How to Write & Do Proofs
This Study Guide has been teaching students how to write & do proofs for over 30 years. This text provides an excellent approach for teaching students how to read, understand, and do proofs. The various examples and techniques explains when each technique is likely to be used, based on certain key words that appear in the problem under consideration. Doing so enables students to choose a technique based on the form of the problem. The goal is to enable students to learn advanced mathematics on their own. This book is suitable as: (1) a text for a transition-to-advanced-math course, (2) a supplement to any mathematics course, and (3) self-guided teaching.
Think Like a Molecule
Despite their complex structures, molecules most likely do not take time to ponder the ways they fit into the big scheme of things. They just are. But when zillions of molecules bond into organized, functional systems, we get everything, including you and me - and some seven billion others. Chuck Champlin, a writer, journalist, and a former Walt Disney Co. communications executive, seeks inspiration via deep imaginative journeys into the infinitely vast and invisibly tiny realms of the cosmos in this small book with a big message. In observing molecular assemblies, we can see that physically matter came together, possibly all on its own, to create life and thinking minds. It is profound that our minds, perhaps born from accidental creativity, can intentionally assemble marvelous new things. To think like a molecule is to be aware of the physical foundations in matter that have given rise to our thoughts - and from there, it's onward into the realm of pure imaginations and the twinkling stars of our infinite potential.
Functional Analysis
This comprehensive introduction to functional analysis covers both the abstract theory and applications to spectral theory, the theory of partial differential equations, and quantum mechanics. It starts with the basic results of the subject and progresses towards a treatment of several advanced topics not commonly found in functional analysis textbooks, including Fredholm theory, form methods, boundary value problems, semigroup theory, trace formulas, and a mathematical treatment of states and observables in quantum mechanics. The book is accessible to graduate students with basic knowledge of topology, real and complex analysis, and measure theory. With carefully written out proofs, more than 300 problems, and appendices covering the prerequisites, this self-contained volume can be used as a text for various courses at the graduate level and as a reference text for researchers in the field.
The Secret Formula
The legendary Renaissance math duel that ushered in the modern age of algebra The Secret Formula tells the story of two Renaissance mathematicians whose jealousies, intrigues, and contentious debates led to the discovery of a formula for the solution of the cubic equation. Niccol簷 Tartaglia was a talented and ambitious teacher who possessed a secret formula--the key to unlocking a seemingly unsolvable, two-thousand-year-old mathematical problem. He wrote it down in the form of a poem to prevent other mathematicians from stealing it. Gerolamo Cardano was a physician, gifted scholar, and notorious gambler who would not hesitate to use flattery and even trickery to learn Tartaglia's secret. Set against the backdrop of sixteenth-century Italy, The Secret Formula provides new and compelling insights into the peculiarities of Renaissance mathematics while bringing a turbulent and culturally vibrant age to life. It was an era when mathematicians challenged each other in intellectual duels held outdoors before enthusiastic crowds. Success not only enhanced the winner's reputation, but could result in prize money and professional acclaim. After hearing of Tartaglia's spectacular victory in one such contest in Venice, Cardano invited him to Milan, determined to obtain his secret by whatever means necessary. Cardano's intrigues paid off. In 1545, he was the first to publish a general solution of the cubic equation. Tartaglia, eager to take his revenge by establishing his superiority as the most brilliant mathematician of the age, challenged Cardano to the ultimate mathematical duel. A lively account of genius, betrayal, and all-too-human failings, The Secret Formula reveals the epic rivalry behind one of the fundamental ideas of modern algebra.
Tutor Book's
Need help with Geometry? Tutor Book's Geometry is extremely thorough. This book skillfully cover the many concepts that students need to master. Examples, including examples using numbers, are included for those theorems and definitions that skilled tutors and teachers know students find more difficult to understand. Many teaching tips and hints are included to support student learning. Memory tips are given where useful.
Separation of Variables and Exact Solutions to Nonlinear PDEs
The book is devoted to describing and applying methods of generalized and functional separation of variables used to find exact solutions of nonlinear PDEs. It also presents the direct method of symmetry reductions and its more general version.
