An Introduction to the Operations With Series
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Slide Rule Simplified
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Anthemius of Tralles
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
50 Mathematical Puzzles and Oddities
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Outlines of a Formalist Philosophy of Mathematics
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Fuzzy Sets, Fuzzy Logic and Their Applications 2020
The present book contains the 24 total articles accepted and published in the Special Issue "Fuzzy Sets, Fuzzy Logic and Their Applications, 2020" of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of fuzzy sets and systems of fuzzy logic and their extensions/generalizations. These topics include, among others, elements from fuzzy graphs; fuzzy numbers; fuzzy equations; fuzzy linear spaces; intuitionistic fuzzy sets; soft sets; type-2 fuzzy sets, bipolar fuzzy sets, plithogenic sets, fuzzy decision making, fuzzy governance, fuzzy models in mathematics of finance, a philosophical treatise on the connection of the scientific reasoning with fuzzy logic, etc. It is hoped that the book will be interesting and useful for those working in the area of fuzzy sets, fuzzy systems and fuzzy logic, as well as for those with the proper mathematical background and willing to become familiar with recent advances in fuzzy mathematics, which has become prevalent in almost all sectors of the human life and activity.
International Perspectives on Mathematics Teacher Education
Mathematics teacher education includes the mathematics content teachers need to understand, ways that pedagogical approaches are developed, messages about the nature of mathematics teaching and learning, and interfaces between tertiary preparation and school contexts. Scholars from Sweden, France, Malawi, Singapore, New Zealand, Brazil, the USA, and Canada provide insights for the mathematics education community's understanding of how teacher educators structure, develop, and implement their respective mathematics teacher education programs. Several themes emerged across the chapters, including: varied approaches to developing culturally responsive pedagogies and/or Indigenous perspectives; issues and challenges in fostering partnerships and collaborations; strategies for developing mathematics knowledge for teaching; and preparing flexible and resourceful teachers.
Information Bottleneck
The celebrated information bottleneck (IB) principle of Tishby et al. has recently enjoyed renewed attention due to its application in the area of deep learning. This collection investigates the IB principle in this new context. The individual chapters in this collection: - provide novel insights into the functional properties of the IB; - discuss the IB principle (and its derivates) as an objective for training multi-layer machine learning structures such as neural networks and decision trees; and - offer a new perspective on neural network learning via the lens of the IB framework. Our collection thus contributes to a better understanding of the IB principle specifically for deep learning and, more generally, of information-theoretic cost functions in machine learning. This paves the way toward explainable artificial intelligence.
International Perspectives on Mathematics Teacher Education
Mathematics teacher education includes the mathematics content teachers need to understand, ways that pedagogical approaches are developed, messages about the nature of mathematics teaching and learning, and interfaces between tertiary preparation and school contexts. Scholars from Sweden, France, Malawi, Singapore, New Zealand, Brazil, the USA, and Canada provide insights for the mathematics education community's understanding of how teacher educators structure, develop, and implement their respective mathematics teacher education programs. Several themes emerged across the chapters, including: varied approaches to developing culturally responsive pedagogies and/or Indigenous perspectives; issues and challenges in fostering partnerships and collaborations; strategies for developing mathematics knowledge for teaching; and preparing flexible and resourceful teachers.
Thinking About Space and Time
This volume offers an integrated understanding of how the theory of general relativity gained momentum after Einstein had formulated it in 1915. Chapters focus on the early reception of the theory in physics and philosophy and on the systematic questions that emerged shortly after Einstein's momentous discovery. They are written by physicists, historians of science, and philosophers, and were originally presented at the conference titled Thinking About Space and Time: 100 Years of Applying and Interpreting General Relativity, held at the University of Bern from September 12-14, 2017. By establishing the historical context first, and then moving into more philosophical chapters, this volume will provide readers with a more complete understanding of early applications of general relativity (e.g., to cosmology) and of related philosophical issues. Because the chapters are often cross-disciplinary, they cover a wide variety of topics related to the general theory of relativity. These include: Heuristics used in the discovery of general relativityMach's PrincipleThe structure of Einstein's theoryCosmology and the Einstein worldStability of cosmological modelsThe metaphysical nature of spacetimeThe relationship between spacetime and dynamicsThe Geodesic PrincipleSymmetriesThinking About Space and Time will be a valuable resource for historians of science and philosophers who seek a deeper knowledge of the (early and later) uses of general relativity, as well as for physicists and mathematicians interested in exploring the wider historical and philosophical context of Einstein's theory.
