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
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.
Orbital Mechanics using Python and R
This book describes the mechanics or physics of resident space objects (RSOs) in orbits due to the gravitational force of the central mass, like the Earth. In other words, it's about the obit of satellites and other RSOs. Part 1 applies the laws of Newton and Kepler, considers 2-body and N-body problems, and explores Jacobi's constant and Lagrangian points. Using calculus, geometry, trigonometry, and algebra, it develops the equations of orbits and motion, transforms reference frames to other frames, like Cartesian to True Equator, Mean Equinox (TEME). The book investigates orbital maneuvers with applications like Hohmann transfers, and interplanetary trajectories hyperbolic departures. We develop the orbital parameters, like the semilatus rectum, mean anomaly, eccentricity, inclination, and argument of periapsis. Part 2 explores and implements the NORAD two-line element (TLE) set and uses the content to propagate state vectors( position and velocity) to plot orbits and ground tracks. We employ the SGD4 (LEO) propagator and SPD4 (deep space) propagator to validate orbits against Revisiting Spacetrack Report #3. We then use the results to project orbits forward in time and to simulate from selected orbital elements.
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
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 .
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.
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.
Graph Data Science with Neo4j
Supercharge your data with the limitless potential of Neo4j 5, the premier graph database for cutting-edge machine learningPurchase of the print or Kindle book includes a free PDF eBookKey Features: Extract meaningful information from graph data with Neo4j's latest version 5Use Graph Algorithms into a regular Machine Learning pipeline in PythonLearn the core principles of the Graph Data Science Library to make predictions and create data science pipelines.Book Description: Neo4j, along with its Graph Data Science (GDS) library, is a complete solution to store, query, and analyze graph data. As graph databases are getting more popular among developers, data scientists are likely to face such databases in their career, making it an indispensable skill to work with graph algorithms for extracting context information and improving the overall model prediction performance.Data scientists working with Python will be able to put their knowledge to work with this practical guide to Neo4j and the GDS library that offers step-by-step explanations of essential concepts and practical instructions for implementing data science techniques on graph data using the latest Neo4j version 5 and its associated libraries. You'll start by querying Neo4j with Cypher and learn how to characterize graph datasets. As you get the hang of running graph algorithms on graph data stored into Neo4j, you'll understand the new and advanced capabilities of the GDS library that enable you to make predictions and write data science pipelines. Using the newly released GDSL Python driver, you'll be able to integrate graph algorithms into your ML pipeline.By the end of this book, you'll be able to take advantage of the relationships in your dataset to improve your current model and make other types of elaborate predictions.What You Will Learn: Use the Cypher query language to query graph databases such as Neo4jBuild graph datasets from your own data and public knowledge graphsMake graph-specific predictions such as link predictionExplore the latest version of Neo4j to build a graph data science pipelineRun a scikit-learn prediction algorithm with graph dataTrain a predictive embedding algorithm in GDS and manage the model storeWho this book is for: If you're a data scientist or data professional with a foundation in the basics of Neo4j and are now ready to understand how to build advanced analytics solutions, you'll find this graph data science book useful. Familiarity with the major components of a data science project in Python and Neo4j is necessary to follow the concepts covered in this book.
Information Retrieval and Natural Language Processing
This book gives a comprehensive view of graph theory in informational retrieval (IR) and natural language processing(NLP). This book provides number of graph techniques for IR and NLP applications with examples. It also provides understanding of graph theory basics, graph algorithms and networks using graph. The book is divided into three parts and contains nine chapters. The first part gives graph theory basics and graph networks, and the second part provides basics of IR with graph-based information retrieval. The third part covers IR and NLP recent and emerging applications with case studies using graph theory. This book is unique in its way as it provides a strong foundation to a beginner in applying mathematical structure graph for IR and NLP applications. All technical details that include tools and technologies used for graph algorithms and implementation in Information Retrieval and Natural Language Processing with its future scope are explained in a clear and organized format.
