Fluid Flow and Stability
Modelling of flow and transport is an essential component of many scientific and engineering applications, with increased interests in recent years. Application areas vary widely and include groundwater contamination, carbon dioxide sequestration, air pollution, petroleum exploration and recovery, weather prediction, and chemical separation processes. However, accurate mathematical and numerical simulation of flow and transport remains a challenging topic from many aspects of physical modelling, numerical analysis, and scientific computation. In the present book, a study is made to understand the flow dynamics in porous medium and its transition behavior in a horizontal layer.
Systems theory and system analysis in economy
Systems theory and systems analysis in economics: Tutorial /A.V.Tyurin, A.Yu. Akhmerov ‒ D羹sseldorf: LAP LAMBERT Academic Publishing GmbH & Co.KG., 2020. - 164 p. - ISBN 978-620-2-55443-5 .The manual is written in accordance with the syllabus of the course "Theory of Systems and Systems Analysis", which is read by masters in the specialty "Economics". The basics of systems theory and systems analysis are presented with the purpose of mastering students' knowledge of the laws and models of systems, methods of analysis and synthesis of systems; developing the ability to apply the laws, models and methods of systems; problem-solving skills by system analysis methods.
Fuzzy ahp with trapezoidal fuzzy numbers and topsis
Analytical Hierarchy Process (AHP) is a popular multi criteria decision making developed by Thomas L. Saaty. A method was explained by synthesizing the concepts of Fuzzy Analytical Hierarchy Process and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) with Trapezoidal Fuzzy Numbers which are used to rank the alternatives with respect to different criteria. A case study on problem of student drop outs in schools was conducted to identify and rank the alternatives with respect to different criteria. It can be concluded that Implementation of Infrastructure has highest weight which curbs student dropouts, based on opinions of the experts.
Ensemble Algorithms and Their Applications
In recent decades, the development of ensemble learning methodologies has gained a significant attention from the scientific and industrial community, and found their application in various real-word problems. Theoretical and experimental evidence proved that ensemble models provide a considerably better prediction performance than single models. The main aim of this collection is to present the recent advances related to ensemble learning algorithms and investigate the impact of their application in a diversity of real-world problems. All papers possess significant elements of novelty and introduce interesting ensemble-based approaches, which provide readers with a glimpse of the state-of-the-art research in the domain.
Fixed Point Theory
The purpose of this book is to provide a primary resource for anyone interested in fixed point theory in Non-Archimedean Menger Probabilistic Metric Space. The book presents information for those wishing to find results that might apply to their own work and for those wishing to obtain a deeper understanding of the theory. The book should be of interest to a wide range of researchers in Mathematical Analysis as well as to those whose primary interest is the study of fixed point theory and the underlying spaces. The level of exposition is directed to a wide audience, including students and established researchers. The topics treated range from fairly standard results (such as Banach contraction principle, Brouwer's and Schauder's fixed point theorems) to the frontier of what is known, but I have not tried to achieve maximal generality in all possible directions. I hope that the reference quoted may be useful for this purpose. The point of view adapted in this book is that of functional analysis. A knowledge of functional analysis is not a prerequisite, although a knowledge of an introductory course in functional analysis would be profitable.
Fractional Calculus - Application to Physical Problems
Our endeavour is to study fractional calculus from a different angle, starting from elementary to higher level of research. This is an entirely new topic different from the traditional system of mathematics. It started from the work of Leibniz in the 17th century but remained untouched till the beginning of the 20th century. The development of the subject started seriously by the researchers at the end of the last quarter of the 20th century, that is why fractional calculus is called calculus of the 20th century. The theory and application of fractional calculus are now tested in the areas of Science, Engineering, Technology, Rheology, Viscoelasticity, Chemical Physics, Electromagnetic Waves, Acoustics, Finance, Statistics and Economics.The physical problems involved in the study of fractional differential equations are both linear and nonlinear in nature. The solution of the types of problems appeared in the discussion of the fractional differential equations needs new types of methods. For this reason new methods like Adomian Decomposition Method, Homotopy Analysis Method, Variational Itaration Method, Generalized Differential Transform Method etc.have been applied in this conne
Mathematics Handbook to Electronics Engineering
The following book is a recollection of superior mathematics to electronics engineering and scientists through resolved problems, in which are exposed many applications and research exercises to electronics and their prospective as are micro-electronics, sensor technology, electronic nano-components, semi-conductors, photonics, opto-electronics and spintronics. The corresponding specialized mathematics to these disciplines are conformed in several mathematics areas as are special functions and integral transforms, Fourier analysis (harmonic and non-harmonic), control theory, complex variable, differential equations (partial and ordinary), vector and tensor calculus, rational electronics and quantum field theory. Also is precisely consider the physics fundamentals though of the electromagnetic theory, solid state, physical optics, thermodynamics, physical systems dynamics, Lagrangian dynamics, and QED (Quantum Electrodynamics) and quantum mechanics, these last as part of quantum field theory.
