Advanced Exponents and Powers volume 1
This book covers over 1000+ problems of practice in the core areas of 1. Exponents Multiplication2. Exponents Division3. Exponents Powers4. Scientific Notations5. Multiplying Scientific Notations6. Dividing Scientific Notations7. Plotting Exponential Graphs8. Writing Exponential EquationsVisit www.math-knots.com for more books.Questions? e-mail: mathknots.help@gmail.com Mastering the concepts is a very important part of the academic excellence of students.1000+ problems to practice and master the concepts
Hyers-Ulam Stability of Function Equations and Fractional Differential Equations
The main purpose of this book is to present some of the old and recent results on Hyers-Ulam stability of function equations and differential equations in Banach spaces, quasi-Banach spaces, F-spaces and group. The book provides a survey of both the latest and new results especially on the following topics: (1)Stability theory for several new functional equations in Banach spaces.(2)Stability of some functional equations and some properties of groups.(3)Hyers-Ulam Stability of functional differential equations and partial differential equations.(4)Stability of nonlinear fractional differential equations.(5)Stability of differential equations on time scales
Integers
This book reinforces the concepts of integers. This is the basic block for pre-algebra and Algebra 1. 1. Addition of Integers2. Subtraction Integers3. Multiplication of Integers4. Division of IntegersMastering the concepts is a very important part of the academic excellence of students.1000+ PROBLEMS TO PRACTICE AND MASTER THE CONCEPTS
Whole Numbers
This book reinforces the concepts of whole numbers. These are some of the basic blocks for mastering elementary math.1) Additions2) Subtractions3) Multiplications4) Divisions5) Rounding the Numbers6) Write in words and numbersMastering the concepts is a very important part of the academic excellence of students.1000+ problems to practice and master the concepts
Mathematical Analysis in Interdisciplinary Research
This contributed volume provides an extensive account of research and expository papers in a broad domain of mathematical analysis and its various applications to a multitude of fields. Presenting the state-of-the-art knowledge in a wide range of topics, the book will be useful to graduate students and researchers in theoretical and applicable interdisciplinary research. The focus is on several subjects including: optimal control problems, optimal maintenance of communication networks, optimal emergency evacuation with uncertainty, cooperative and noncooperative partial differential systems, variational inequalities and general equilibrium models, anisotropic elasticity and harmonic functions, nonlinear stochastic differential equations, operator equations, max-product operators of Kantorovich type, perturbations of operators, integral operators, dynamical systems involving maximal monotone operators, the three-body problem, deceptive systems, hyperbolic equations, strongly generalized preinvex functions, Dirichlet characters, probability distribution functions, applied statistics, integral inequalities, generalized convexity, global hyperbolicity of spacetimes, Douglas-Rachford methods, fixed point problems, the general Rodrigues problem, Banach algebras, affine group, Gibbs semigroup, relator spaces, sparse data representation, Meier-Keeler sequential contractions, hybrid contractions, and polynomial equations. Some of the works published within this volume provide as well guidelines for further research and proposals for new directions and open problems.
Mathematical Essays and Recreations
Mathematical Essays and Recreations, has been acknowledged as a major work throughout human history, and we have taken precautions to assure its preservation by republishing this book in a modern manner for both present and future generations. This book has been completely retyped, revised, and reformatted. The text is readable and clear because these books are not created from scanned copies.
Fractional Calculus on Special Functions
The subject of fractional calculus has applications in diverse and widespread fields of engineering and science such as electromagnetics, viscoelasticity, fluid mechanics, electrochemistry, biological population models, optics, and signals processing. It has been used to model physical and engineering processes that are found to be best described by fractional differential equations. The fractional derivative models are used for accurate modeling of those systems that require accurate modeling of damping. In these fields, various analytical and numerical methods including their applications to new problems have been proposed in recent years. In the present book, we present some fractional derivatives, integrals and solutions of fractional differential equations.
Network Models for Data Science
This text on the theory and applications of network science is aimed at beginning graduate students in statistics, data science, computer science, machine learning, and mathematics, as well as advanced students in business, computational biology, physics, social science, and engineering working with large, complex relational data sets. It provides an exciting array of analysis tools, including probability models, graph theory, and computational algorithms, exposing students to ways of thinking about types of data that are different from typical statistical data. Concepts are demonstrated in the context of real applications, such as relationships between financial institutions, between genes or proteins, between neurons in the brain, and between terrorist groups. Methods and models described in detail include random graph models, percolation processes, methods for sampling from huge networks, network partitioning, and community detection. In addition to static networks the book introduces dynamic networks such as epidemics, where time is an important component.
