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| understanding maths basic mathematics explained graham lawler: Understanding Maths Graham Lawler, 2011 Who else wants to spend less time studying and be able to calculate correctly each time? Now in its fourth edition, this book has proved highly successful, selling thousands of copies per year over the last ten years. It is ideal for student nurses, engineers, primary school student teachers and parents who wish to help their children with maths. |
| understanding maths basic mathematics explained graham lawler: Mathematics: Bullet Guides Sophie Goldie, 2012-01-13 Open this book and you will Be numerate Understand key principles Conquer difficult problems Handle data confidently |
| understanding maths basic mathematics explained graham lawler: Understanding Maths Graham Lawler, 2006 Written by an experienced maths teacher, this book will help you master number and data handling. Whether you are just starting at college or university, or a mature student, it explains all you need to know. |
| understanding maths basic mathematics explained graham lawler: Maths for Chemistry Paul Monk, Lindsey J. Munro, 2021-08-11 Mathematical skills and concepts lie at the heart of chemistry, yet they are the aspect of the subject that many students fear the most. Maths for Chemistry recognizes the challenges faced by many students in equipping themselves with the maths skills necessary to gain a full understanding of chemistry. Working from foundational principles, the book builds the student's confidence by leading them through the subject in a steady, progressive way from basic algebra to quantum mathematics. Opening with the core mathematics of algebra, logarithms and trigonometry, the book goes on to cover calculus, matrices, vectors, complex numbers, and laboratory mathematics to cover everything that a chemistry student needs. With its modular structure, the book presents material in short, manageable sections to keep the content as accessible and readily digestible as possible. Maths for Chemistry is the perfect introduction to the essential mathematical concepts which all chemistry students should master. |
| understanding maths basic mathematics explained graham lawler: Understanding Maths Graham Lawler, |
| understanding maths basic mathematics explained graham lawler: The British National Bibliography Arthur James Wells, 2003 |
| understanding maths basic mathematics explained graham lawler: 50th IMO - 50 Years of International Mathematical Olympiads Hans-Dietrich Gronau, Hanns-Heinrich Langmann, Dierk Schleicher, 2011-01-03 In July 2009 Germany hosted the 50th International Mathematical Olympiad (IMO). For the very first time the number of participating countries exceeded 100, with 104 countries from all continents. Celebrating the 50th anniversary of the IMO provides an ideal opportunity to look back over the past five decades and to review its development to become a worldwide event. This book is a report about the 50th IMO as well as the IMO history. A lot of data about all the 50 IMOs are included. We list the most successful contestants, the results of the 50 Olympiads and the 112 countries that have ever taken part. It is impressive to see that many of the world’s leading research mathematicians were among the most successful IMO participants in their youth. Six of them gave presentations at a special celebration: Bollobás, Gowers, Lovász, Smirnov, Tao and Yoccoz. This book is aimed at students in the IMO age group and all those who have interest in this worldwide leading competition for highschool students. |
| understanding maths basic mathematics explained graham lawler: Introduction to Embedded Systems, Second Edition Edward Ashford Lee, Sanjit Arunkumar Seshia, 2016-12-30 An introduction to the engineering principles of embedded systems, with a focus on modeling, design, and analysis of cyber-physical systems. The most visible use of computers and software is processing information for human consumption. The vast majority of computers in use, however, are much less visible. They run the engine, brakes, seatbelts, airbag, and audio system in your car. They digitally encode your voice and construct a radio signal to send it from your cell phone to a base station. They command robots on a factory floor, power generation in a power plant, processes in a chemical plant, and traffic lights in a city. These less visible computers are called embedded systems, and the software they run is called embedded software. The principal challenges in designing and analyzing embedded systems stem from their interaction with physical processes. This book takes a cyber-physical approach to embedded systems, introducing the engineering concepts underlying embedded systems as a technology and as a subject of study. The focus is on modeling, design, and analysis of cyber-physical systems, which integrate computation, networking, and physical processes. The second edition offers two new chapters, several new exercises, and other improvements. The book can be used as a textbook at the advanced undergraduate or introductory graduate level and as a professional reference for practicing engineers and computer scientists. Readers should have some familiarity with machine structures, computer programming, basic discrete mathematics and algorithms, and signals and systems. |
| understanding maths basic mathematics explained graham lawler: Self-Efficacy in Changing Societies Albert Bandura, 1997-05-13 The volume addresses important issues of human adaptation and change. |
