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Introduction to Data Science: A Python Approach to Concepts, Techniques and Applications (Undergraduate Topics in Computer Science)
by Laura Igual Santi SeguíThis accessible and classroom-tested textbook/reference presents an introduction to the fundamentals of the interdisciplinary field of data science. The coverage spans key concepts from statistics, machine/deep learning and responsible data science, useful techniques for network analysis and natural language processing, and practical applications of data science such as recommender systems or sentiment analysis. Topics and features: Provides numerous practical case studies using real-world data throughout the book Supports understanding through hands-on experience of solving data science problems using Python Describes concepts, techniques and tools for statistical analysis, machine learning, graph analysis, natural language processing, deep learning and responsible data scienceReviews a range of applications of data science, including recommender systems and sentiment analysis of text data Provides supplementary code resources and data at an associated website This practically-focused textbook provides an ideal introduction to the field for upper-tier undergraduate and beginning graduate students from computer science, mathematics, statistics, and other technical disciplines. The work is also eminently suitable for professionals on continuous education short courses, and to researchers following self-study courses.
Introduction to Data Science in Biostatistics: Using R, the Tidyverse Ecosystem, and APIs
by Thomas W. MacFarlandIntroduction to Data Science in Biostatistics: Using R, the Tidyverse Ecosystem, and APIs defines and explores the term "data science" and discusses the many professional skills and competencies affiliated with the industry. With data science being a leading indicator of interest in STEM fields, the text also investigates this ongoing growth of demand in these spaces, with the goal of providing readers who are entering the professional world with foundational knowledge of required skills, job trends, and salary expectations. The text provides a historical overview of computing and the field's progression to R as it exists today, including the multitude of packages and functions associated with both Base R and the tidyverse ecosystem. Readers will learn how to use R to work with real data, as well as how to communicate results to external stakeholders. A distinguishing feature of this text is its emphasis on the emerging use of APIs to obtain data.
An Introduction to Dynamical Systems and Chaos (University Texts in the Mathematical Sciences)
by G. C. LayekThis book discusses continuous and discrete nonlinear systems in systematic and sequential approaches. The unique feature of the book is its mathematical theories on flow bifurcations, nonlinear oscillations, Lie symmetry analysis of nonlinear systems, chaos theory, routes to chaos and multistable coexisting attractors. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, featuring a multitude of detailed worked-out examples alongside comprehensive exercises. The book is useful for courses in dynamical systems and chaos and nonlinear dynamics for advanced undergraduate, graduate and research students in mathematics, physics and engineering. The second edition of the book is thoroughly revised and includes several new topics: center manifold reduction, quasi-periodic oscillations, Bogdanov–Takens, period-bubbling and Neimark–Sacker bifurcations, and dynamics on circle. The organized structures in bi-parameter plane for transitional and chaotic regimes are new active research interest and explored thoroughly. The connections of complex chaotic attractors with fractals cascades are explored in many physical systems. Chaotic attractors may attain multiple scaling factors and show scale invariance property. Finally, the ideas of multifractals and global spectrum for quantifying inhomogeneous chaotic attractors are discussed.
Introduction to Finite Element Analysis: A Textbook for Engineering Students
by S. Unnikrishnan Nair S. SomanathThis textbook covers the basic concepts and applications of finite element analysis. It is specifically aimed at introducing this advanced topic to undergraduate-level engineering students and practicing engineers in a lucid manner. It also introduces a structural and heat transfer analysis software FEASTSMT which has wide applications in civil, mechanical, nuclear and automobile engineering domains. This software has been developed by generations of scientists and engineers of Vikram Sarabhai Space Centre and Indian Space Research Organisation. Supported with many illustrative examples, the textbook covers the classical methods of estimating solutions of mathematical models. The book is written in an easy-to-understand manner. This textbook also contains numeral exercise problems to aid self-learning of the students. The solutions to these problems are demonstrated using finite element software. Furthermore, the textbook contains several tutorials and associated online resources on usage of the FEASTSMT software. Given the contents, this textbook is highly useful for the undergraduate students of various disciplines of engineering. It is also a good reference book for the practicing engineers.