Visual Category Theory, CoPart 3
This CoPart is a dual complement to Visual Category Theory Brick by Brick, Part 3. The original series translated abstract categorical concepts into the language of LEGO(R) bricks, and the CoPart series implement the opposite way of translating brick constructions to the standard diagram language of category theory that should benefit comprehension of definitions. Since usual categorical diagrams are black and white and occupy less space on paper, CoParts include additional color-enhanced diagrams in the spirit of brick constructions when arrow source and target parts use different colors. These CoParts from CoSeries (named after opposite categories with reversed arrows) keep the same 1-to-1 page correspondence between Parts and CoParts. Page layout is also similar: location of explanatory notes (written using standard mathematical notation) is the same - only bricks are replaced by letters, dots, and arrows. Therefore, this CoSeries can be used independently from the original series or together. The third CoPart covers adjoint functors, diagram shapes and categories, cones and cocones, limits and colimits, pullbacks and pushouts.
Optimization of Integer/Fractional Order Chaotic Systems by Metaheuristics and Their Electronic Realization
The book describes the application of different numerical methods to simulate integer/fractional-order chaotic systems. These methods are used within optimization loops to maximize positive Lyapunov exponents, Kaplan-Yorke dimension, and entropy.
Algebra II for Beginners
Algebra II for Beginners provides students with the essential tools and skills necessary for success in Algebra II courses. This comprehensive guide includes hundreds of examples, over 1,500 skill-building exercises, and two practice tests to ensure thorough preparation for the Algebra II final exam. It will help improve math abilities, increase confidence, and sharpen problem-solving skills. Algebra II for Beginners offers complete coverage of all Algebra II concepts and aligns with national and state standards. The dynamic design and interactive activities make learning engaging and concrete, while targeted practices build essential skills. All exercise solutions are included, allowing students to check their understanding and progress.This comprehensive textbook for Algebra II is the perfect resource for students looking to review core content, refine their math skills, and achieve their best results on the Algebra II course. Key Features of Algebra II for Beginners: In-Depth Understanding: The book provides the essential tools and skills necessary for success in Algebra II courses, presenting hundreds of examples and over 1,500 skill-building exercises to ensure comprehensive preparation for the Algebra II final exam.Boost Confidence and Skills: This guide is designed to enhance math abilities, increase confidence, and sharpen problem-solving skills, ultimately leading to improved academic performance.Comprehensive Coverage: All Algebra II concepts are thoroughly covered in alignment with national and state standards.Engaging and Interactive: The book's dynamic design and interactive activities make learning engaging and concrete. It turns abstract concepts into tangible knowledge, making learning more enjoyable and effective.Targeted Practices: The book includes targeted practices that help build essential skills. Students can immediately apply what they have learned, thereby reinforcing understanding.Solutions Provided: All exercise solutions are included, allowing students to check their understanding and monitor their progress.Perfect for Review and Refinement: This comprehensive textbook for Algebra II is ideal for students looking to review core content, refine their math skills, and achieve their best results on the Algebra II course.Suitable for Self-Study and Classroom Use: Algebra II for Beginners offers a comprehensive approach to excelling in Algebra II, whether studying individually or being used as a classroom resource.Digital Support: The book includes a unique online resource feature. For each topic covered, a QR code and link are provided, directing to a web page that offers further information, supplementary exercises, and explanatory videos. This digital integration enhances understanding and caters to various learning styles.Full-Length Practice Tests: Two full-length Algebra II practice tests are provided at the end of the book. These tests simulate the format and difficulty of the actual exam, helping students gauge their readiness, identify areas of improvement, and build confidence for their Algebra II final exam.This comprehensive textbook for Algebra II is the perfect resource for students looking to review core content, refine their math skills, and achieve their best results on the Algebra II course. Ideal for both self-study and classroom use, Algebra II for Beginners offers a comprehensive approach to excelling in Algebra II.
Gini Inequality Index
Gini Inequality Index: Methods and Applications features original high-quality peer-reviewed chapters prepared by internationally acclaimed researchers.
Differential Geometry and Its Visualization
This book is suitable for graduate level courses in differential geometry, serving both students and teachers. It can also be used as a supplementary reference for research in mathematics and the natural and engineering sciences.
Advanced Problem Solving Using Maple
The advanced text covers dynamical systems, single variable and multi-variable optimization, linear algebra, advanced model fitting techniques, game theory, and multi-attribute decision processes.
Lateral Solutions to Mathematical Problems
This book offers a fresh approach to mathematical problem solving via lateral thinking. This book is appropriate for interested high school students, undergraduates and postgraduates, looking for relief from technical material and also looking for insight into the methodology of mathematics.