Inverse Optimal Control and Inverse Noncooperative Dynamic Game Theory
This book presents a novel unified treatment of inverse problems in optimal control and noncooperative dynamic game theory. It provides readers with fundamental tools for the development of practical algorithms to solve inverse problems in control, robotics, biology, and economics. The treatment involves the application of Pontryagin's minimum principle to a variety of inverse problems and proposes algorithms founded on the elegance of dynamic optimization theory. There is a balanced emphasis between fundamental theoretical questions and practical matters. The text begins by providing an introduction and background to its topics. It then discusses discrete-time and continuous-time inverse optimal control. The focus moves on to differential and dynamic games and the book is completed by consideration of relevant applications. The algorithms and theoretical results developed in Inverse Optimal Control and Inverse Noncooperative Dynamic Game Theory provide new insights into information requirements for solving inverse problems, including the structure, quantity, and types of state and control data. These insights have significant practical consequences in the design of technologies seeking to exploit inverse techniques such as collaborative robots, driver-assistance technologies, and autonomous systems. The book will therefore be of interest to researchers, engineers, and postgraduate students in several disciplines within the area of control and robotics.
Spatial Networks
This book provides a complete introduction into spatial networks. It offers the mathematical tools needed to characterize these structures and how they evolve in time and presents the most important models of spatial networks.The book puts a special emphasis on analyzing complex systems which are organized under the form of networks where nodes and edges are embedded in space. In these networks, space is relevant, and topology alone does not contain all the information. Characterizing and understanding the structure and the evolution of spatial networks is thus crucial for many different fields, ranging from urbanism to epidemiology.This subject is therefore at the crossroad of many fields and is of potential interest to a broad audience comprising physicists, mathematicians, engineers, geographers or urbanists. In this book, the author has expanded his previous book ("Morphogenesis of Spatial Networks") to serve as a textbook and reference on this topic for a wide range of students and professional researchers.
Formal Methods Teaching
This book constitutes the proceedings of the 5th International Workshop on Formal Methods Teaching, FMTea 2023, which was held in L羹beck, Germany, in March 2023.The 7 full papers presented in this volume were carefully reviewed and selected from 10 submissions. FMTea 2023 aim is to support a worldwide improvement in learning Formal Methods, mainly by teaching but also via self-learning.
Contemporary Mathematical Thinking
This book deals with the evolution of mathematical thought during the 20th century. Representing a unique point of view combining mathematics, philosophy and history on this issue, it presents an original analysis of key authors, for example Bourbaki, Grothendieck and Husserl. As a product of 19th and early 20th century science, a canon of knowledge or a scientific ideology, mathematical structuralism had to give way. The succession is difficult, still in progress, and uncertain. To understand contemporary mathematics, its progressive liberation from the slogans of "modern mathematics" and the paths that remain open today, it is first necessary to deconstruct the history of this long dominant current. Another conception of mathematical thought emerged in the work of mathematicians such as Hilbert or Weyl, which went beyond the narrow epistemological paths of science in the making. In this tradition, mathematical thought was accompanied by a philosophical requirement. Modernity teaches us to revive it. The book is intended for a varied public: mathematicians concerned with understanding their discipline, philosophers of science, and the erudite public curious about the progress of mathematics.
Why Accounting Is Not Boring
I wrote the first edition long before I went on the Path of the Peacemaker- The Iroquois Legend. When first published in 1975 I had founded Second City in Toronto but that is another story. Just ask Andrew Alexander. For the past 47 Years I have been on an adventure that will be covered in the Sequel to this Book. This book is a book of humor even though the Tax department insisted that it was a notebook. I won my case and was exempt from excise tax in Canada. The sequel will introduce you to information you do not know you do not know, this book is the introduction.
Why Accounting Is Not Boring
I wrote the first edition long before I went on the Path of the Peacemaker- The Iroquois Legend. When first published in 1975 I had founded Second City in Toronto but that is another story. Just ask Andrew Alexander. For the past 47 Years I have been on an adventure that will be covered in the Sequel to this Book. This book is a book of humor even though the Tax department insisted that it was a notebook. I won my case and was exempt from excise tax in Canada. The sequel will introduce you to information you do not know you do not know, this book is the introduction.
Journal of Applied Logics. The IfCoLog Journal of Logics and their Applications. Volume 10, number 1, January 2023
The Journal of Applied Logics - IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are free open access, and available via the College Publications website. This Journal is open access, puts no limit on the number of pages of any article, puts no limit on the number of papers in an issue and puts no limit on the number of issues per year. We insist only on a very high academic standard, and will publish issues as they come.