Introduction to Mathematical Models in Operations Planning
by Halit Alper TayalıDiscover the intricate nature of a company's production function and the comprehensive principles of planning operations in this book. Through practical applications and enriched by numerical examples, readers gain essential knowledge of elementary mathematical methods in operations planning. The inclusion of the powerful R programming language, accompanied by code scripts and real-world examples, enhances the learning experience. Blending theory with practice, this resource equips readers with the tools necessary to optimize production systems, make informed decisions, and gain a competitive edge in today's dynamic business landscape.
Introduction to NFL Analytics with R (Chapman & Hall/CRC Data Science Series)
by Bradley J. CongelioIt has become difficult to ignore the analytics movement within the NFL. An increasing number of coaches openly integrate advanced numbers into their game plans, and commentators, throughout broadcasts, regularly use terms such as air yards, CPOE, and EPA on a casual basis. This rapid growth, combined with an increasing accessibility to NFL data, has helped create a burgeoning amateur analytics movement, highlighted by the NFL’s annual Big Data Bowl. Because learning a coding language can be a difficult enough endeavor, Introduction to NFL Analytics with R is purposefully written in a more informal format than readers of similar books may be accustomed to, opting to provide step-by-step instructions in a structured, jargon-free manner.Key Coverage:• Installing R, RStudio, and necessary packages• Working and becoming fluent in the tidyverse• Finding meaning in NFL data with examples from all the functions in the nflverse family of packages• Using NFL data to create eye-catching data visualizations• Building statistical models starting with simple regressions and progressing to advanced machine learning models using tidymodels and eXtreme Gradient BoostingThe book is written for novices of R programming all the way to more experienced coders, as well as audiences with differing expected outcomes. Professors can use Introduction to NFL Analytics with R to provide data science lessons through the lens of the NFL, while students can use it as an educational tool to create robust visualizations and machine learning models for assignments. Journalists, bloggers, and arm-chair quarterbacks alike will find the book helpful to underpin their arguments by providing hard data and visualizations to back up their claims.
Introduction to Non-linear Mechanics: A Unified Energetical Approach (Springer Series in Solid and Structural Mechanics #14)
by Claude StolzThis book presents an introduction to the non-linear mechanics of materials, focusing on a unified energetical approach. It begins by summarizing the framework of a thermodynamic description of continua, including a description of the kinematics of deformation, and a summary of the equations of motion. After a short description of the motion of the system and the mechanical interaction, the book introduces the Lagrangean and Hamiltonian functionals of the system, transitioning to the quasistatic characterization with emphasis on the role of potential energy and pseudo-potential of dissipation. The framework is then extended to fracture and damage mechanics with a similar energetical approach proposed for material damage and wear. The book looks at homogenization in non-linear mechanics for locally plastic or damaged material with an analysis of stability and bifurcation of the equilibrium path. Lastly, inverse problems in non-linear mechanics are introduced using optimal control theory. All the concepts introduced in the book are illustrated using analytical solutions on beams, rods, plates, or using spherical and cylindrical symmetries. Graduate students and researchers working on continuum mechanics and interested in a deeper understanding of materials damage, wear, and fatigue will find this book instructive and informative.