Advanced Calculus
Advanced Calculus: Theory and Practice, Second Edition offers a text for a one- or two-semester course on advanced calculus or analysis. The text improves students' problem-solving and proof-writing skills, familiarizes them with the historical development of calculus concepts, and helps them understand the connections among different topics. The book explains how various topics in calculus may seem unrelated but have common roots. Emphasizing historical perspectives, the text gives students a glimpse into the development of calculus and its ideas from the age of Newton and Leibniz to the twentieth century. Nearly 300 examples lead to important theorems.Features of the Second Edition: Improved Organization. Chapters are reorganized to address common preferences.Enhanced Coverage of Axiomatic Systems. A section is added to include Peano's system of axioms for the set of natural numbers and their use in developing the well-known properties of the set N. Expanded and Organized Exercise Collection. There are close to 1,000 new exercises, many of them with solutions or hints. Exercises are classified based on the level of difficulty. Computation-oriented exercises are paired and solutions or hints provided for the odd-numbered questions.Enrichment Material. Historical facts and biographies of over 60 mathematicians.Illustrations. Thirty-five new illustrations are added in order to guide students through examples or proofs.About the Author: John Srdjan Petrovic is a professor at Western Michigan University.
Real-Variable Theory of Hardy Spaces Associated with Generalized Herz Spaces of Rafeiro and Samko
A Full Axiomatic Development of High School Geometry
This textbook provides a full and complete axiomatic development of exactly that part of plane Euclidean geometry that forms the standard content of high school geometry. It begins with a set of points, a measure of distance between pairs of points and ten simple axioms. From there the notions of length, area and angle measure, along with congruence and similarity, are carefully defined and their properties proven as theorems. It concludes with a proof of the consistency of the axioms used and a full description of their models. It is provided in guided inquiry (inquiry-based) format with the intention that students will be active learners, proving the theorems and presenting their proofs to their class with the instructor as a mentor and a guide.The book is written for graduate and advanced undergraduate students interested in teaching secondary school mathematics, for pure math majors interested in learning about the foundations of geometry, for faculty preparing future secondary school teachers and as a reference for any professional mathematician. It is written with the hope of anchoring K-12 geometry in solid modern mathematics, thereby fortifying the teaching of secondary and tertiary geometry with a deep understanding of the subject.
Spatial Econometric Methods in Agricultural Economics Using R
The book describes methods and techniques of spatial data and its use in monitoring agricultural resources, farms management and regional markets. Spatial econometrics models for different data types relevant to statistical units adopted in typical agricultural economics analyses, are introduced.
Essential Mathematics for Undergraduates
This textbook covers topics of undergraduate mathematics in abstract algebra, geometry, topology and analysis with the purpose of connecting the underpinning key ideas. It guides STEM students towards developing knowledge and skills to enrich their scientific education. In doing so it avoids the common mechanical approach to problem-solving based on the repetitive application of dry formulas. The presentation preserves the mathematical rigour throughout and still stays accessible to undergraduates. The didactical focus is threaded through the assortment of subjects and reflects in the book's structure.Part 1 introduces the mathematical language and its rules together with the basic building blocks. Part 2 discusses the number systems of common practice, while the backgrounds needed to solve equations and inequalities are developed in Part 3. Part 4 breaks down the traditional, outdated barriers between areas, exploring in particular the interplay between algebra and geometry. Two appendices form Part 5: the Greek etymology of frequent terms and a list of mathematicians mentioned in the book. Abundant examples and exercises are disseminated along the text to boost the learning process and allow for independent work.Students will find invaluable material to shepherd them through the first years of an undergraduate course, or to complement previously learnt subject matters. Teachers may pick'n'mix the contents for planning lecture courses or supplementing their classes.