| understanding maths basic mathematics explained graham lawler: Scheduling Algorithms Peter Brucker, 2013-04-17 Besides scheduling problems for single and parallel machines and shop scheduling problems the book covers advanced models involving due-dates, sequence dependent change over times and batching. Also multiprocessor task scheduling and problems with multi-purpose machines are discussed. The methods used to solve these problems are polynomial algorithms, dynamic programming procedures, branch-and-bound algorithms and local search heuristics. Also complexity issues are addressed. |
| understanding maths basic mathematics explained graham lawler: Mathematics Minus Fear Lawrence Potter, 2021-11-15 Forget your classroom nightmares and discover how numbers can enhance and illuminate your world! How can math help you bet on horses or win in Vegas? What’s the foolproof way to solve Sudoku? How can probability teach you to calculate your chances of survival in Russian roulette? In this irreverent and entertaining guide to mathematics, Lawrence Potter takes the fear out of everything from long division to percentages. Using fascinating puzzles and surprising examples, from M.C. Escher to Pascal, he shows us how math is connected with the world we encounter every day, from how the VAT works to why weather forecasts are wrong, from winning at Monopoly to improving your mental arithmetic. Along the way you’ll also discover who invented numbers, whether animals can count, and what nuns have to do with multiplication. |
| understanding maths basic mathematics explained graham lawler: The Challenge of Developing Statistical Literacy, Reasoning and Thinking Dani Ben-Zvi, Joan Garfield, 2004-07-29 Unique in that it collects, presents, and synthesizes cutting edge research on different aspects of statistical reasoning and applies this research to the teaching of statistics to students at all educational levels, this volume will prove of great value to mathematics and statistics education researchers, statistics educators, statisticians, cognitive psychologists, mathematics teachers, mathematics and statistics curriculum developers, and quantitative literacy experts in education and government. |
| understanding maths basic mathematics explained graham lawler: Human Accomplishment Charles Murray, 2009-10-13 “Readers . . . are sure to enjoy [the] arguments and elegant presentation” of this “engaging” cultural survey by the controversial co-author of The Bell Curve (Kirkus Reviews). “At irregular times and in scattered settings, human beings have achieved great things. Human Accomplishment is about those great things, falling in the domains known as the arts and sciences, and the people who did them.’ So begins Charles Murray’s unique account of human excellence, from the age of Homer to our own time. Murray compiles inventories of the people who have been essential to the stories of literature, music, art, philosophy, and the sciences—a total of 4,002 men and women from around the world, ranked according to their eminence. The heart of Human Accomplishment is a series of enthralling descriptive chapters: on the giants in the arts and what sets them apart from the merely great. Charles Murray takes on some controversial questions. Why has accomplishment been so concentrated in Europe? Among men? Since 1400? He presents evidence that the rate of great accomplishment has been declining in the last century, asks what it means, and offers a rich framework for thinking about the conditions under which the human spirit has expressed itself most gloriously. “Well-written and informative.” —Publishers Weekly |
| understanding maths basic mathematics explained graham lawler: The William Lowell Putnam Mathematical Competition 1985-2000 Kiran Sridhara Kedlaya, Bjorn Poonen, Ravi Vakil, 2002 A collection of problems from the William Lowell Putnam Competition which places them in the context of important mathematical themes. |
| understanding maths basic mathematics explained graham lawler: Open Middle Math Robert Kaplinsky, 2023-10-10 This book is an amazing resource for teachers who are struggling to help students develop both procedural fluency and conceptual understanding.. --Dr. Margaret (Peg) Smith, co-author of5 Practices for Orchestrating Productive Mathematical Discussions Robert Kaplinsky, the co-creator of Open Middle math problems, brings hisnew class of tasks designed to stimulate deeper thinking and lively discussion among middle and high school students in Open Middle Math: Problems That Unlock Student Thinking, Grades 6-12. The problems are characterized by a closed beginning,- meaning all students start with the same initial problem, and a closed end,- meaning there is only one correct or optimal answer. The key is that the middle is open- in the sense that there are multiple ways to approach and ultimately solve the problem. These tasks have proven enormously popular with teachers looking to assess and deepen student understanding, build student stamina, and energize their classrooms. Professional Learning Resource for Teachers: Open Middle Math is an indispensable resource for educators interested in teaching student-centered mathematics in middle and high schools consistent with the national and state standards. Sample Problems at Each Grade: The book demonstrates the Open Middle concept with sample problems ranging from dividing fractions at 6th grade to algebra, trigonometry, and calculus. Teaching Tips for Student-Centered Math Classrooms: Kaplinsky shares guidance on choosing problems, designing your own math problems, and teaching for multiple purposes, including formative assessment, identifying misconceptions, procedural fluency, and conceptual understanding. Adaptable and Accessible Math: The tasks can be solved using various strategies at different levels of sophistication, which means all students can access the problems and participate in the conversation. Open Middle Math will help math teachers transform the 6th -12th grade classroom into an environment focused on problem solving, student dialogue, and critical thinking. |