Classification Theory. Second Edition with a new introduction
This book is for readers who have learned about first order logic; G繹del's completeness theorem; the L繹wenheim-Skolem theorem; the Tarski-Vaught criterion for being elementary sub-model; and who know naive set theory. A graduate course in model theory will be helpful. The thesis of the book is that we can find worthwhile dividing lines among complete first order theories T; mainly countable. That is, properties dividing them in some sense between understandable and complicated ones.The main test problem is the number of models of T of the infinite cardinal l as a function of l. This culminates in the so-called main gap theorem saying the number is either maximal or quite small in suitable sense. Toward this, other properties are introduced and investigated, such as being stable or being super stable, where can we define dimension and weight, particularly for super stable theories.
Marks’ first lessons in geometry; In two parts. Objectively presented, and designed for the use of primary classes in grammar schools, academies, etc.
Marks' first lessons in geometry; In two parts. Objectively presented, and designed for the use of primary classes in grammar schools, academies, etc., has been regarded as significant work throughout human history, and in order to ensure that this work is never lost, we have taken steps to ensure its preservation by republishing this book in a contemporary format for both current and future generations. This entire book has been retyped, redesigned, and reformatted. Since these books are not made from scanned copies, the text is readable and clear.
Theories of Paradox in the Middle Ages
Paradoxes seized the attention of logicians in the middle ages, and were used both as tests for the viability of theories of logic, language, epistemology, and possibly every philosophical issue, and also in the specific genre of insolubles as needing a theoretical solution, usually involving issues about signification, truth, knowledge and modality. Numerous theories were developed, not only in the Latin West, but also in the Islamic world and in the Byzantine tradition. Some of these theories are well known, others barely investigated, if at all. The papers in this volume discuss and contrast a range of these theories and consider their advantages and drawbacks, and their relation to more recent theories of paradox and antinomy. Several of the papers were presented at a workshop organised at the University of St Andrews, Scotland, as part of the Leverhulme-funded project 'Theories of Paradox in Fourteenth-Century Logic: Edition and Translation of Key Texts'.
Investigations into the Predicate Calculus
Oiva Ketonen (1913--2000) was the closest to a student the creator of modern proof theory Gerhard Gentzen ever had. Their encounter took place in 1938--39 in G繹ttingen, with Ketonen hoping to receive a suitable topic for a doctoral dissertation and Gentzen instead deeply immersed in attempts at proving the consistency of analysis. Ketonen's thesis of 1944, his only work in logic, introduced what is today called the G3-sequent calculus. It is his best-known discovery, a sequent calculus for classical propositional logic the logical rules of which are all invertible. Few read his thesis, the results of which were instead made available through a long review by Paul Bernays. Ketonen's calculus is the basis of Evert Beth's tableau method and of the sequent calculi in Stephen Kleene's influential {\it Introduction to Metamathematics}. A second result was a sharpening of the midsequent theorem, by which the number of quantifier inferences with eigenvariables could be minimized. The existence of a weakest possible midsequent followed, in the sense that if any midsequent is derivable, a weakest one is. Turning this into a contrapositive, Ketonen found a purely syntactic method for proofs of underivability that he applied to affine plane geometry. His result, in modern terms, was a positive solution to the word problem for the universal fragment of plane affine geometry, with a syntactic proof of underivability of the parallel postulate from the rest of the affine axioms as a corollary.
A Lambda Calculus Satellite
In 1936 the notion of intuitive computability was operationalized in two different ways: via Turing machines and via lambda-calculus. The difference consisted in manipulating beads (bits) for the former approach versus manipulating trees (rewriting lambda-terms) for the latter. Both proposals turned out to formalize the same notion of computability, and led to the Church-Turing Thesis, claiming that intuitive computability is captured in the correct way.This resulted in the foundation of imperative and functional programming. Variants of lambda-calculus are being used in another powerful field of applications, namely proof-checking, the basis for certifying mathematical theorems and thereby high tech industrial products. These two areas of research are still being actively investigated and make lambda-calculus a major tool in the present stages of science and of the industrial revolution.In this book lambda-calculus is considered from another angle: as a study of these tree-like structures, investigating the relation between their shape and their action. This is like studying numbers qualitatively, rather than for their applications dealing quantitatively with objects and phenomena in the world.Barendregt's book 'The Lambda Calculus, its Syntax and Semantics' (1981/84), does treat the subject from the same methodological viewpoint, and includes several open conjectures. In the more than four decades that have passed, most - but not all - of these conjectures have been solved, sometimes in ingenious PhD theses. This 'Satellite' to the aforementioned book presents these solutions in a uniform style and adds other topics of interest.