Multivariable and Vector Calculus
This book is designed primarily for undergraduates in mathematics, engineering, and the physical sciences. Rather than concentrating on technical skills, it focuses on a deeper understanding of the subject by providing many unusual and challenging examples. The basic topics of vector geometry, differentiation and integration in several variables are explored. Furthermore, it can be used to impower the mathematical knowledge for Artificial Intelligence (AI) concepts. It also provides numerous computer illustrations and tutorials using MATLAB(R) and Maple(R), that bridge the gap between analysis and computation. Partial solutions and instructor ancillaries available for use as a textbook. FEATURESIncludes numerous computer illustrations and tutorials using MATLAB(R) and Maple(R) Covers the major topics of vector geometry, differentiation, and integration inseveral variablesInstructors' ancillaries available upon adoption
The ASQ Metrology Handbook
The ever-changing fields of science and technology have made huge leaps, thanks in part to improvements in measurements. Without metrology, these areas may not have experienced exponential growth. Developed by experts in the field as a comprehensive and practical reference, The ASQ Metrology Handbook, Third Edition provides a foundation for understanding metrology as well as calibration principles and practices. This handbook is ideal for not only metrology professionals, but also calibration professionals including calibration technicians and technologists, quality professionals, workers in testing laboratories, consultants, and instructors. Whether you are entering a new phase of your career field, investing in your own continuous improvement journey, training your fellow calibration practitioners, or preparing for ASQ's Certified Calibration Technician (CCT) exam, this handbook provides the information, guidance, and knowledge to help you achieve your goals. New to this Third Edition: - A thorough explanation of ISO/IEC 17025:2017 - The 2019 Redefinition of the International System of Units - Updated and expanded chapters, including information about training and competency, software validation, statistics, decision rules and risk, uncertainty in measurement, mass and weighing, force, and chemical and biological measurements and uncertainties
Some new constants in problem solutions of Mathematical Analysis
This is the mathematical reference book for the students, the graduates and researchers who are interested in the mathematical constants as Euler constants γ, Glaisher-Kinkelin's constant, and Bendersky-Adamchik's constants arising in the mathematical analysis.The book contains various problems concerning important items of mathematical analysis: series and integrals.Our new constants plays important role for calculating singular integrals and the sum of multi series which has the multi power in general term.This book can be widely used by students in mathematics and physics, and everyone who is interested in mathematical analysis.It is certain that this will be contributed to the students, the graduates and researchers who are going to mathematically analyze the physical situations arise in advanced science and technology .
Directed Quantities in Electrodynamics
This monograph explores classical electrodynamics from a geometrical perspective with a clear visual presentation throughout. Featuring over 200 figures, readers will delve into the definitions, properties, and uses of directed quantities in classical field theory. With an emphasis on both mathematical and electrodynamic concepts, the author's illustrative approach will help readers understand the critical role directed quantities play in physics and mathematics. Chapters are organized so that they gradually scale in complexity, and carefully guide readers through important topics. The first three chapters introduce directed quantities in three dimensions with and without the metric, as well as the development of the algebra and analysis of directed quantities. Chapters four through seven then focus on electrodynamics without the metric, such as the premetric case, waves, and fully covariant four-dimensional electrodynamics. Complementing the book's careful structure, exercises are included throughout for readers seeking further opportunities to practice the material. Directed Quantities in Electrodynamics will appeal to students, lecturers, and researchers of electromagnetism. It is particularly suitable as a supplement to standard textbooks on electrodynamics.
Oral Communication Excellence for Engineers and Scientists
Many of us have implemented oral communication instruction in our design courses, lab courses, and other courses where students give presentations. Others have students give presentations without instruction on how to become a better presenter. Many of us, then, could use a concise book that guides us on what instruction on oral communication should include, based on input from executives from different settings. This instruction will help our students get jobs and make them more likely to move up the career ladder, especially in these hard economic times. Oral Communication Excellence for Engineers and Scientists: Based on Executive Input is the tool we need. It is based on input from over 75 executives with engineering or science degrees, leading organizations that employ engineers and scientists. For the presentation chapter, the executives described what makes a "stellar presentation." And for every other chapter, they gave input--on, for example, how to effectively communicate in meetings and in teams, how to excel at phone communication, how to communicate electronically to supplement oral communication, and how to meet the challenges of oral communication. They also provided tips on cross-cultural communication, listening, choosing the appropriate medium for a communication, elevator pitches, and posters; and using oral communication to network on the job. Oral Communication Excellence for Engineers and Scientists includes exercises and activities for students and professionals, based on instruction that has improved Georgia Tech's students' presentation skills at a statistically significant level. Slides demonstrating best practices are included from Capstone Design students around the country. Table of Contents: Introduction / Background Preparation / Presentation: Customizing to your Audience / Presentation: Telling your Story / Presentation: Displaying Key Information / Delivering the Presentation / Other Oral Communication Skills / Advanced Oral Communication Skills / References
Differential Geometry
This book combines the classical and contemporary approaches to differential geometry. An introduction to the Riemannian geometry of manifolds is preceded by a detailed discussion of properties of curves and surfaces.The chapter on the differential geometry of plane curves considers local and global properties of curves, evolutes and involutes, and affine and projective differential geometry. Various approaches to Gaussian curvature for surfaces are discussed. The curvature tensor, conjugate points, and the Laplace-Beltrami operator are first considered in detail for two-dimensional surfaces, which facilitates studying them in the many-dimensional case. A separate chapter is devoted to the differential geometry of Lie groups.
