Problems & Solutions in Stochastic Calculus with Appln
Problems and Solutions in Stochastic Calculus with Applications exposes readers to simple ideas and proofs in stochastic calculus and its applications. It is intended as a companion to the successful original title Introduction to Stochastic Calculus with Applications (Third Edition) by Fima Klebaner. The current book is authored by three active researchers in the fields of probability, stochastic processes, and their applications in financial mathematics, mathematical biology, and more. The book features problems rooted in their ongoing research. Mathematical finance and biology feature pre-eminently, but the ideas and techniques can equally apply to fields such as engineering and economics.The problems set forth are accessible to students new to the subject, with most of the problems and their solutions centring on a single idea or technique at a time to enhance the ease of learning. While the majority of problems are relatively straightforward, more complex questions are also set in order to challenge the reader as their understanding grows. The book is suitable for either self-study or for instructors, and there are numerous opportunities to generate fresh problems by modifying those presented, facilitating a deeper grasp of the material.
Solitons, Instantons, and Twistors
Most nonlinear differential equations arising in natural sciences admit chaotic behaviour and cannot be solved analytically. Integrable systems lie on the other extreme. They possess regular, stable, and well-behaved solutions known as solitons and instantons. These solutions play important roles in pure and applied mathematics as well as in theoretical physics where they describe configurations topologically different from vacuum. While integrable equations in lower space-time dimensions can be solved using the inverse scattering transform, the higher-dimensional examples of anti-self-dual Yang-Mills and Einstein equations require twistor theory. Both techniques rely on an ability to represent nonlinear equations as compatibility conditions for overdetermined systems of linear differential equations. The book provides a self-contained and accessible introduction to the subject. It starts with an introduction to integrability of ordinary and partial differential equations. Subsequent chapters explore symmetry analysis, gauge theory, vortices, gravitational instantons, twistor transforms, and anti-self-duality equations. The three appendices cover basic differential geometry, complex manifold theory, and the exterior differential system.
Intro to Calcul Varia (4th Ed)
The calculus of variations is one of the oldest subjects in mathematics, and it is very much alive and still evolving. Besides its mathematical importance and its links to other branches of mathematics, such as geometry or differential equations, it is widely used in physics, engineering, economics and biology.This book serves both as a guide to the expansive existing literature and as an aid to the non-specialist -- mathematicians, physicists, engineers, students or researchers -- in discovering the subject's most important problems, results and techniques. Despite the aim of addressing non-specialists, mathematical rigor has not been sacrificed; most of the theorems are either fully proved or proved under more stringent conditions.This new edition offers an entirely new chapter, as well as the addition of several new exercises. The book, containing a total of 147 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels.
Intro to Calcul Varia (4th Ed)
The calculus of variations is one of the oldest subjects in mathematics, and it is very much alive and still evolving. Besides its mathematical importance and its links to other branches of mathematics, such as geometry or differential equations, it is widely used in physics, engineering, economics and biology.This book serves both as a guide to the expansive existing literature and as an aid to the non-specialist -- mathematicians, physicists, engineers, students or researchers -- in discovering the subject's most important problems, results and techniques. Despite the aim of addressing non-specialists, mathematical rigor has not been sacrificed; most of the theorems are either fully proved or proved under more stringent conditions.This new edition offers an entirely new chapter, as well as the addition of several new exercises. The book, containing a total of 147 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels.