Linear Algebra
This book is written to give instructors a tool to teach students to develop a mathematical concept from first principles. The text is organized around and offers the standard topics expected in a first undergraduate course in linear algebra.
Applied Regression and ANOVA Using SAS
Designed for researchers primarily interested in what their data are revealing, this book presents statistical methods without burdening readers with matrix algebra and calculus. The book shows how high resolution, publication-ready graphics associated with regression and ANOVA methods are produced with virtually no effort by the SAS user.
Non-commutative Algebras. Pseudo-BCK Algebras versus m-pseudo-BCK Algebras
This monograph is devoted mainly to the author's results in her research on non-commutative algebras related to logic started on October 17, 2022, results never published. It would not be written in so little time and with so many important results and examples without the help of the computer program Prover9-Mace4, developed by William W. McCune (1953 - 2011).There exist a frame-work of non-commutative algebras of logic, having in its `center' the pseudo-BCK algebra.In this monograph, the author mainly has generalized to the non-commutative case the m-BCK algebra and its related algebras, as particular cases of unital magmas, thus creating a new frame-work of non-commutative algebras, having in its `center' the new m-pseudo-BCK algebra. The pseudo-MV algebras are particular cases of m-pseudo-BCK algebras, the groups belong to this new frame-work. But, the goal of her research was to define and study the quantum-pseudo-MV algebra, the non-commutative generalization of quantum-MV algebra. She was able to reach her goal only because she has discovered the`principle' that governs the non-commutative algebras, called `transposition' principle (`m-transposition' principle, for magmas). She has also introduced and studied other non-commutative generalizations of quantum algebras: the bounded involutive pseudo-lattices, the pseudo-De Morgan algebras and the ortho-pseudo-lattices. The book has 18 chapters, divided into three parts: Part I (centered on pseudo-BCK algebras: Chapters 1 - 7), Part II (the core of the monograph, centered on m-pseudo-BCK algebras: Chapters 8 - 16) and Part III (`bridge' theorems: Chapters 17, 18).
Vedic Tricks Made Mathematics Easy
Unveiling the Power of Vedic Mathematics: Essential InsightsEfficiency in Calculation: Vedic Mathematics provides highly efficient techniques for mental calculations, enabling individuals to perform complex computations quickly. This efficiency is particularly valuable in situations where rapid calculation is crucial.Versatility Across Mathematical Operations: The techniques in Vedic Mathematics are versatile and applicable across various mathematical operations, including addition, subtraction, multiplication, division, algebraic equations, and even advanced mathematical concepts.Promote Skills of Mental Calculations: Vedic Mathematics strongly emphasizes mental calculations, fostering the development of strong mental calculation skills. It not only enhances cognitive abilities but also makes mathematical tasks more accessible without the reliance on external tools.Applicability to Competitive Exams: Many of the Vedic Mathematics techniques are designed to streamline calculations in competitive exams where time is a critical factor. As a result, students find these methods beneficial for solving problems quickly and accurately in exam settings.Mental Calculation: Vedic Mathematics emphasizes mental calculation, promoting the development of mental agility and mathematical intuition.Universality and Speed: The techniques are not limited to specific types of problems; they can be applied universally, making them adaptable to various mathematical scenarios. The methods are designed to be straightforward and can often lead to faster calculations compared to conventional methods.Educational Applications: Vedic Mathematics is often used as an educational tool to make learning mathematics more engaging, accessible, and enjoyable for students.Connection to Profound Wisdom: Vedic Mathematics is sometimes considered a part of the broader Vedic tradition, with enthusiasts believing it embodies a profound approach to mathematics.
Nicknames, nicknames and nicknames in the Tumaque簽a Speech
The Colombian Pacific is one of the largest and most biodiverse territories in the country. It is inhabited by Afro-descendants and indigenous people from different groups, but has little or no relevant and inclusive education. Here, we intend to reflect on the importance of ethno-educational work that starts from the speech and oral tradition to reach the knowledge of Afro-Pacific culture from elementary school, showing the obvious importance of endogenous ethnopedagogical work to achieve cementing ethnic and cultural identity in the early stages of academic life.
