to harness this powerful technique further to unlock new insights and embrace the intricacies of natural processes. Researchers and graduate students at various levels interested in learning about the Stieltjes differential calculus and related fields will find this text a valuable resource of both introductory and advanced material.
Abelian Model Category Theory
Offering a unique resource for advanced graduate students and researchers, this book treats the fundamentals of Quillen model structures on abelian and exact categories. Building the subject from the ground up using cotorsion pairs, it develops the special properties enjoyed by the homotopy category of such abelian model structures. A central result is that the homotopy category of any abelian model structure is triangulated and characterized by a suitable universal property - it is the triangulated localization with respect to the class of trivial objects. The book also treats derived functors and monoidal model categories from this perspective, showing how to construct tensor triangulated categories from cotorsion pairs. For researchers and graduate students in algebra, topology, representation theory, and category theory, this book offers clear explanations of difficult model category methods that are increasingly being used in contemporary research.
Combinatorial Knot Theory
A classic knot is an embedded simple loop in 3-dimensional space. It can be described as a 4-valent planar graph or network in the horizontal plane, with the vertices or crossings corresponding to double points of a projection. At this stage we have the shadow of the knot defined by the projection. We can reconstruct the knot by lifting the crossings into two points in space, one above the other. This information is preserved at the vertices by cutting the arc which appears to go under the over crossing arc. We can then act on this diagram of the knot using the famous Reidemeister moves to mimic the motion of the knot in space. The result is classic combinatorial knot theory. In recent years, many different types of knot theories have been considered where the information stored at the crossings determines how the Reidemeister moves are used, if at all.In this book, we look at all these new theories systematically in a way which any third-year undergraduate mathematics student would understand. This book can form the basis of an undergraduate course or as an entry point for a postgraduate studying topology.
Mathematical Legends
This book is not only about the history of mathematics, but also by telling the story of some of the most distinctive personalities in the history of mathematics, it goes on to reveal the various strange treasures, bright flowers and hidden passions of the mathematical kingdom. Some of these mathematicians were thinkers, writers, poets, musicians, painters, politicians, judges, soldiers, clerks, young men of society or even prisoners. The mathematical world constructed by these geniuses is exquisite, and a walk in such a world not only expands our mathematical horizons and imagination, but also raises our humanistic cultivation to a higher level. Written for general audience, this book will be of interest to anyone who's studied mathematics in university or even high school, while also benefiting researchers in mathematics and the humanities. The readers will also enjoy reading the beautiful and simple language of all the articles and interviews.
Trigonometry and analytic geometry
The book centres on the basic concepts of trigonometry and analytic geometry.It is prepared most especially for the undergraduates, in universities, polytechnics, monotechnic, colleges of education, as well as other higher education.. The book is very much indispensable for those who desires to learn and develop themselves with good foundation in both Mathematic and mathematical sciences.Students and learners in Physical, chemical and earth sciences are very well privileged to have a copy of the book.
Dynamical System and Stochastic Analysis
Almost all real-world systems are inevitably subject to random structures, parameters, and noises, and stochastic systems have been playing increasingly important roles in all areas of science and engineering.The purpose of this Special Issue is to solicit the recent achievements of control theory and applications of stochastic systems so as to further improve and develop the theoretical methods of stochastic system estimation, fault diagnosis, prognostics, and optimization, among others.
Cauchy problems for the generalized system of Maxwell's equations
The monograph is devoted to the study of non-correct problems for a system of Maxwell-type equations with an elliptic complex in a bounded region. We consider the Cauchy problem for an elliptic system of equations of Maxwell type in "n" dimensional space. And also the construction of the matrix of the left fundamental solution of the system of electrodynamics equations of a special kind is given. The generalized Stratton-Chu formula is obtained here, the solvability conditions are proved and the Carleman formula is constructed using the method of bases with double orthogonality, i.e. an explicit formula is constructed which restores the solution of the system of Maxwell's equations in a bounded region.
Malliavin Calculus in Finance
This book aims to bridge the gap between theory and practice and demonstrate the practical value of Malliavin calculus. It offers readers the chance to discover an easy-to-apply tool that allows us to recover, unify, and generalize several previous results in the literature on stochastic volatility modeling.
