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Transition to Advanced Mathematics (Textbooks in Mathematics)
by Stephen Lovett Danilo R. DiedrichsThis unique and contemporary text not only offers an introduction to proofs with a view towards algebra and analysis, a standard fare for a transition course, but also presents practical skills for upper-level mathematics coursework and exposes undergraduate students to the context and culture of contemporary mathematics. The authors implement the practice recommended by the Committee on the Undergraduate Program in Mathematics (CUPM) curriculum guide, that a modern mathematics program should include cognitive goals and offer a broad perspective of the discipline. Part I offers: An introduction to logic and set theory. Proof methods as a vehicle leading to topics useful for analysis, topology, algebra, and probability. Many illustrated examples, often drawing on what students already know, that minimize conversation about "doing proofs." An appendix that provides an annotated rubric with feedback codes for assessing proof writing. Part II presents the context and culture aspects of the transition experience, including: 21st century mathematics, including the current mathematical culture, vocations, and careers. History and philosophical issues in mathematics. Approaching, reading, and learning from journal articles and other primary sources. Mathematical writing and typesetting in LaTeX. Together, these Parts provide a complete introduction to modern mathematics, both in content and practice. Table of Contents Part I - Introduction to Proofs Logic and Sets Arguments and Proofs Functions Properties of the Integers Counting and Combinatorial Arguments RelationsPart II - Culture, History, Reading, and Writing Mathematical Culture, Vocation, and Careers History and Philosophy of Mathematics Reading and Researching Mathematics Writing and Presenting Mathematics Appendix A. Rubric for Assessing Proofs Appendix B. Index of Theorems and Definitions from Calculus and Linear Algebra Bibliography Index Biographies Danilo R. Diedrichs is an Associate Professor of Mathematics at Wheaton College in Illinois. Raised and educated in Switzerland, he holds a PhD in applied mathematical and computational sciences from the University of Iowa, as well as a master’s degree in civil engineering from the Ecole Polytechnique Fédérale in Lausanne, Switzerland. His research interests are in dynamical systems modeling applied to biology, ecology, and epidemiology. Stephen Lovett is a Professor of Mathematics at Wheaton College in Illinois. He holds a PhD in representation theory from Northeastern University. His other books include Abstract Algebra: Structures and Applications (2015), Differential Geometry of Curves and Surfaces, with Tom Banchoff (2016), and Differential Geometry of Manifolds (2019).
A Transition to Advanced Mathematics (7th Edition)
by Douglas Smith Maurice Eggen Richard St. AndreThe main goal of the book is to improve the student's ability to think and write in a mature mathematical fashion and to provide a solid understanding of the material most useful for advanced courses.
Transition to Analysis with Proof (Textbooks in Mathematics)
by Steven Krantz<p>Transition to Real Analysis with Proof provides undergraduate students with an introduction to analysis including an introduction to proof. The text combines the topics covered in a transition course to lead into a first course on analysis. This combined approach allows instructors to teach a single course where two were offered. <p>The text opens with an introduction to basic logic and set theory, setting students up to succeed in the study of analysis. Each section is followed by graduated exercises that both guide and challenge students. The author includes examples and illustrations that appeal to the visual side of analysis. The accessible structure of the book makes it an ideal reference for later years of study or professional work.</p>
The Transition to Chaos: Conservative Classical and Quantum Systems (Fundamental Theories of Physics #200)
by Linda ReichlBased on courses given at the universities of Texas and California, this book treats an active field of research that touches upon the foundations of physics and chemistry. It presents, in as simple a manner as possible, the basic mechanisms that determine the dynamical evolution of both classical and quantum systems in sufficient generality to include quantum phenomena. The book begins with a discussion of Noether's theorem, integrability, KAM theory, and a definition of chaotic behavior; continues with a detailed discussion of area-preserving maps, integrable quantum systems, spectral properties, path integrals, and periodically driven systems; and concludes by showing how to apply the ideas to stochastic systems. The presentation is complete and self-contained; appendices provide much of the needed mathematical background, and there are extensive references to the current literature; while problems at the ends of chapters help students clarify their understanding. This new edition has an updated presentation throughout, and a new chapter on open quantum systems.