Digital Smile Design
In essence the entire concept rests on the analysis of the your facial and dental proportions and by incorporating a preselected series of high quality digital photographs and videos into a systematic, effective communicative approach. That supports the evaluation, diagnostic, planning - implementation, of treatment processes unique to your specific case. DSD has been structured with an amazingly simple set of protocols. Any standard laptop, desktop, notebook or tablet will be sufficient and the MS Power-point or Apple Keynote software, available in most dental clinics for basic presentation purposes can all be used in the Digital Design process.Digital Smile Design's (DSD) multi-purpose communication methods stimulate consistent levels of excellence to achieve highly satisfying results.
The Daring Invention of Logarithm Tables
*** This is the black and white edition. There is also a color edition. *** In the early 17th century, both Jost B羹rgi and John Napier dared to invent a logarithm table whose construction required tens of thousands of computing steps. These tables reduced computing effort for multiplication and division by an order of magnitude. Indeed, their invention launched a computing revolution that continues to this day. The book tells the story of B羹rgi's and Napier's work, and how Henry Briggs built on Napier's idea, creating a table of logarithms that was easier to use. John Napier and Henry Briggs described their methods in detail; distribution of their results was widespread. In contrast, Jost B羹rgi did not leave detailed records of his work. Just a few copies of his table and terse handwritten instructions for its use have survived. To fill this gap, the book reconstructs B羹rgi's thinking leading up to his table. The reader looks over his shoulder, so to speak, and learns how B羹rgi came upon the idea, how he decided on the specific format of the table, and how his instructions should be interpreted. And so the reader experiences the magic of the invention of logarithms. The final chapters examine the question "Who invented logarithms?". For centuries, few people were aware of B羹rgi's work; John Napier was considered to be the sole inventor. This changed at the middle of the 19th century when Jost B羹rgi's work became more widely known. Since then there has been extensive debate whether B羹rgi should be considered an independent co-inventor. Careful parsing of the history of logarithm going back to Archimedes of antiquity then reveals that, without doubt, John Napier and Jost B羹rgi are independent co-inventors of logarithms. This book is also available in German: Die wagemutige Erfindung der Logarithmentafeln
Numerical Solutions and Stability Analysis of Brusselator System
In this work, we studied the numerical solution of the Brusselator model in one dimension using FDM including explicit and implicit methods; FEM with weighted residual methods and iterative methods. Also, we studied the numerical solution of the Brusselator model in two dimensions using ADI ( Alternating Direction Implicit) and ADE (Alternating Direction Explicit) methods. Besides, we studied the numerical stability of FDM (explicit and implicit methods); the numerical stability analysis of the Brusselator system was done in one-dimensional space and two-dimensional spaces. For one dimensional space, we have studied the numerical stability for explicit and implicit (Crank- Nicolson) methods and we have found the stability condition for explicit method, whereas the implicit method is unconditionally stable. For two dimensional space, we found the stability condition for ADE method, while ADI is unconditionally stable.
Soft Fuzzy and fuzzy soft set theory With applications
we classify the fuzzy sets families which produced seven different families and two new definitions for fuzzy points. A definition of families which is called soft sets and by using the composition technique between fuzzy points and soft points we get new three different fuzzy soft points also via nine combinations between soft points and fuzzy points, new five soft fuzzy points are extracted .For the new three different fuzzy soft points, fuzzy soft topological space also for the new five different soft fuzzy points, soft fuzzy topological space is studied respectively. It worth to say that it is possible to define adherence, accumulation, exterior, interior and boundary points according to fuzzy soft sets and on the soft fuzzy sets with studying the separation axioms on them added to the above as well .Soft probability and soft fuzzy reliability in topological spaces are presented in light of concepts of soft sets and probability theory, to show the relation between soft probability and topology is presented via an illustrative example. Evaluation of reliability for different types of systems as an application concern different kind of uncertainty by using distinct mathematical tools as vague sets, intuitionistic fuzzy sets, fuzzy soft sets and soft fuzzy set is presented and added to this applications to clarify the relation between the topology and the confidence interval through an example.