Circles, Spheres and Spherical Geometry
This textbook focuses on the geometry of circles, spheres, and spherical geometry. Various classic themes are used as introductory and motivating topics. The book begins very simply for the reader in the first chapter discussing the notions of inversion and stereographic projection. Here, various classical topics and theorems such as Steiner cycles, inversion, Soddy's hexlet, stereographic projection and Poncelet's porism are discussed. The book then delves into Bend formulas and the relation of radii of circles, focusing on Steiner circles, mutually tangent four circles in the plane and other related notions. Next, some fundamental concepts of graph theory are explained. The book then proceeds to explore orthogonal-cycle representation of quadrangulations, giving detailed discussions of the Brightwell-Scheinerman theorem (an extension of the Koebe-Andreev-Thurston theorem), Newton's 13-balls-problem, Casey's theorem (an extension of Ptolemy's theorem) and its generalizations. The remainder of the book is devoted to spherical geometry including a chapter focusing on geometric probability on the sphere. The book also contains new results of the authors and insightful notes on the existing literature, bringing the reader closer to the research front. Each chapter concludes with related exercises of varying levels of difficulty. Solutions to selected exercises are provided. This book is suitable to be used as textbook for a geometry course or alternatively as basis for a seminar for both advanced undergraduate and graduate students alike.
Elliptic Partial Differential Equations Elementary Viewpoint
This is a textbook that covers several selected topics in the theory of elliptic partial differential equations which can be used in an advanced undergraduate or graduate course.The book considers many important issues such as existence, regularity, qualitative properties, and all the classical topics useful in the wide world of partial differential equations. It also includes applications with interesting examples.The structure of the book is flexible enough to allow different chapters to be taught independently.The book is friendly, welcoming, and written for a newcomer to the subject.It is essentially self-contained, making it easy to read, and all the concepts are fully explained from scratch, combining intuition and rigor, and therefore it can also be read independently by students, with limited or no supervision.
Cleaning Up the Human Skeleton and Genome
This is a work traversed by scientific and technical themes in which the indispensable irrationality interacts: African Art and Spirituality (an element of stability in any science so that the latter does not cross the boundaries of ethics, morality... I reread this precious thesis with great interest, during which it is not so easy to tackle all the themes, analyses and reflections. The skilful and ingenious researcher Audrey KIBAMBA had a head start, for he constructed his thesis in such a way that all the themes dealt with converged like guidelines towards the same vanishing point. In biology, we know that bacteria cooperate, exchange information, evolve and even advance their ability to evolve. Ants do the same. Human beings must do the same too, to evolve better in this fast-paced, dizzying world. This world is making spectacular progress in many areas, and we are in the midst of a major transition in our evolution.
Introduction to Data Science
Unlike the first edition, the new edition has been split into two books.Thoroughly revised and updated, this is the first book of the second edition of Introduction to Data Science: Data Wrangling and Visualization with R. It introduces skills that can help you tackle real-world data analysis challenges. These include R programming, data wrangling with dplyr, data visualization with ggplot2, file organization with UNIX/Linux shell, version control with Git and GitHub, and reproducible document preparation with Quarto and knitr. The new edition includes additional material on data.table, locales, and accessing data through APIs. The book is divided into four parts: R, Data Visualization, Data Wrangling, and Productivity Tools. Each part has several chapters meant to be presented as one lecture and includes dozens of exercises. The second book will cover topics including probability, statistics and prediction algorithms with R.Throughout the book, we use motivating case studies. In each case study, we try to realistically mimic a data scientist's experience. For each of the skills covered, we start by asking specific questions and answer these through data analysis. Examples of the case studies included in the book are: US murder rates by state, self-reported student heights, trends in world health and economics, and the impact of vaccines on infectious disease rates.This book is meant to be a textbook for a first course in Data Science. No previous knowledge of R is necessary, although some experience with programming may be helpful. To be a successful data analyst implementing these skills covered in this book requires understanding advanced statistical concepts, such as those covered the second book. If you read and understand all the chapters and complete all the exercises in this book, and understand statistical concepts, you will be well-positioned to perform basic data analysis tasks and you will be prepared to learn the more advanced concepts and skills needed to become an expert.