Doc Lambacher hilft! Deine Unterst羹tzung zum Mathebuch - Gymnasium/Gesamtschule Einf羹hrungsphase (NRW)
Du brauchst Hilfe, dem Stoff des Matheunterrichts zu folgen? Es f瓣llt dir nicht leicht, den Inhalt des Lambacher Schweizer zu verstehen? Doc Lambacher hilft! Mit diesem Buch m繹chte ich dir helfen, den Lernstoff auf einfache Weise zu wiederholen. Anhand von zahlreichen Beispielaufgaben gehen wir zusammen noch einmal den gesamten Lernstoff durch. Damit wird dir garantiert der Schrecken vor der n瓣chsten Mathearbeiten genommen: Du wirst bestens vorbereitet sein! In diesem 2. Band behandeln wir die Themen: - Vektoren - Wahrscheinlichkeit - Potenzen in Termen und Funktionen (Referenz: NRW-Ausgabe des Lambacher Schweizer)
The Center and Focus Problem
This book focuses on an old problem of the qualitative theory of differential equations, called the Center and Focus Problem. The book reflects the results obtained by the authors in the last decades.
Spaces of Measures and Their Applications to Structured Population Models
Structured population models are transport-type equations often applied to describe evolution of heterogeneous populations of biological cells, animals or humans, including phenomena such as crowd dynamics or pedestrian flows. This book introduces the mathematical underpinnings of these applications, providing a comprehensive analytical framework for structured population models in spaces of Radon measures. The unified approach allows for the study of transport processes on structures that are not vector spaces (such as traffic flow on graphs) and enables the analysis of the numerical algorithms used in applications. Presenting a coherent account of over a decade of research in the area, the text includes appendices outlining the necessary background material and discusses current trends in the theory, enabling graduate students to jump quickly into research.
Mathematical Research in the last 20 years
No detailed description available for "Mathematical Research in the last 20 years".
Handbook of Formal Argumentation, Volume 2
The Handbook of Formal Argumentation is a community effort aimed at providing a comprehensive and up-to-date view of the state of the art and current trends in the lively research field of formal argumentation. In recent years, this field has matured to a central area in Artificial Intelligence in general, and Knowledge Representation and Applied Logics in particular.The second volume of the Handbook is organised into three parts, containing thirteen chapters in all, each written by leading experts in the field. The first part contains surveys and personal views on extensions to abstract argumentation frameworks, such as bipolar argumentation, value-based argumentation, and many more. The second part is about dynamic aspects of argumentation and argumentative dialogues. Finally, the third part provides some meta-level investigations on formal argumentation issues, such as a logical analysis of formal argumentation and empirical cognitive studies.The Handbook of Formal Argumentation is an open-ended initiative of which the present volume is the second outcome. Further volumes are planned to cover topics not included in the first one or the present one and the initiative is conceived to grow by the support and feeding it receives from the community members.