A Transition to Proof: An Introduction to Advanced Mathematics (Textbooks in Mathematics)
by Neil R. NicholsonA Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of the proof takes place: thought processes, scratch work and ways to attack problems. Readers will learn not just how to write mathematics but also how to do mathematics. They will then learn to communicate mathematics effectively. The text emphasizes the creativity, intuition, and correct mathematical exposition as it prepares students for courses beyond the calculus sequence. The author urges readers to work to define their mathematical voices. This is done with style tips and strict "mathematical do’s and don’ts", which are presented in eye-catching "text-boxes" throughout the text. The end result enables readers to fully understand the fundamentals of proof. Features: The text is aimed at transition courses preparing students to take analysis Promotes creativity, intuition, and accuracy in exposition The language of proof is established in the first two chapters, which cover logic and set theory Includes chapters on cardinality and introductory topology
Transitional Mathematics: Understanding Algebraic Expressions, Student Textbook
by John Woodward Mary StrohNIMAC-sourced textbook
Transitioning to Microsoft Power Platform: An Excel User Guide to Building Integrated Cloud Applications in Power BI, Power Apps, and Power Automate
by David DingWelcome to this step-by-step guide for Excel users, data analysts, and finance specialists. It is designed to take you through practical report and development scenarios, including both the approach and the technical challenges. This book will equip you with an understanding of the overall Power Platform use case for addressing common business challenges. While Power BI continues to be an excellent tool of choice in the BI space, Power Platform is the real game changer. Using an integrated architecture, a small team of citizen developers can build solutions for all kinds of business problems. For small businesses, Power Platform can be used to build bespoke CRM, Finance, and Warehouse management tools. For large businesses, it can be used to build an integration point for existing systems to simplify reporting, operation, and approval processes.The author has drawn on his15 years of hands-on analytics experience to help you pivot from the traditional Excel-based reporting environment. By using different business scenarios, this book provides you with clear reasons why a skill is important before you start to dive into the scenarios. You will use a fast prototyping approach to continue to build exciting reporting, automation, and application solutions and improve them while you acquire new skill sets. The book helps you get started quickly with Power BI. It covers data visualization, collaboration, and governance practices. You will learn about the most practical SQL challenges. And you will learn how to build applications in PowerApps and Power Automate.The book ends with an integrated solution framework that can be adapted to solve a wide range of complex business problems.What You Will LearnDevelop reporting solutions and business applicationsUnderstand the Power Platform licensing and development environmentApply Data ETL and modeling in Power BIUse Data Storytelling and dashboard design to better visualize dataCarry out data operations with SQL and SharePoint listsDevelop useful applications using Power AppsDevelop automated workflows using Power AutomateIntegrate solutions with Power BI, Power Apps, and Power Automate to build enterprise solutionsWho This Book Is ForNext-generation data specialists, including Excel-based users who want to learn Power BI and build internal apps; finance specialists who want to take a different approach to traditional accounting reports; and anyone who wants to enhance their skill set for the future job market.
Transitions in Mathematics Education
by Ghislaine Gueudet Marianna Bosch Andrea A. A. Disessa Oh Nam Nam Kwon Lieven VerschaffelThis book examines the kinds of transitions that have been studied in mathematics education research. It defines transition as a process of change, and describes learning in an educational context as a transition process. The book focuses on research in the area of mathematics education, and starts out with a literature review, describing the epistemological, cognitive, institutional and sociocultural perspectives on transition. It then looks at the research questions posed in the studies and their link with transition, and examines the theoretical approaches and methods used. It explores whether the research conducted has led to the identification of continuous processes, successive steps, or discontinuities. It answers the question of whether there are difficulties attached to the discontinuities identified, and if so, whether the research proposes means to reduce the gap to create a transition. The book concludes with directions for future research on transitions in mathematics education. "
Translating Statistics to Make Decisions
by Victoria CoxExamine and solve the common misconceptions and fallacies that non-statisticians bring to their interpretation of statistical results. Explore the many pitfalls that non-statisticians—and also statisticians who present statistical reports to non-statisticians—must avoid if statistical results are to be correctly used for evidence-based business decision making. Victoria Cox, senior statistician at the United Kingdom’s Defence Science and Technology Laboratory (Dstl), distills the lessons of her long experience presenting the actionable results of complex statistical studies to users of widely varying statistical sophistication across many disciplines: from scientists, engineers, analysts, and information technologists to executives, military personnel, project managers, and officials across UK government departments, industry, academia, and international partners. The author shows how faulty statistical reasoning often undermines the utility of statistical results even among those with advanced technical training. Translating Statistics teaches statistically naive readers enough about statistical questions, methods, models, assumptions, and statements that they will be able to extract the practical message from statistical reports and better constrain what conclusions cannot be made from the results. To non-statisticians with some statistical training, this book offers brush-ups, reminders, and tips for the proper use of statistics