A Celebration of the Edge Program’s Impact on the Mathematics Community and Beyond
The Enhancing Diversity in Graduate Education (EDGE) Program began twenty years ago to provide support for women entering doctoral programs in the mathematical sciences. With a steadfast commitment to diversity among participants, faculty, and staff, EDGE initially alternated between Bryn Mawr and Spelman Colleges. In later years, EDGE has been hosted on campuses around the nation and expanded to offer support for women throughout their graduate school and professional careers. The refereed papers in A Celebration of the EDGE Program's Impact on the Mathematics Community and Beyond range from short memoirs, to pedagogical studies, to current mathematics research. All papers are written by former EDGE participants, mentors, instructors, directors, and others connected to EDGE. Together, these papers offer compelling testimony that EDGE has produced a diverse new generation of leaders in the mathematics community. This volume contains technical and non-technical works, and it is intended for a far-reaching audience, including mathematicians, mathematics teachers, diversity officers, university administrators, government employees writing educational or science policy, and mathematics students at the high school, college, and graduate levels. By highlighting the scope of the work done by those supported by EDGE, the volume offers strong evidence of the American Mathematical Society's recognition that EDGE is "a program that makes a difference."This volume offers unique testimony that a 20-year old summer program has expanded its reach beyond the summer experience to produce a diverse new generation of women leaders, nearly half of whom are underrepresented women. While some books with a women-in-math theme focus only on one topic such as research or work-life balance, this book's broad scope includes papers on mathematics research, teaching, outreach, and career paths.
Differential and Difference Equations
This Special Issue deals with the theory and applications of differential and difference equations, and includes papers for different branches of differential equations, such as - Boundary Value Problems for Fractional Differential Equations and Inclusions - Spectral Theory for Fractional Differential Equations - Generalized Abel's Integral Equations - Oscillation Results for Higher Order Differential Equations - Stability of Equilibria under Stochastic Perturbations - Harmonic Functions - Coincidence Continuation Theory for Multivalued Maps - Generalized Briot-Bouquet Differential Equation - Nonlocal Inverse Problem - Lyapunov Type Theorems for Exponential Stability - Fuzzy Functions on Time Scales - Modified Helmholtz Equation on a Regular Hexagon
Correct Antidifferentiation: The Change of Variable Well Done
A typical source of mistakes that frequently lead to a wrong or incomplete solution for the antiderivative of a given real function of one real variable is a misuse of the technique of change of variable. The increasing implementation of software in apparently mechanic tasks such as the calculation of antiderivatives has not improved the situation, yet those software packages issue generic warnings such as "the answer's is not guaranteed to be continuous" or "the solution might be only valid for parts of the function". The practical meaning of those vague machine messages is clearly envisaged in this book, which shows how to handle the technique of change of variable in order to provide correct solutions.This book is monographically focused on elementary antidifferentiation and reasonably self-contained, yet it is written in a "hand-book" style: it has plenty of examples and graphics in an increasing level of difficulty; the most standard changes of variable are studied and the hardest theoretic parts are included in a final Appendix. Each practical chapter has a list of exercises and solutions.This book is intended for instructors and university students of Mathematics of first and second year.
Fluctuation Relations and Nonequilibrium Thermodynamics in Classical and Quantum Systems
This Special Issue contains novel results in the area of out-of-equilibrium classical and quantum thermodynamics. Contributions are from different areas of physics, including statistical mechanics, quantum information and many-body systems.
The Architecture of Convnets and Data Processing. Advantages of Convolutional Neural Networks
Essay from the year 2020 in the subject Mathematics - Miscellaneous, grade: 1,3, University of Ulm, language: English, abstract: In the past two decades in particular, artificial neural networks have led to new approaches and processes in machine learning in many areas. They have replaced many existing processes. In some areas, they even exceed human performance. Impressive progress has been made in the area of image recognition and classification. Above all, this includes the introduction of convolutional neural networks (ConvNets). They belong to the class of neural networks. The first ConvNet was developed by LeCun et al. in 1989. ConvNets were especially developed to enhance image processing. Therefore, they provide a unique architecture. Due to their structure and functionality, ConvNets are particularly well suited within this field of application compared to other methods.
Diagonal Chromatic Number of Maximal Planar Graphs of Diameter Three with Twelve Vertices
This thesis is an exploration of the diagonal chromatic number of maximal planar graphs of diameter less than four. A maximal planar graph is a graph that consists of vertices and edges such that no new edge can be added without intersecting another edge. This thesis will aim to show that if a graph is maximal planar of diameter less than four with twelve vertices, then the diagonal chromatic number of the graph is six.