Electricity and Magnetism
All electrical actions are referred to force, are consequently expressed by the aid of three fundamental quantities, length, mass, and time. To measure these quantities is approximately the billionth part of the centimetre, the gram, and the second as units. The Centimetre is approximately the billionth part of the terrestrial quardant; rigorogusly speaking, it is the hundreadth part of the standard metr
Data Analytics Made Easy
Use data analytics and data storytelling in your work without writing any codeKey Features: Learn the art of telling stories with your dataGet ahead in your career by thinking like a data scientistStart working with data to get better insightsBook Description: Data Analytics Made Easy is an accessible guide for anyone new to working with data. It focuses on how to generate insights from your data at a click of a button using popular tools, without having to write a line of code! The book helps you start analyzing data and quickly apply these skills to your work.Data analytics has become a necessity in modern business, and skills such as data visualization, machine learning, and digital storytelling are now essential in every field. If you want to make sense of your data and add value with informed decisions, this is the book for you.The book introduces the concepts of data analytics and shows you how to get your data ready and apply algorithms. Implement analytics solutions to predict future trends and assess their levels of accuracy. Create impressive visualizations and learn the greatest secret in successful analytics - how to tell a story with your data. You'll connect the dots on the various stages of the data-to-insights process.By the end of this book, you will have learned how to get your data talking and sell the results to your customers without writing a line of code.What You Will Learn: Understand the potential of data and its impact on any businessInfluence business decisions with effective data storytelling when delivering insightsImport, clean, transform, combine data feeds, and automate your processesLearn the basics of machine learning to add value to your organizationCreate professional-looking and business-centric visuals and dashboardsWho this book is for: If you are new to working with data and you want to progress in your career, you'll find this book an effective way to add analytics to your skill stack.No previous math, statistics, or computer science knowledge is required.
The Discrete Mathematical Charms of Paul Erdős
Paul Erdős published more papers during his lifetime than any other mathematician, especially in discrete mathematics. He had a nose for beautiful, simply-stated problems with solutions that have far-reaching consequences across mathematics. This captivating book, written for students, provides an easy-to-understand introduction to discrete mathematics by presenting questions that intrigued Erdős, along with his brilliant ways of working toward their answers. It includes young Erdős's proof of Bertrand's postulate, the Erdős-Szekeres Happy End Theorem, De Bruijn-Erdős theorem, Erdős-Rado delta-systems, Erdős-Ko-Rado theorem, Erdős-Stone theorem, the Erdős-R矇nyi-S籀s Friendship Theorem, Erdős-R矇nyi random graphs, the Chv獺tal-Erdős theorem on Hamilton cycles, and other results of Erdős, as well as results related to his work, such as Ramsey's theorem or Deza's theorem on weak delta-systems. Its appendix covers topics normally missing from introductory courses. Filled with personal anecdotes about Erdős, this book offers a behind-the-scenes look at interactions with the legendary collaborator.
The Discrete Mathematical Charms of Paul Erdős
Paul Erdős published more papers during his lifetime than any other mathematician, especially in discrete mathematics. He had a nose for beautiful, simply-stated problems with solutions that have far-reaching consequences across mathematics. This captivating book, written for students, provides an easy-to-understand introduction to discrete mathematics by presenting questions that intrigued Erdős, along with his brilliant ways of working toward their answers. It includes young Erdős's proof of Bertrand's postulate, the Erdős-Szekeres Happy End Theorem, De Bruijn-Erdős theorem, Erdős-Rado delta-systems, Erdős-Ko-Rado theorem, Erdős-Stone theorem, the Erdős-R矇nyi-S籀s Friendship Theorem, Erdős-R矇nyi random graphs, the Chv獺tal-Erdős theorem on Hamilton cycles, and other results of Erdős, as well as results related to his work, such as Ramsey's theorem or Deza's theorem on weak delta-systems. Its appendix covers topics normally missing from introductory courses. Filled with personal anecdotes about Erdős, this book offers a behind-the-scenes look at interactions with the legendary collaborator.
Symbols and Things
In the steam-powered mechanical age of the eighteenth and nineteenth centuries, the work of late Georgian and early Victorian mathematicians depended on far more than the properties of number. British mathematicians came to rely on industrialized paper and pen manufacture, railways and mail, and the print industries of the book, disciplinary journal, magazine, and newspaper. Though not always physically present with one another, the characters central to this book--from George Green to William Rowan Hamilton--relied heavily on communication technologies as they developed their theories in consort with colleagues. The letters they exchanged, together with the equations, diagrams, tables, or pictures that filled their manuscripts and publications, were all tangible traces of abstract ideas that extended mathematicians into their social and material environment. Each chapter of this book explores a thing, or assembling of things, mathematicians needed to do their work--whether a textbook, museum, journal, library, diagram, notebook, or letter--all characteristic of the mid-nineteenth-century British taskscape, but also representative of great change to a discipline brought about by an industrialized world in motion.