Philosophy of Mathematics in Antiquity and in Modern Times
罈Philosophy of Mathematics竄 is understood, in this book, as an effort to clarify such questions that mathematics itself raises but cannot answer with its own methods. These include, for example, questions about the ontological status of mathematical objects (e.g., what is the nature of mathematical objects?) and the epistemological status of mathematical theorems (e.g., from what sources do we draw when we prove mathematical theorems?). The answers given by Plato, Aristotle, Euclid, Descartes, Locke, Leibniz, Kant, Cantor, Frege, Dedekind, Hilbert and others will be studied in detail. This will lead us to deep insights, not only into the history of mathematics, but also into the conception of mathematics as it is commonly held in the present time. The book is a translation from the German, however revised and considerably expanded. Various chapters have been completely rewritten.
Differential Equations on Manifolds and Mathematical Physics
Parametrix and localized solutions for linearized equations of gas dynamics.- Laplacians on generalized smooth distributions as C*-algebra multipliers.- C*-algebras generated by dynamical systems, and applications to nonlocal PDO.- The equivariant Atiyah-Patodi-Singer theorem.- Representations of Maslov's canonical operator in a neighborhood of caustics.- Resurgent analysis of singularly perturbed differential systems.- Dual linear programming problem and one-dimensional Gromov minimal fillings.- Complete semiclassical spectral asymptotics for periodic and almost periodic perturbations of constant operators.- Analytic properties of the H繹rmander solution of the wave equation.- Derivations of group algebras and Hohschild cohomology.- Mellin operators in weighted corner Sobolev spaces.- Quantum Hall effect and noncommutative geometry.- Flat vector bundles and open coverings.- A class of Fredholm boundary value problems for the wave equation with conditions on the entire boundary.- Motion of mechanical systems across the singular points.- Large-time decay of solutions to the Kawahara equation.- Applications of the Maslov index to phase reconstruction problems.- The complex homotopy principle of Grauert and Gromov for algebras of pseudo differential operators.- On the Fredholm solvability of operators associated with Morse-Smale diffeomorphisms.- Geometrical model of the one-dimensional double pendulum phase space.- Solutions for a nonlinear elliptic problem involving a variable exponent and measure data in unbounded domains.- Periodic internal layers in reaction-diffusion-advection equations with modular type advection.- Model of protosphera.- Pseudo-differential operators, equations, and elliptic boundary value problems.
Discrete Quantum Walks on Graphs and Digraphs
Discrete quantum walks are quantum analogues of classical random walks. They are an important tool in quantum computing and a number of algorithms can be viewed as discrete quantum walks, in particular Grover's search algorithm. These walks are constructed on an underlying graph, and so there is a relation between properties of walks and properties of the graph. This book studies the mathematical problems that arise from this connection, and the different classes of walks that arise. Written at a level suitable for graduate students in mathematics, the only prerequisites are linear algebra and basic graph theory; no prior knowledge of physics is required. The text serves as an introduction to this important and rapidly developing area for mathematicians and as a detailed reference for computer scientists and physicists working on quantum information theory.
Logic and Its Applications
Edited in collaboration with FoLLI, this book constitutes the refereed proceedings of the 10th Indian Conference on Logic and Its Applications, ICLA 2023, which was held in Indore, India, in March 2023.Besides 6 invited papers presented in this volume, there are 9 contributed full papers which were carefully reviewed and selected from 18 submissions. The volume covers a wide range of topics. These topics are related to modal and temporal logics, intuitionistic connexive and imperative logics, systems for reasoning with vagueness and rough concepts, topological quasi-Boolean logic and quasi-Boolean based rough set models, and first-order definability of path functions of graphs.