Math 1060 Trigonometry Notes
This book is meant to be used as guided notes for Stacy Clark's Math 1060 Trigonometry Class (Snow College).
Number Theory and Symmetry
According to Carl Friedrich Gauss (1777-1855), mathematics is the queen of the sciences-and number theory is the queen of mathematics. Numbers (integers, algebraic integers, transcendental numbers, p-adic numbers) and symmetries are investigated in the nine refereed papers of this MDPI issue. This book shows how symmetry pervades number theory. In particular, it highlights connections between symmetry and number theory, quantum computing and elementary particles (thanks to 3-manifolds), and other branches of mathematics (such as probability spaces) and revisits standard subjects (such as the Sieve procedure, primality tests, and Pascal's triangle). The book should be of interest to all mathematicians, and physicists.
Reassessing Riemann’s Paper
In this book, the author pays tribute to Bernhard Riemann (1826-1866), a mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc. contributed immensely to mathematical physics. The text concentrates in particular on Riemann's only work on prime numbers, including ideas - new at the time - such as analytical continuation into the complex plane and the product formula for entire functions. A detailed analysis of the zeros of the Riemann zeta-function is presented. The impact of Riemann's ideas on regularizing infinite values in field theory is also emphasized. This revised and enhanced new edition contains three new chapters, two on the application of Riemann's zeta-function regularization to obtain the partition function of a Bose (Fermi) oscillator and one on the zeta-function regularization in quantum electrodynamics. Appendix A2 has been re-written to make the calculations more transparent. A summary of Euler-Riemann formulae completes the book.
Applied Functional Analysis and Its Applications
Applied functional analysis has an extensive history. In the last century, this field has often been used in physical sciences, such as wave and heat phenomena. In recent decades, with the development of nonlinear functional analysis, this field has been used to model a variety of engineering, medical, and computer sciences. Two of the most significant issues in this area are modeling and optimization. Thus, we consider some recently published works on fixed point, variational inequalities, and optimization problems. These works could lead readers to obtain new novelties and familiarize them with some applications of this area.
Mathematics in Ancient Egypt
A survey of ancient Egyptian mathematics across three thousand years Mathematics in Ancient Egypt traces the development of Egyptian mathematics, from the end of the fourth millennium BC-and the earliest hints of writing and number notation-to the end of the pharaonic period in Greco-Roman times. Drawing from mathematical texts, architectural drawings, administrative documents, and other sources, Annette Imhausen surveys three thousand years of Egyptian history to present an integrated picture of theoretical mathematics in relation to the daily practices of Egyptian life and social structures. Imhausen shows that from the earliest beginnings, pharaonic civilization used numerical techniques to efficiently control and use their material resources and labor. Even during the Old Kingdom, a variety of metrological systems had already been devised. By the Middle Kingdom, procedures had been established to teach mathematical techniques to scribes in order to make them proficient administrators for their king. Imhausen looks at counterparts to the notation of zero, suggests an explanation for the evolution of unit fractions, and analyzes concepts of arithmetic techniques. She draws connections and comparisons to Mesopotamian mathematics, examines which individuals in Egyptian society held mathematical knowledge, and considers which scribes were trained in mathematical ideas and why. Of interest to historians of mathematics, mathematicians, Egyptologists, and all those curious about Egyptian culture, Mathematics in Ancient Egypt sheds new light on a civilization's unique mathematical evolution.
Fast Track to Forcing
This quick yet detailed introduction to set theory and forcing builds the reader's intuition about it as much as the mathematical detail. Intuition, rather absent from the existing literature on the subject, here plays a large role. The reader will not only learn the facts, but will understand why they are true and will be brought to ask: what else could be true? Having presented forcing in Part I, the second part of the book discusses contemporary issues in the theory of forcing. It includes known and some previously unpublished results as well as many open questions. This is ideal for those who want to start a research career in forcing but do not have a personal interlocutor. Obviously, not everything about forcing is in this book. Many references are included to help the reader further explore the vast amount of research literature available on the subject.
Applied Mathematics: Principles and Techniques
The application of mathematical methods in different fields such as engineering, science, industry, business and computer science is known as applied mathematics. It combines mathematical science with specialized knowledge. Applied mathematics is broadly subdivided into three parts- applied analysis, approximation theory and applied probability. These categorizations are made complex due to the changes in mathematics and science over time. Numerical analysis, algebra, logic, decision theory, financial mathematics are some of the areas of mathematics which are widely applied to the domains of scientific computing, actuarial science, computer science and mathematical economics. This book discusses the fundamentals as well as modern approaches to the field of applied mathematics, and its various principles and techniques. Students, researchers, experts and all associated with applied mathematics will benefit alike from this book.