An Invitation to Combinatorics
Active student engagement is key to this classroom-tested combinatorics text, boasting 1200+ carefully designed problems, ten mini-projects, section warm-up problems, and chapter opening problems. The author - an award-winning teacher - writes in a conversational style, keeping the reader in mind on every page. Students will stay motivated through glimpses into current research trends and open problems as well as the history and global origins of the subject. All essential topics are covered, including Ramsey theory, enumerative combinatorics including Stirling numbers, partitions of integers, the inclusion-exclusion principle, generating functions, introductory graph theory, and partially ordered sets. Some significant results are presented as sets of guided problems, leading readers to discover them on their own. More than 140 problems have complete solutions and over 250 have hints in the back, making this book ideal for self-study. Ideal for a one semester upper undergraduate course, prerequisites include the calculus sequence and familiarity with proofs.
A Short Account of the History of Mathematics
The subject-matter of this book is a historical summary of the development of mathematics, illustrated by the lives and discoveries of those to whom the progress of the science is mainly due. It may serve as an introduction to more elaborate works on the subject, but primarily it is intended to give a short and popular account of those leading facts in the history of mathematics which many who are unwilling, or have not the time, to study it systematically may yet desire to know. The first edition was substantially a transcript of some lectures which I delivered in the year 1888 with the object of giving a sketch of the history, previous to the nineteenth century, that should be intelligible to any one acquainted with the elements of mathematics. In the second edition, issued in 1893, I rearranged parts of it, and introduced a good deal of additional matter.
In Pursuit of Zeta-3
An engrossing look at the history and importance of a centuries-old but still unanswered math problem For centuries, mathematicians the world over have tried, and failed, to solve the zeta-3 problem. Math genius Leonhard Euler attempted it in the 1700s and came up short. The straightforward puzzle considers if there exists a simple symbolic formula for the following: 1+(1/2)^3+(1/3)^3+(1/4)^3+. . . . But why is this issue--the sum of the reciprocals of the positive integers cubed--so important? With In Pursuit of Zeta-3, popular math writer Paul Nahin investigates the history and significance of this mathematical conundrum. Drawing on detailed examples, historical anecdotes, and even occasionally poetry, Nahin sheds light on the richness of the nature of zeta-3. He shows its intimate connections to the Riemann hypothesis, another mathematical mystery that has stumped mathematicians for nearly two centuries. He looks at its links with Euler's achievements and explores the modern research area of Euler sums, where zeta-3 occurs frequently. An exact solution to the zeta-3 question wouldn't simply satisfy pure mathematical interest: it would have critical ramifications for applications in physics and engineering, such as quantum electrodynamics. Challenge problems with detailed solutions and MATLAB code are included at the end of each of the book's sections. Detailing the trials and tribulations of mathematicians who have approached one of the field's great unsolved riddles, In Pursuit of Zeta-3 will tantalize curious math enthusiasts everywhere.
Analytic Geometry and Calculus
The present work is a revision and abridgment of the authors' "Course in Mathematics for Students of Engineering and Applied Science". The condensation of a two-volume work into a single volume has been made possible partly by the omission of some topics, but more especially by a rearrangement of subject matter and new methods of treatment. Among the subject omitted are determinations, much of the general theory of equations, the general equation of the conic sections, polars and diameters related to conics, center of curvature, evolutes, certain special methods, of integration, complex numbers, and some types of differential, can well be postponed to a latter course, of subjects which are more immediately important.
Geometry and Trigonometry Geometry, Plane Trigonometry,
The volume of the International Library of Technology are made up of Instruction Papers, or Sections, comprising the various courses of instruction for students of the International Correspondence Schools. The original manuscripts are prepared by persons thoroughly qualified both technically and by experience to write with authority, and in may cases they are regularly employed elsewhere in practical work as experts.
The Elements of the Integral Calculus
The work here submitted to the notice of the public forms the third volume of a course intended to furnish to the mathematical student a pretty comprehensive view of the principles of modern analytical science. To complete this design will require a fourth volume, in some measure supplementary to the three now completed, and to contain the subject of Finite Differences, a fuller inquiry into the theory of Partial Differential Equations, and a chapter on Definite Integrals. This final volume I hope hereafter to be able to prepare, although I do not propose to enter immediately upon the undertaking.