An Introduction to Optimization: With Applications to Machine Learning (Wiley Series In Discrete Mathematics And Optimization Ser. #77)
by Edwin K. Chong Wu-Sheng Lu Stanislaw H. ŻakAn Introduction to Optimization Accessible introductory textbook on optimization theory and methods, with an emphasis on engineering design, featuring MATLAB® exercises and worked examples Fully updated to reflect modern developments in the field, the Fifth Edition of An Introduction to Optimization fills the need for an accessible, yet rigorous, introduction to optimization theory and methods, featuring innovative coverage and a straightforward approach. The book begins with a review of basic definitions and notations while also providing the related fundamental background of linear algebra, geometry, and calculus. With this foundation, the authors explore the essential topics of unconstrained optimization problems, linear programming problems, and nonlinear constrained optimization. In addition, the book includes an introduction to artificial neural networks, convex optimization, multi-objective optimization, and applications of optimization in machine learning. Numerous diagrams and figures found throughout the book complement the written presentation of key concepts, and each chapter is followed by MATLAB® exercises and practice problems that reinforce the discussed theory and algorithms. The Fifth Edition features a new chapter on Lagrangian (nonlinear) duality, expanded coverage on matrix games, projected gradient algorithms, machine learning, and numerous new exercises at the end of each chapter. An Introduction to Optimization includes information on: The mathematical definitions, notations, and relations from linear algebra, geometry, and calculus used in optimization Optimization algorithms, covering one-dimensional search, randomized search, and gradient, Newton, conjugate direction, and quasi-Newton methods Linear programming methods, covering the simplex algorithm, interior point methods, and duality Nonlinear constrained optimization, covering theory and algorithms, convex optimization, and Lagrangian duality Applications of optimization in machine learning, including neural network training, classification, stochastic gradient descent, linear regression, logistic regression, support vector machines, and clustering. An Introduction to Optimization is an ideal textbook for a one- or two-semester senior undergraduate or beginning graduate course in optimization theory and methods. The text is also of value for researchers and professionals in mathematics, operations research, electrical engineering, economics, statistics, and business.
An Introduction to Optimization with Applications in Machine Learning and Data Analytics (Textbooks in Mathematics)
by Jeffrey Paul WheelerThe primary goal of this text is a practical one. Equipping students with enough knowledge and creating an independent research platform, the author strives to prepare students for professional careers. Providing students with a marketable skill set requires topics from many areas of optimization. The initial goal of this text is to develop a marketable skill set for mathematics majors as well as for students of engineering, computer science, economics, statistics, and business. Optimization reaches into many different fields. This text provides a balance where one is needed. Mathematics optimization books are often too heavy on theory without enough applications; texts aimed at business students are often strong on applications, but weak on math. The book represents an attempt at overcoming this imbalance for all students taking such a course. The book contains many practical applications but also explains the mathematics behind the techniques, including stating definitions and proving theorems. Optimization techniques are at the heart of the first spam filters, are used in self-driving cars, play a great role in machine learning, and can be used in such places as determining a batting order in a Major League Baseball game. Additionally, optimization has seemingly limitless other applications in business and industry. In short, knowledge of this subject offers an individual both a very marketable skill set for a wealth of jobs as well as useful tools for research in many academic disciplines. Many of the problems rely on using a computer. Microsoft’s Excel is most often used, as this is common in business, but Python and other languages are considered. The consideration of other programming languages permits experienced mathematics and engineering students to use MATLAB® or Mathematica, and the computer science students to write their own programs in Java or Python.
Introduction to Probability, Statistical Methods, Design of Experiments and Statistical Quality Control (University Texts in the Mathematical Sciences)
by Dharmaraja Selvamuthu Dipayan DasThis revised book provides an accessible presentation of concepts from probability theory, statistical methods, the design of experiments, and statistical quality control. It is shaped by the experience of the two teachers teaching statistical methods and concepts to engineering students. Practical examples and end-of-chapter exercises are the highlights of the text, as they are purposely selected from different fields. Statistical principles discussed in the book have a great relevance in several disciplines like economics, commerce, engineering, medicine, health care, agriculture, biochemistry, and textiles to mention a few.Organised into 16 chapters, the revised book discusses four major topics—probability theory, statistical methods, the design of experiments, and statistical quality control. A large number of students with varied disciplinary backgrounds need a course in basics of statistics, the design of experiments and statistical quality control at an introductory level to pursue their discipline of interest. No previous knowledge of probability or statistics is assumed, but an understanding of calculus is a prerequisite. The whole book also serves as a master level introductory course in all the three topics, as required in textile engineering or industrial engineering.