Differential Equations: Concepts and Applications
Differential Equation is a mathematical equation which denotes the relationship between a function and its derivatives. The functions usually represent physical quantities in the applications and the derivatives are used to show the rate of change. The study of differential equations involves pure and applied mathematics, physics and engineering. There are various types of differential equations such as ordinary differential equations, partial differential equations, linear differential equations and non - linear differential equations. Ordinary differential equation is an equation that contains unknown function of one real or complex variable. Partial differential equations are the differential equations that involve unknown multivariable functions and their partial derivatives. Linear differential equations are linear in the unknown function and its derivatives, whereas non - linear differential equations are formed by the products of the unknown function. This book unravels the recent studies in the field of differential equations. It elucidates new concepts and their applications in a multidisciplinary manner. It will serve as a valuable source of reference for graduate and post graduate students.
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.
Applied Principles of Mathematical Analysis
Mathematical analysis is a domain of mathematics that deals with limits and other related theories such as, measure, infinite series, differentiation, integration, and analytical functions. All of these theories are often studied in the context of real and complex numbers along with their functions. The main branches of mathematical analysis include real analysis, complex analysis and functional analysis. The fundamental concepts of this field are metric spaces and sequences and limits. Mathematical analysis has evolved from calculus that includes elementary techniques and concepts of analysis. It can be applied to any space of those mathematical objects that have a topological space or a metric space. This book contains some path-breaking studies in the field of mathematical analysis. It studies and analyzes various principles of mathematical analysis. It is appropriate for students seeking detailed information in this area as well as for experts.
Reminiscing on Basics
Discover the wonders of science and math in this accessible and engaging book. With fascinating concepts made simple, this book sparks curiosity and invites readers of all backgrounds to embark on their own intellectual adventure.
Adventures of Mind and Mathematics
This monograph uses the concept and category of "event" in the study of mathematics as it emerges from an interaction between levels of cognition, from the bodily experiences to symbolism. It is subdivided into three parts.The first moves from a general characterization of the classical approach to mathematical cognition and mind toward laying the foundations for a view on the mathematical mind that differs from going approaches in placing primacy on events.The second articulates some common phenomena-mathematical thought, mathematical sign, mathematical form, mathematical reason and its development, and affect in mathematics-in new ways that are based on the previously developed ontology of events. The final part has more encompassing phenomena as its content, most prominently the thinking body of mathematics, the experience in and of mathematics, and the relationship between experience and mind. The volume is well-suited for anyone with a broad interest in educationaltheory and/or social development, or with a broad background in psychology.
Fractional-Order Integral and Derivative Operators and Their Applications
In recent years, various families of fractional-order integral and derivative operators, such as those named after Riemann-Liouville, Weyl, Hadamard, Grunwald-Letnikov, Riesz, Erdelyi-Kober, Liouville-Caputo, and so on, have been found to be remarkably important and fruitful, due mainly to their demonstrated applications in numerous seemingly diverse and widespread areas of the mathematical, physical, chemical, engineering, and statistical sciences. Many of these fractional-order operators provide interesting, potentially useful tools for solving ordinary and partial differential equations, as well as integral, differintegral, and integro-differential equations; fractional-calculus analogues and extensions of each of these equations; and various other problems involving special functions of mathematical physics and applied mathematics, as well as their extensions and generalizations in one or more variables. For this Special Issue, we invite and welcome review, expository, and original research articles dealing with the recent advances in the theory of fractional-order integral and derivative operators and their multidisciplinary applications.
Advances in Differential and Difference Equations with Applications 2020
It is very well known that differential equations are related with the rise of physical science in the last several decades and they are used successfully for models of real-world problems in a variety of fields from several disciplines. Additionally, difference equations represent the discrete analogues of differential equations. These types of equations started to be used intensively during the last several years for their multiple applications, particularly in complex chaotic behavior. A certain class of differential and related difference equations is represented by their respective fractional forms, which have been utilized to better describe non-local phenomena appearing in all branches of science and engineering. The purpose of this book is to present some common results given by mathematicians together with physicists, engineers, as well as other scientists, for whom differential and difference equations are valuable research tools. The reported results can be used by researchers and academics working in both pure and applied differential equations.
Culture That Counts
This compilation of articles celebrating the tenth anniversary of the Journal of Mathematics & Culture examines the intersections between mathematics and culture in western and non-western societies, and among math professionals and non-professionals. Authors from early editions of the JMC were asked to write and share their respective research insights after ten years. This collection is in response to requests for Ethnomathematics curriculum materials.