The Foundation of Geometry
Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry. The present book is a new attempt to choose for geometry a simple and complete set of independent axioms and to deduce from these the most important geometrical theorems in such a manner as to bring out as clearly as possible the significance of the different groups of axioms and the scope of the conclusionsto be derived from the individual axioms.
The Theory of Numbers
The purpose of this little book is to give the reader a convenientintroduction to the theory of numbers, one of the most extensiveand most elegant disciplines in the whole body of mathematics. The treatment throughout is madeas brief as ispossible consistent with clearness and is confinedentirely to fundamental matters. This is done because it is believedthat in this way the book may best be made to serve its purposeas an introduction to the theory of numbers.Numerous problems are supplied throughout the text. The exercises marked with a star are moredifficult than the others; they will doubtlessly appeal to the beststudents. Finally, this book is made up from thematerial used by the author in lectures in Indiana University during thepast two years; and the selection of matter, especially of exercises, has been based on the experience gained in this way
Heuristische Strategien in Der Schulmathematik
Mathematik lehren hei?t Denken lehren und nicht nur das rezepthafte Abarbeiten von Kalk羹len. Wie kann dies gelingen? In diesem Buch werden einige Antworten auf Grundlage heuristischer Strategien gegeben. Diese stellen einen wesentlichen Teil der Methode der Mathematik dar und sind damit zentral f羹r das Verst瓣ndnis mathematischer Handlungen und Kompetenzen. Die Anwendung dieses fachdidaktisch fundierten theoretischen Konzeptes wird durch vielf瓣ltige detaillierte Beispiele aus der Schulmathematik illustriert. Das Buch richtet sich an Fachdidaktiker, Lehrerbildner, Studierende des Lehramtes sowie praktizierende Lehrerinnen und Lehrer und zeigt viele M繹glichkeiten auf, wie heuristischen Strategien in der Schule konkret f羹r den Unterricht genutzt werden k繹nnen. Dabei wird deutlich, dass diese Strategien sowohl in der Schulmathematik als auch in der Universit瓣tsmathematik omnipr瓣sent sind. Auf diese Weise wird ein roter Faden von der Mathematik in der Grundschule羹ber die weiterf羹hrende Schule bis zur Universit瓣t sichtbar.
Attractors of Hamiltonian Nonlinear Partial Differential Equations
This monograph is the first to present the theory of global attractors of Hamiltonian partial differential equations. A particular focus is placed on the results obtained in the last three decades, with chapters on the global attraction to stationary states, to solitons, and to stationary orbits. The text includes many physically relevant examples and will be of interest to graduate students and researchers in both mathematics and physics. The proofs involve novel applications of methods of harmonic analysis, including Tauberian theorems, Titchmarsh's convolution theorem, and the theory of quasimeasures. As well as the underlying theory, the authors discuss the results of numerical simulations and formulate open problems to prompt further research.
Analyse Von Transferprozessen in Der Entwicklung Des Bruchzahlbegriffs
Sebastian Kollhoff rekonstruiert und analysiert in diesem Open-Access-Buch in einer Feldstudie mit F羹nftkl瓣sslerinnen und F羹nftkl瓣sslern Transferprozesse in der Entwicklung von Grundvorstellungen zu Br羹chen. Anhand von umfassenden Detailanalysen der Bearbeitungen von Lernenden im allt瓣glichen Unterricht charakterisiert der Autor den Verlauf von Prozessen des Transfers, die das Potenzial haben fachlich optimiertes Lernen zu initiieren, aber auch die Gefahr bergen dieses zu behindern. Dabei arbeitet er heraus, dass sich bereits bei ersten elementaren Transferschritten erhebliche individuelle Unterschiede in der Auspr瓣gung des Transfers ergeben.