Advances in Modal Logic 15
Since ancient times, philosophers have recognised that truth comes in many 'modes', so that a proposition can be not only true or false, but also, for example, 'necessary' or 'possible'. These ideas led to the modern field of modal logic, a lively area of research at the interface of philosophy, mathematics and computer science. Nowadays, the term 'modal logic' is understood in a broad sense, allowing it to encompass logics for reasoning about seemingly unrelated phenomena such as knowledge, obligations, time, space, and proofs, among many others. Contemporary research in modal logic draws on techniques from many disciplines, including complexity theory, combinatorics, universal algebra, category theory, topology, and proof theory. These proceedings record the papers presented at Advances in Modal Logic 2024, the 15th in a series of biennial conferences that aim to report on important new developments in pure and applied modal logic. Topics in this issue include epistemic modal logic, constructive and many-valued modal logic, unification, algebraic and neighbourhood semantics, proof theory and complexity of modal logics, conditional and quantified modal logic.
Semitopology. Decentralised Collaborative Action via Topology, Algebra, and Logic
We develop semitopologies, a new topological structure which gives a mathematical foundation to heterogeneous, decentralised, permissionless, computing systems. Semitopologies help to model consensus problems that commonly arise in designing cutting-edge peer-to-peer, blockchain, and other decentralised systems; especially when different such systems need to interact. Points correspond to participants in the system, and open sets correspond to the ways in which participants can cooperate.This text is aimed at mathematicians and advanced students interested in a new topology-adjacent field with strong practical applications; and at engineers working to build decentralised systems who could use a mathematical foundation for designing the relevant tools. It aims to offer pleasant surprises and new ideas for researchers; and for practitioners, it aims to help build the next generation of better, safer, more scalable decentralised systems.
Abstract Algebra
This textbook intends to serve as a first course in abstract algebra. The selection of topics serves both of the common trends in such a course: a balanced introduction to groups, rings, and fields; or a course that primarily emphasizes group theory. This book offers a unique feature in the lists of projects at the end of each section.
Asymptotic formulas in the Esterman problem
This monograph is a study in analytical number theory, related to the field of the theory of short trigonometric sums, and its applications to classical additive problems with more stringent conditions, namely, when the terms are almost equal. Short trigonometric sums that arise when solving additive problems with almost equal terms were first studied by I. M. Vinogradov. The relevance and appropriateness of this monograph are determined by the fact that it- studied the behavior of G. Weyl's short trigonometric sums of the formT(α, x, y)=∑_(x-yin large arcs;- the results obtained made it possible to find an asymptotic formula for the number of representations of a sufficiently large natural number as a sum of three almost equal terms, two of which are prime numbers, and the third is the fourth power of a natural number.
Direct and Inverse Spectral Problems for Ordinary Differential and Functional-Differential Operators
This reprint contains a collection of research papers on spectral theory for differential and functional differential operators. Spectral theory plays a fundamental role in mathematics and has applications in various fields of science and engineering, e.g., in quantum and classical mechanics, geophysics, acoustics, and electronics. The collection includes recent studies on a variety of topics such as analytical and numerical methods for solving direct and inverse spectral problems, new developments in the theory of partial differential equations, pseudo-differential equations with fractional derivatives, asymptotical analysis for solutions of differential equations, spectral theory for abstract operators in Hilbert spaces, and inverse nodal problems.
Mathematical Innovation
The transition to a competency-based approach in mathematics education is based on the need for students to acquire competencies that go beyond mere theoretical knowledge. This approach focuses on the practical application of knowledge, developing in students the ability to solve problems, think critically and work in teams. Traditional assessment, based on written tests, has proven to be insufficient to measure these competencies effectively. In contrast, competency-based assessment methods, such as performance tests and projects, allow for a more holistic and contextualized assessment of student learning. Gamification, on the other hand, defined as the use of game elements in non-game contexts, has gained popularity as a pedagogical strategy in teaching and learning. This strategy is based on the premise that gaming can make learning more attractive and motivating for students, gamification allows teachers to adapt their strategies to the needs and preferences of students, awakening their love and interest for the subject.