| understanding maths basic mathematics explained graham lawler: Understanding Physical Education Ken Green, 2008-01-24 `This book will prove an invaluable resource for students wanting to engage with any or all of the issues covered, and who need to get an authoritative ′quick fix′ on particular fields of research. It′s thorough, contemporary in its choice of issues and comprehensive in its coverage of them. The author is to be congratulated on making a very thoughtful and important contribution to the literature in PE′ - Professor John Evans, Loughborough University, UK. This easy-to-use introduction explores all of the contemporary issues and enduring themes in physical education, focusing on the United Kingdom but incorporating a global dimension. The wide range of topics covered include: o the requirements of National Curriculum Physical Education o the current ′state′ of physical education o the relationship between physical education and sport o extra-curricular physical education o lifelong participation in sport and physical activity o assessment and examinations in physical education o social class, gender, ethnicity and inclusion in relation to physical education o teacher training and continuing professional development. This book is an essential read for anyone embarking upon an undergraduate or postgraduate course in physical education. |
| understanding maths basic mathematics explained graham lawler: Design and Analysis of Algorithms Sandeep Sen, Amit Kumar, 2019-05-23 The text covers important algorithm design techniques, such as greedy algorithms, dynamic programming, and divide-and-conquer, and gives applications to contemporary problems. Techniques including Fast Fourier transform, KMP algorithm for string matching, CYK algorithm for context free parsing and gradient descent for convex function minimization are discussed in detail. The book's emphasis is on computational models and their effect on algorithm design. It gives insights into algorithm design techniques in parallel, streaming and memory hierarchy computational models. The book also emphasizes the role of randomization in algorithm design, and gives numerous applications ranging from data-structures such as skip-lists to dimensionality reduction methods. |
| understanding maths basic mathematics explained graham lawler: The Logic of Logistics David Simchi-Levi, Xin Chen, Julien Bramel, 2007-07-03 Fierce competition in today's global market provides a powerful motivation for developing ever more sophisticated logistics systems. This book, written for the logistics manager and researcher, presents a survey of the modern theory and application of logistics. The goal of the book is to present the state-of-the-art in the science of logistics management. As a result, the authors have written a timely and authoritative survey of this field that many practitioners and researchers will find makes an invaluable companion to their work. |
| understanding maths basic mathematics explained graham lawler: Infinite Powers Steven Strogatz, 2019 This is the captivating story of mathematics' greatest ever idea: calculus. Without it, there would be no computers, no microwave ovens, no GPS, and no space travel. But before it gave modern man almost infinite powers, calculus was behind centuries of controversy, competition, and even death. Taking us on a thrilling journey through three millennia, professor Steven Strogatz charts the development of this seminal achievement from the days of Aristotle to today's million-dollar reward that awaits whoever cracks Reimann's hypothesis. Filled with idiosyncratic characters from Pythagoras to Euler, Infinite Powers is a compelling human drama that reveals the legacy of calculus on nearly every aspect of modern civilization, including science, politics, ethics, philosophy, and much besides. |
| understanding maths basic mathematics explained graham lawler: Ramsey Theory on the Integers Bruce M. Landman, Aaron Robertson, 2004 Ramsey theory is the study of the structure of mathematical objects that is preserved under partitions. In its full generality, Ramsey theory is quite powerful, but can quickly become complicated. By limiting the focus of this book to Ramsey theory applied to the set of integers, the authors have produced a gentle, but meaningful, introduction to an important and enticing branch of modern mathematics.Ramsey Theory on the Integers offers students something quite rare for a book at this level: a glimpse into the world of mathematical research and the opportunity for them to begin pondering unsolved problems. In addition to being the first truly accessible book on Ramsey theory, this innovative book also provides the first cohesive study of Ramsey theory on the integers. It contains perhaps the most substantial account of solved and unsolved problems in this blossoming subarea of Ramsey theory. The result is a breakthrough book that will engage students, teachers, and researchers alike. |