Polyadic Transcendental Number Theory
The existence of transcendental numbers was first proved in 1844, by Joseph Liouville. Advances were made by Charles Hermite, proving the transcendence of the number e, and Ferdinand von Lindemann, proving the transcendence of the number π. The consequence of these discoveries was the negative solution to the problem of squaring the circle, which has stood for many years. In the 20th century, the theory of transcendental numbers developed further, with general methods of investigating the arithmetic nature of various classes of numbers. One of these methods is the Siegel-Shidlovskii method, previously used for the so-called E- and G-functions.Polyadic Transcendental Number Theory outlines the extension of the Siegel-Shidlovskii method to a new class of F-series (also called Euler-type series). Analogues of Shidlovskii's famous theorems on E-functions are obtained. Arithmetic properties of infinite-dimensional vectors are studied, and therefore elements of direct products of rings of integer p-adic numbers are considered. Hermite-Pad矇 approximations are used to investigate the values of hypergeometric series with algebraic irrational parameters. Moreover, the book describes how to use Hermite-Pad矇 approximations to obtain results on the values of hypergeometric series with certain transcendental (polyadic Liouville) parameters. Based on recent results, this book contains indications of promising areas in a new field of research. The methods described will allow readers to obtain many new results.
Heat Source and Radiation on MHD Fluid Flow Over a Porous plate
The study of magnetohydrodynamic (MHD) fluid flow has garnered significant attention due to its wide range of applications in engineering, astrophysics, and industrial processes. When considering high-temperature systems, it becomes crucial to understand the impact of thermal radiation and heat sources on the flow characteristics. These factors play a pivotal role in processes such as nuclear reactor cooling, geothermal energy extraction, and in various metallurgical applications.In MHD flows, the interaction between the magnetic field and the electrically conducting fluid introduces complex dynamics, which are further influenced by the presence of a heat source and thermal radiation. The heat source can represent internal heating mechanisms such as chemical reactions or external sources like solar radiation. Thermal radiation, on the other hand, is essential in understanding the energy transport in high-temperature flows.
Domination Numbers and Radius in Trapezoidal Graphs
Trapezoidal graphs, a significant class of intersection graphs, have garnered interest due to their applicability in various real-world scenarios. Defined as intersection graphs of trapezoids between two parallel lines, these graphs are useful in scheduling problems, bioinformatics, and network design.Understanding the relationships between different domination numbers and the radius of a graph can provide deeper insights into its structure and properties. In this context, we explore three specific domination numbers: the Roman domination number, the total domination number, and the distance-2 domination number. These parameters offer different ways of measuring how subsets of vertices can influence or dominate the entire graph.
Journal of Applied Logics. IfCoLog Journal of Logics and their Applications. Volume 11, number 4, August 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 Polls Weren't Wrong
This book will equip readers with the tools to navigate the mismatch of expectations. It is not intended to replace more technical applications of statistics but is accessible to those interested in learning about how poll data should be understood.
Fuzzy Sets Applications, Methodological Approaches, and Results
No detailed description available for "Fuzzy Sets Applications, Methodological Approaches, and Results".
Landau Equation, Boltzmann-type Equations, Discrete Models, and Numerical Methods
This two-volume monograph is a comprehensive and up-to-date presentation of the theory and applications of kinetic equations. The second volume covers discrete velocity models of the Boltzmann equation, results on the Landau equation, and numerical (deterministic and stochastic) methods for the solution of kinetic equations.
Artificial Intelligence in Pancreatic Disease Detection and Diagnosis, and Personalized Incremental Learning in Medicine
This volume constitutes the refereed proceedings of the First International Workshop on Artificial Intelligence in Pancreatic Disease Detection and Diagnosis, AIPAD 2024 and the First International Workshop on Personalized Incremental Learning in Medicine, PILM 2024, held in conjunction with MICCAI 2024, in Marrakesh, Morocco, in October 2024. The 8 full papers included in these proceedings were carefully reviewed and selected from 9 submissions. They were organized in topical sections as follows: artificial intelligence in pancreatic disease detection and diagnosis; and personalized incremental learning in medicine.
School assessment from the point of view of maths teachers and students
This work brings together the conceptions of school assessment held by public school maths teachers working in the final grades of primary school, as well as students' views on school assessment in the final grades of primary school in the public school system in the state of Paran獺. The educational institutions where the questionnaires were administered were spread across various regions of Paran獺.