Application of Artificial Intelligence Methods in Processing of Emotions, Decisions and Opinions
During recent years, social infrastructure has become irreversibly linked to the Internet through its everyday manifestations, such as social networking services (Twitter, Facebook, etc.). Every second, this new tangible information-based reality provides large amounts of data filled with 1) emotional expressions; 2) people's opinions on various topics; and 3) their reasoning, revealing their decision-making processes. As these three categories are also closely interrelated with each other, they should be studied together to obtain a more robust view on all of the topics involved. This, as never before, provides an opportunity for the development and application of natural language processing methods, in particular those regarding such topics as emotion processing, decision-making, and opinion mining.
Geometry of Crystallographic Groups (Second Edition)
It is eleven years since the First Edition of Geometry of Crystallographic Groups appeared. This Second Edition expands on the first, providing details of a new result of automorphism of crystallographic groups, and on Hantzsche-Wendt groups/manifolds.Crystalographic groups are groups which act via isometries on some n-dimensional Euclidean space, so-named because in three dimensions they occur as the symmetry groups of a crystal. There are short introductions to the theme before every chapter, and a list of conjectures and open projects at the end of the book.Geometry of Crystallographic Groups is suitable as a textbook for students, containing basic theory of crystallographic groups. It is also suitable for researchers in the field, discussing in its second half more advanced and recent topics.
Machine Learning for Pattern Recognition
In recently arisen digital age, machine learning technology has made huge significant progress, revolutionizing applications in fields such as image recognition, speech processing, and natural language processing. These technologies have not only changed our daily lives, but have also had a profound impact on medicine, finance, transportation and other fields. However, pattern recognition, as an important branch of machine learning, still faces many challenges and problems. This reprint brings together contributions from leading experts in their fields. Each paper provides valuable insights into the latest trends, methods, and challenges in state-of-the-art applications of machine learning for pattern recognition. In addition, the research in each paper not only showcases the latest advancements in machine learning algorithms but also discusses their successful applications and the challenges encountered in real-world scenarios. As editors, we are honored to present this reprint, and we hope that readers, whether they be researchers, engineers, and students, will find inspiration and guidance in these papers as they explore the growing field of machine learning for pattern recognition. We express our gratitude to the authors for their outstanding contributions, to the reviewers for their critical evaluation, and to the assistant editor Mr. Musea Wu for his enthusiastic help. We are also sincerely grateful to our readers, whose curiosity and enthusiasm continue to drive innovation in this exciting field.
Reciprocity and contrapositive in the Pythagorean theorem
The reciprocal of the Pythagorean theorem is the same as explaining that a triangle is right-angled. For example, consider a triangle whose lengths are 3, 4 and 5. To explain that this triangle is a right-angled triangle, we need to use the reciprocal of the Pythagorean theorem. On the one hand, we have 32+42=9+16=25. On the other hand, it's true that 52=25. So 32+42=52 and, by the reciprocal of the Pythagorean theorem, it's a right-angled triangle. If we want to explain that a triangle is a right-angled triangle, we need to sum the squares of the two shortest lengths and check whether this sum is equal to the square of the longest side.
Every Tree is a Subtree of a Graceful Unicyclic Graph
A decomposition of a graph K into a set of graphs {G1, G2, ..., Gt} is a partition (E1, E2, ..., Et) of E(K) such that ∼= Gi, for i,1
Algebraic Systems
No detailed description available for "Algebraic Systems".
Trustworthy Artificial Intelligence for Healthcare
This book constitutes the proceedings of Second International Workshop on Trustworthy Artificial Intelligence for Healthcare, TAI4H 2024, held in Jeju, South Korea, in August 2024, in conjunction with the International Joint Conference on Artificial Intelligence, IJCAI 2024. The 13 full papers included in this book were carefully reviewed and selected from 21 submissions. They focus on trustworthy artificial intelligence, healthcare, generalization, explainability, fairness, privacy, multi-modal fusion, foundation models.
Preparing for Calculus
The book will enable the reader to assess their readiness for calculus. It provides a review and practice with the math needed for early success in a calculus course.High school, home-schooled and college students who face calculus as their next math course will benefit from this book.