Inverse Linear Problems on Hilbert Space and Their Krylov Solvability
This book presents a thorough discussion of the theory of abstract inverse linear problems on Hilbert space. Given an unknown vector f in a Hilbert space H, a linear operator A acting on H, and a vector g in H satisfying Af=g, one is interested in approximating f by finite linear combinations of g, Ag, A2g, A3g, ... The closed subspace generated by the latter vectors is called the Krylov subspace of H generated by g and A. The possibility of solving this inverse problem by means of projection methods on the Krylov subspace is the main focus of this text.After giving a broad introduction to the subject, examples and counterexamples of Krylov-solvable and non-solvable inverse problems are provided, together with results on uniqueness of solutions, classes of operators inducing Krylov-solvable inverse problems, and the behaviour of Krylov subspaces under small perturbations. An appendix collects material on weaker convergence phenomena in general projection methods.This subject of this book lies at the boundary of functional analysis/operator theory and numerical analysis/approximation theory and will be of interest to graduate students and researchers in any of these fields.
Mathematics and Music
Mathematics and Music: Composition, Perception, and Performance, Second Edition includes many new sections and more consistent expectations of a student's experience. The new edition of this popular text is more accessible for students with limited musical backgrounds and only high school mathematics is required. The new edition includes more illustrations than the previous one and the added sections deal with the XronoMorph rhythm generator, musical composition, and analyzing personal performance. The text teaches the basics of reading music, explaining how various patterns in music can be described with mathematics, providing mathematical explanations for musical scales, harmony, and rhythm. The book gives students a deeper appreciation showing how music is informed by both its mathematical and aesthetic structures. Highlights of the Second Edition: Now updated for more consistent expectations of students' backgrounds More accessible for students with limited musical backgrounds Full-color presentation Includes more thorough coverage of spectrograms for analyzing recorded music Provides a basic introduction to reading music Features new coverage of building and evaluating rhythms
Variational Views in Mechanics
This volume provides a timely survey of interactions between the calculus of variations and theoretical and applied mechanics. Chapters have been significantly expanded since preliminary versions appeared in a special issue of the Journal of Optimization Theory and Applications (184(1), 2020) on "Calculus of Variations in Mechanics and Related Fields". The variety of topics covered offers researchers an overview of problems in mechanics that can be analyzed with variational techniques, making this a valuable reference for researchers in the field. It also presents ideas for possible future areas of research, showing how the mastery of these foundational mathematical techniques can be used for many exciting applications. Specific topics covered include: Topology optimizationIdentification of material propertiesOptimal controlPlastic flowsGradient polyconvexityObstacle problemsQuasi-monotonicity Variational Views in Mechanics will appeal to researchers in mathematics, solid-states physics, and mechanical, civil, and materials engineering.
Mathematics of Public Health
Curated by the Fields Institute for Research in Mathematical Sciences from their COVID-19 Math Modelling Seminars, this first in a series of volumes on the mathematics of public health allows readers to access the dominant ideas and techniques being used in this area, while indicating problems for further research. This work brings together experts in mathematical modelling from across Canada and the world, presenting the latest modelling methods as they relate to the COVID-19 pandemic. A primary aim of this book is to make the content accessible so that researchers share the core methods that may be applied elsewhere. The mathematical theories and technologies in this book can be used to support decision makers on critical issues such as projecting outbreak trajectories, evaluating public health interventions for infection prevention and control, developing optimal strategies to return to a new normal, and designing vaccine candidates and informing mass immunization program. Topical coverage includes: basic susceptible-exposed-infectious-recovered (SEIR) modelling framework modified and applied to COVID-19 disease transmission dynamics; nearcasting and forecasting for needs of critical medical resources including personal protective equipment (PPE); predicting COVID-19 mortality; evaluating effectiveness of convalescent plasma treatment and the logistic implementation challenges; estimating impact of delays in contact tracing; quantifying heterogeneity in contact mixing and its evaluation with social distancing; modelling point of care diagnostics of COVID-19; and understanding non-reporting and underestimation. Further, readers will have the opportunity to learn about current modelling methodologies and technologies for emerging infectious disease outbreaks, pandemic mitigation rapid response, and the mathematics behind them. The volume will help the general audience and experts to better understand the important role that mathematics has been playing during this on-going crisis in supporting critical decision-making by governments and public health agencies.
Approximation and Computation in Science and Engineering
In recent years, extensive research has been conducted by eminent mathematicians and engineers whose results and proposed problems are presented in this new volume. It is addressed to graduate students, research mathematicians, physicists, and engineers. Individual contributions are devoted to topics of approximation theory, functional equations and inequalities, fixed point theory, numerical analysis, theory of wavelets, convex analysis, topology, operator theory, differential operators, fractional integral operators, integro-differential equations, ternary algebras, super and hyper relators, variational analysis, discrete mathematics, cryptography, and a variety of applications in interdisciplinary topics. Several of these domains have a strong connection with both theories and problems of linear and nonlinear optimization. The combination of results from various domains provides the reader with a solid, state-of-the-art interdisciplinary reference to theory and problems. Some of the works provide guidelines for further research and proposals for new directions and open problems with relevant discussions.