Study of the impact of factors on returns on financial assets
This dissertation is an internship report for Typhoon Partner, a UK-based proprietary investment firm specializing in the development of quantitative investment strategies. We focus on intra-sector and inter-sector returns relative to the fundamental characteristics of US equities. After a thorough analysis of the basic concepts of risk and the issues involved in risk management, we will first look at the various risk measures associated with each sector (VaR, Expected Shortfall, etc.). Secondly, using the relevant literature, we apply a statistical model to explain cross-asset returns in the equity universe using the financial ratios selected, with the aim of studying the performance of equities within a sector and between several sectors. Finally, we look at the comparison of investment strategies and portfolio insurance.
Writers of the Cold
This study analyses the literary construction of space. More specifically, we analyse the artistic construction of the city and the means used to give it high relevance in the text. To this end, we chose the work of Argentinian writer Jorge Luis Borges, published in the 1920s and 1930s. We also analysed how Vitor Ramil (a reader and self-confessed admirer of Borges) constructs his own Satolep from the city of Pelotas. For this analysis, we used his novels that thematise the city: Pequod (1999) and Satolep (2008).
Introduction to the Spectral Theory of Operators in Spaces with an Indefinite Metric
No detailed description available for "Introduction to the Spectral Theory of Operators in Spaces with an Indefinite Metric".
Singularly Perturbed Differential Equations
No detailed description available for "Singularly Perturbed Differential Equations".
Mathematical Modeling
The co-infection of tuberculosis (TB) and malaria poses significant challenges for public health, particularly in regions where both diseases are endemic. This study presents a mathematical model to elucidate the dynamics of TB and malaria co-infection, considering the influence of interference treatments and vaccination resistance. The model incorporates compartmental dynamics for susceptible, latent TB-infected, active TB-infected, malaria-exposed, symptomatic malaria-infected, co-infected, and recovered individuals. Additionally, it integrates mechanisms of interference between treatments for TB and malaria, as well as compartments representing vaccinated individuals and those resistant to vaccination.
Study on Posbist Reliability Theory and Its Applications
"Imprecision" here is meant in the sense of vagueness rather than the lack of knowledge about the value of a parameter as in tolerance analysis. Fuzzy set theory provides a strict mathematical framework (there is nothing fuzzy about fuzzy set theory!) in which vague conceptual phenomena can be precisely and rigorously studied. It can also be considered as a modeling language well suited for situations in which fuzzy relations, criteria, and phenomena exist. Fuzziness has so far not been defined uniquely semantically, and probably never will. It will mean different things, depending on the application area and the way it is measured. This book entitled "Study on Posbist Reliability Theory and its Applications" present some important aspects Fuzzy Set theory and some recent results in its development. This embodies four chapters . The first chapter consists of an introduction on fuzzy set theory and different ideas with definitions that lead to the growth and extension of Fuzzy Set Theory. In second chapter we describe fuzzy variables. The third chapter consists of study on Posbist systems. At last chapter, we have presented a brief description on application of Fuzzy Set Theory.
Linear Algebra for Teaching Activities
In this second volume of Linear Algebra you will find topics related to Matrices and Determinants, making reference to great authors of books focused on linear algebra, such as Baldor (Baldor, 2019) with authorships on Algebra, and other expert authors on the subject (David C. Lay, Ron Larson, Grossman, Estrada, Guzm獺n, among others) that is why, the topics related to Matrices and Determinants; are essential for the application in real life, with the demonstration of exercises related to the methods and an annex of proposed exercises for practice.
Laplace Substitution Method
There are several methods to solve linear and nonlinear partial differential equations. However, these methods are not effective for solving nonlinear partial differential and integral equations involving mixed partial derivatives. Therefore, we focused on developing a new method to obtain exact solutions for these equations with fewer computations and in a shorter time. This method is called the Laplace Substitution Method. We derived the idea for this method from the Adomian Decomposition Method (ADM) and the Differential Transform Method (DTM). In this book, we address initial value problems of nonlinear partial differential and integral equations involving mixed partial derivatives of any order using our developed method, the Laplace Substitution Method. This study includes both linear and nonlinear partial differential and integral equations with mixed partial derivatives.
