Generalized Radon Transforms and Imaging by Scattered Particles
A generalized Radon transform (GRT) maps a function to its weighted integrals along a family of curves or surfaces. Such operators appear in mathematical models of various imaging modalities. The GRTs integrating along smooth curves and surfaces (lines, planes, circles, spheres, amongst others) have been studied at great lengths for decades, but relatively little attention has been paid to transforms integrating along non-smooth trajectories. Recently, an interesting new class of GRTs emerged at the forefront of research in integral geometry. The two common features of these transforms are the presence of a 'vertex' in their paths of integration (broken rays, cones, and stars) and their relation to imaging techniques based on physics of scattered particles (Compton camera imaging, single scattering tomography, etc).This book covers the relevant imaging modalities, their mathematical models, and the related GRTs. The discussion of the latter comprises a thorough exploration of their known mathematical properties, including injectivity, inversion, range description and microlocal analysis. The mathematical background required for reading most of the book is at the level of an advanced undergraduate student, which should make its content attractive for a large audience of specialists interested in imaging. Mathematicians may appreciate certain parts of the theory that are particularly elegant with connections to functional analysis, PDEs and algebraic geometry.
Mathematical Logic
This book gathers together a colorful set of problems on classical Mathematical Logic, selected from over 30 years of teaching. The initial chapters start with problems from supporting fields, like set theory (ultrafilter constructions), full-information game theory (strategies), automata, and recursion theory (decidability, Kleene's theorems). The work then advances toward propositional logic (compactness and completeness, resolution method), followed by first-order logic, including quantifier elimination and the Ehrenfeucht- Fra簿ss矇 game; ultraproducts; and examples for axiomatizability and non-axiomatizability. The Arithmetic part covers Robinson's theory, Peano's axiom system, and G繹del's incompleteness theorems. Finally, the book touches universal graphs, tournaments, and the zero-one law in Mathematical Logic. Instructors teaching Mathematical Logic, as well as students who want to understand its concepts and methods, can greatly benefit from this work. The style and topics have been specially chosen so that readers interested in the mathematical content and methodology could follow the problems and prove the main theorems themselves, including G繹del's famous completeness and incompleteness theorems. Examples of applications on axiomatizability and decidability of numerous mathematical theories enrich this volume.
Basic Topology 3
This third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, and algebra. Topics covered in this volume include homotopy theory, homology and cohomology theories, homotopy theory of fiber bundles, Euler characteristic, and the Betti number. It also includes certain classic problems such as the Jordan curve theorem along with the discussions on higher homotopy groups and establishes links between homotopy and homology theories, axiomatic approach to homology and cohomology as inaugurated by Eilenberg and Steenrod. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power and active learning of the subject, all the while covering a wide range of theory and applications in a balanced unified way.
An Introduction to the Math of Voting Methods
Some modern political discussions are focused on electoral reform and the mechanics of democracy. For instance, Maine and Alaska recently adopted new procedures for statewide elections that involve Ranked Choice Voting, while a similar ballot measure in Massachusetts was only narrowly defeated. Meanwhile, countries all over the world use other voting methods with runoffs or scores. It's important for people to be aware of how different voting methods work in practice so that we can have productive debates about which to use in various situations.​Accordingly, this book will teach you about a variety of voting methods through concrete examples and clear explanations. Each chapter illustrates a different type of voting method using basic definitions, real-world examples, a list of pros and cons, and detailed practice problems with solutions. No prior mathematical or political knowledge is assumed. In fact, the prose is designed for a wide audience, making this book ideal for a general education mathematics course or anyone else who is curious to learn about different methods of voting.
Gauss Nodes Revolution
Radical insight into how and why Gauss nodes work using alternative non-polynomial vectors presented in a simple argument. In fact, the Runge-vector solution (arguably the most important solution presented in GNR), is fully accessible to high school mathematics. And conventional Gauss-Legendre nodes generate as one of an infinite number of approaches to the Runge-vector solution.
Stem Education Now More Than Ever
In response to "these unconventional and uncertain years," veteran educator Rodger W. Bybee has written a book that's as thought-provoking as it is constructive. Now more than ever, he writes, America needs reminders of both the themes that made it great in the first place and STEM's contributions to its citizens." Science educators must address STEM issues at local, national, and global levels. And teachers should help students tackle today's problems with new approaches to STEM learning that complement traditional single-discipline programs. STEM Education Now More Than Ever addresses these themes through four wide-ranging sections. Parts of the book are what you might expect from a longtime thought leader in science education. In light of the 2016 election and recent assaults on science's validity, Bybee strongly asserts the need for a new case for STEM education. Other parts may not seem typical for a book on STEM. He writes about the Enlightenment, the U.S. Constitution, democracy, and citizenship as reminders of the effects of STEM disciplines on America's foundational ideas and values. In the end, Bybee ties it all together with positive, practical recommendations. A major one involves newer, faster ways to help teachers develop STEM units that address contemporary challenges in their classes. Another involves the importance of strong leadership from teachers and the STEM education community--leadership Bybee believes we need now more than ever.