Paradoxes Between Truth and Proof
This book is a collection of essays that offer original logical and philosophical investigations into the century-long endeavor to understand paradoxes. It bridges the gap between the two most prominent traditions in the analysis of paradoxes: the truth-theoretic and proof-theoretic approaches. The truth-theoretic tradition stems from Alfred Tarski's solution to the semantic paradoxes, while the proof-theoretic tradition dates back to Dag Prawitz's analysis of set-theoretic paradoxes in terms of structural proof theory. Rather than viewing these traditions as competing perspectives, this volume advocates for the idea that a deeper understanding of paradoxes requires insights from both truth-theoretic and proof-theoretic conceptions of language and meaning. Although the collection does not aim to be exhaustive, it seeks to highlight the vast scope of the subject and its deep connections to various fields of inquiry. The essays are organized into four sections: the first focuses on methodology, the second and third examine paradoxes through the conventional lenses of logical investigation-semantics and syntax-, and the fourth presents a selection of paradoxes that extend beyond the interplay between syntax and semantics, exploring other dimensions of human rationality.
Four Open Questions for the N-Body Problem
The N-body problem has been investigated since Isaac Newton, however vast tracts of the problem remain open. Showcasing the vibrancy of the problem, this book describes four open questions and explores progress made over the last 20 years. After a comprehensive introduction, each chapter focuses on a different open question, highlighting how the stance taken and tools used vary greatly depending on the question. Progress on question one, 'Are the central configurations finite?', uses tools from algebraic geometry. Two, 'Are there any stable periodic orbits?', is dynamical and requires some understanding of the KAM theorem. The third, 'Is every braid realised?', requires topology and variational methods. The final question, 'Does a scattered beam have a dense image?', is quite new and formulating it precisely takes some effort. An excellent resource for students and researchers of mathematics, astronomy, and physics interested in exploring state-of-the-art techniques and perspectives on this classical problem.
Journal of Applied Logics. IfCoLog Journal of Logics and their Applications. Volume 11, number 6, November 2024
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 of any article, puts no limit on the number of papers 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.
The Story of Euclid
Euclid's name echoes through the halls of geometry, but who was the man behind the theorems that have shaped mathematical understanding for centuries? Journey back to ancient Greece and uncover the story of a scholar whose work has transcended time, influencing everything from architecture to art.In "The Story of Euclid," you'll be transported to a world of groundbreaking ideas and timeless principles. Delve into the life of this enigmatic figure and witness the birth of geometric concepts that continue to shape our world today. Explore the elegance of his proofs, the power of his postulates, and the enduring legacy of a man whose contributions to mathematics are immeasurable.Whether you're a seasoned mathematician or simply curious about the origins of geometry, "The Story of Euclid" will ignite your passion for this fascinating subject. Let this captivating narrative guide you through the foundations of a discipline that has shaped our understanding of the world around us.
The Story of Euclid
Euclid's name echoes through the halls of geometry, but who was the man behind the theorems that have shaped mathematical understanding for centuries? Journey back to ancient Greece and uncover the story of a scholar whose work has transcended time, influencing everything from architecture to art.In "The Story of Euclid," you'll be transported to a world of groundbreaking ideas and timeless principles. Delve into the life of this enigmatic figure and witness the birth of geometric concepts that continue to shape our world today. Explore the elegance of his proofs, the power of his postulates, and the enduring legacy of a man whose contributions to mathematics are immeasurable.Whether you're a seasoned mathematician or simply curious about the origins of geometry, "The Story of Euclid" will ignite your passion for this fascinating subject. Let this captivating narrative guide you through the foundations of a discipline that has shaped our understanding of the world around us.
Brief historical overview of the concept of number
This book offers a historical journey through various moments of antiquity, exploring how some civilizations developed strategies to understand and use the notion of number. It covers from the earliest attempts at counting in prehistoric times to the mathematical developments in Greece and Rome. It examines the thinking of ancient cultures such as Mesopotamia, Egypt, Babylon, Greece, Rome, and China. It addresses the evolution of numerical notations and their importance in the development of science and technology. Examples of irrational numbers are presented, such as those of the Pythagorean theorem, the number π and some square roots, showing their relevance in the civilizations mentioned. This book is a valuable resource for high school mathematics teachers, as it provides interesting historical data and the compilation of various authors on the subject, seeking attractive elements for students and strengthening pedagogical practices. It is essential for educators who seek to connect mathematical knowledge with its historical and cultural development, raising the quality of mathematics teaching in their classrooms.
Complex Analysis
In this book we introduce the main concepts of complex analysis as The Set of Complex Numbers, Euler's Formula, Polar Form, De Moivers Formula, Roots of Complex Numbers, Complex Functions, Limits of Complex Functions, Continuity of Complex Functions, Analytic Functions, Differentiation Rules, Cauchy- Riemann Equations, Elementary Complex Functions, Trigonometric Complex Functions, Hyperbolic Complex Functions, Logarithmic Complex Functions, Inverse Trigonometric Complex Functions and Inverse Hyperbolic Complex Functions, Mappings, Integration, Definite Integral, Line Integral, Theorems of Integration, Antiderivatives, Cauchy Integral Formulas, Sequences of Complex Numbers, Complex Serie, Complex Power Series, Laurant Series, Residue Theory, Application of Residue Theory.