Introduction to Probability, Statistics & R: Foundations for Data-Based Sciences
by Sujit K. SahuA strong grasp of elementary statistics and probability, along with basic skills in using R, is essential for various scientific disciplines reliant on data analysis. This book serves as a gateway to learning statistical methods from scratch, assuming a solid background in high school mathematics. Readers gradually progress from basic concepts to advanced statistical modelling, with examples from actuarial, biological, ecological, engineering, environmental, medicine, and social sciences highlighting the real-world relevance of the subject. An accompanying R package enables seamless practice and immediate application, making it ideal for beginners. The book comprises 19 chapters divided into five parts. Part I introduces basic statistics and the R software package, teaching readers to calculate simple statistics and create basic data graphs. Part II delves into probability concepts, including rules and conditional probability, and introduces widelyused discrete and continuous probability distributions (e.g., binomial, Poisson, normal, log-normal). It concludes with the central limit theorem and joint distributions for multiple random variables. Part III explores statistical inference, covering point and interval estimation, hypothesis testing, and Bayesian inference. This part is intentionally less technical, making it accessible to readers without an extensive mathematical background. Part IV addresses advanced probability and statistical distribution theory, assuming some familiarity with (or concurrent study of) mathematical methods like advanced calculus and linear algebra. Finally, Part V focuses on advanced statistical modelling using simple and multiple regression and analysis of variance, laying the foundation for further studies in machine learning and data science applicable to various data and decision analytics contexts. Based on years of teaching experience, this textbook includes numerousexercises and makes extensive use of R, making it ideal for year-long data science modules and courses. In addition to university courses, the book amply covers the syllabus for the Actuarial Statistics 1 examination of the Institute and Faculty of Actuaries in London. It also provides a solid foundation for postgraduate studies in statistics and probability, or a reliable reference for statistics.
Introduction to Quantum Mechanics: With a Focus on Physics and Operator Theory (Synthesis Lectures on Engineering, Science, and Technology)
by Horst R. BeyerThis book presents an introduction to quantum mechanics that consistently uses the methods of operator theory, allowing readers to develop a physical understanding of quantum mechanical systems. The methods of operator theory are discussed throughout the book and presented with a mathematically rigorous approach. The author describes in detail how to use the methods of operator theory for analyzing quantum mechanical systems, starting with the definition of the involved physical operators (observables) up to the calculation of their spectra, spectral measures, and functional calculus. In addition, the book includes the construction of exponential functions of the involved Hamilton operators that solve the problem of time evolution.
An Introduction to Spatial Data Science with GeoDa: Volume 1: Exploring Spatial Data
by Luc AnselinThis book is the first in a two-volume series that introduces the field of spatial data science. It offers an accessible overview of the methodology of exploratory spatial data analysis. It also constitutes the definitive user’s guide for the widely adopted GeoDa open-source software for spatial analysis. Leveraging a large number of real-world empirical illustrations, readers will gain an understanding of the main concepts and techniques, using dynamic graphics for thematic mapping, statistical graphing, and, most centrally, the analysis of spatial autocorrelation. Key to this analysis is the concept of local indicators of spatial association, pioneered by the author and recently extended to the analysis of multivariate data.The focus of the book is on intuitive methods to discover interesting patterns in spatial data. It offers a progression from basic data manipulation through description and exploration to the identification of clusters and outliers by means of local spatial autocorrelation analysis. A distinctive approach is to spatialize intrinsically non-spatial methods by means of linking and brushing with a range of map representations, including several that are unique to the GeoDa software. The book also represents the most in-depth treatment of local spatial autocorrelation and its visualization and interpretation by means of GeoDa.The book is intended for readers interested in going beyond simple mapping of geographical data to gain insight into interesting patterns. Some basic familiarity with statistical concepts is assumed, but no previous knowledge of GIS or mapping is required.Key Features:• Includes spatial perspectives on cluster analysis• Focuses on exploring spatial data• Supplemented by extensive support with sample data sets and examples on the GeoDaCenter websiteThis book is both useful as a reference for the software and as a text for students and researchers of spatial data science.Luc Anselin is the Founding Director of the Center for Spatial Data Science at the University of Chicago, where he is also the Stein-Freiler Distinguished Service Professor of Sociology and the College, as well as a member of the Committee on Data Science. He is the creator of the GeoDa software and an active contributor to the PySAL Python open-source software library for spatial analysis. He has written widely on topics dealing with the methodology of spatial data analysis, including his classic 1988 text on Spatial Econometrics. His work has been recognized by many awards, such as his election to the U.S. National Academy of Science and the American Academy of Arts and Science.