The Making of Mathematics
This book offers an alternative to current philosophy of mathematics: heuristic philosophy of mathematics. In accordance with the heuristic approach, the philosophy of mathematics must concern itself with the making of mathematics and in particular with mathematical discovery. In the past century, mainstream philosophy of mathematics has claimed that the philosophy of mathematics cannot concern itself with the making of mathematics but only with finished mathematics, namely mathematics as presented in published works. On this basis, mainstream philosophy of mathematics has maintained that mathematics is theorem proving by the axiomatic method. This view has turned out to be untenable because of G繹del's incompleteness theorems, which have shown that the view that mathematics is theorem proving by the axiomatic method does not account for a large number of basic features of mathematics. By using the heuristic approach, this book argues that mathematics is not theorem provingby the axiomatic method, but is rather problem solving by the analytic method. The author argues that this view can account for the main items of the mathematical process, those being: mathematical objects, demonstrations, definitions, diagrams, notations, explanations, applicability, beauty, and the role of mathematical knowledge.
Star-Critical Ramsey Numbers for Graphs
This text is a comprehensive survey of the literature surrounding star-critical Ramsey numbers. First defined by Jonelle Hook in her 2010 dissertation, these numbers aim to measure the sharpness of the corresponding Ramsey numbers by determining the minimum number of edges needed to be added to a critical graph for the Ramsey property to hold. Despite being in its infancy, the topic has gained significant attention among Ramsey theorists.This work provides researchers and students with a resource for studying known results and their complete proofs. It covers typical results, including multicolor star-critical Ramsey numbers for complete graphs, trees, cycles, wheels, and n-good graphs, among others. The proofs are streamlined and, in some cases, simplified, with a few new results included. The book also explores the connection between star-critical Ramsey numbers and deleted edge numbers, which focus on destroying the Ramsey property by removing edges.The book concludes with open problems and conjectures for researchers to consider, making it a valuable resource for those studying the field of star-critical Ramsey numbers.
Operation Research
Operations research (OR) is an analytical method of problem-solving and decision-making that is useful in the management of organizations. In operations research, problems are broken down into basic components and then solved in defined steps by mathematical analysis.The concept of operations research arose during World War II by military planners. After the war, the techniques used in their operations research were applied to addressing problems in business, the government and society.
The Mathematical Field
While writing this book, I felt intuitively that readers would want to know whether the Creator knew about the Mathematical Field. I have answered the question in one section of this book. Unfortunately, I do not know whether you will agree with me because as I mention in the book, human beings have free will. The book shows the beauty and purity of the Mathematical Field, particularly how the numbers follow specific rules to form different systems like Binary, Octal, Decimal, Duodecimal, and Hexadecimal, where they can have different place values. It is significant that the decimal system suits human beings and our design of 10 fingers and 10 toes for counting seems to be no accident. The rules of the decimal system allows the numbers to be easily added, subtracted, multiplied and divided. Even the higher functions of calculating square roots, cube roots, Sine, Cosine, Tan, logarithms, and exponentials can be easily calculated using a simple calculating machine. The numbers form sequences and series. The arithmetic and geometric series enable easy calculation of numbers using formulae. All the periodic functions like Sine, Cosine, Tan, and ex can be expressed as a series. The Algebraic Arm has shown us how lines and curves can be expressed as simple equations, which we can visualise on the Cartesian Plane in two dimensions. Through differentiation and integration, we can sketch curves and calculate areas and volumes. In the Geometric Arm, we can visualise the points forming lines and the lines forming different slopes and different angles. Geometry also shows the different formations the lines can take-three lines to form triangles, four lines to form quadrilaterals, five lines to form pentagons, and many other shapes with more lines. Geometry also shows the purity of the conic sections forming hyperbolas, ellipses, parabolas, and circles with specific equations and characteristics that enable them to be easily sketched. The manner in which the two foci of the ellipse can come together to form the beautiful circle with one centre and one radius is amazing. Although the Cartesian Plane is more of an algebraic way of showing points in terms of x and y coordinates from an origin of (0,0), the Geometric Arm has shown that points can be described geometrically, as a distance and an angle from an origin. Geometry has also shown us how points around a circle can be drawn as Sine and Cosine waves, which generate the numerous trigonometric identities. The Mathematical Field shows the importance of measurements, which has led to standardisation and mass production of goods and services. This has obviously made things easy for the large populations supported in the cities and towns all over the world. The Mathematical Field has also made it possible to draw and design objects before manufacture and construction; this eliminates errors and wastage. Numbers are essentially pure producing the same results when put in equations and formulae. Human beings and the Fields of Knowledge can produce uncertain results because of the free will issue. Mathematics allows for this in Probability Theory, a branch of Arithmetic Arm. The Sporting Field is full of probability associated with the results. If five horses are running in a race, there is only a certain probability that a particular horse will win. Also, if one tossed a coin, there is only a 50% chance of getting a head and a 50% chance of not getting a head. Probability Theory shows how to calculate the chances of certain events occurring. Finally, the Mathematical Field shows us how to sort the data accumulated in many of Fields of Knowledge to produce useful statistical data and generate formulae and applications in many other Fields of Knowledge, some of which will be considered in my next book.