Supporting Maths & English in Post-14 Education & Training
This book offers a practical solution to the challenges trainee teachers and practising teachers face when asked to address English and maths across the further education curriculum. Aimed firmly at non-specialist teachers of English and maths, each chapter has activities to raise your own awareness of English or maths concepts, as well as examples of activities that you can use in your teaching to ensure English and maths are appropriately embedded. Key features include: - Accessible explanations of English and maths concepts to support both you and your learners- Tasks to get you thinking about the general principles of embedding English and maths- Specific ideas for embedding English and maths in a range of vocational subject contexts- Tips and ideas for your lessons- General advice together with "Dos and don'ts" - Helpful commentaries about suggested teacher activities- Recommendations for further readingIf you are training to teach in the education and training sector, this book offers a number of tasks and activities to help you address English and maths in your subject area and is an excellent resource to support the planning and teaching of your subject. "These experts in English and Maths have ensured that their advice is well conceived and carefully explained but also that it is practical. Written with enthusiasm and flair, this book is valuable and very welcome."Professor Kevin Orr, School of Education and Professional Development, University of Huddersfield, UK"From reading aloud to pronunciation on the one hand; and from measurement and data handling on the other, the authors present workable strategies, ideas and exercises that are easy to use. Jargon-free and user-friendly, this book offers valuable insights and ideas."Dr Rebecca Eliahoo, Principal Lecturer (Lifelong Learning), University of Westminster, UK "The book has helpful embedding ideas and reminders throughout and the reflection and practice tasks would be very useful for trainee teachers or for vocational teachers working on their own or with colleagues to develop their awareness of English and maths.For non-specialists in both English and maths it is particularly challenging to embed these skills, and this book will go a long way to helping those teachers support their students."NATECLA News, Spring 2017, Issue 113
Turnpike Conditions in Infinite Dimensional Optimal Control
This book provides a comprehensive study of turnpike phenomenon arising in optimal control theory. The focus is on individual (non-generic) turnpike results which are both mathematically significant and have numerous applications in engineering and economic theory. All results obtained in the book are new. New approaches, techniques, and methods are rigorously presented and utilize research from finite-dimensional variational problems and discrete-time optimal control problems to find the necessary conditions for the turnpike phenomenon in infinite dimensional spaces. The semigroup approach is employed in the discussion as well as PDE descriptions of continuous-time dynamics. The main results on sufficient and necessary conditions for the turnpike property are completely proved and the numerous illustrative examples support the material for the broad spectrum of experts. Mathematicians interested in the calculus of variations, optimal control and in applied functional analysis will find this book a useful guide to the turnpike phenomenon in infinite dimensional spaces. Experts in economic and engineering modeling as well as graduate students will also benefit from the developed techniques and obtained results.
Combinatorial and Additive Number Theory III
Based on talks from the 2017 and 2018 Combinatorial and Additive Number Theory (CANT) workshops at the City University of New York, these proceedings offer 17 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003, the workshop series surveys state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. Topics featured in this volume include sumsets, partitions, convex polytopes and discrete geometry, Ramsey theory, commutative algebra and discrete geometry, and applications of logic and nonstandard analysis to number theory. Each contribution is dedicated to a specific topic that reflects the latest results by experts in the field. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.
Student Solutions Manual for College Algebra in Context with Applications for the Managerial, Life, and Social Sciences
Pi (π) In Nature, Art, and Culture
In Pi (π) in Nature, Art, and Culture Marcel Danesi revisits the importance of π as a pattern in the structure of reality, fitting in with the Pythagorean view of Order. Pi has cropped up in formulas that describe natural and physical structures which, on the surface, seem to have nothing to do with a circle, but might harbor the archetype of circularity as a principle. Through π, this book thus revisits the implicit ancient Greek view that geometry was a 'hermeneutic science, ' a discipline aiming to investigate the connectivity among numbers, shapes, and natural phenomena. It also examines its manifestations in aesthetic, symbolic and cultural structures, which point to an abiding fascination with the circle as an unconscious archetype. Hermeneutic geometry is ultimately about the exploration of the meanings of geometric-mathematical notions to science and human life.