Fundamentals of Probability
Praise for the fourth edition: "This book is an excellent primer on probability .... The flow of the text aids its readability, and the book is indeed a treasure trove of set and solved problems. --Dalia Chakrabarty, Brunel University, UK "This textbook provides a thorough and rigorous treatment of fundamental probability, including both discrete and continuous cases. The book's ample collection of exercises gives instructors and students a great deal of practice and tools to sharpen their understanding." --Joshua Stangle, University of Wisconsin - Superior, USA This one- or two-term calculus-based basic probability text is written for majors in mathematics, physical sciences, engineering, statistics, actuarial science, business and finance, operations research, and computer science. It presents probability in a natural way: through interesting and instructive examples and exercises that motivate the theory, definitions, theorems, and methodology. This book is mathematically rigorous and, at the same time, closely matches the historical development of probability. Whenever appropriate, historical remarks are included, and the 2096 examples and exercises have been carefully designed to arouse curiosity and hence encourage students to delve into the theory with enthusiasm. New to the Fifth Edition: In this edition, a significant change has been made in the order of material presentation. The topics such as the joint probability mass function, joint probability density functions, independence of random variables, sums of random variables, the central limit theorem, and certain other materials have been covered earlier in the book, enabling students to grasp these crucial concepts from the start. These changes have considerable merit, particularly the idea of covering the celebrated central limit theorem immediately after discussing the normal distribution. Additionally, discussions on sigma fields are provided and an in-depth section on characteristic functions is added. The central limit theorem has been proven using both moment-generating functions and characteristic functions. In the present edition, numerous new figures are included that were drawn for the first time, specifically to aid in students' understanding of the material. These fresh illustrations, along with all the previous ones in the book, have been meticulously crafted by the technical support team at CRC. Instructors who prefer the content arrangement used in previous editions can still teach the material in the same order as those editions. Moreover, the homepage of this book contains a whole chapter with comprehensive coverage on Stochastic Processes as well as additional contents for Chapters 1 to 10, such as extra examples, supplementary topics, and practical applications to facilitate in-depth exploration. Furthermore, it offers thorough solutions for all self-tests and self-quiz problems, empowering students to assess their progress and grasp of this demanding subject. In this new edition, at the end of select chapters, sections are included dedicated to exploring approximate solutions for complex probabilistic problems using simulation techniques. These simulations are conducted using the R software, a powerful tool well-suited for probabilistic simulations due to its extensive collection of built-in functions and numerous specialized libraries designed for various simulation purposes. In the homepage of the book, a chapter, titled "Algorithm-Driven Simulations," is presented in which we delve deeply into the concept of simulation using algorithms exclusively, without being tied to any specific programming language.
A Treatise on the Theory of Invariants
A Treatise on the Theory of Invariants, a classical book, 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.
An Introduction to Panel Data QCA in R
This book discusses and compares four different approaches towards analyzing panel data in QCA. It introduces QCA as a research approach, then discusses the most important assumptions, and steps like set-calibration and theory-testing, and demonstrates each of the four panel data approaches.
Probably the Best Book on Statistics Ever Written
Taking an amusing and digestible look at the usually dry world of probability and statistics, this is the ultimate guide to how you can incorporate them into everyday life, from one of the world's most sought-after experts in game theory. This is the only book you need to become a statistics whizz! Numbers are everywhere - food packaging, weather forecasts, social media, adverts, and more. You can't escape them. But you can learn to understand them - and avoid being fooled! This book breaks down the key fundamentals in statistics in a fun and accessible way so that you can understand the numbers that occupy your life. - Make sense of sports stats - discover who is the greatest scorer of all time - Learn to interpret scientific studies and how they're reported in the media so you're never misled again - Discover tips and tricks to make you a more successful gambler - Explore what role stats has to play in flat-earth conspiracy arguments - Read about misunderstood probabilities in the Sally Clarke and OJ Simpson trials With easy-to-follow explanations, tables, graphs, and real-life examples, this book helps you evaluate your options, calculate your chances of success, and make better decisions.