An Introduction to Spatial Data Science with GeoDa: Volume 2: Clustering Spatial Data
by Luc AnselinThis book is the second in a two-volume series that introduces the field of spatial data science. It moves beyond pure data exploration to the organization of observations into meaningful groups, i.e., spatial clustering. This constitutes an important component of so-called unsupervised learning, a major aspect of modern machine learning.The distinctive aspects of the book are both to explore ways to spatialize classic clustering methods through linked maps and graphs, as well as the explicit introduction of spatial contiguity constraints into clustering algorithms. Leveraging a large number of real-world empirical illustrations, readers will gain an understanding of the main concepts and techniques and their relative advantages and disadvantages. The book also constitutes the definitive user’s guide for these methods as implemented in the GeoDa open source software for spatial analysis.It is organized into three major parts, dealing with dimension reduction (principal components, multidimensional scaling, stochastic network embedding), classic clustering methods (hierarchical clustering, k-means, k-medians, k-medoids and spectral clustering), and spatially constrained clustering methods (both hierarchical and partitioning). It closes with an assessment of spatial and non-spatial cluster properties.The book is intended for readers interested in going beyond simple mapping of geographical data to gain insight into interesting patterns as expressed in spatial clusters of observations. Familiarity with the material in Volume 1 is assumed, especially the analysis of local spatial autocorrelation and the full range of visualization methods.Luc Anselin is the Founding Director of the Center for Spatial Data Science at the University of Chicago, where he is also Stein-Freiler Distinguished Service Professor of Sociology and the College, as well as a member of the Committee on Data Science. He is the creator of the GeoDa software and an active contributor to the PySAL Python open-source software library for spatial analysis. He has written widely on topics dealing with the methodology of spatial data analysis, including his classic 1988 text on Spatial Econometrics. His work has been recognized by many awards, such as his election to the U.S. National Academy of Science and the American Academy of Arts and Science.
Introduction to Supply Chain Analytics: With Examples in AnyLogic and anyLogistix Software (Classroom Companion: Business)
by Dmitry IvanovThe book offers a concise yet comprehensive introduction to supply chain analytics covering management, modeling, and technology perspectives. Designed to accompany the textbook “Global Supply Chain and Operations Management”, it addresses the topics of supply chain analytics in more depth. The book describes descriptive, predictive, and prescriptive supply chain analytics explaining methodologies, illustrating method applications with the use of training exercises, and providing numerous examples in AnyLogic and anyLogistix software. Throughout the book, numerous practical examples and short case studies are given to illustrate theoretical concepts. Along with AnyLogic and anyLogistix model development guidelines and examples, the book has two other distinct features. First, it reviews and explains novel frameworks and concepts related to data-driven decision-making and digital twins. Second, it shows how to use analytics to improve supply chain resilience.Without relying heavily on mathematical derivations, the book offers a structured presentation and explanation of major supply chain analytics techniques and principles in a simple, predictable format to make it easy to understand for students and professionals with both management and engineering backgrounds. Graduate/Ph.D. students and supply chain professionals alike would benefit from a structured and didactically-oriented concise presentation of the concepts, principles, and methods of supply chain analytics. Providing graduate students and supply chain managers with working knowledge of basic and advanced supply chain analytics, this book contributes to improving knowledge-awareness of decision-making in increasingly data-driven and digital environments. The book is supplemented by a companion website offering interactive exercises with the use of AnyLogic and anyLogistix software as well as Spreadsheet Modeling.