Contemporary Research in Elliptic Pdes and Related Topics
This volume collects contributions from the speakers at an INdAM Intensive period held at the University of Bari in 2017. The contributions cover several aspects of partial differential equations whose development in recent years has experienced major breakthroughs in terms of both theory and applications. The topics covered include nonlocal equations, elliptic equations and systems, fully nonlinear equations, nonlinear parabolic equations, overdetermined boundary value problems, maximum principles, geometric analysis, control theory, mean field games, and bio-mathematics. The authors are trailblazers in these topics and present their work in a way that is exhaustive and clearly accessible to PhD students and early career researcher. As such, the book offers an excellent introduction to a variety of fundamental topics of contemporary investigation and inspires novel and high-quality research.
Nonlinear Combinatorial Optimization
Graduate students and researchers in applied mathematics, optimization, engineering, computer science, and management science will find this book a useful reference which provides an introduction to applications and fundamental theories in nonlinear combinatorial optimization. Nonlinear combinatorial optimization is a new research area within combinatorial optimization and includes numerous applications to technological developments, such as wireless communication, cloud computing, data science, and social networks. Theoretical developments including discrete Newton methods, primal-dual methods with convex relaxation, submodular optimization, discrete DC program, along with several applications are discussed and explored in this book through articles by leading experts.
The Inspirational Untold Stories of Secondary Mathematics Teachers (hc)
Personal story telling is a powerful and interesting medium through which one can share experiences, insights, successes, and difficulties in meaningful contexts. Teaching in general, and mathematics teaching in particular, is much more than what meets the eye. Most people have only experienced teaching from the vantage point of a student and have impressions of teachers and teaching that are simplistic and usually totally incorrect. The lives of mathematics teachers are varied and contrary to what one might think they are. The journeys of exemplary in-service teachers are not linear; there are many bends, potholes, and detours through which they have navigated. The "road conditions" of teaching are fodder for the 12 untold stories collected in this volume, whose authors graduated from a special four-year undergraduate mathematics teacher preparation program, containing innovative components, many of which are revealed through the experiences described in their stories. The range of narratives vary in every possible way, from the reasons they became mathematics teachers, to the number of years teaching, to the experiences encountered while teaching, to the different roles they have assumed throughout their careers. Nevertheless, one strand permeates all of the stories: their passion for what they do and their ability to reflect on early college experiences that contribute to their performance. These inspiring narratives will shed light on the developmental processes of mathematics teachers, what it means to teach mathematics, and the components of a secondary mathematics teacher preparation program that can contribute to their expertise.
Studies in Indian Mathematics and Astronomy
This volume presents a collection of some of the seminal articles of Professor K. S. Shukla who made immense contributions to our understanding of the history and development of mathematics and astronomy in India. It consists of six parts: Part I constitutes introductory articles which give an overview of the life and work of Prof. Shukla, including details of his publications, reminiscences from his former students, and an analysis of his monumental contributions. Part II is a collection of important articles penned by Prof. Shukla related to various aspects of Indian mathematics. Part III consists of articles by Bibhutibhusan Datta and Avadhesh Narayan Singh--which together constitute the third unpublished part of their History of Hindu Mathematics--that were revised and updated by Prof. Shukla. Parts IV and V consist of a number of important articles of Prof. Shukla on different aspects of Indian astronomy. Part VI includes some important reviews authored by him and a few reviews of his work. Given the sheer range and depth of Prof. Shukla's scholarship, this volume is essential reading for scholars seeking to deepen their understanding of the rich and varied contributions made by Indian mathematicians and astronomers.
The Inspirational Untold Stories of Secondary Mathematics Teachers
Personal story telling is a powerful and interesting medium through which one can share experiences, insights, successes, and difficulties in meaningful contexts. Teaching in general, and mathematics teaching in particular, is much more than what meets the eye. Most people have only experienced teaching from the vantage point of a student and have impressions of teachers and teaching that are simplistic and usually totally incorrect. The lives of mathematics teachers are varied and contrary to what one might think they are. The journeys of exemplary in-service teachers are not linear; there are many bends, potholes, and detours through which they have navigated. The "road conditions" of teaching are fodder for the 12 untold stories collected in this volume, whose authors graduated from a special four-year undergraduate mathematics teacher preparation program, containing innovative components, many of which are revealed through the experiences described in their stories. The range of narratives vary in every possible way, from the reasons they became mathematics teachers, to the number of years teaching, to the experiences encountered while teaching, to the different roles they have assumed throughout their careers. Nevertheless, one strand permeates all of the stories: their passion for what they do and their ability to reflect on early college experiences that contribute to their performance. These inspiring narratives will shed light on the developmental processes of mathematics teachers, what it means to teach mathematics, and the components of a secondary mathematics teacher preparation program that can contribute to their expertise.