The E. M. Stein Lectures on Hardy Spaces
​The book The E. M. Stein Lectures on Hardy Spaces is based on a graduate course on real variable Hardy spaces which was given by E.M. Stein at Princeton University in the academic year 1973-1974. Stein, along with C. Fefferman and G. Weiss, pioneered this subject area, removing the theory of Hardy spaces from its traditional dependence on complex variables, and to reveal its real-variable underpinnings.This book is based on Steven G. Krantz's notes from the course given by Stein. The text builds on Fefferman's theorem that BMO is the dual of the Hardy space. Using maximal functions, singular integrals, and related ideas, Stein offers many new characterizations of the Hardy spaces. The result is a rich tapestry of ideas that develops the theory of singular integrals to a new level. The final chapter describes the major developments since 1974.This monograph is of broad interest to graduate students and researchers in mathematical analysis. Prerequisites for the book include a solid understanding of real variable theory and complex variable theory. A basic knowledge of functional analysis would also be useful.
The Math Book
Learn about the most important mathematical ideas, theorems, and movements in The Math Book. Part of the fascinating Big Ideas series, this book tackles tricky topics and themes in a simple and easy to follow format. Learn about Math in this overview guide to the subject, brilliant for novices looking to find out more and experts wishing to refresh their knowledge alike! The Math Book brings a fresh and vibrant take on the topic through eye-catching graphics and diagrams to immerse yourself in. This captivating book will broaden your understanding of Math, with: - More than 85 ideas and events key to the development of mathematics- Packed with facts, charts, timelines and graphs to help explain core concepts- A visual approach to big subjects with striking illustrations and graphics throughout- Easy to follow text makes topics accessible for people at any level of understanding The Math Book is a captivating introduction to the world's most famous theorems, mathematicians and movements, aimed at adults with an interest in the subject and students wanting to gain more of an overview. Charting the development of math around the world from Babylon to Bletchley Park, this book explains how math help us understand everything from patterns in nature to artificial intelligence.Your Math Questions, Simply Explained What is an imaginary number? Can two parallel lines ever meet? How can math help us predict the future? This engaging overview explores answers to big questions like these and how they contribute to our understanding of math. If you thought it was difficult to learn about topics like algebra and statistics, The Math Book presents key information in an easy to follow layout. Learn about the history of math, from ancient ideas such as magic squares and the abacus to modern cryptography, fractals, and the final proof of Fermat's Last Theorem. The Big Ideas Series With millions of copies sold worldwide, The Math Book is part of the award-winning Big Ideas series from DK. The series uses striking graphics along with engaging writing, making big topics easy to understand.
Fractional Differential Equations and Inclusions
This monograph is devoted to the existence and stability (Ulam-Hyers-Rassias stability and asymptotic stability) of solutions for various classes of functional differential equations or inclusions involving the Hadamard or Hilfer fractional derivative. Some equations present delay which may be finite, infinite, or state-dependent. Others are subject to impulsive effect which may be fixed or non-instantaneous.Readers will find the book self-contained and unified in presentation. It provides the necessary background material required to go further into the subject and explores the rich research literature in detail. Each chapter concludes with a section devoted to notes and bibliographical remarks and all abstract results are illustrated by examples. The tools used include many classical and modern nonlinear analysis methods such as fixed-point theorems, as well as some notions of Ulam stability, attractivity and the measure of non-compactness as well as the measure of weak noncompactness. It is useful for researchers and graduate students for research, seminars, and advanced graduate courses, in pure and applied mathematics, physics, mechanics, engineering, biology, and all other applied sciences.
The Stieltjes Integral
This book provides a detailed, rigorous treatment of the Stieltjes integral. It offers an accessible treatment of the subject to students who have had a one semester course in analysis. This book is suitable for a second semester course in analysis, and also for independent study or as the foundation for a senior thesis or Masters project.
Multiaxial Notch Fracture and Fatigue
This book presents unified fatigue life prediction equations for a low/medium/high cycle fatigue of metallic materials, relevant to plain materials and notched components.