Introduction to the Development of Web Applications Using ASP .Net (Synthesis Lectures on Computer Science)
by Razvan Alexandru MezeiThis book introduces a simplified approach to web application development using the open-source ASP .Net Core MVC framework. Readers will learn to implement web applications using the following languages and frameworks: HTML, JavaScript, CSS, Bootstrap, C#, ASP .Net, and Entity Framework Core. In addition, this book addresses how to build a web application to create user accounts, store data in a database, manipulate data, and how to allow controlled access to certain parts of the application functionality. The author also covers both client-side and server-side development and the use of an object relational mapper to work with persistent data (using a database). Topics include: models, views, controllers, routing, entity framework core, identity, layouts, dependency injection and services, model binder, among others. This book: Introduces the development of web applications using the open-source ASP .Net Core MVC frameworkImplements web applications including HTML, JavaScript, CSS, Bootstrap, C#, ASP .Net, and Entity Framework CoreFeatures client-side development, server-side development, and object relational mapper software
Introduction to the Maths and Physics of Quantum Mechanics
by Lucio PiccirilloIntroduction to the Maths and Physics of Quantum Mechanics details the mathematics and physics that are needed to learn the principles of quantum mechanics. It provides an accessible treatment of how to use quantum mechanics and why it is so successful in explaining natural phenomena. This book clarifies various aspects of quantum physics such as ‘why quantum mechanics equations contain “I”, the imaginary number?’, ‘Is it possible to make a transition from classical mechanics to quantum physics without using postulates?’ and ‘What is the origin of the uncertainty principle?’. A significant proportion of discussion is dedicated to the issue of why the wave function must be complex to properly describe our “real” world. The book also addresses the different formulations of quantum mechanics. A relatively simple introductory treatment is given for the “standard” Heisenberg matrix formulation and Schrodinger wave-function formulation and Feynman path integrals and second quantization are then discussed. This book will appeal to first- and second-year university students in physics, mathematics, engineering and other sciences studying quantum mechanics who will find material and clarifications not easily found in other textbooks. It will also appeal to self-taught readers with a genuine interest in modern physics who are willing to examine the mathematics and physics in a simple but rigorous way. Key Features: • Written in an engaging and approachable manner, with fully explained mathematics and physics concepts. <p class="MsoListParagraphCxSpMiddle" style="text-in
Introduction to the New Statistics: Estimation, Open Science, and Beyond
by Geoff Cumming Robert Calin-JagemanThis fully revised and updated second edition is an essential introduction to inferential statistics. It is the first introductory statistics text to use an estimation approach from the start and also to explain the new and exciting Open Science practices, which encourage replication and enhance the trustworthiness of research. The estimation approach, with meta-analysis (“the new statistics”), is exactly what’s needed for Open Science.Key features of this new edition include: Even greater prominence for Open Science throughout the book. Students easily understand basic Open Science practices and are guided to use them in their own work. There is discussion of the latest developments now being widely adopted across science and medicine. Integration of new open-source esci (Estimation Statistics with Confidence Intervals) software, running in jamovi. This is ideal for the book and extends seamlessly to what’s required for more advanced courses, and also by researchers. See www.thenewstatistics.com/itns/esci/jesci/. Colorful interactive simulations, including the famous dances, to help make key statistical ideas intuitive. These are now freely available through any browser. See www.esci.thenewstatistics.com/. Coverage of both estimation and null hypothesis significance testing (NHST) approaches, with full guidance on how to translate between the two. Effective learning strategies and pedagogical features to promote critical thinking, comprehension and retention Designed for introduction to statistics, data analysis, or quantitative methods courses in psychology, education, and other social and health sciences, researchers interested in understanding Open Science and the new statistics will also appreciate this book. No familiarity with introductory statistics is assumed.A comprehensive website offers data sets, key term flashcards, learning guides, and videos describing key concepts and demonstrating the use of esci. For instructors, there are guides for teaching the new statistics and Open Science, assessment exercises, question banks, downloadable slides, and more. Altogether, the website provides engaging learning resources for traditional or flipped classrooms. See www.routledge.com/cw/cumming.
