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.
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.
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.
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.
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.
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.
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.
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.
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.
"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.
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.
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)
Boundary Elements and Other Mesh Reduction Methods XLVII
Theoretical advances and new foundations are reported which contribute to expanding the range of applications as well as the type of materials modelled in response to current industrial and professional requirements. The contents of the volume reflect the ability of the subject matter to evolve and the establishment of a continuously renewed community of stakeholders.As design, analysis and manufacture become more integrated, the chances are that the users of computational software will be less aware of the capabilities of the analytical techniques that are at the core of the process. This reinforces the need to retain expertise in certain specialised areas of numerical methods, such as BEM/MRM, to ensure that all new tools perform satisfactorily in the integrated process.The maturity of BEM since 1978 has resulted in a substantial number of industrial applications which demonstrate the accuracy, robustness and easy use of the technique. Their range is still being widened, taking advantage of the potentialities of the Mesh Reduction techniques in general. This volume constitutes an important reference base from which to discuss new ideas and critically compare results before developed solutions and tools are released to end professional users.
Introduction to Potential Theory
This monograph is devoted to harmonic analysis and potential theory. The authors study these essentials carefully and present recent researches based on the papers including by authors in an accessible manner for graduate students and researchers in pure and applied analysis.
Differential Geometry and Its Application, 2nd Edition
This Special Issue provides a platform to showcase the latest achievements in many branches of theoretical and practical mathematical studies. These relate to Riemannian theories, generalized Riemannian spaces and their mappings. The scope of this Special Issue also includes Finsler geometry, Kenmotsu manifolds, Kaehler manifolds, manifolds with non-symmetric linear connections, cosymplectic manifolds, contact manifolds, statistical manifolds, Minkowski spaces, geodesic mappings, almost-geodesic mappings, holomorphically projective mappings, warped products of manifolds, complex space forms, quaternionic space forms, golden manifolds, inequalities, invariants, immersions, etc. Potential authors are encouraged to submit papers that present new ideas in the field of differential geometry, in addition to the above topics. Given the broad scope and widespread interest in this topic, more works should be published in this area.
Some insights on surface calculus
This book is about calculus of surfaces. Firstly, we present and prove the main results on surface integration in a clear and readable fashion. The following chapters are dedicated to solving new problems on the theory of surface integration of scalar and vector fields over parameterized regular surfaces. The book ends with a chapter on proposed problems and their solutions which many of them were used in classroom and in assessment in the last 20 years.
Artificial Intelligence of Neuromorphic Systems
This book argues for neuromorphic systems as a technology of the future, which are oriented towards the energy efficiency of natural brains. Energy efficiency is a dramatic claim in times of environmental and climate challenges which should consider the sustainability goals of the United Nations (UN). Mathematically, neuromorphic computing is connected to analogue ('real') computing, which theoretically overcomes the limits of digital Turing computability. Therefore, the book also considers material sciences and engineering sciences which start to realize neuromorphic computing in hardware. Other mathematical formalisms such as quantum mechanics also open up new solutions (e.g., quantum computing) beyond the limits of digital Turing computability. These research fields are no longer merely of theoretical interest, they promise increasing innovation power of market interest. Nevertheless, neuromorphic computing is connected with deep logical, mathematical, and epistemic questions. Does it open new avenues to Artificial General Intelligence (AGI)? All these tendencies of research and innovation demonstrate that we need more integrated research in the foundations of logic, mathematics, physics, engineering sciences, cognitive science, and philosophy. The book is a plea for this kind of research.