Maths in Construction
This work is the result of Marcelo Azevedo de Souza's dissertation in natural sciences and maths at the University of Blumenau (FURB) - Blumenau/Santa Catarina - Brazil. The main purpose of this book is to show readers, teachers and students of youth and adult education and ethnomathematics researchers, that the everyday mathematics used in construction can be related to the mathematics taught in schools and that both can go hand in hand in an organised way, with the aim of developing excellence in the teaching and learning of this subject. The subjects chosen in this book are varied and come from the student's everyday life, so they can be applied in any classroom in basic and higher education. The book features a brief introduction, explaining the choice of topic, general and specific objectives, the structure of each chapter, followed by creative and challenging activities, a timetable for application, research methods, data collection, resources to be used, mathematical games for the construction industry, and finally, tips for future application.
Formal Methods Teaching
This book constitutes the proceedings of the 6th International Workshop on Formal Methods Teaching, FMTea 2024, which was held in Milan, Italy, on September 10, 2024. The 7 full papers included in these proceedings were carefully reviewed and selected from 9 submissions. The book also contains one invited talk in full paper length. The papers focus on learning formal methods for the purpose of teaching and self-learning.
Information Theoretic Measures
Communication system is vital for message transmission, affected by noise. Researchers contribute to improving communication. Information theory development is significant, enhanced by C. E. Shannon's work. Shannon model encodes and decodes messages. Researchers generalize information measures for various applications. This book focuses on information theoretic measures, their analysis and applications. Information measures are applied in data mining, including weighted residual information measure. Classification methods and results are compared for improvement. Information theoretic measures in ID3 algorithm find information gain as splitting criteria for data. ID3 algorithm applied to census 2011 data of India to classify attributes into States and Union Territories. Decision tree made using Renyi entropy, rules developed to decide project implementation region. Varma entropy based ID3 algorithm used to analyze health services in India up to 2015. C4.5 algorithm applied on same data with discrete attribute values to develop decision tree. Weighted generalized residual information measure of order α and type β developed as extension of information theoretic measures.
Weighted Morrey Spaces
This monograph is a testament to the potency of the method of singular integrals of layer potential type in solving boundary value problems for weakly elliptic systems in the setting of Muckenhoupt-weighted Morrey spaces and their pre-duals. A functional analytic framework for Muckenhoupt-weighted Morrey spaces in the rough setting of Ahlfors regular sets is built from the ground up and subsequently supports a Calder籀n-Zygmund theory on this brand of Morrey space in the optimal geometric environment of uniformly rectifiable sets. A thorough duality theory for such Morrey spaces is also developed and ushers in a never-before-seen Calder籀n-Zygmund theory for Muckenhoupt-weighted Block spaces. Both weighted Morrey and Block spaces are also considered through the lens of (generalized) Banach function spaces, and ultimately, a variety of boundary value problems are formulated and solved with boundary data arbitrarily prescribed from either scale of space. The fairly self-contained nature of this monograph ensures that graduate students, researchers, and professionals in a variety of fields, e.g., function space theory, harmonic analysis, and PDE, will find this monograph a welcome and valuable addition to the mathematical literature.
Differential Geometry
This textbook offers a different approach to classical textbooks in Differential Geometry. It includes practical examples and over 300 advanced problems designed for graduate students in various fields, such as fluid mechanics, gravitational fields, nuclear physics, electromagnetism, solid-state physics, and thermodynamics. Additionally, it contains problems tailored for students specializing in chemical, civil, and electrical engineering and electronics. The book provides fully detailed solutions to each problem and includes many illustrations to help visualize theoretical concepts. The book introduces Frenet equations for plane and space curves, presents the basic theory of surfaces, and introduces differentiable maps and differentials on the surface. It also provides the first and second fundamental forms of surfaces, minimal surfaces, and geodesics. Furthermore, it contains a detailed analysis of covariant derivatives and manifolds. The book covers many classical results, such as the Lancret Theorem, Shell Theorem, Joachimsthal Theorem, and Meusnier Theorem, as well as the fundamental theorems of plane curves, space curves, surfaces, and manifolds.