An Introduction to Traffic Flow Theory (Springer Optimization and Its Applications #84)
by Lily ElefteriadouThis second edition of An Introduction to Traffic Flow Theory adds new material in several chapters related to advanced technologies including autonomy, the use of sensors and communications, and particularly congestion mitigation solutions that leverage connected and autonomous vehicles (CAVs). It also includes a new chapter that briefly outlines several mathematical analysis techniques commonly used in traffic flow theory, aiming to introduce students to some of the most frequently used tools available for traffic operational-related analysis. This new edition also includes several updates related to the most recent versions of the Highway Capacity Manual and the Green Book. This textbook is meant for use in advanced undergraduate/graduate level courses in traffic flow theory with prerequisites including two semesters of calculus, statistics, and an introductory course in transportation. The text would also be of interest to transportation professionals as a refresherin traffic flow theory or as a reference. Students and engineers of diverse backgrounds will find this text accessible and applicable to today’s traffic issues.This text provides a comprehensive and concise treatment of the topic of traffic flow theory and includes several topics relevant to today’s highway transportation system. It provides the fundamental principles of traffic flow theory as well as applications of those principles for evaluating specific types of facilities (freeways, intersections, etc.). Newer concepts of Intelligent transportation systems (ITS) and their potential impact on traffic flow are discussed. State-of-the-art traffic flow research, microscopic traffic analysis, and traffic simulation have significantly advanced and are also discussed in this text. Real-world examples and useful problem sets complement each chapter.
Intuitive Axiomatic Set Theory (Textbooks in Mathematics)
by José L GarciáSet theory can be rigorously and profitably studied through an intuitive approach, thus independently of formal logic. Nearly every branch of Mathematics depends upon set theory, and thus, knowledge of set theory is of interest to every mathematician. This book is addressed to all mathematicians and tries to convince them that this intuitive approach to axiomatic set theory is not only possible but also valuable.The book has two parts. The first one presents, from the sole intuition of "collection" and "object", the axiomatic ZFC-theory. Then, we present the basics of the theory: the axioms, well-orderings, ordinals and cardinals are the main subjects of this part. In all, one could say that we give some standard interpretation of set theory, but this standard interpretation results in a multiplicity of universes. The second part of the book deals with the independence proofs of the continuum hypothesis (CH) and the axiom of choice (AC), and forcing is introduced as a necessary tool, and again the theory is developed intuitively, without the use of formal logic. The independence results belong to the metatheory, as they refer to things that cannot be proved, but the greater part of the arguments leading to the independence results, including forcing, are purely set-theoretic. The book is self-contained and accessible to beginners in set theory. There are no prerequisites other than some knowledge of elementary mathematics. Full detailed proofs are given for all the results.
An Invitation to Mathematical Logic (Graduate Texts in Mathematics #301)
by David MarkerIn addition to covering the essentials, the author’s intention in writing this text is to entice the reader to further study mathematical logic. There is no current “standard text” for a first graduate course in mathematical logic and this book will fill that gap. While there is more material than could be covered in a traditional one semester course, an instructor can cover the basics and still have the flexibility to choose several weeks’ worth of interesting advanced topics that have been introduced. The text can and will be used by people in various courses with different sorts of perspectives. This versatility is one of the many appealing aspects of this book. A list of suggested portions to be covered in a single course is provided as well as a useful chart which maps chapter dependencies. Additionally, a motivated student will have ample material for further reading. New definitions, formalism, and syntax have been streamlined to engage thereader quickly into the heart of logic and to more sophisticated topics. Part I and Part IV center on foundational questions, while Part III establishes the fundamentals of computability. Part II develops model theory, highlighting the model theory of the fields of real and complex numbers. The interplay between logic and other areas of mathematics, notably algebra, number theory, and combinatorics, are illustrated in Chapters 5, 6, 8, 14, and 16. For most of the text, the only prerequisite is mathematical maturity. The material should be accessible to first year graduate students or advanced undergraduates in mathematics, graduate students in philosophy with a solid math background, or students in computer science who want a mathematical introduction to logic. Prior exposure to logic is helpful but not assumed.