| understanding maths basic mathematics explained graham lawler: Discrete Mathematics with Applications Thomas Koshy, 2004-01-19 This approachable text studies discrete objects and the relationsips that bind them. It helps students understand and apply the power of discrete math to digital computer systems and other modern applications. It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract algebra and for computer science courses in data structures, algorithms, programming languages, compilers, databases, and computation.* Covers all recommended topics in a self-contained, comprehensive, and understandable format for students and new professionals * Emphasizes problem-solving techniques, pattern recognition, conjecturing, induction, applications of varying nature, proof techniques, algorithm development and correctness, and numeric computations* Weaves numerous applications into the text* Helps students learn by doing with a wealth of examples and exercises: - 560 examples worked out in detail - More than 3,700 exercises - More than 150 computer assignments - More than 600 writing projects* Includes chapter summaries of important vocabulary, formulas, and properties, plus the chapter review exercises* Features interesting anecdotes and biographies of 60 mathematicians and computer scientists* Instructor's Manual available for adopters* Student Solutions Manual available separately for purchase (ISBN: 0124211828) |
| understanding maths basic mathematics explained graham lawler: Gender Change in Academia Birgit Riegraf, Brigitte Aulenbacher, Edit Kirsch-Auwärter, Ursula Müller, 2010-07-15 Editors’ Foreword The fundamental changes currently taking place in the national and international science landscapes can no longer be overlooked. Within those changes, reforms do not go ‘as planned’ but, as is always the case with processes of rationali- tion, have a series of unintended effects. At the same time it becomes incre- ingly clear who in this process are the winners and who are the losers, although this is still subject to fluctuation and change. This can be illustrated by two - amples from current events: Where the range of taught courses is concerned, as part of the Bologna Process the new structuring of student study paths and their organisation is aimed at unifying the European area of science to ensure a study that is equally permissive and efficient. However, it is to be deplored that the mobility of s- dents has become more restricted because of an increasing specialisation in the available study paths. Also, bachelor degrees do not meet with the anticipated high response from the labour market in all countries, so that the master’s degree is becoming more or less a ‘must’, while at the same time the number of study places on master’s courses is limited. Instead of the intended reduction in the duration of study time in comparison to the previous German ‘Magister’ and ‘Diplom’, rather a prolongation in the duration of studies has been recorded. |
| understanding maths basic mathematics explained graham lawler: International Handbook of Educational Policy Nina Bascia, Alister Cumming, Amanda Datnow, Kenneth Leithwood, David Livingstone, 2008-05-14 Nina Bascia, Alister Cumming, Amanda Datnow, Kenneth Leithwood and David Livingstone This Handbook presents contemporary and emergent trends in educational policy research, in over ?fty chapters written by nearly ninety leading researchers from a number of countries. It is organized into ?ve broad sections which capture many of the current dominant educational policy foci and at the same time situate current understandings historically, in terms of both how they are conceptualized and in terms of past policy practice. The chapters themselves are empirically grounded, providing illustrations of the conceptual implications c- tained within them as well as allowing for comparisons across them. The se- re?exivity within chapters with respect to jurisdictional particularities and c- trasts allows readers to consider not only a range of approaches to policy analysis but also the ways in which policies and policy ideas play out in di?erent times and places. The sections move from a focus on prevailing policy tendencies through increasingly critical and ‘‘outsider’’ perspectives on policy. They address, in turn, the contemporary strategic emphasis on large-scale reform; substantive emphases at several levels – on leadership and governance, improving teacher quality and conceptualizing learning in various domains around the notion of literacies and concluding, ?nally, with a contrasting topic, workplace learning, which has had less policy attention and thus allows readers to consider both the advantages and disadvantages of learning and teaching under the bright gaze of policy. |
| understanding maths basic mathematics explained graham lawler: Parabolic Geometries I Andreas Čap, Jan Slovák, 2024-07-29 Parabolic geometries encompass a very diverse class of geometric structures, including such important examples as conformal, projective, and almost quaternionic structures, hypersurface type CR-structures and various types of generic distributions. The characteristic feature of parabolic geometries is an equivalent description by a Cartan geometry modeled on a generalized flag manifold (the quotient of a semisimple Lie group by a parabolic subgroup). Background on differential geometry, with a view towards Cartan connections, and on semisimple Lie algebras and their representations, which play a crucial role in the theory, is collected in two introductory chapters. The main part discusses the equivalence between Cartan connections and underlying structures, including a complete proof of Kostant's version of the Bott–Borel–Weil theorem, which is used as an important tool. For many examples, the complete description of the geometry and its basic invariants is worked out in detail. The constructions of correspondence spaces and twistor spaces and analogs of the Fefferman construction are presented both in general and in several examples. The last chapter studies Weyl structures, which provide classes of distinguished connections as well as an equivalent description of the Cartan connection in terms of data associated to the underlying geometry. Several applications are discussed throughout the text. |