The Perfect Handbook for Science
Embark on a captivating journey through the vast realms of science with our comprehensive handbook, meticulously crafted to be your perfect companion. Whether you're a curious novice or a seasoned enthusiast, this book is designed to unlock the mysteries of the universe and deepen your understanding of the natural world. Discover the wonders of physics, unravel the complexities of chemistry, explore the intricacies of biology, and delve into the mysteries of astronomy and earth sciences. Each chapter is expertly curated to provide clear explanations, captivating illustrations, and practical insights into key scientific concepts. Navigate effortlessly through our alphabetical index, ensuring quick access to a wealth of topics-from Acids and Bases to Quantum Mechanics, from Genetics to Plate Tectonics. Thematic groupings further enhance accessibility, guiding you through interconnected fields such as ecology, space exploration, and mathematical foundations. So lets take a leap of faith towards this profound and legible book.
Maths and Technologies in Teaching Practice
This book shows through existing literature how information and communication technologies (ICT) are used as a form of production in the school environment and how those involved in the process make use of these tools in teaching practice. As it is a new tool, it is necessary to encourage older teachers to use these new means in order to achieve excellence, as the Internet can help with guided school research, as well as the use of numerous software programmes to support teachers and students. The book demonstrates the use of ICT and seminars in maths and other subjects.
Likelihood Methods in Survival Analysis
Many conventional survival analysis methods, such as the Kaplan-Meier method for survival function estimation and the partial likelihood method for Cox model regression coefficients estimation, were developed under the assumption that survival times are subject to right censoring only. However, in practice, survival time observations may include interval-censored data, especially when the exact time of the event of interest cannot be observed. When interval-censored observations are present in a survival dataset, one generally needs to consider likelihood-based methods for inference. If the survival model under consideration is fully parametric, then likelihood-based methods impose neither theoretical nor computational challenges. However, if the model is semi-parametric, there will be difficulties in both theoretical and computational aspects.Likelihood Methods in Survival Analysis: With R Examples explores these challenges and provides practical solutions. It not only covers conventional Cox models where survival times are subject to interval censoring, but also extends to more complicated models, such as stratified Cox models, extended Cox models where time-varying covariates are present, mixture cure Cox models, and Cox models with dependent right censoring. The book also discusses non-Cox models, particularly the additive hazards model and parametric log-linear models for bivariate survival times where there is dependence among competing outcomes.Features Provides a broad and accessible overview of likelihood methods in survival analysis Covers a wide range of data types and models, from the semi-parametric Cox model with interval censoring through to parametric survival models for competing risks Includes many examples using real data to illustrate the methods Includes integrated R code for implementation of the methods Supplemented by a GitHub repository with datasets and R code The book will make an ideal reference for researchers and graduate students of biostatistics, statistics, and data science, whose interest in survival analysis extend beyond applications. It offers useful and solid training to those who wish to enhance their knowledge in the methodology and computational aspects of biostatistics.
Statistical Methods Using SPSS
Statistical Methods Using SPSS provides a practical approach for better understanding of the advanced statistical concepts that are applied in business, economics, epidemiology, public health, agriculture and other areas of data analytics.
Markov Decision Problems with Countable State Spaces
No detailed description available for "Markov Decision Problems with Countable State Spaces".
The World through the Lens of Mathematics
This amazing book aims to shatter the barrier between students and mathematics. By encouraging students to look at mathematics from a different perspective, build a bridge between their surroundings and mathematics and, at the same time, enrich them with the culture, history, customs, and geography of different parts of the world.
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.