Teaching Knowledge and Inclusive Mathematics Education
"Even with the advances in Brazilian legislation related to Inclusive Education, the daily practice of schools and teacher training courses is still a long way from what is desirable. In the specific case of teaching mathematics to deaf students, despite the obligation to have interpreters in schools and the subject of Libras in degree courses, the scenario is not very different. Training teachers to work in this scenario is an urgent task, both in degree courses and in spaces dedicated to continuing education. The purpose of this book, which is the result of qualitative research, is to analyse the possible contributions of an extension course to the mobilization of teaching knowledge related to the inclusion of deaf students in Mathematics classes in regular classes".(...) Viviane C.Costa*
Enhancing Security in Fuzzy Networks Through Efficient Domination
Let G(V, E) be a finite simple connected graph of order m with vertex set V and edge set E. A dominating set S ⊆ V(G) is called an efficiently dominating set if, for every vertex u ∈ V(G), N[u] ∩ S = 1, where N[u] denotes the closed neighborhood of the vertex. Using efficient domination techniques and labeling, we constructed the different types of fuzzy networks. An algorithm has been framed to encrypt and decrypt the secret information present in the network. The mathematical modeling of a strong type of fuzzy network is defined and constructed to elude the burgeoning intruder. Using the study of efficient domination on types of fuzzy graphs, this domination parameter plays a nuanced role in encrypting and decrypting the framed network. The main purpose of types of fuzzy network are encryption and decryption, our contributions to this research is to build a novel combinatorial technique to encrypt and decrypt the built-in fuzzy network with a secret number utilizing effective domination. An illustration with an appropriate secret message is provided, along with the encryption and decryption algorithms.
Statistics and reality in students' daily lives
Statistics is a part of applied mathematics that studies methods for collecting, organising, analysing and interpreting data, since its study is aimed, among other things, at decision-making. So we have to experience it so that we can understand it better without skipping any steps. In this way we will better interpret and consequently improve the skills and competences that, although important, should not be measured only through a written test, but through the application of a concept constructed and experienced by the student in everyday life. Statistics therefore seeks situations in which problem-solving is meaningful for the student and mobilises their cognitive resources. According to the PCN's (2002), the teaching of mathematics can help students develop skills related to representation, comprehension and investigation, as well as socio-cultural contextualisation. This means placing students in a teaching-learning process that values mathematical (statistical) reasoning and also enables the teacher to work on content in an interdisciplinary way and broaden the understanding of its meanings, thus contributing to the formation of knowledge.
Game-Theoretical Models in Biology
Covering the major topics of evolutionary game theory, this book presents both abstract and practical mathematical models of real biological situations. It discusses the static aspects of game theory in a mathematically rigorous way that is appealing to mathematicians. The text is also useful to biologists.
Math Mammoth Grade 8 Answer Keys, Canadian Version
This book includes answers for Math Mammoth Grade 8-A and 8-B student worktexts (Canadian version), for all of the chapter tests, and for the cumulative reviews. The other parts of the curriculum may be purchased separately.
Introduction to Calculus
Introduction to Calculus provides a comprehensive introduction to fundamental concepts in calculus and their applications, covering all of Calculus 1 and some of Calculus 2. The book starts with functions and limits, followed by differential calculus, and then moves on to integral calculus and a brief discussion of differential equations. It ends with the complete solution for a sample exam based on the AP Calculus AB course. Students can access a free, interactive ebook version of the text using a URL provided inside the print version. Further supplemental materials, including videos, practice problems, exercises and quizzes, are available online in the companion Wolfram U course.
Transition to Advanced Mathematics
This unique and contemporary text not only offers an introduction to proofs with a view towards algebra and analysis, a standard fare for a transition course, but also presents practical skills for upper-level mathematics coursework and exposes undergraduate students to the context and culture of contemporary mathematics.
Handbook of Complex Analysis
The Handbook of Complex Analysis will be an entree for advanced undergraduates and beginning graduate students in the subject of complex analysis. The subject of complex analysis of increasing importance. Even the function theory of several complex variables has seen applications in cosmology, geophysics, and engineering.
Introduction to Probability and Statistics
This book aims to be a manual for understanding problems in probability and statistics. The main emphasis is the random variables (discrete and continuous), their distributions, the basics of statistics, the law of large numbers, the central limit theorem, statistical models, least squares estimation, confidence intervals for the mean, testing hypothesis, and statistics with datasets.The book is aimed at junior students in the field of applied mathematics, physics, computer engineering, economics, artificial intelligence, and data science & analytics in science and engineering disciplines.