| understanding maths basic mathematics explained graham lawler: Researching Design Learning Richard Kimbell, Kay Stables, 2008-09-27 The product of ongoing research projects in design and technology teaching, this book summarizes the lessons learned. The book focuses on the design activity, on learning, teaching and assessment, and, more widely, on what can be learnt about the research process itself. The authors aim to answer questions such as how active, concrete learning enables cognitive and emotional growth? Researching such questions, the authors integrate the conceptual, the practical and the pedagogic. |
| understanding maths basic mathematics explained graham lawler: Transforming a University Angela Brew, Judyth Sachs, 2007-06-21 This unique collection shows what happens when one university takes on the challenge of developing the scholarship of teaching and learning with a view to enhancing students' learning experiences. |
| understanding maths basic mathematics explained graham lawler: Scheduling Theory. Single-Stage Systems Vi︠a︡cheslav Sergeevich Tanaev, Valeriĭ Sergeevich Gordon, 1994-05-31 Scheduling theory is an important branch of operations research. Problems studied within the framework of that theory have numerous applications in various fields of human activity. As an independent discipline scheduling theory appeared in the middle of the fifties, and has attracted the attention of researchers in many countries. In the Soviet Union, research in this direction has been mainly related to production scheduling, especially to the development of automated systems for production control. In 1975 Nauka (Science) Publishers, Moscow, issued two books providing systematic descriptions of scheduling theory. The first one was the Russian translation of the classical book Theory of Scheduling by American mathematicians R. W. Conway, W. L. Maxwell and L. W. Miller. The other one was the book Introduction to Scheduling Theory by Soviet mathematicians V. S. Tanaev and V. V. Shkurba. These books well complement each other. Both. books well represent major results known by that time, contain an exhaustive bibliography on the subject. Thus, the books, as well as the Russian translation of Computer and Job-Shop Scheduling Theory edited by E. G. Coffman, Jr., (Nauka, 1984) have contributed to the development of scheduling theory in the Soviet Union. Many different models, the large number of new results make it difficult for the researchers who work in related fields to follow the fast development of scheduling theory and to master new methods and approaches quickly. |
| understanding maths basic mathematics explained graham lawler: Combinatorial Optimization Bernhard Korte, Jens Vygen, 2009-09-02 This well-written textbook on combinatorial optimization puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. The book contains complete (but concise) proofs, as well as many deep results, some of which have not appeared in any previous books. |
| understanding maths basic mathematics explained graham lawler: Mathematics Education as a Research Domain: A Search for Identity Anna Sierpinska, Jeremy Kilpatrick, 2013-03-14 No one disputes how important it is, in today's world, to prepare students to un derstand mathematics as well as to use and communicate mathematics in their future lives. That task is very difficult, however. Refocusing curricula on funda mental concepts, producing new teaching materials, and designing teaching units based on 'mathematicians' common sense' (or on logic) have not resulted in a better understanding of mathematics by more students. The failure of such efforts has raised questions suggesting that what was missing at the outset of these proposals, designs, and productions was a more profound knowledge of the phenomena of learning and teaching mathematics in socially established and culturally, politically, and economically justified institutions - namely, schools. Such knowledge cannot be built by mere juxtaposition of theories in disci plines such as psychology, sociology, and mathematics. Psychological theories focus on the individual learner. Theories of sociology of education look at the general laws of curriculum development, the specifics of pedagogic discourse as opposed to scientific discourse in general, the different possible pedagogic rela tions between the teacher and the taught, and other general problems in the inter face between education and society. Mathematics, aside from its theoretical contents, can be looked at from historical and epistemological points of view, clarifying the genetic development of its concepts, methods, and theories. This view can shed some light on the meaning of mathematical concepts and on the difficulties students have in teaching approaches that disregard the genetic development of these concepts. |
| understanding maths basic mathematics explained graham lawler: Programming with Mathematica® Paul Wellin, 2013-01-10 This practical, example-driven introduction teaches the foundations of the Mathematica language so it can be applied to solving concrete problems. |