Stability and Robustness in Data-Driven Predictive Control
Spray polymerisation has a long time been discussed as a promising process, yet, with little knowledge on cause-and-effect relationships between drying and chemical reactions. This work develops a new single droplet model of combined solution drying and free radical homopolymerisation, based on the method of moments. New, consistent approaches for moments' diffusion and the reaction-diffusion system are derived to ensure conservation. Simulations reveal peculiarities of the process such as that, due to drying, polymerisation happens mostly in bulk and monomer evaporation leads to a poor yield. Various process variants and simulation models are discussed. The impact of process parameters is examined by means of numerical DoEs. The second part presents a novel approach for the simulation of structure evolution in suspension drying. The meshfree SPH method is used to model the relevant physical effects on a detailed scale during the first and second drying period. New implementations of physical effects are derived: heat and mass transfer based on linear driving forces, an implicit solution of the heat equation, several approaches for crust formation and a new formulation of surface tension by pairwise forces. The formation of dense structures as well as hollow granules can be simulated. Model parameters influence crust formation during the second drying period concerning shape and microporosity and can be interpreted in a physical sense.
Analyzing Mathematical Patterns - Detection & Formulation
The book's objectives are to expose students to analyzing and formulating various patterns such as linear, quadratic, geometric, piecewise, alternating, summation-type, product-type, recursive and periodic patterns. The book will present various patterns graphically and analytically and show the connections between them. Graphical presentations include patterns at same scale, patterns at diminishing scale and alternating patterns.The book's goals are to train and expand students' analytical skills by presenting numerous repetitive-type problems that will lead to formulating results inductively and to the proof by induction method. These will start with formulating basic sequences and piecewise functions and transition to properties of Pascal's Triangle that are horizontally and diagonally oriented and formulating solutions to recursive sequences. The book will start with relatively straight forward problems and gradually transition to more challenging problems and open-ended research questions. The book's aims are to prepare students to establish a base of recognition and formulation of patterns that will navigate to study further mathematics such as Calculus, Discrete Mathematics, Matrix Algebra, Abstract Algebra, Difference Equations, and to potential research projects. The primary aims out of all are to make mathematics accessible and multidisciplinary for students with different backgrounds and from various disciplines.
Analyzing Mathematical Patterns - Detection & Formulation
The book's objectives are to expose students to analyzing and formulating various patterns such as linear, quadratic, geometric, piecewise, alternating, summation-type, product-type, recursive and periodic patterns. The book will present various patterns graphically and analytically and show the connections between them. Graphical presentations include patterns at same scale, patterns at diminishing scale and alternating patterns.The book's goals are to train and expand students' analytical skills by presenting numerous repetitive-type problems that will lead to formulating results inductively and to the proof by induction method. These will start with formulating basic sequences and piecewise functions and transition to properties of Pascal's Triangle that are horizontally and diagonally oriented and formulating solutions to recursive sequences. The book will start with relatively straight forward problems and gradually transition to more challenging problems and open-ended research questions. The book's aims are to prepare students to establish a base of recognition and formulation of patterns that will navigate to study further mathematics such as Calculus, Discrete Mathematics, Matrix Algebra, Abstract Algebra, Difference Equations, and to potential research projects. The primary aims out of all are to make mathematics accessible and multidisciplinary for students with different backgrounds and from various disciplines.
Bornologies and Lipschitz Analysis
Bornologies are a useful tool in studying problems in mathematical analysis and general topology.　For example, they can be used to characterize those metric spaces on which the real-valued uniformly continuous functions are stable under pointwise products.　 　
International & Multidisciplinary Pedagogy
The book's primary objectives are to welcome you to the abundant and meaningful international and multidisciplinary education discovery journey. You will grow from exposure to other cultures and their practices and I daresay, become better teachers in your local as well as on-line environments. Most every local classroom is multi-cultural as well. The students have different backgrounds and different ways of internalizing information meaningfully.The book will provide practical examples how to design, promote and teach various courses and seminars abroad. Examples are those the author experienced with a specific pedagogical idea that is successful in one system, however, the same concept may face unexpected challenges or fail in another system. Most importantly, the book will focus on applying feedback as vital tools that will guide us to the designing, promoting and teaching mathematics and multidisciplinary courses and seminars. The book's most important goal is to make international and multidisciplinary education accessible to everyone.The book will compare several educational systems as well as their similarities and differences. These include different teaching and learning styles, students' preparation levels, and students' interests and value orientations. The goal is to inspire you to embark on your own innovative discovery journey, seek out multi-cultural and international teaching opportunities and to effectively reach, effectively communicate information and help students learn.