Solving Diophantine Problems
The name Diophantus has long been attached to what we call under-determined algebraic problems with more unknowns than information. He himself was short of good methods of attack but his work has been the jump off point for a great and hugely productive range of mathematical developments. His choice of word problems remains a source of fascination to this day and that is the topic of this book..
Teaching the Quadrivium
Reviving an educational tradition involves a double task. A new generation of students must be taught, and at the same time the teachers themselves must learn. This book addresses the teachers who seek to hand on the quadrivium-the four mathematical liberal arts of arithmetic, geometry, music, and astronomy-at the same time as they acquire it.Two components run in parallel throughout the book. The first component is practical. Weekly overviews and daily lesson plans explain how to complete the study of A Brief Quadrivium in the course of a single school year, and suggestions for weekly assessments make it easy to plan tests and monitor student progress. The second component is directed to the continuing education of the teacher. Short essays explore the history, philosophy, and practice of mathematics. The themes of these essays are coordinated with the simultaneous mathematical work being done by students, allowing the teacher to instruct more reflectively.Some users of this book are confident in their grasp of mathematics and natural science. For them, the essays will clarify the unity of mathematical activity over time and reveal the old roots of new developments. Other users of this book, including some parents who school their children at home, find mathematics intimidating. The clear structure of the lesson plans, and the support of the companion essays, give them the confidence to lead students through a demanding but doable course of study.The British mathematician John Edensor Littlewood remarked that one finds in the ancient mathematicians not "clever schoolboys" but rather "Fellows of another College." This guide invites all teachers of the quadrivium to join the enduring mathematical culture of Littlewood and his predecessors, and to witness for themselves the significance and vitality of a tradition as old as Pythagoras.
A Brief Quadrivium
Mathematics occupies a central place in the traditional liberal arts. The four mathematical disciplines of the quadrivium-arithmetic, geometry, music, and astronomy-reveal their enduring significance in this work, which offers the first unified, textbook treatment of these four subjects. Drawing on fundamental sources including Euclid, Boethius, and Ptolemy, this presentation respects the proper character of each discipline while revealing the relations among these liberal arts, as well as their connections to later mathematical and scientific developments.This book makes the quadrivium newly accessible in a number of ways. First, the careful choice of material from ancient sources means that students receive a faithful, integral impression of the classical quadrivium without being burdened or confused by an unwieldy mass of scattered results. Second, the terminology and symbols that are used convey the real insights of older mathematical approaches without introducing needless archaism. Finally, and perhaps most importantly, the book is filled with hundreds of exercises. Mathematics must be learned actively, and the exercises structured to complement the text, and proportioned to the powers of a learner to offer a clear path by which students make quadrivial knowledge their own.Many readers can profit from this introduction to the quadrivium. Students in high school will acquire a sense of the nature of mathematical proof and become confident in using mathematical language. College students can discover that mathematics is more than procedure, while also gaining insight into an intellectual current that influenced authors they are already reading: authors such as Plato, Aristotle, Augustine, Thomas Aquinas, and Dante. All will find a practical way to grasp a body of knowledge that, if long neglected, is never out of date.
Random Graphs and Networks: A First Course
Networks surround us, from social networks to protein-protein interaction networks within the cells of our bodies. The theory of random graphs provides a necessary framework for understanding their structure and development. This text provides an accessible introduction to this rapidly expanding subject. It covers all the basic features of random graphs - component structure, matchings and Hamilton cycles, connectivity and chromatic number - before discussing models of real-world networks, including intersection graphs, preferential attachment graphs and small-world models. Based on the authors' own teaching experience, it can be used as a textbook for a one-semester course on random graphs and networks at advanced undergraduate or graduate level. The text includes numerous exercises, with a particular focus on developing students' skills in asymptotic analysis. More challenging problems are accompanied by hints or suggestions for further reading.