and solutions to common errors. To fellow statisticians, the author demonstrates how to present statistical output to non-statisticians to ensure that the statistical results are correctly understood and properly applied to real-world tasks and decisions. The book avoids algebra and proofs, but it does supply code written in R for those readers who are motivated to work out examples. Pointing along the way to instructive examples of statistics gone awry, Translating Statistics walks readers through the typical course of a statistical study, progressing from the experimental design stage through the data collection process, exploratory data analysis, descriptive statistics, uncertainty, hypothesis testing, statistical modelling and multivariate methods, to graphs suitable for final presentation. The steady focus throughout the book is on how to turn the mathematical artefacts and specialist jargon that are second nature to statisticians into plain English for corporate customers and stakeholders. The final chapter neatly summarizes the book’s lessons and insights for accurately communicating statistical reports to the non-statisticians who commission and act on them. What You'll LearnRecognize and avoid common errors and misconceptions that cause statistical studies to be misinterpreted and misused by non-statisticians in organizational settingsGain a practical understanding of the methods, processes, capabilities, and caveats of statistical studies to improve the application of statistical data to business decisionsSee how to code statistical solutions in RWho This Book Is ForNon-statisticians—including both those with and without an introductory statistics course under their belts—who consume statistical reports in organizational settings, and statisticians who seek guidance for reporting statistical studies to non-statisticians in ways that will be accurately understood and will inform sound business and technical decisions
Translational Bioinformatics and Its Application
by Dong-Qing Wei Yilong Ma William C. S. Cho Qin Xu Fengfeng ZhouThis book offers a detailed overview of translational bioinformatics together with real-case applications. Translational bioinformatics integrates the areas of basic bioinformatics, clinical informatics, statistical genetics and informatics in order to further our understanding of the molecular basis of diseases. By analyzing voluminous amounts of molecular and clinical data, it also provides clinical information, which can then be applied. Filling the gap between clinic research and informatics, the book is a valuable resource for human geneticists, clinicians, health educators and policy makers, as well as graduate students majoring in biology, biostatistics, and bioinformatics.
Translational Recurrences
by Norbert Marwan Michael Riley Alessandro Giuliani Charles L. WebberThis book features 13 papers presented at the Fifth International Symposium on Recurrence Plots, held August 2013 in Chicago, IL. It examines recent applications and developments in recurrence plots and recurrence quantification analysis (RQA) with special emphasis on biological and cognitive systems and the analysis of coupled systems using cross-recurrence methods. Readers will discover new applications and insights into a range of systems provided by recurrence plot analysis and new theoretical and mathematical developments in recurrence plots. Recurrence plot based analysis is a powerful tool that operates on real-world complex systems that are nonlinear, non-stationary, noisy, of any statistical distribution, free of any particular model type and not particularly long. Quantitative analyses promote the detection of system state changes, synchronized dynamical regimes or classification of system states. The book will be of interest to an interdisciplinary audience of recurrence plot users and researchers interested in time series analysis of complex systems in general.
TransMath: Innovative Solutions from Mathematical Technology
by María Teresa Sánchez Adela Martínez Peregrina Quintela Guadalupe Parente Ana Belén FernándezThe book "TransMath - Innovative Solutions from Mathematical Technology" has been conceived as a tool for the dissemination of scientific knowledge. This publication is addressed to those companies with innovation needs that could be met through mathematical technology. The book maps both existing and possible interactions and connections that enable technology transfer between Spanish mathematical research and industrial and business sectors. Businesses can determine the level of implementation and demand for such technology within their sector and understand the benefits and innovations achieved in other companies and industries with the application of mathematical techniques. The information is classified into eleven sectors of economic activity: Biomedicine & Health; Construction; Economics & Finance; Energy & Environment; Food; ICT; Logistics & Transport; Management & Tourism; Metal & Machinery; Public Administration; and Technical Services.
TransMath®: Expressions, Equations, and Functions
by John Woodward Mary StrohNIMAC-sourced textbook
TransMath: Developing Number Sense, Interactive Text
by John Woodward Mary StrohNIMAC-sourced textbook
TRANSMATHTM: Developing Number Sense
by John Woodward Mary StrohTransMath (2nd Edition) Developing Number Sense Student Text (Level 1)
Transmission Dynamics of Tick-Borne Diseases with Co-Feeding, Developmental and Behavioural Diapause (Lecture Notes on Mathematical Modelling in the Life Sciences)
by Jianhong Wu Xue ZhangThis monograph introduces some current developments in the modelling of the spread of tick-borne diseases. Effective modelling requires the integration of multiple frameworks. Here, particular attention is given to the previously neglected issues of tick developmental and behavioral diapause, tick-borne pathogen co-feeding transmission, and their interactions. An introduction to the required basics of structured population formulations and delay differential equations is given, and topics for future study are suggested. The described techniques will also be useful in the study of other vector-borne diseases. The ultimate aim of this project is to develop a general qualitative framework leading to tick-borne disease risk predictive tools and a decision support system. The target audience is mathematical biologists interested in modelling tick population dynamics and tick-borne disease transmission, and developing computational tools for disease prevention and control.