Irrationality, Transcendence and the Circle-Squaring Problem: An Annotated Translation of J. H. Lambert’s Vorläufige Kenntnisse and Mémoire (Logic, Epistemology, and the Unity of Science #58)
by Eduardo Dorrego López Elías Fuentes GuillénThis publication, now in its second edition, includes an unabridged and annotated translation of two works by Johann Heinrich Lambert (1728–1777) written in the 1760s: Vorläufige Kenntnisse für die, so die Quadratur und Rectification des Circuls suchen and Mémoire sur quelques propriétés remarquables des quantités transcendentes circulaires et logarithmiques. The translations, as in the first edition, are accompanied by a contextualised study of each of these works and provide an overview of Lambert’s contributions, showing both the background and the influence of his work. In addition, by adopting a biographical approach, it allows readers to better get to know the scientist himself.Lambert was a highly relevant scientist and polymath in his time, admired by the likes of Kant, who despite having made a wide variety of contributions to different branches of knowledge, later faded into an undeserved secondary place with respect to other scientists of the eighteenth century. In mathematics, in particular, he is famous for his research on non-Euclidean geometries, although he is likely best known for having been the first who proved the irrationality of pi. In his Mémoire, he conducted one of the first studies on hyperbolic functions, offered a surprisingly rigorous proof of the irrationality of pi, established for the first time the modern distinction between algebraic and transcendental numbers, and based on such distinction, he conjectured the transcendence of pi and therefore the impossibility of squaring the circle.
Isolated Objects in Quadratic Gravity: From Action Principles to Observations (Springer Theses)
by Samuele SilvervalleOne of the main unanswered question of modern Physics is "How does gravity behave at small scales?". The aim of this thesis is to illustrate in a comprehensive but accessible way how to look for deviations from Einstein's theory of General Relativity in this regime, looking at the simplest celestial bodies: static and spherically symmetric ones.With a conservative and bottom-up approach, at smaller scales the first corrections to the action of General Relativity are generally considered to be terms quadratic in the curvature tensors; while these modifications do not cure the inconsistency between gravity and quantum mechanics, the solutions of this theory are plausible candidates to be the first-order corrections of the classical ones.Even with such simple modifications, a striking picture emerges from the study of isolated objects: the unique Schwarzschild solution of General Relativity is only a rare bird in the set of solutions, with non-Schwarzschild black holes, wormholes and naked singularities appearing as possible substitutes.Tailored to graduate students and researchers entering this field, this thesis shows how to construct these new solutions from action principles, how to characterize their metric, how to study their physical properties, such as their stability or Thermodynamics, and how to look for phenomenological signatures.
IT Crisisology Models: Object-Based Optimization for Sustainable Development (Smart Innovation, Systems and Technologies #381)
by Sergey V. ZykovThe book focuses on modeling real-world crisis management in digital product development. This includes models and methods for forecasting, responding, and agile engineering/managing for sustainable product development. This book suggests an approach that contains principles, formal models, and semi-formal practice-oriented methods, patterns and techniques to efficiently manage these crises and provide sustainable development. The book also introduces a set of principles, models, and methods for sustainable management as a blend, the components of which have been carefully selected from a few domains adjacent to digital production such as IT-intensive operation, human resource management, and knowledge engineering, to name a few. The key ingredients of this crisis management framework include smart data modeling, trade-off optimizing, agile product controlling, and knowledge transferring.
Janusz Czelakowski on Logical Consequence (Outstanding Contributions to Logic #27)
by Jacek Malinowski Rafał PalczewskiThis book is dedicated to the life and work of logician Janusz Czelakowski on the topic of logical consequence. It consists of three parts – a biography, a survey and research sections. The volume begins with an autobiographic chapter by Janusz Czelakowski followed by a historical chapter written by Jacek Malinowski. The survey section forms the backbone of the volume with each chapter covering one of Janusz Czelakowski’s results. They focus on his results in the area of logical consequence, demonstrate how his results influenced following research, and presents potential future results, problems and applications. This volume is of interest to logicians and mathematicians.