Random Graphs and Networks: A First Course
Networks surround us, from social networks to protein-protein interaction networks within the cells of our bodies. The theory of random graphs provides a necessary framework for understanding their structure and development. This text provides an accessible introduction to this rapidly expanding subject. It covers all the basic features of random graphs - component structure, matchings and Hamilton cycles, connectivity and chromatic number - before discussing models of real-world networks, including intersection graphs, preferential attachment graphs and small-world models. Based on the authors' own teaching experience, it can be used as a textbook for a one-semester course on random graphs and networks at advanced undergraduate or graduate level. The text includes numerous exercises, with a particular focus on developing students' skills in asymptotic analysis. More challenging problems are accompanied by hints or suggestions for further reading.
Mental Maths
This series on Mental Maths has been developed to improve mathematical skills of young children. The books include various mathematical problems and the correct methodology for solving them, several illustrative examples and many unsolved problems for practice which will help strengthen the basic concepts of mathematics.
Mental Maths
This series on Mental Maths has been developed to improve mathematical skills of young children. The books include various mathematical problems and the correct methodology for solving them, several illustrative examples and many unsolved problems for practice which will help strengthen the basic concepts of mathematics.
Mental Maths
This series on Mental Maths has been developed to improve mathematical skills of young children. The books include various mathematical problems and the correct methodology for solving them, several illustrative examples and many unsolved problems for practice which will help strengthen the basic concepts of mathematics.
Numerical Modelling and Simulation of Fractals in C++
In Euclidean Geometry, the simplest and best known figures are studied, such as: straight lines, squares, circles, cones, pyramids, among others. In this context, many phenomena and shapes are found in nature, which cannot be explained in the conventional mathematical molds, requiring a special theory to explain and characterize them, known as fractal geometry. According to (TRICOT, 1955) fractal means "broken", which are geometric shapes with some special characteristics that define and distinguish them from other shapes, such as self-similarity at different levels of scale. Currently, fractal geometry, especially the fractal dimension, has been used in several areas of knowledge, such as the study of chaotic systems, image analysis and pattern recognition, texture analysis, among others. This book presents numerical simulation along with mathematical concepts with object oriented programming languages, allowing the topological representation of fractals.
On Cantor and the Transfinite
A set in mathematics is just a collection of elements; an example is the set of natural numbers {1, 2, 3, ...}. Simplifying somewhat, the theory of sets can be regarded as the foundation on which the whole of mathematics is built; and the founder of set theory is the German logician and mathematician Georg Cantor (1845-1918). However, the aspect of Cantor's work that's most widely known-or most controversial, at any rate-isn't so much set theory in general, but rather those parts of that theory that have to do with infinite sets in particular. Cantor claimed among other things that the infinite set of real numbers contains strictly more elements than the infinite set of natural numbers. From this result, he concluded that there's more than one kind of infinity; in fact, he claimed that there are an infinite number of different infinities, or transfinite numbers. (He also believed these results had been communicated to him by God.) The aim of this book is to explain and investigate these claims of Cantor's in depth (and question them, where appropriate). It's not a textbook, though; instead, it's a popular account-it tells a story-and the target audience is interested lay readers, not mathematicians or logicians. What little mathematics is needed to understand the story is explained in the book itself.
