Metrical and Ergodic Theory of Continued Fraction Algorithms
This monograph presents the work of the authors in metrical theory of continued fractions in the last two decades. The monograph cuts a particular path through this extensive theory and describes the theory in its current form for three families of continued fractions, namely, θ-continued fractions, N-continued fractions, and generalized R矇nyi continued fractions. The book systematically lays out the required preliminaries, making the book easy to read. This monograph provides a solid introduction into the theory of continued fractions. The book is intended for researchers in metrical theory, as well as advanced graduate students and mathematicians interested in this field.
The Vedic Math Bible
The Vedic Math Way is more than a guide to faster calculations-it's a revolutionary journey into the timeless intelligence of ancient Indian mathematics, reimagined for today's learners, educators, and problem-solvers. Whether you're a student aiming to ace competitive exams, a teacher seeking innovative methods to spark numerical intuition, or an adult wishing to rekindle mental sharpness, this book delivers powerful techniques that are as practical as they are profound.Rooted in the 16 foundational Sutras of Vedic Mathematics, this book unveils a system that fosters mental clarity, speed, flexibility, and confidence-not by memorisation, but through intuitive insight. It breaks down complex arithmetic into effortless steps, nurtures logical thinking through pattern recognition, and builds numerical literacy without dependence on calculators or rote learning.What makes this book essential is its structure: every chapter is crafted to demystify the principles, offer real-world applications, and develop scalable skills through practice drills, brain games, and strategy frameworks tailored for timed tests and daily use. From basic operations to Olympiad-level challenges, the content evolves with the reader-making it a true "from beginner to master" experience.This book will be a game-changer for: Students preparing for competitive exams (SAT, GMAT, GRE, CAT, Olympiads, etc.)Educators looking to enrich classrooms with dynamic, ancient-meets-modern methodologyParents supporting their children's learning with logic-based strategiesLifelong learners who want to sharpen their minds and rediscover joy in numbersIn a world obsessed with shortcuts, The Vedic Math Way offers something deeper-a mindset of mastery. It's not just about how fast you solve; it's about how clearly you think. Whether you're battling number anxiety or aiming for mental agility, this book provides the tools, the history, and the roadmap to awaken the inner mathematician in you.
Probability, Statistics, and Reliability for Engineers and Scientists
Virtually every engineer and scientist must be able to collect, analyze, interpret, and properly use vast arrays of data. This means acquiring a solid foundation in the methods of data analysis and synthesis. Understanding the theoretical aspects is important, but learning to properly apply the theory to real-world problems is essential.The goal of this popular and proven book is to introduce the fundamentals of probability, statistics, reliability, and risk methods to engineers and scientists for the purpose of data and uncertainty analysis and modeling in support of decision-making.The primary objectives to the author's approach include: (1) introducing probability, statistics, reliability, and risk methods to students and practicing professionals in engineering and the sciences; (2) emphasizing the practical use of these methods; and (3) establishing the limitations, advantages, and disadvantages of the methods. The book was developed with an emphasis on solving real-world technological problems that engineers and scientists are asked to solve as part of their professional responsibilities.Upon graduation, engineers and scientists must have a solid academic foundation in methods of data analysis and synthesis, as the analysis and synthesis of complex systems are common tasks that confront even entry-level professionals.The underlying theory, especially the assumptions central to the methods, is presented, but then the proper application of the theory is presented through realistic examples, often using actual data. Every attempt is made to show that methods of data analysis are not independent of each other. Instead, we show that real-world problem-solving often involves applying many of the methods presented in different chapters.Probability, Statistics, and Reliability for Engineers and Scientists, here in its fourth edition, is a very popular textbook. Ultimately, readers will find its content of great value in problem-solving and decision-making, particularly in practical applications.
Causal Analysis for Climate Study
This book offers the theory of causal analysis and its applications. The authors have developed this book in relation its applications to four climatological phenomena, to prove the theory of causal analysis in time sequential data analysis.