| understanding maths basic mathematics explained graham lawler: Teaching and Learning Mathematics in Multilingual Classrooms Anjum Halai, Philip Clarkson, 2015-12-17 Contemporary concerns in mathematics education recognize that in the increasingly technological and globalized world, with concomitant change in population demographics (e.g. immigration, urbanization) and a change in the status of languages (e.g. English as a dominant language of science and technology) multilingualism in classrooms is a norm rather than an exception. Shifts in perspective also view language not simply as an instrument for cognition with all learners equipped with this instrument in service of learning, although clearly in the classroom that remains of importance. Rather, it is now also being acknowledged that language use is inherently political, so that the language that gets official recognition in the classroom is invariably the language of the powerful elite, or the dominant societal language, or in the case of post-colonial contexts the language of the colonisers. From this socio-political role of language in learning quite different issues arise for teaching, learning and curriculum for linguistically marginalized learners than that of cognition (e.g. immigrants, second language learners, other). Policies on language in education are being considered and re-considered with specific reference to mathematics teaching and learning. Given the policy environment, globally the proposed publication is timely. This edited collection draws on recent, emerging insights and understandings about the approaches to improving policy and practice in mathematics education and mathematics teacher education in multilingual settings. It presents, and discusses critically, examples of work from a range of contexts and uses these examples to draw out key issues for research in education in language diverse settings including teaching, learning, curriculum and fit these with appropriate policy and equity approaches. With contributions from all over the world, especially novice researchers in low income countries, this book is a valuable resource for courses in Mathematics Education and related social sciences both at the graduate and undergraduate levels, as well as for students of international development. |
| understanding maths basic mathematics explained graham lawler: Math with Bad Drawings Ben Orlin, 2018-09-18 A hilarious reeducation in mathematics-full of joy, jokes, and stick figures-that sheds light on the countless practical and wonderful ways that math structures and shapes our world. In Math With Bad Drawings, Ben Orlin reveals to us what math actually is; its myriad uses, its strange symbols, and the wild leaps of logic and faith that define the usually impenetrable work of the mathematician. Truth and knowledge come in multiple forms: colorful drawings, encouraging jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Orlin shows us how to think like a mathematician by teaching us a brand-new game of tic-tac-toe, how to understand an economic crises by rolling a pair of dice, and the mathematical headache that ensues when attempting to build a spherical Death Star. Every discussion in the book is illustrated with Orlin's trademark bad drawings, which convey his message and insights with perfect pitch and clarity. With 24 chapters covering topics from the electoral college to human genetics to the reasons not to trust statistics, Math with Bad Drawings is a life-changing book for the math-estranged and math-enamored alike. |
| understanding maths basic mathematics explained graham lawler: Miseducation Diane Reay, 2017-10-11 In this book Diane Reay, herself working-class-turned-Cambridge-professor, presents a 21st-century view of education and the working classes. Drawing on over 500 interviews, the book includes vivid stories from working-class children and young people. It looks at class identity, and the effects of wider economic and social class relationships on working-class educational experiences. The book reveals how we have ended up with an educational system that still educates the different social classes in fundamentally different ways and, vitally, what we can do to achieve a fairer system. Book jacket. |
| understanding maths basic mathematics explained graham lawler: Parabolic Equations with Irregular Data and Related Issues Claude Le Bris, Pierre-Louis Lions, 2019-06-17 This book studies the existence and uniqueness of solutions to parabolic-type equations with irregular coefficients and/or initial conditions. It elaborates on the DiPerna-Lions theory of renormalized solutions to linear transport equations and related equations, and also examines the connection between the results on the partial differential equation and the well-posedness of the underlying stochastic/ordinary differential equation. |
| understanding maths basic mathematics explained graham lawler: Mathematical Modelling Murray S. Klamkin, 1987-01-01 Designed for classroom use, this book contains short, self-contained mathematical models of problems in the physical, mathematical, and biological sciences first published in the Classroom Notes section of the SIAM Review from 1975-1985. The problems provide an ideal way to make complex subject matter more accessible to the student through the use of concrete applications. Each section has extensive supplementary references provided by the editor from his years of experience with mathematical modelling. |
| understanding maths basic mathematics explained graham lawler: Affect and Mathematical Problem Solving Douglas B McLeod, Verna M Adams, 1989-05-01 |