Geometry
This book covers over 1000+ problems of practice in the core areas of 1. Various types of Angles2. Finding a missing Angle3. Areas of 2-D figures4. Volumes of 3-D figures5. Total surface Areas of 3-D figures Visit 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
Pre-Algebra
The Pre-Algebra practice sets are developed to help teachers and counselors make informed decisions about the initial placement of students in the secondary mathematics curriculum.Math-Knots Pre-Algebra Books, designed to harnesses a child's Pre-Algebra skills.Math-Knots Pre-Algebra Work Book Includes: Topics covering Pre-algebra skills extensively1000 + questionsAnswer key is included.The content has been successfully used by many kids over the years to ace the test.Also availablePre-Algebra Work book - Vol 1a4ace offers an online comprehensive test prep course for students .The most effective online test prep course for boosting your Pre-Algebra skillsPractice test series with 9, 12, 21 or 32 practice testsVarious packages to chooseDetailed step by step solutionsStrategies to improve speed & accuracy on the testStudents can practice as many times as they needTime based assessments simulating the real test.Many of our students got highest scoresVisit https: //a4ace.comPurchase ONLY our latest edition books. If you see any issues, please email us mathknots.help@gmail.com. For more practice tests visit www.a4ace.com
Pre-Algebra
The Pre-Algebra practice sets are developed to help teachers and counselors make informed decisions about the initial placement of students in the secondary mathematics curriculum.Math-Knots Pre-Algebra Books, designed to harnesses a child's Pre-Algebra skills.Math-Knots Pre-Algebra Work Book Includes: Topics covering Pre-algebra skills extensively1000 + questionsAnswer key is included.The content has been successfully used by many kids over the years to ace the test.Also availablePre-Algebra Work book - Vol 2a4ace offers an online comprehensive test prep course for students .The most effective online test prep course for boosting your Pre-Algebra skillsPractice test series with 9, 12, 21 or 32 practice testsVarious packages to chooseDetailed step by step solutionsStrategies to improve speed & accuracy on the testStudents can practice as many times as they needTime based assessments simulating the real test.Many of our students got highest scoresVisit https: //a4ace.comPurchase ONLY our latest edition books. If you see any issues, please email us mathknots.help@gmail.com. For more practice tests visit www.a4ace.com
Fractions
This book reinforces the concepts of Fractions. This is the basic block for mastering elementary mathThis book containsAdditions of FractionsSubtractions of FractionsMultiplications of FractionsDivisions of FractionsMixed NumbersVisit 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 concept
Basic Algebra 1
This book covers over 1000+ problems of practice in the core areas of1. Verbal expressions and Equations2. Variable Expressions3. Variable Equations4. Variable Inequalities5. Least Common Multiples6. Simplification of ExponentsVisit www.math-knots.com for more books.Questions?e-mail: mathknots.help@gmail.comMastering the concepts is a very important part of the academic excellence of students.1000+ problems to practice and master the concepts
Decimals
This book reinforces the concepts of Decimal numbers: 1. Additions2. Subtractions3. Multiplications4. Divisions5. Rounding a place value6. Write in words and numbersMastering the concepts is a very important part of the academic excellence of students.
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
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
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
Advanced Algebra 1 vol 1
This book covers over 1000+ problems of practice in the core areas of1. Literal Equations2. Absolute value Equations and Inequalities3. Slope of a Straight line4. Parallel and Perpendicular lines5. Graphing Linear, Absolute value Equations and Inequalities6. Graphing System of Equations and InequalitiesVisit 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
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.
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.
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
Discourse on the Method of Rightly Conducting the Reason And Seeking Truth in the Sciences
Discourse on the Method of Rightly Conducting One's Reason and of Seeking Truth in the Sciences (French: Discours de la M矇thode Pour bien conduire sa raison, et chercher la v矇rit矇 dans les sciences) is a philosophical and autobiographical treatise by Ren矇 Descartes. Discourse on the Method is one of the most influential works in the history of modern philosophy, and important to the development of natural sciences. In this work, Descartes tackles the problem of skepticism, which had previously been studied by other philosophers. While addressing some of his predecessors and contemporaries, Descartes modified their approach to account for a truth he found to be incontrovertible; he started his line of reasoning by doubting everything, so as to assess the world from a fresh perspective, clear of any preconceived notions. Together with Meditations on First Philosophy, Principles of Philosophy and Rules for the Direction of the Mind, it forms the base of the epistemology known as Cartesianism.
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 .
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
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
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.
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.
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
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.
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.
Time-Delay Systems and Their Applications
Time-delay systems occupy a place of central importance in all areas of science. Time-delays are often related to Physico-chemical processes, electric networks, hydraulic networks, heredity in population growth, the economy, and other related industries. Such time-delay systems can be represented by delay differential equations, delay discrete equations, or delay fractional differential equations. Some real-world problems can be modeled in a more accurate way by including time-delays. Such systems are often used to model phenomena in scientific and technological problems. These models are used in computer engineering, viscoelastic systems, diffusion processes, signal analysis, biology, forced oscillations, control theory, disease modeling, finance, and population dynamics. Recently, several attempts have been made to find an analytical solution for time-delay systems under different conditions, which leads to results on stability analysis, control problems, observability, and iterative learning control for linear or nonlinear continuous delay systems, discrete delay systems, impulsive delay systems or fractional order delay systems. The first objective of this work is to obtain the exact solutions of linear or nonlinear continuous delay systems, discrete delay systems, and fractional order delay systems. After that, as an application, the representation of solutions of these systems is used to derive the finite time stability, Hyers-Ulam stability, and controllability results. To prove the effectiveness of the proposed approach, the obtained results will be illustrated by applications, and compared with the outcomes in the existing literature.