Bridging Eigenvalue Theory and Practice - Applications in Modern Engineering
Computational Intelligence and Industrial Applications
This two-volume set CCIS 2465-2466, constitutes of the proceedings of 11th International Symposium on Computational Intelligence and Industrial Applications, ISCIIA 2024, held in Beijing, China, during November 1-5, 2024. The 55 full papers and 5 short papers included in this volume were carefully reviewed and selected from 135 submissions. The topics cover the following fields connected to computational intelligence and intelligent informatics: intelligent information processing, pattern recognition and computer vision, intelligent optimization and decision-making, advanced control, multi-agent systems, robotics and various applications of computational intelligence methods such as neural networks, fuzzy reasoning, evolutionary computing, machine learning and deep learning.
AI in Banking
Big data and artificial intelligence (AI) cannot remain limited to academic theoretical research. It is crucial to utilize them in practical business scenarios, enabling cutting-edge technology to generate tangible value. This book delves into the application of AI from theory to practice, offering detailed insights into AI project design and code implementation across eleven business scenarios in four major sectors: retail banking, e-banking, bank credit, and tech operations. It provides hands-on examples of various technologies, including automatic machine learning, integrated learning, graph computation, recommendation systems, causal inference, generative adversarial networks, supervised learning, unsupervised learning, computer vision, reinforcement learning, fuzzy control, automatic control, speech recognition, semantic understanding, Bayesian networks, edge computing, and more. This book stands as a rare and practical guide to AI projects in the banking industry. By avoiding complex mathematical formulas and theoretical analyses, it uses plain language to illustrate how to apply AI technology in commercial banking business scenarios. With its strong readability and practical approach, this book enables readers to swiftly develop their own AI projects.
Combining Expert Knowledge and Deep Learning with Case-Based Reasoning for Predictive Maintenance
If a manufacturing company's main goal is to sell products profitably, protecting production systems from defects is essential and has led to vast documentation and expert knowledge. Industry 4.0 has facilitated access to sensor and operational data across the shop floor, enabling data-driven models that detect faults and predict failures, which are crucial for predictive maintenance to minimize unplanned downtimes and costs. Commonly, a universally applicable machine learning (ML) approach is used without explicitly integrating prior knowledge from sources beyond training data, risking incorrect rediscovery or neglecting already existing knowledge. Integrating expert knowledge with ML can address the scarcity of failure examples and avoid the learning of spurious correlations, though it poses technical challenges when combining Semantic Web-based knowledge graphs with neural networks (NNs) for time series data. For his research, a physical smart factory model with condition monitoring sensors and a knowledge graph was developed. This setup generated the required data for exploring the integration of expert knowledge with (Siamese) NNs for similarity-based fault detection, anomaly detection, and automation of root cause analysis. Patrick Klein applied symbolic and sub-symbolic AI techniques, demonstrating that integrating expert knowledge with NNs enhances prediction performance and confidence in them while reducing the number of learnable parameters and failure examples.
Image Schema Theory and Mathematical Cognition
This book uses blending theory in math cognition, and assesses the main aspect of this theory, called image schema theory. Applied work in math pedagogy has used this theory, but no work has assessed its validity. This book provides an overall assessment of the theory with regard to its validity in the study of math cognition. Overall, this book presents image schema theory as it has evolved today to mathematicians, cognitive scientists, and math educators, deriving from it any concrete implications for modeling math in computer science and, on the other side, for making math pedagogy more effective.
Python for Mathematics
Python for Mathematics introduces readers to effective methods for doing mathematics using the Python programming language
Set Theory
Contemporary students of mathematics differ considerably from those of half a century ago. In spite of this, many textbooks written and now considered to be "classics" decades ago are still prescribed for students today. These texts are not suitable for today's students. This text is meant for and written to today's mathematics students.
Floating Point Numerics for Games and Simulations
Floating point is ubiquitous in computers, where it is the default way to represent non-integer numbers. However, few people understand it. We all see weird behavior sometimes, and many programmers treat it as a mystical and imprecise system of math that just works until it sometimes doesn't.
Statistical Inference Via Data Science
Offers a comprehensive guide to learning statistical inference with data science tools widely used in industry, academia, and government. Ideal for those new to statistics or looking to deepen their knowledge, this edition provides a clear entry point into data science and modern statistical methods.