Transmutation Operators and Applications (Trends in Mathematics)
by Vladislav V. Kravchenko Sergei M. SitnikTransmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones. Accordingly, they represent an important mathematical tool in the theory of inverse and scattering problems, of ordinary and partial differential equations, integral transforms and equations, special functions, harmonic analysis, potential theory, and generalized analytic functions. This volume explores recent advances in the construction and applications of transmutation operators, while also sharing some interesting historical notes on the subject.
Transnational and Borderland Studies in Mathematics Education (Studies in Mathematical Thinking and Learning Series)
by Richard S. Kitchen Marta CivilEvery year, significant numbers of immigrant children from Mexico enter classrooms in the United States. These immigrants comprise a heterogeneous group of students with diverse needs, abilities, and experiences. Transnational and Borderland Studies in Mathematics Education is the first collection to offer research studies across these communities. Providing invaluable research on both sending and receiving communities in Mexico and the US, this collection considers the multiple aspects of children’s experiences with mathematics, including curriculum, classroom participation structures, mathematical reasoning and discourse – both in and out of school – and parents’ perceptions and beliefs about mathematics instruction. An important treatment of an insufficiently documented subject, this collection brings together researchers on both sides of the border to foster and support an interest in documenting evidence that will set the stage for future studies in mathematics education.
Transnational Family Relations of German Emigrants (Familienforschung)
by Karsten Hank Marcel ErlinghagenDrawing on unique data from the German Emigration and Remigration Panel Study (GERPS), the present book comprises empirical studies on various aspects of recent German emigrants’ transnational relationships to core family members, specifically intimate partners, parents, and children. Moreover, we reflect on conceptual and empirical challenges in previous work on transnational family relations, suggesting avenues for future research. We thereby aim to strengthen the integration of two closely related strands of social research – the sociologies of migration and families – and add an important new facet to the study of transnational families more generally.
Transnational Synergies in School Mathematics and Science Debates (Palgrave Studies in Excellence and Equity in Global Education)
by Roger Openshaw Margaret WalshawThis book highlights and interrogates the continued interest and scrutiny of mathematics and science education. National debates on excellence and equity tend to focus largely on underachievement in mathematics and science rather than subjects in the arts or music: this is due to a belief that these curriculum areas are central to individual workplace success and national development in a competitive economic environment. The authors explore the history of these assumptions, as well as the debates based around claims that student achievement levels in these subjects has fallen. Spanning the United States, New Zealand, Australia and the United Kingdom, the chapters question how such debates are sustained and amplified: how has this perceived ‘crisis’ been articulated and spread across national borders? This comprehensive book will be of interest and value to scholars of mathematics and science education, as well as international education debates.
Transport and Fluctuations in Granular Fluids
by Andrea PuglisiThis brief offers a concise presentation of granular fluids from the point of view of non-equilibrium statistical physics. The emphasis is on fluctuations, which can be large in granular fluids due to the small system size (the number of grains is many orders of magnitude smaller than in molecular fluids). Firstly, readers will be introduced to the most intriguing experiments on fluidized granular fluids. Then granular fluid theory, which goes through increasing levels of coarse-graining and emerging collective phenomena, is described. Problems and questions are initially posed at the level of kinetic theory, which describes particle densities in full or reduced phase-space. Some answers become clear through hydrodynamics, which describes the evolution of slowly evolving fields. Granular fluctuating hydrodynamics, which builds a bridge to the most recent results in non-equilibrium statistical mechanics, is also introduced. Further and more interesting answers come when the dynamics of a massive intruder are discussed. Such non-equilibrium stochastic process offers a more precise and compact picture of the features foreseen at the more detailed levels of description. The dynamics of an intruder diffusing in a granular fluid reveal the clearest connection with recent theories on stochastic energetics and stochastic thermodynamics.
Transport of Energetic Electrons in Solids
by Maurizio DaporThis book presents the potential of the Monte Carlo (MC) technique to solve mathematical and physical problems of great complexity. This book focusses on the study of the electron-solid interaction (transport MC) and presents some physical problems related to the transport of hot electrons in solid targets using transport MC. The numerical and theoretical results are validated through a comparison with experimental results. The author also addresses methodological aspects. In particular, systematic comparisons among different calculation schemes are presented. Different expressions for the calculation of cross sections and/or stopping power and different simulation methods are described and discussed.