Introduction to Topology
Chapter 1. Topological Spaces.- Chapter 2. Continuity and Products.- Chapter 3. Connectedness.- Chapter 4. Convergence.- Chapter 5. Countability axioms.- Chapter 6. Compactness.- Chapter 7. Topological Constructions.- Chapter 8. Separation Axioms.- Chapter 9. Paracompactness and Metrisability.- Chapter 10. Completeness.- Chapter 11. Function Spaces.- Chapter 12. Topological Groups.- Chapter 13. Transformation Groups.- Chapter 14. The fundamental Group.- Chapter 15. Covering Spaces.
Magic SquaresTheir History and Construction from Ancient Times to Ad 1600
The science of magic squares witnessed an important development in the Islamic world during the Middle Ages, with a great variety of construction methods being created and ameliorated. The initial step was the translation, in the ninth century, of an anonymous Greek text containing the description of certain highly developed arrangements, no doubt the culmination of ancient research on magic squares.
A Primer for a Secret Shortcut to Pdes of Mathematical Physics
​This book presents a concise introduction to a unified Hilbert space approach to the mathematical modelling of physical phenomena which has been developed over recent years by Picard and his co-workers. The main focus is on time-dependent partial differential equations with a particular structure in the Hilbert space setting that ensures well-posedness and causality, two essential properties of any reasonable model in mathematical physics or engineering.However, the application of the theory to other types of equations is also demonstrated. By means of illustrative examples, from the straightforward to the more complex, the authors show that many of the classical models in mathematical physics as well as more recent models of novel materials and interactions are covered, or can be restructured to be covered, by this unified Hilbert space approach.The reader should require only a basic foundation in the theory of Hilbert spaces and operators therein. For convenience, however, some of the more technical background requirements are covered in detail in two appendices The theory is kept as elementary as possible, making the material suitable for a senior undergraduate or master's level course. In addition, researchers in a variety of fields whose work involves partial differential equations and applied operator theory will also greatly benefit from this approach to structuring their mathematical models in order that the general theory can be applied to ensure the essential properties of well-posedness and causality.
Grade Five Competition from the Leningrad Mathematical Olympiad
This unique book presents mathematical competition problems primarily aimed at upper elementary school students, but are challenging for students at any age. These problems are drawn from the complete papers of the legendary Leningrad Mathematical Olympiads that were presented to the city's Grade Five students. The period covered is between 1979 - the earliest year for which relevant records could be retrieved - and 1992, when the former Soviet Union was dissolved.The respective chapters reflect the famous four-step approach to problem solving developed by the great Hungarian mathematics educator Gyorgy P籀lya. In Chapter One, the Grade Five Competition problems from the Leningrad Mathematical Olympiads from 1979 to 1992 are presented in chronological order. In Chapter Two, the 83 problems are loosely divided into 26 sets of three or four related problems, and an example is provided for each one. Chapter Three provides full solutions to all problems, while Chapter Four offers generalizations of the problems.This book can be used by any mathematically advanced student at the upper elementary school level. Teachers and organizers of outreach activities such as mathematical circles will also find this book useful. But the primary value of the book lies in the problems themselves, which were crafted by experts; therefore, anyone interested in problem solving will find this book a welcome addition to their library.
Coalgebraic Methods in Computer Science
This book constitutes the thoroughly refereed post-conference proceedings of the 15th International Workshop on Coalgebraic Methods in Computer Science, CMCS 2020, colocated with ETAPS 2020, held in Dublin, Ireland, in April 2020. The conference was held as several online events in September and October due to the COVID-19 pandemic. The 9 revised full papers were carefully reviewed and selected from 13 submissions. Also included is one invited talk. The papers cover a wide range of topics in the theory, logics, and applications of coalgebras.
Dos Problemas Matem獺ticos
DR. ADALBERTO GARCIA DE MENDOZA (1900-1963). La concepci籀n del c獺lculo infinitesimal ha sido la m獺s sorprendente del intelecto humano. Su absoluta generalidad, basada en la realidad, la 繳nica dial矇ctica de lo verdadero, es sin duda la base m獺s s籀lida de cuantas exiten, para el fundamento de la ciencia. Creo firmemente que en una 矇poca no lejana, la unidad matem獺tica ser獺 el calculo infinitesimal, y de 矇l se desprender獺n las incoherentes, contingentes y diversas teor穩as de las series de las imaginarias. Vendr獺 una 矇poca de sincretismo en que se ver獺 el conjunto maravilloso, espl矇ndido, formado de partes perfectamente distintas y claras y todas con el mismo matiz, con el mismo car獺cter, armonizando el profundo y noble conocimiento de la ciencia matem獺tica.