International & Multidisciplinary Pedagogy
The book's primary objectives are to welcome you to the abundant and meaningful international and multidisciplinary education discovery journey. You will grow from exposure to other cultures and their practices and I daresay, become better teachers in your local as well as on-line environments. Most every local classroom is multi-cultural as well. The students have different backgrounds and different ways of internalizing information meaningfully.The book will provide practical examples how to design, promote and teach various courses and seminars abroad. Examples are those the author experienced with a specific pedagogical idea that is successful in one system, however, the same concept may face unexpected challenges or fail in another system. Most importantly, the book will focus on applying feedback as vital tools that will guide us to the designing, promoting and teaching mathematics and multidisciplinary courses and seminars. The book's most important goal is to make international and multidisciplinary education accessible to everyone.The book will compare several educational systems as well as their similarities and differences. These include different teaching and learning styles, students' preparation levels, and students' interests and value orientations. The goal is to inspire you to embark on your own innovative discovery journey, seek out multi-cultural and international teaching opportunities and to effectively reach, effectively communicate information and help students learn.
Logically Speaking. A Festschrift for Marie Duz穩
This Festschrift is in honour of Professor Marie Duz穩, VSB - Technical University of Ostrava. The 16 contributions, authored by 24 colleagues, runthe gamut from foundations in logic and theoretical computer science through philosophical logic, multi-agent systems and theory of communicationto personal recollections. Marie Duz穩 is best known for her profound and extensive work on both the foundations and multiple applications of Transparent Intensional Logic, originally developed by Pavel Tich羸 in the late 1960s. Her work, whether single-authored or co-authored, has appeared in various high-level journals. In 2008 the Rector of her home university granted Marie the award Outstanding Results in the Development of Science and Research.The 2010 monograph Procedural Semantics for Hyperintensional Logic earned Marie and her coauthors the prestigious Award for OutstandingResults of Major Scientific Importance from the Academy of Sciences of the Czech Republic. The major achievements of Transparent IntensionalLogic that Marie has been involved in over the last decade have been compiled into the volume Transparent Intensional Logic: Selected RecentEssays, also published by College Publications.
The Logic of Knowledge Bases
The idea of a knowledge base lies at the heart of symbolic or "good old-fashioned" artificial intelligence (GOFAI). A knowledge-based systemdecides how to act by running formal reasoning procedures over a body of explicitly represented knowledge, its knowledge base. The system isnot programmed for specific tasks; rather, it is told what it needs to know, and expected to infer the rest.This book is about the logic of such knowledge bases. It describes in detail the relationship between symbolic representations of knowledge and abstract states of knowledge, exploring along the way, the foundations of knowledge, knowledge bases, knowledge-based systems, and knowledge representation and reasoning. Assuming some familiarity with first-order predicate logic, the book offers a rigorous mathematical model of knowledge that is general and expressive, yet more workable in practice than previous models.The first edition of the book appeared in the year 2000, and since then its model of knowledge has been applied and extended in a number of ways.This second edition incorporates a number of new results about the logic of knowledge bases, including default reasoning, reasoning about actionand change, and tractable reasoning.Hector Levesque is Professor Emeritus in the Department of Computer Science, University of Toronto. Gerhard Lakemeyer is Professor and Chair of the Department of Computer Science, RWTH Aachen University, and Professor (status only) in the Department of Computer Science, University of Toronto.
An Elementary Course on Partial Differential Equations
Partial differential equations are a vital part of any course in pure or applied mathematics. This book will be invaluable to anyone looking for a lucid but comprehensive introduction to PDEs. Designed to strike a balance between theory and practical problems, it covers all major methods as well as their historical backgrounds, theoretical rigour, and geometric significance. The book is divided into three parts. It starts with basic topics like ordinary differential equations, multivariable calculus, and geometry. This is followed by important techniques to solve certain types of partial differential equations. The last part is devoted to first, second, and higher-order PDEs. The chapters have been arranged to help students develop their knowledge gradually and systematically. Each method is discussed through theoretical descriptions in the form of theorems followed by illustrative problems to help the readers. Finally, numerous solved examples and practice problems helps the student learn to apply this knowledge.