Math for English Majors
In this trailblazing work from the internet's most empathetic math teacher, Ben Orlin unravels the secrets behind the world's most confounding language. Math, it is said, is the "universal language." But if a language brings people together, why does math make so many of us feel so alone? In Math for English Majors, bestselling author Ben Orlin (Math with Bad Drawings) offers fresh insights for the mathematically perplexed and mathematical masters alike. As Orlin reveals, the "universal language" is precisely that: a language. It has nouns (numbers), verbs (calculations), and grammar (algebra). It has funny idioms ("exponential"), quirky etymologies ("squaring"), and peculiar ambiguities ("PEMDAS"). It even has its own form of literature, with equations ranging from the simple wisdom of A2 + B2 = C2 to the startling profundity of eπi + 1 = 0. Along the way, he shares relatable stories of his own mathematical misunderstandings and epiphanies, as well as the trials and triumphs of his students. And, as always, he sheds further light and levity on the subject with his inept--yet strangely effective--drawings.
Mathematical Modelling and Numerical Analysis in Electrical Engineering
This special issue focuses on the mathematical modelling and numerical analysis methods employed in electrical engineering applications. The 11 manuscripts included utilize various analytical and computational techniques such as parameter modelling methods and numerical analyses to solve engineering problems in domains such as electric motors, power systems. One of these papers investigates line-start permanent magnet synchronous motors and explores the starting performance when parameters such as the supply voltage and cable length are varied; in addition, simulation and experimental methods are employed to characterize the motor behavior. Another study employs the finite element modelling technique to study the electric field distributions for lightning rod design. Additionally, optimization techniques such as the Nelder-Mead algorithm are applied to optimize a synchronous homopolar motor. Mathematical and numerical analyses of the induction and flux-switching motors are also presented. Transient simulations of the starting and synchronization processes, which incorporate the lumped parameter motor models of a line-start permanent magnet synchronous motor, are also undertaken. Other studies employ accurate models that have been developed for adjustable permanent magnet couplers, external magnetic fields and switched reluctance motors. Validation using finite element analyses and experiments demonstrates the feasibility and superiority of the proposed modelling approaches. The broad range of topics addressed reflects the extensive application of analytical techniques in electrical engineering research.
AI Empowered Sentiment Analysis
With the popularity of the social media, a large amount of user-generated content, such as comments, is emerging, which is crucial for all industries. Recently, the development of deep learning and computing power have made it possible to handle complex data. However, there are still some including (but are not limited to): (1) How can we construct a multi-modal sentiment analysis framework? (2) How can we accurately extract aspect-sentiment quadruples? (3) How can we generate fine-grained sentiment text? To tackle these challenges, this Special Issue focuses on multi-modal sentiment analysis, aspect-sentiment extraction, interpretability, and so on. In the following, we briefly summarize the selected two papers that we believe will make significant contributions. (1) "Generative Aspect Sentiment Quad Prediction with Self-Inference Template" by Li et al., considered that current research predominantly confines templates to single sentences, limiting the model's reasoning opportunities. Therefore, the authors introduce a self-inference template (SIT) to guide the model in thoughtful reasoning. (2) "Interpretability in Sentiment Analysis: A Self-Supervised Approach to Sentiment Cue Extraction" by Sun et al., proposes a new sentiment cue extraction (SCE) self-supervised framework, aimed at improving the interpretability of models. In conclusion, we extend our heartfelt appreciation to all the authors and reviewers who selflessly put their energy to ensure the successful completion of this Special Issue.
Advanced Guidance and Control of Flight Vehicle
The application of advanced guidance and control to missiles, hypersonic vehicles, and unmanned aerial vehicles has long represented a research hotspot in academia, and the development of more advanced and intelligent guidance and control technology for flight vehicles has become a focus of research in recent years. In this reprint, studies on the mathematical theory and application of flight vehicle guidance and control are presented. This includes trajectory optimization, online planning, advanced intermediate guidance theoretical methods, terminal guidance theoretical methods, intercept guidance and pursuit and escape guidance, and other topics.
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.
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.
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.
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.
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.
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.
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.
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.
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).
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.
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.
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.
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.
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.