| understanding maths basic mathematics explained graham lawler: Critical Mathematics Education Paul Ernest, Bharath Sriraman, Nuala Ernest, 2016-01-01 Mathematics is traditionally seen as the most neutral of disciplines, the furthest removed from the arguments and controversy of politics and social life. However, critical mathematics challenges these assumptions and actively attacks the idea that mathematics is pure, objective, and value?neutral. It argues that history, society, and politics have shaped mathematics—not only through its applications and uses but also through molding its concepts, methods, and even mathematical truth and proof, the very means of establishing truth. Critical mathematics education also attacks the neutrality of the teaching and learning of mathematics, showing how these are value?laden activities indissolubly linked to social and political life. Instead, it argues that the values of openness, dialogicality, criticality towards received opinion, empowerment of the learner, and social/political engagement and citizenship are necessary dimensions of the teaching and learning of mathematics, if it is to contribute towards democracy and social justice. This book draws together critical theoretic contributions on mathematics and mathematics education from leading researchers in the field. Recurring themes include: The natures of mathematics and critical mathematics education, issues of epistemology and ethics; Ideology, the hegemony of mathematics, ethnomathematics, and real?life education; Capitalism, globalization, politics, social class, habitus, citizenship and equity. The book demonstrates the links between these themes and the discipline of mathematics, and its critical teaching and learning. The outcome is a groundbreaking collection unified by a shared concern with critical perspectives of mathematics and education, and of the ways they impact on practice. |
| understanding maths basic mathematics explained graham lawler: The William Lowell Putnam Mathematical Competition Gerald L. Alexanderson, Leonard F. Klosinski, Loren C. Larson, 2003 The Putnam Competition has since 1928 been providing a challenge to gifted college mathematics students. This book, the second of the Putnam Competition volumes, contains problems with their solutions for the years 1965-1984. Additional solutions are presented for many of the problems. Included is an essay on recollections of the first Putnam Exam by Herbert Robbins, as well as appendices listing the winning teams and students from 1965 through 1984. This volume offers the problem solver an enticing sample of challenging problems and their solutions. In 1980, the MAA published the first William Lowell Putnam Mathematical Competition book, covering the contest from 1938 to 1964. In 2002 the third of the Putnam problem books appeared, covering the years 1985 through 2000. All three of these books belong on the bookshelf of students, teachers, and all interested in problem solving. |
| understanding maths basic mathematics explained graham lawler: How Mathematicians Think William Byers, 2010-05-02 To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a final scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself. |
| understanding maths basic mathematics explained graham lawler: Learning Futures Keri Facer, 2011-03-29 In the twenty-first century, educators around the world are being told that they need to transform education systems to adapt young people for the challenges of a global digital knowledge economy. Too rarely, however, do we ask whether this future vision is robust, achievable or even desirable, whether alternative futures might be in development, and what other possible futures might demand of education. Drawing on ten years of research into educational innovation and socio-technical change, working with educators, researchers, digital industries, students and policy-makers, this book questions taken-for-granted assumptions about the future of education. Arguing that we have been working with too narrow a vision of the future, Keri Facer makes a case for recognizing the challenges that the next two decades may bring, including: the emergence of new relationships between humans and technology the opportunities and challenges of aging populations the development of new forms of knowledge and democracy the challenges of climate warming and environmental disruption the potential for radical economic and social inequalities. This book describes the potential for these developments to impact critical aspects of education – including adult-child relationships, social justice, curriculum design, community relationships and learning ecologies. Packed with examples from around the world and utilising vital research undertaken by the author while Research Director at the UK’s Futurelab, the book helps to bring into focus the risks and opportunities for schools, students and societies over the coming two decades. It makes a powerful case for rethinking the relationship between education and social and technological change, and presents a set of key strategies for creating schools better able to meet the emerging needs of their students and communities. An important contribution to the debates surrounding educational futures, this book is compelling reading for all of those, including educators, researchers, policy-makers and students, who are asking the question 'how can education help us to build desirable futures for everyone in the context of social and technological change?' |
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The meaning of UNDERSTANDING is a mental grasp : comprehension. How to use understanding in a sentence.