Analytic Methods of Spectral Representations of Non-Selfadjoint (Non-Unitary) Operators
Indirect Methods of Data Collection and Analysis from Surveys
Mathematical Study for Approximation Models in Radiation Hydrodynamics
Computational Structural Bioinformatics
This book constitutes the proceedings of the Computational Structural Bioinformatics Workshop, CMSB 2024, which took place in Boston, MA, USA, on November 16, 2024. The 7 papers presented in this book were carefully reviewed and selected for inclusion in the proceedings. They deal with relevant problems in classification, modeling and analyzing protein structures and complexes.
Special Integrals
Targeted to upper-undergraduate and graduate students of mathematics, this book discusses special integrals and their applications in finding certain series sums. It starts with the differentiation and the integration methods for summing a series that is applied to find the sum of various binomial and trigonometrical series. It also discusses methods to find the sum of series involving the variables having exponents in integral or fractional powers of 2. Complex variables are freely used to derive several theorems, which result in several special integrals and series sums. Bessel coefficients, Bessel functions, and their various generalizations are also discussed in the book. As a particular case of generalized Bessel functions, pseudo-exponential functions are defined, and their properties are studied in the book. Broadly divided into two parts--Part 1 and Part 2--the book has six chapters in Part 1, whereas Part 2 has six chapters on solutions to the problems in Part 1. To understand the topics in the book, the minimum prerequisites are the knowledge of calculus, complex analysis, and Fourier series.
The Krasnoselskii-Mann Method for Common Fixed Point Problems
This book delves into the intricate world of fixed point theory, focusing on the Krasnoselskii-Mann method to tackle common fixed point problems within a finite family of quasi-nonexpansive mappings in hyperbolic metric spaces. By exploring various iterative algorithms, including the Cimmino algorithm and dynamic string-averaging methods, this volume offers a comprehensive study of convergence and approximate solutions amidst computational errors. Key concepts such as W-hyperbolic spaces, convex combinations, and set-valued inclusions are meticulously examined. The author presents a detailed analysis of iterative methods, highlighting their effectiveness in solving complex fixed-point problems. Readers will encounter critical discussions on the behavior of exact and inexact iterates, the role of computational errors, and innovative approaches like remotest set control. This book invites readers to engage with challenging questions about convergence and solution accuracy in mathematical spaces. Ideal for researchers and scholars in mathematics and related fields, this book provides valuable insights into advanced iterative methods for solving fixed-point problems. Whether you are a mathematician specializing in nonlinear analysis or an academic exploring optimization theory, this volume is an essential resource for understanding the latest developments in fixed point theory.
Lectures on Mathematics for Economic and Financial Analysis
Linear Models with R
Linear Models with R, Third Edition explains how to use linear models in physical science, engineering, social science, and business applications. The book incorporates several improvements that reflect how the world of R has expanded since the publication of the second edition.
The Secret World of Flexagons
The hexaflexagon is a folded paper strip of colored triangles that has long delighted people with how it "magically" changes its appearance when "flexed". This hands-on, comprehensive book goes beyond the hexaflexagon, the standard version of this folded puzzle, exponentially expanding the barely explored field of flexagons as it brings new options and fresh insights to light.● Learn over a dozen different flexes, and make dozens of different flexagons with the aid of step-by-step illustrated directions and templates to copy and print.● Delve into the internal structure of flexagons and discover a universal way to describe and predict their behavior.● Learn how to create your own custom flexagons with a special computer program.● Understand how flexagons are connected to group theory, computer science, and topology.● Have fun decorating flexagons and make flexagon books, puzzles, pop-ups, mazes, and more.Written in a clear, easy-to-understand, and conversational style and enhanced with challenges and tips to broaden your flexagon skills and spark creativity, The Secret World of Flexagons: Fascinating Folded Paper Puzzles is a must for flexagon enthusiasts, teachers, students, libraries, mathematicians, and everyone who loves to solve a good puzzle.
Applied Survey Data Analysis
Building on the wealth of material on practical approaches to descriptive analysis and regression modeling from the first and second editions, this third edition further expands the topics covered and presents more step-by-step examples of modern approaches to the analysis of survey data using the newest statistical software procedures.
Biofuel Production, Performance, and Emission Optimization