Numerical Methods
This anthology presents a selection of the fundamental concepts and methods that students of Numerical Methods should master. Although it does not cover all topics, it seeks to illustrate how each method, whether open or closed interval, offers advantages and disadvantages that can lead to the same result. It is important to note that the functions discussed in this text have a higher level of complexity than those studied in high school, so it is necessary to resort to numerical techniques that provide approximate, but as accurate as possible, results in order to make informed decisions.The methods described in the following sections will show various ways to obtain approximate values of the roots of a function, including estimating the percentage error. This will allow students to understand the importance of Numerical Methods in solving complex problems.
"Viral hepatitis A
This Practical Guide for Students is a tool designed to help you optimize your academic career. Hepatitis A is a viral liver disease caused by the hepatitis A virus. Although most cases are benign and recovery is usually complete, it can lead to serious complications, especially in certain at-risk populations. Hepatitis A can also lead to high healthcare costs, loss of productivity due to absenteeism, and affect the local and national economy.An educational guide on hepatitis A can serve several purposes:1 Awareness: to inform the public about the causes, modes of transmission and symptoms of hepatitis A.2 Prevention: Provide advice on hygiene and vaccination practices to reduce the risk of infection.3 Education: Explain the issues surrounding hepatitis A, including its health consequences and the importance of screening and treatment.4 Resources: Provide educators with tools and resources to facilitate learning and the dissemination of information.5 Community support: Strengthen support for people affected by hepatitis A.
The Friction of Life
Naples, May 8, 1959. Renato Caccioppoli, a mathematical genius, prodigious pianist, captivating storyteller, highly cultured and multilingual, believed to be the grandson of the anarchist movement founder Mikhail Bakunin, takes his own life by shooting himself in the back of the head in his residence at Palazzo Cellammare.Adored by students and colleagues, a symbol of freedom and non-conformity for an entire generation, Caccioppoli enchanted not only some of the most celebrated intellectuals of the century - Andr矇 Gide, Pablo Neruda, Eduardo De Filippo, Benedetto Croce, Alberto Moravia, Elsa Morante - but also, and above all, the people of Naples, who have always regarded him with amazed admiration. Persecuted by the fascist regime, afflicted by what the writer and friend Paola Masino would describe as "the friction of life," his death permanently places him in the city's history.This meticulous and well-documented investigation tells us who Caccioppoli truly was and offers us an un-stereotyped and, in some ways, unprecedented portrayal of a legendary Naples.
Cone Fuzzy Systems and Their Application to Modeling Nonlinear Systems
Fuzzy systems can effectively model complex nonlinear systems with uncertainties, fuzzy system can make full use of the experience knowledge of domain experts and make it easy to understand. Theoretically, the modeling precision of fuzzy model is related to the number of fuzzy rules. The more fuzzy rules, the higher the precision of the fuzzy model. However, in practice, when modeling fuzzy models for some nonlinear systems, the improvement of fuzzy model precision is limited by simply increasing the number of fuzzy rules, which, on the contrary, greatly increases the calculation amount of the entire modeling process, leading to redundancy of the fuzzy rules and overfitting of the models, so the balance and compromise between complexity and precision has become a hot issue in the research of fuzzy system identification. Therefore, how to design a simple and effective fuzzy system, improve its approximation performance and reduce its computational complexity become the main starting points of this paper.
Application of Partials Differential Equations in Plasma Physics
Authors introduced advanced applications of partial differential equations in plasma physics using analytical methods based on Boltzmann-Maxwell equations. The book creates theoretical tools for predicting and controlling plasma behavior in many outstanding applications. To the best of our knowledge, we introduced a new mathematical model for calculating the thermodynamic forces, kinetic coefficients, and flux variables as two new scientific achievements. Second, with reasonable accuracy, we determined the equilibrium time of electrons and positive ions under an electromagnetic forces. Authors clarify the difference between an equilibrium velocity distribution function and a perturbed one. The book introduces the extended Gibbs equation, which predicts ratios between various contributions to the internal energy change for diamagnetic and paramagnetic plasmas. A standard laboratory argon plasma model is used to apply the results. This book advances our understanding of plasma physics and holds immense potential for practical applications in aerospace engineering, plasma technology, materials science. This book lays the groundwork for future innovations and technological advance.
Algebraic Number Theory and Fermat's Last Theorem
Updated to reflect current research and extended to cover more advanced topics as well as the basics, this book introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematics-the quest for a proof of Fermat's Last Theorem.
Theory of Recursive Functions and Effective Computability
(Reprint of the 1967 edition)