Nonlinear Fractional Differential Equations. Some Exact Solitary Wave Solutions
Master's Thesis from the year 2021 in the subject Mathematics - Applied Mathematics, grade: 99/110, University of Verona, language: English, abstract: The current study deals with distinct kinds of solitary wave solutions for the fractional generalized Duffing model and fractional diffusion reaction model with novel truncated M-fractional derivative. We are also interested in studying some special cases of the fractional generalized Duffing model. These are known as fractional Landau-Ginzburg-Higgs equation, classical fractional Klein-Gordon equation, the Phi-4 equation, the Sine-Gordon equation and the Duffing equation. The obtained results can be used in describing these models in some better way. The novel fractional derivative operator namely M-fractional derivative is used to study the above-mentioned models. Also, the obtained results are verified via symbolic software Mathematica. A modified integration method, the extended Sinh-Gordon equation expansion method (EShGEEM) is employed to secure the aforesaid solitary wave solutions. Furthermore, the obtained results show that the suggested approach have broadened capacity to obtain the different wave solutions of the fractional differential equations effectively. At the end, the results are also explained through their graphical representations.
Differential Equations
This book follows an innovative approach of inculcating linear algebra and elementary functional analysis in the backdrop of even the simple methods of solving ordinary differential equations. It is made user-friendly through concise useful theoretical discussions and numerous illustrative examples practical and pathological.
Mathe ganz einfach
Der vorliegende Band "Mathe ganz einfach" enth瓣lt die ele-mentare Arithmetik und Algebra in ihren Grundz羹gen mit Einschluss der quadratischen Gleichun-gen und der Rechnungsarten dritter Stufe. Komplexere Rechnungsarten und Randgebiete der Algebra und Arithmetik wurden nicht aufgenommen. So eignet sich der Band zur Einf羹hrung, Wiederholung oder Schlie?ung grundlegender L羹cken, insbesondere auch wegen der zahlreichen ?bungsaufgaben.
Doc Lambacher hilft! Deine Unterst羹tzung zum Mathebuch - Gymnasium/Gesamtschule Einf羹hrungsphase (NRW)
Du brauchst Hilfe, dem Stoff des Matheunterrichts zu folgen? Es f瓣llt dir nicht leicht, den Inhalt des Lambacher Schweizer zu verstehen? Doc Lambacher hilft! Mit diesem Buch m繹chte ich dir helfen, den Lernstoff auf einfache Weise zu wiederholen. Anhand von zahlreichen Beispielaufgaben gehen wir zusammen noch einmal den gesamten Lernstoff durch. Damit wird dir garantiert der Schrecken vor der n瓣chsten Mathearbeiten genommen: Du wirst bestens vorbereitet sein! In diesem 1. Band behandeln wir die Themen: - Funktionen - Ableitungen - Funktionsuntersuchungen (Referenz: NRW-Ausgabe des Lambacher Schweizer)
Research Trends in Graph Theory and Applications
The Workshop for Women in Graph Theory and Applications was held at the Institute for Mathematics and Its Applications (University of Minnesota, Minneapolis) on August 19-23, 2019. During this five-day workshop, 42 participants performed collaborative research, in six teams, each focused on open problems in different areas of graph theory and its applications. The research work of each team was led by two experts in the corresponding area, who prior to the workshop, carefully selected relevant and meaningful open problems that would yield high-quality research and results of strong impact. As a result, all six teams have made significant contributions to several open problems in their respective areas. The workshop led to the creation of the Women in Graph Theory and Applications Research Collaboration Network, which provided the framework to continue collaborating and to produce this volume.This book contains six chapters, each of them on one of the different areas of research at the Workshop for Women in Graph Theory and Applications, and written by participants of each team.
The Mental Arithmetic
Practical mathematics for everyday lifeWhile there is no shortage of math textbooks available to parents and educators, much of the common material today is neither practical nor related to real everyday life. Math is a practical and useful subject, and should be learned in such a manner. This little volume, originally written by educational reformer and pioneer Dr. Edward Sutherland, will be an enjoyable study to the student of nearly any age. It is not a textbook in the traditional sense, but will be most helpful to the parent or teacher seeking to teach math from a practical and useful standpoint and with wholesome principles and subjects.