UNDERSTANDING | English meaning - Cambridge Dictionary
UNDERSTANDING definition: 1. knowledge about a subject, situation, etc. or about how something works: 2. a particular way in…. Learn more.
Understanding - Wikipedia
Understanding is a cognitive process related to an abstract or physical object, such as a person, situation, or message whereby one is able to use concepts to model that object. …
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characterized by understanding; prompted by, based on, or demonstrating comprehension, intelligence, discernment, empathy, or the like.
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The sum of your knowledge of a certain topic, is your understanding of it. This can change, or deepen as you learn more. But being an understanding person doesn't take a lot of studying …
understanding noun - Definition, pictures, pronunciation and …
Definition of understanding noun from the Oxford Advanced Learner's Dictionary. [uncountable, singular] understanding (of something) the knowledge that somebody has about a particular …
UNDERSTANDING definition and meaning | Collins English …
If you have an understanding of something, you know how it works or know what it means. If you are understanding towards someone, you are kind and forgiving. Her boss, who was very …
Understanding - definition of understanding by ... - The Free …
1. the mental process of a person who understands; comprehension; personal interpretation. 2. intellectual faculties; intelligence. 3. knowledge of or familiarity with a particular thing. 5. a …
What does Understanding mean? - Definitions.net
Understanding is a relation between the knower and an object of understanding. Understanding implies abilities and dispositions with respect to an object of knowledge sufficient to support …
514 Synonyms & Antonyms for UNDERSTAND | Thesaurus.com
He described a "mismatch" between the expectation and understanding of the shared owner and the landlord. "It is important that the fate of pesticides and other chemicals in the environment …
UNDERSTANDING Definition & Meaning - Merriam-Webster
The meaning of UNDERSTANDING is a mental grasp : comprehension. How to use understanding in a sentence.
UNDERSTANDING | English meaning - Cambridge Dictionary
UNDERSTANDING definition: 1. knowledge about a subject, situation, etc. or about how something works: 2. a particular way in…. Learn more.
Understanding - Wikipedia
Understanding is a cognitive process related to an abstract or physical object, such as a person, situation, or message whereby one is able to use concepts to model that object. …
UNDERSTANDING Definition & Meaning - Dictionary.com
characterized by understanding; prompted by, based on, or demonstrating comprehension, intelligence, discernment, empathy, or the like.
Understanding - Definition, Meaning & Synonyms
The sum of your knowledge of a certain topic, is your understanding of it. This can change, or deepen as you learn more. But being an understanding person doesn't take a lot of studying …
understanding noun - Definition, pictures, pronunciation and …
Definition of understanding noun from the Oxford Advanced Learner's Dictionary. [uncountable, singular] understanding (of something) the knowledge that somebody has about a particular …
UNDERSTANDING definition and meaning | Collins English …
If you have an understanding of something, you know how it works or know what it means. If you are understanding towards someone, you are kind and forgiving. Her boss, who was very …
Understanding - definition of understanding by ... - The Free …
1. the mental process of a person who understands; comprehension; personal interpretation. 2. intellectual faculties; intelligence. 3. knowledge of or familiarity with a particular thing. 5. a …
What does Understanding mean? - Definitions.net
Understanding is a relation between the knower and an object of understanding. Understanding implies abilities and dispositions with respect to an object of knowledge sufficient to support …
514 Synonyms & Antonyms for UNDERSTAND | Thesaurus.com
He described a "mismatch" between the expectation and understanding of the shared owner and the landlord. "It is important that the fate of pesticides and other chemicals in the environment …