Grade 6 Common Core Math
This book is your comprehensive workbook for 6th Grade Common Core Math.Practice makes it perfect. Practice questions on each concept helps the students master over the topic, Students get familiar with the state math aligned to common core standards and moreThis book contains Multiple choice and free response questions. This 6th Grade Common Core Math Workbook includes the below32 weeks of Math26 weeks of practice questions6 Assessments2500+ Math questionsChallenge QuestionsAligned to common core curriculumMultiple choice and Free response questionsDetailed notes on topics with solved examplesEnd of Year assessment onlineChallenge QuestionsThis book has following topics covered: Number sense - Decimal AdditionNumber sense - Decimal SubtractionNumber sense - Decimal MultiplicationNumber sense - Decimal DivisionNumber sense - Decimal MultistepNumber sense - Integer AdditionNumber sense - Integer SubtractionNumber sense - Integer MultiplicationNumber sense - Integer DivisionNumber sense - Integer MultistepFactors & MultiplesGreatest Common Factor (GCF)Least Common Multiple (LCM)Word Problems on LCM nd GCFNumber sense - Fraction AdditionNumber sense - Fraction SubtractionNumber sense - Fraction MultiplicationNumber sense - Fraction DivisionAssessment #1RatiosUnit RatiosPercentagesAssessment #2ExponentsLike term simplificationOrder of OperationsLinear variable substitutionsLinear variable expressionsOne and Two step EquationsAssessment #3Verbal InequalitiesOne and Two step InequalitiesAssessment #4Absolute valueArea of 2-D figures with mixed unitsPerimeter of 2-DArea of 2-DCo-ordinatesVolume: PrismsSimilar RatioSurface Area: Prisms3-D NetsAssessment #5Dot plots, Box plots & Bar graphsHistograms, Line graphs, CirclesStatistical data measuresTransformationsAssessment #6END of YEAR ASSESSMENT #1 ( www.a4ace.com)Math-Knots Weekly practice Math Workbook, Grade 6: Common Core (6th Grade) 2023 EditionSharpening Minds Strengthening Skills
History of Modern Mathematics
History of Modern Mathematics is an unchanged, high-quality reprint of the original edition of 1896. Hansebooks is editor of the literature on different topic areas such as research and science, travel and expeditions, cooking and nutrition, medicine, and other genres. As a publisher we focus on the preservation of historical literature. Many works of historical writers and scientists are available today as antiques only. Hansebooks newly publishes these books and contributes to the preservation of literature which has become rare and historical knowledge for the future.
Modeling and Simulation for Collective Dynamics
The thematic program Quantum and Kinetic Problems: Modeling, Analysis, Numerics and Applications was held at the Institute for Mathematical Sciences at the National University of Singapore, from September 2019 to March 2020. Leading experts presented tutorials and special lectures geared towards the participating graduate students and junior researchers.Readers will find in this significant volume four expanded lecture notes with self-contained tutorials on modeling and simulation for collective dynamics including individual and population approaches for population dynamics in mathematical biology, collective behaviors for Lohe type aggregation models, mean-field particle swarm optimization, and consensus-based optimization and ensemble Kalman inversion for global optimization problems with constraints.This volume serves to inspire graduate students and researchers who will embark into original research work in kinetic models for collective dynamics and their applications.
Stochastic Komatu-Loewner Evolutions
The present monograph on stochastic Komatu-Loewner evolutions (SKLEs) provides the first systematic extension of the Schramm-Loewner evolution (SLE) theory from a simply connected planar domain to multiply connected domains by using the Brownian motion with darning (BMD) that has arisen in a recent study of the boundary theory of symmetric Markov processes.This volume is presented in an accessible manner for the interested researchers and graduate students. It also brings new insights into SLEs as special cases of SKLEs. Mathematically, it can be viewed as a powerful application of stochastic analysis via BMDs to complex analysis.
Introductory Statistics for Data Analysis
This book describes the probability theory associated with frequently used statistical procedures and the relation between probability theory and statistical inference. The first third of the book is dedicated to probability theory including topics relating to events, random variables, and the Central Limit Theorem. Statistical topics then include parameter estimation with confidence intervals, hypothesis testing, chi-square tests, t tests, and several non-parametric tests. Flow charts are frequently used to facilitate an understanding of the material considered. The examples and problems in the book all concern simple data sets which can be analyzed with a simple calculator; however, the R code required to complete many examples and problems is provided as well for those that are interested.