Epistemological Beliefs and Critical Thinking in Mathematics
Epistemological beliefs--i.e. beliefs on the nature of knowledge, its limits, sources, and justification--play an important role both in everyday life and in learning processes. This book comprises several studies dealing with such beliefs in the domain of mathematics; amongst others a qualitative interview study, and quantitative studies for which a new questionnaire has been developed. In this new instrument, belief position (e.g. "mathematical knowledge is certain" vs. "uncertain") and belief argumentation (the way those positions are justified) are differentiated. Additionally, a test for mathematical critical thinking has been designed.The results show significant correlations between sophisticated belief argumentations and high scores in the critical thinking test, but no correlations regarding belief positions.
Students’ Understanding of Mathematical Concepts
This book presents four research papers, the first three based on the APOS Theory framework and the last one on the type of problems that need to be formulated to aid the development of mental structures for students. It is an attempt to illustrate how APOS Theory could give insight into the development of mental structures during the teaching and learning of some undergraduate mathematics concepts/topics; namely the derivative, integration and solving a system of linear equations. The published papers that follow in this book are based on the author's understanding of what APOS Theory is, how it could be used as a theoretical framework to guide research into a better understanding of how mental structures could probably develop during the teaching and learning of mathematics concepts.
My Number Workbook
The Number Workbook was created with my grandchildren in mind. They are at the age where they are beginning to hold pens and pencils and trying to write. It is all scribble. So we decided to create individual books, with only a few set of numbers so the children can learn a few numbers at a time. This book has tracing numbers and a place where they can try to write the number without tracing. It also has activities for the children at the bottom of every number page and a few pages that are activities only. This book will help your child develop their cognitive and motor skills.
Handbook for the Brain Dynamics Toolbox
The Brain Dynamics Toolbox is an open software tool for simulating dynamical systems in matlab. It allows custom dynamical models to be explored in an intuitive graphical application while retaining the ability to script large-scale simulations. It can be applied to initial-value problems in any domain that involves systems of Ordinary Differential Equations (ODEs), Delay Differential Equations (DDEs), Stochastic Differential Equations (SDEs) or Partial Differential Equations (PDEs). This book is for researchers and students who wish to use the toolbox to simulate their own dynamical models. It describes how to define the dynamical equations and load them into the graphical interface from where interchangeable solvers and visualisations can be applied with no additional programming effort. The source code for the final model can be published independently of the toolbox.Dr Stewart Heitmann is a Senior Staff Scientist at the Victor Chang Cardiac Research Institute. He studies cardiac arrhythmogenesis using mathematical and computational models of excitable systems.Professor Michael Breakspear is Head of the Systems Neuroscience Group at the University of Newcastle, Australia. He studies the principles of adaptive large-scale brain dynamics in health, and the impact of their disturbance in brain disorders.
Argumentieren in Mathematischen Spielsituationen Im Kindergarten
Einhergehend mit der zunehmenden Bedeutung fr羹hkindlicher Bildung r羹ckte in der mathematikdidaktischen Forschung auch die fr羹he mathematische Bildung in den Fokus. Ein Schwerpunkt liegt auf der Erforschung spielbasierter mathematischer F繹rderung und dabei entstehender Lerngelegenheiten. Ein Schl羹ssel zur Wissenskonstruktion beim mathematischen Lernen sind verbale und nonverbale Interaktionen und damit einhergehend auch Argumentationen, die als spezifische Form der Interaktion gelten. An diesem Punkt setzt die Studie an, die als Teilprojekt des von der Internationalen Bodenseehochschule (IBH) gef繹rderten Projekts "Spielintegrierte mathematische Fr羹hf繹rderung (spimaf)" durchgef羹hrt wurde. Julia B繹hringer untersucht, wie sich Interaktions- und Argumentationsprozesse in mathematischen Spielsituationen unter Kindergartenkindern gestalten. ?bergeordnete Ziele der qualitativen Studie sind die Erfassung und Beschreibung von strukturellen und inhaltlichen Aspekten der Interaktionen sowie die Analyse deren Qualit瓣t in Form von Argumentationstiefen. Insgesamt lassen die Ergebnisse darauf schlie?en, dass sich speziell konzipierte, arithmetische Regelspiele zur Anregung und F繹rderung von mathematischen Interaktionen und Argumentationen eignen.