The Language of Mathematics
A marvelous compendium of mathematical symbols and their fascinating histories Galileo famously wrote that the book of nature is written in mathematical language. The Language of Mathematics is a wide-ranging and beautifully illustrated collection of short, colorful histories of the most commonly used symbols in mathematics, providing readers with an engaging introduction to the origins, evolution, and conceptual meaning of each one. In dozens of lively and informative entries, Ra繳l Rojas shows how today's mathematics stands on the shoulders of giants, mathematicians from around the world who developed mathematical notation through centuries of collective effort. He tells the stories of such figures as al-Khwārizmī, Ren矇 Descartes, Joseph-Louis Lagrange, Carl Friedrich Gauss, Augustin-Louis Cauchy, Karl Weierstrass, Sofia Kovalevskaya, David Hilbert, and Kenneth Iverson. Topics range from numbers and variables to sets and functions, constants, and combinatorics. Rojas describes the mathematical problems associated with different symbols and reveals how mathematical notation has sometimes been an accidental process. The entries are self-contained and can be read in any order, each one examining one or two symbols, their history, and the variants they may have had over time. An essential companion for math enthusiasts, The Language of Mathematics shows how mathematics is a living and evolving entity, forever searching for the best symbolism to express relationships between abstract concepts and to convey meaning.
General Quantum Variational Calculus
Quantum calculus is the modern name for the investigation of calculus without limits. The quantum calculus or q-calculus began with FH Jackson in the early twentieth century, but this kind of calculus had already been worked out by Euler and Jacobi.
Handbook of Mathematical and Digital Engineering Foundations for Artificial Intelligence
Artificial intelligence (AI) and digital engineering have become prevalent in business, industry, government, and academia. However, the workforce still has a lot to learn on how to leverage them. This handbook presents the preparatory and operational foundations for the efficacy, applicability, risk, and how to take advantage of these tools and techniques. Handbook of Mathematical and Digital Engineering Foundations for Artificial Intelligence: A Systems Methodology provides a guide for using digital engineering platforms for advancing AI applications. The book discusses an interface of education and research in the pursuit of AI developments and highlights the facilitation of advanced education through AI and digital engineering systems. It presents an integration of soft and hard skills in developing and using AI and offers a rigorous systems approach to understanding and using AI. This handbook will be the go-to resource for practitioners and students on applying systems methodology to the body of knowledge of understanding, embracing, and using digital engineering tools and techniques.The recent developments and emergence of Chatbots (AI tools) all have mathematical foundations for their efficacy. Such AI tools include ChatGPT, GPT-4, Bard, Tidio Support Bot, Kuki AI Companion, Meena, BlenderBot, Rose AI Chatbot, Replika: AI Friend, Eviebot, and Tay. This handbook highlights the importance of mathematical and digital foundations for AI developments. The handbook will enhance the understanding and appreciation of readers about the prevailing wave of artificial intelligence products, and, thereby, fitting the current market needs.
Fractals and Chaotic Phenomena in Chemical Reactor Models
The heart of most chemical plants is a chemical reactor. Basically there are two types of reactors: tubular and tank. Depending on the type, they are described by system of partial differential equations or by system of ordinary differential equations. Each of these models can generate complex solutions, including chaos. Analysis of this type of equations requires using sophisticated mathematical methods and complex numerical algorithms. In this study these phenomena and methods of analysis were presented. Particular attention is paid to the bifurcation problem and chaotic oscillations. Different mathematical - numerical methods were presented which were used to solve above mention problems. The following concepts as: bifurcation, Lyapunov's exponent, Lyapunov's time and power spectrum were used for this purpose. The way of chaos crisis prediction was presented and optimization of reactor's process by relaxation method. At the end, it was presented two-parameter continuation method for Hopf bifurcation. This book is an extension of my previously published book "Chaotic Dynamics and Fractals in Chemical Reactor Systems" from 2019 (LAP).
Ethnomathematics and Law 10.639/03 in the Quilombola Community of Curia繳
This book is the result of research carried out in the school of the Quilombola Community of Curia繳, in the city of Macap獺, in the state of Amap獺, Brazil. The main focus was to investigate the teaching and learning of mathematics in this school. We reflect on the perceptions of some researchers in Ethnomathematics, regarding the production and dissemination of knowledge, with regard to the history of black education, more specifically education in Quilombola Communities. To answer some of these questions, we reported on the work carried out by teachers at the community school. We interviewed teachers, school staff and rural workers in their work environment and analyzed the mathematical knowledge that exists in their work activities, checking how it happens and whether it is related to Law 10.639/03. The records made during the field activities served to confirm that different mathematical knowledges can be worked on by math teachers in the classroom, and that these knowledges produced by the workers in the community answer important existential questions for the cultural group in question.