The Theory of Zeta-Functions of Root Systems
The contents of this book was created by the authors as a simultaneous generalization of Witten zeta-functions, Mordell-Tornheim multiple zeta-functions, and Euler-Zagier multiple zeta-functions. Zeta-functions of root systems are defined by certain multiple series, given in terms of root systems. Therefore, they intrinsically have the action of associated Weyl groups. The exposition begins with a brief introduction to the theory of Lie algebras and root systems and then provides the definition of zeta-functions of root systems, explicit examples associated with various simple Lie algebras, meromorphic continuation and recursive analytic structure described by Dynkin diagrams, special values at integer points, functional relations, and the background given by the action of Weyl groups. In particular, an explicit form of Witten's volume formula is provided. It is shown that various relations among special values of Euler-Zagier multiple zeta-functions-which usually are called multiple zeta values (MZVs) and are quite important in connection with Zagier's conjecture-are just special cases of various functional relations among zeta-functions of root systems. The authors further provide other applications to the theory of MZVs and also introduce generalizations with Dirichlet characters, and with certain congruence conditions. The book concludes with a brief description of other relevant topics.
Analytical Methods of HPLC, LCMS/MS
HPLC, LCMS/MS has become the preferred analytical methods for the Estimation of Pharmaceutical Drugs and related compounds due to its versatility, specificity and selectivity. And as Such the objectives of the present work are detailed as under.* To develop and validate Stability indicating analytical methods for separation, identification and Simultaneous estimation of some Pharmaceutical drugs using RP-HPLC, LCMS/MS, analytical methods.* To develop new analytical methods for some of the important drugs in pure and Pharmaceuticals dosage forms.* To conduct pharmacokinetic studies.The results collected from the above studies are useful for the proper review and assessment of the effectiveness and safety data obtained for the estimation of Pharmaceutical drugs.
Elliptic Curves
This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in first-year graduate courses.An elliptic curve is a plane curve defined by a cubic polynomial. Although the problem of finding the rational points on an elliptic curve has fascinated mathematicians since ancient times, it was not until 1922 that Mordell proved that the points form a finitely generated group. There is still no proven algorithm for finding the rank of the group, but in one of the earliest important applications of computers to mathematics, Birch and Swinnerton-Dyer discovered a relation between the rank and the numbers of points on the curve computed modulo a prime. Chapter IV of the book proves Mordell's theorem and explains the conjecture of Birch and Swinnerton-Dyer.Every elliptic curve over the rational numbers has an L-series attached to it.Hasse conjectured that this L-series satisfies a functional equation, and in 1955 Taniyama suggested that Hasse's conjecture could be proved by showing that the L-series arises from a modular form. This was shown to be correct by Wiles (and others) in the 1990s, and, as a consequence, one obtains a proof of Fermat's Last Theorem. Chapter V of the book is devoted to explaining this work.The first three chapters develop the basic theory of elliptic curves.For this edition, the text has been completely revised and updated.
Lectures on Variational Analysis
This book presents an introduction to variational analysis, a field which unifies theories and techniques developed in calculus of variations, optimization, and control, and covers convex analysis, nonsmooth analysis, and set-valued analysis. It focuses on problems with constraints, the analysis of which involves set-valued mappings and functions that are not differentiable. Applications of variational analysis are interdisciplinary, ranging from financial planning to steering a flying object. The book is addressed to graduate students, researchers, and practitioners in mathematical sciences, engineering, economics, and finance. A typical reader of the book should be familiar with multivariable calculus and linear algebra. Some basic knowledge in optimization, control, and elementary functional analysis is desirable, but all necessary background material is included in the book.
Principles and Applications of Dimensional Analysis and Similarity
The book provides a summary of the historical evolution of dimensional analysis, and frames the problem of dimensions, systems of units and similarity in a vision dominated by the conventions that formalise even the exact sciences.The first four chapters address the definitions, with few dimensional analysis theorems and similarity criteria. There is also the analysis of self-similarity, both of first and second kind, with a couple of completely solved problems, framed within the group theory. From chapter 5 onward, the focus is on applications in some of the engineering sectors. The number of topics is necessarily limited, but, almost always, there are details, calculations and treatment of assumptions. The book contains descriptions of some of the experimental apparatuses currently used for the realisation of physical models, such as the wind tunnel, the shaking table, the centrifuge, and with the exclusion of many others, which can be found in specialist monographies. Measurement techniques and instrumentation and statistical data processing is also available in other books. Some more specific notions, required by the context, are reported in the appendix, where appears also the description of numerous dimensionless groups, all of engineering interest, but with the exclusion of many others related to physical processes of electrical nature or physics of particles. A glossary lists the meaning of some specific terms typical of dimensional analysis and used in the book.
Women in Numbers Europe III
This volume includes articles spanning several research areas in number theory, such as arithmetic geometry, algebraic number theory, analytic number theory, and applications in cryptography and coding theory. Most of the articles are the results of collaborations started at the 3rd edition of the Women in Numbers Europe (WINE) conference between senior and mid-level faculty, junior faculty, postdocs, and graduate students. The contents of this book should be of interest to graduate students and researchers in number theory.