(Co)End Calculus
The language of ends and (co)ends provides a natural and general way of expressing many phenomena in category theory, in the abstract and in applications. Yet although category-theoretic methods are now widely used by mathematicians, since (co)ends lie just beyond a first course in category theory, they are typically only used by category theorists, for whom they are something of a secret weapon. This book is the first systematic treatment of the theory of (co)ends. Aimed at a wide audience, it presents the (co)end calculus as a powerful tool to clarify and simplify definitions and results in category theory and export them for use in diverse areas of mathematics and computer science. It is organised as an easy-to-cite reference manual, and will be of interest to category theorists and users of category theory alike.
Building Bridges II
This volume collects together research and survey papers written by invited speakers of the conference celebrating the 70th birthday of L獺szl籀 Lov獺sz.The topics covered include classical subjects such as extremal graph theory, coding theory, design theory, applications of linear algebra and combinatorial optimization, as well as recent trends such as extensions of graph limits, online or statistical versions of classical combinatorial problems, and new methods of derandomization.L獺szl籀 Lov獺sz is one of the pioneers in the interplay between discrete and continuous mathematics, and is a master at establishing unexpected connections, "building bridges" between seemingly distant fields. His invariably elegant and powerful ideas have produced new subfields in many areas, and his outstanding scientific work has defined and shaped many research directions in the last 50 years. The 14 contributions presented in this volume, all of which areconnected to L獺szl籀 Lov獺sz's areas of research, offer an excellent overview of the state of the art of combinatorics and related topics and will be of interest to experienced specialists as well as young researchers.
Set-Valued Analysis
This Special Issue contains eight original papers with a high impact in various domains of set-valued analysis. Set-valued analysis has made remarkable progress in the last 70 years, enriching itself continuously with new concepts, important results, and special applications. Different problems arising in the theory of control, economics, game theory, decision making, nonlinear programming, biomathematics, and statistics have strengthened the theoretical base and the specific techniques of set-valued analysis. The consistency of its theoretical approach and the multitude of its applications have transformed set-valued analysis into a reference field of modern mathematics, which attracts an impressive number of researchers.
In the Footsteps of Programming Teachers
"Krzysztof Frankowski has written an unusual book with a fresh look at many of the fundamental ideas behind the digital computer and the algorithms they run. This book should inspire the reader to explore these ideas further." -- Professor Daniel Boley, Data Science Director of Graduate Studies, University of Minnesota. "I enjoyed reading mathematics viewed through the clear lens of a mathematical computer scientist."-- Professor Stanislaw Goldstein, Chair of the Department of Applied Computer Science, University of L籀dź, Poland. This book is a meditation on the history and relationship of mathematics and programming by a pioneer from the early era of computing. Each of 13 chapters focuses on one or two master teachers and something they taught us. The teachings are broad concepts, but also concrete, with a problem defined in each chapter, and implemented in Mathematica (which can also be run in Mathics, a free and open-source tool). Spend a few hours reading some polished programming pearls. "We live in times of awful extravagance and waste of resources. Indeed, our actions and attitudes may be threatening even the beauty and human habitability of the natural environment of our planet. Mindset and values are important from small to large. I want to teach students to recognize the beauty of small pearls rather than tolerate the wasteful tangles that result from laziness."
Something Blue
The truth is out there... This sheer enchantment of mathematics is a meeting of minds that reaches throughout the eras of time and finally makes sense in the form of a present! The power of Exponents becomes clear in this story: Exponents are firmly rooted in the truth of the unknown, and reveal themselves only to a chosen few who seek out to find them.
Something Blue
The truth is out there... This sheer enchantment of mathematics is a meeting of minds that reaches throughout the eras of time and finally makes sense in the form of a present! The power of Exponents becomes clear in this story: Exponents are firmly rooted in the truth of the unknown, and reveal themselves only to a chosen few who seek out to find them.