Innovative practices of the "good math teacher"
To be excellent educators, it's not enough just to "be a teacher", we must have something more, something that transforms us and changes students' lives. We worked together with innovative practices and differentiated methodologies, which were part of the theme of our research. It deals with the innovative practices of the good math teacher, from which we searched through the words of authors who have worked with the theme of the good teacher, the meaning, the basis of the good teacher, and thus we founded our theoretical practical research. We set ourselves the objectives of getting to know their teaching practices, methods that increase the quality of teaching and what pedagogical innovations we are finding in math teachers. We tried to find out what the attributions of a good teacher are from the suggestions made by the students. By analyzing these three problems, we found the characteristics of a good teacher. Our research was initially based on a theoretical foundation, elaborated in order to understand what the main attributes of a good math teacher are, and we sought to formulate some questions to find answers within our journey.
An Introduction to Classical and Modal Logics
Classical logic - which studies the structural features of purported claims of fact - and modal logic - which studies relations of necessity and possibility - are different but complementary areas of logical thought. In this lively and accessible textbook, Adam Bjorndahl provides a comprehensive and unified introduction to the two subjects, treating them with the same level of rigour and detail and showing how they fit together. The core material appears in the main text, with hundreds of supplemental examples, comments, clarifications, and connections presented throughout in easy-to-read sidenotes, giving the book a distinct conversational feel. A detailed, multi-part appendix covers important background mathematical material that some students may lack, such as induction or the concept of countable infinity. A fully self-contained learning resource, this book will be ideal for a semester-long upper-level university course on either or both of the topics.
Mathematics
REVISED AND UPDATED EDITION Here is the latest edition of this essential guide to mathematics, an authoritative reference book and timeline that explores the work of history's greatest mathematicians. These include the teasing genius of Pierre de Fermat, who said he knew the answers but rarely gave them up, the helpful guidance of Fibonacci, whose 13th-century compendium for bookkeepers proved to be a valuable tool for the most high-minded mathematicians, and the fractal pattern discovered by Waclaw Sierpinski now used to plan the route a mailman takes. With a glimpse of the abstract landscapes of infinite numbers and multi-dimensional shapes that these incredible minds explore, we can begin to get beyond school-day sums and understand the true power of mathematics. 100 milestone facts reveal the greatest mathematical breakthroughs through the eyes of the people who made them. Authoritative text, historical imagery, and helpful diagrams are combined with stories and everyday examples to make the complex mathematics accessible to everyone. Includes a 12-page foldout Timeline poster which stretches out to 8.5 feet (2.6 meters) long. Mathematics is part of the bestselling 100 Ponderables series which tackles STEM subjects by partnering lively text about significant milestones with stunning illustrations. Every book includes a timeline/chart poster which puts these milestones in historical context. Perfect for smart kids and curious adults!
An Introduction to Classical and Modal Logics
Classical logic - which studies the structural features of purported claims of fact - and modal logic - which studies relations of necessity and possibility - are different but complementary areas of logical thought. In this lively and accessible textbook, Adam Bjorndahl provides a comprehensive and unified introduction to the two subjects, treating them with the same level of rigour and detail and showing how they fit together. The core material appears in the main text, with hundreds of supplemental examples, comments, clarifications, and connections presented throughout in easy-to-read sidenotes, giving the book a distinct conversational feel. A detailed, multi-part appendix covers important background mathematical material that some students may lack, such as induction or the concept of countable infinity. A fully self-contained learning resource, this book will be ideal for a semester-long upper-level university course on either or both of the topics.
Multidimensional Differential and Integral Calculus
This textbook proposes an informal access to the most important issues of multidimensional differential and integral calculus. The traditional style-characterized by listing definitions, theorems, and proofs-is replaced by a conversational approach, primarily oriented to applications. The topics covered, developing along the usual path of a textbook for undergraduate courses, are always introduced by thoroughly carried out examples. This drives the reader in building the capacity of properly use the theoretical tools to model and solve practical problems. To situate the contents within a historical perspective, the book is accompanied by a number of links to the biographies of all scientists mentioned as leading actors in the development of the theory.
Nonexictence results on the Heisenberg group
This book is devoted to prove a nonexictence theorems for solutions of some nonlinear evolution equations and systems of the same type on the Heisenberg group. The proofs are based on the test function method developed by Mitidieri and Pohozaev, Pohozaev and Tesei, Kirane and L. Ragoub. The method relies on a suitable choice of the test function in the weak formulation of the sought solutions.
Mathematical Analysis for Economists
This book provides economics students with a comprehensive foundation in mathematical analysis, focusing on key concepts necessary for advanced economic models and quantitative methods. Divided into five chapters, it covers essential topics: numerical series, numeric functions of two variables, double integrals, improper integrals, and differential equations. Each chapter is designed with exercises and practical applications relevant to economics, enabling students to build both theoretical understanding and applied skills. Through this approach, students gain a mathematical toolkit vital for advanced studies and future careers in economics.
Application of Statistical Computing to Statistical Learning
The study here is about supervised learning, an aspect of statistical learning. We identified prediction as the mainstay of supervised learning, and further noted that when the outcome of prediction is a categorical variable, classification obtains, otherwise what we have is regression, meaning that the prediction outcome is a continuous variable.A distinguishing aspect of this work is our ability to show both mathematically with a proof, and practically with some real-world datasets, that regression tools can be used as veritable tools for classification.
Fundamentals of Heat & Mass Transfer Analysis due to Stretching Sheet
Many mechanisms can be responsible for the movement of fluid. These mechanisms includes the pressure gradient, movement of surface the fluid is resting upon or the surfaces the fluid is contained in and buoyancy force resulting due to density gradients. Of these, two important mechanisms are studied in this book i.e., the stretching of the surfaces and/or thermal buoyancy or both. These two basic mechanisms, surface motion due to stretching i.e. contracting/expanding walls and buoyancy force, determine the momentum and thermal transport processes for the problems. Considerable interest has been also arisen in these years regarding the flows caused by the buoyant forces such flows have promising applications in engineering such as drawing of wires, laments spinning, extrusion of metal, growth of crystals, continuous casting, fiberglass production, pulsating diaphragms modeling, and separation of isotopes, irrigation, sweet cooling or heating filtration and manufacturing of paper. Due to fluid complexity, it is impossible to provide unique governing linear partial differential equation describing the characteristics of all types of dusty fluids. So, these are discussed in this book.
The effect of heat and mass transfer on MHD flow in channels and ducts
Transport phenomena involving the combined influence of thermal and concentration buoyancy are often encountered in many engineering systems and natural environments. Combined heat and mass transfer problems with chemical reactions are important in many processes and received a considerable amount of attention in recent years. Obviously, an understanding of this transport process is desirable in order to effectively control the overall transport characteristics. In this context, we make an attempt to investigate the effect of dissipation, the Soret effect, and radiation on the unsteady double diffusive flow of a viscous and electrically conducting fluid through a porous medium in a vertical channel. Also, investigated the Heat and Mass transfer of a viscous fluid with radiation effect in channels/ducts. We discuss the effect of radiation, thermo-diffusion, dissipation, and heat sources on the convective heat and mass transfer flow of a viscous fluid through a porous medium in a rectangular duct.
Theory and Applications of Analytical Integration Methods
Dive into a captivating journey through the complex world of integral calculus with this first volume, "Theory and Applications of Analytical Integration Methods: From Mathematical Foundations to Practical Solutions", the first tome of a two-volume series. This first volume delves deeply into analytical integration methods, while the second volume focuses on numerical methods and their implementation in Python. Through nine carefully structured chapters, explore the fundamentals of integral calculus and dive into its numerous practical applications in geometry, statistics, electricity, thermochemistry, and mechanics. Designed for a broad audience, whether you're a novice or an expert, this book offers a comprehensive and accessible approach to mastering integral calculus with little to no external assistance. Each chapter is enriched with clear examples and practical exercises, accompanied by detailed solutions to enhance understanding. The great strength of this series lies in the rigorous validation of results obtained by analytical resolution against those obtained using numerical methods, which are further confirmed by computer-generated results.
