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Bridging the Gap to University Mathematics by Edward Hurst,Martin Gould Pdf
Helps to ease the transition between school/college and university mathematics by (re)introducing readers to a range of topics that they will meet in the first year of a degree course in the mathematical sciences, refreshing their knowledge of basic techniques and focussing on areas that are often perceived as the most challenging. Each chapter starts with a "Test Yourself" section so that readers can monitor their progress and readily identify areas where their understanding is incomplete. A range of exercises, complete with full solutions, makes the book ideal for self-study.
Fundamentals of University Mathematics by Colin McGregor,Jonathan Nimmo,Wilson Stothers Pdf
The third edition of this popular and effective textbook provides in one volume a unified treatment of topics essential for first year university students studying for degrees in mathematics. Students of computer science, physics and statistics will also find this book a helpful guide to all the basic mathematics they require. It clearly and comprehensively covers much of the material that other textbooks tend to assume, assisting students in the transition to university-level mathematics.Expertly revised and updated, the chapters cover topics such as number systems, set and functions, differential calculus, matrices and integral calculus. Worked examples are provided and chapters conclude with exercises to which answers are given. For students seeking further challenges, problems intersperse the text, for which complete solutions are provided. Modifications in this third edition include a more informal approach to sequence limits and an increase in the number of worked examples, exercises and problems.The third edition of Fundamentals of university mathematics is an essential reference for first year university students in mathematics and related disciplines. It will also be of interest to professionals seeking a useful guide to mathematics at this level and capable pre-university students. One volume, unified treatment of essential topics Clearly and comprehensively covers material beyond standard textbooks Worked examples, challenges and exercises throughout
A Focus on Addition and Subtraction by Caroline B. Ebby,Elizabeth T. Hulbert,Rachel M. Broadhead Pdf
This innovative text offers a unique approach to making mathematics education research on addition, subtraction, and number concepts readily accessible and understandable to pre-service and in-service teachers of grades K–3. Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of teachers’ experiences, this book provides educators with the knowledge and tools needed to modify their lessons and improve student learning of additive reasoning in the primary grades. Based on research gathered in the Ongoing Assessment Project (OGAP), this engaging, easy-to-use resource features practical resources such as: A close focus on student work, including 150+ annotated pieces of student work, to help teachers improve their ability to recognize, assess, and monitor their students’ errors and misconceptions, as well as their developing conceptual understanding; A focus on the OGAP Addition, Subtraction, and Base Ten Number Progressions, based on research conducted with hundreds of teachers and thousands of pieces of student work; In-chapter sections on how Common Core State Standards for Math (CCSSM) are supported by math education research; End-of-chapter questions to allow teachers to analyze student thinking and consider instructional strategies for their own students; Instructional links to help teachers relate concepts from each chapter to their own instructional materials and programs; An accompanying eResource, available online, offers an answer key to Looking Back questions, as well as a copy of the OGAP Additive Framework and the OGAP Number Line Continuum. A Focus on Addition and Subtraction marks the fourth installment of the popular A Focus on... collection, designed to aid the professional development of pre-service and in-service mathematics teachers. Following from previous volumes on ratios and proportions, multiplication and division, and fractions, this newest addition is designed to bridge the gap between what math education researchers know and what teachers need to know in order to better understand evidence in student work and make effective instructional decisions.
Mathematics Curriculum Topic Study by Page Keeley,Cheryl M. Rose Pdf
"This book addresses the needs of teachers at every level in their teaching careers, as well as those who support and work with teachers. The processes can be used individually to guide professional learning and teaching, or within almost any professional development structure for facilitating group learning. " -Katherine E. Stiles, Senior Program Associate, WestEd "This resource supports continual professional growth of both content and pedagogical knowledge and will help teachers focus on the appropriate research. What a time saver this is!" -Rhonda Naylor, National Board Certified Mathematics Teacher Campus Middle School, Englewood, CO Attain the tools to plan and incorporate standards-based instruction that positively impacts student achievement! Becoming an accomplished mathematics teacher requires not only a thorough understanding of content, but also a familiarity with mathematics standards and research. However, a strategy for translating standards and research into instructional practice has been lacking since the advent of standards-based education reform. Mathematics Curriculum Topic Study provides a systematic professional development strategy that links mathematics standards and research to curriculum, instruction, and assessment. Developed by authors Page Keeley and Cheryl M. Rose of the Maine Mathematics and Science Alliance, the NSF-funded Curriculum Topic Study (CTS) process can help educators align their practice with research-based concepts and skills required in local, state, and national standards. Successfully field-tested with hundreds of teachers, mathematics coordinators, and staff developers, this book contains 92 ready-to-use CTS guides arranged in seven categories that are aligned with NCTM content and process standards. Designed to work in a variety of contexts, the CTS process will help teachers: Increase their content and pedagogical knowledge Better understand and access mathematics research Translate standards to the classroom in a conscious, scholarly way Learn to recognize and address learning difficulties Increase opportunities for all students to achieve mathematical literacy An essential investment toward improving student achievement in mathematics for K-12 teachers, staff developers, directors of curriculum, department chairs and math educators, this innovative resource is also appropriate for preservice teachers and preservice higher education faculty.
Bridging the Gap: Philosophy, Mathematics, and Physics by Giovanna Corsi,Maria Luisa Dalla Chiara,G. C. Ghirardi Pdf
Foundational questions in logic, mathematics, computer science and physics are constant sources of epistemological debate in contemporary philosophy. To what extent is the transfinite part of mathematics completely trustworthy? Why is there a general malaise' concerning the logical approach to the foundations of mathematics? What is the role of symmetry in physics? Is it possible to build a coherent worldview compatible with a macroobjectivistic position and based on the quantum picture of the world? What account can be given of opinion change in the light of new evidence? These are some of the questions discussed in this volume, which collects 14 lectures on the foundation of science given at the School of Philosophy of Science, Trieste, October 1989. The volume will be of particular interest to any student or scholar engaged in interdisciplinary research into the foundations of science in the context of contemporary debates.
Bridging the Gap: Philosophy, Mathematics, and Physics by G. Corsi,Maria Luisa Dalla Chiara,Giancarlo Ghirardi Pdf
Foundational questions in logic, mathematics, computer science and physics are constant sources of epistemological debate in contemporary philosophy. To what extent is the transfinite part of mathematics completely trustworthy? Why is there a general `malaise' concerning the logical approach to the foundations of mathematics? What is the role of symmetry in physics? Is it possible to build a coherent worldview compatible with a macroobjectivistic position and based on the quantum picture of the world? What account can be given of opinion change in the light of new evidence? These are some of the questions discussed in this volume, which collects 14 lectures on the foundation of science given at the School of Philosophy of Science, Trieste, October 1989. The volume will be of particular interest to any student or scholar engaged in interdisciplinary research into the foundations of science in the context of contemporary debates.
Mathematical Methods For Physics by H. W. Wyld Pdf
This classic book helps students learn the basics in physics by bridging the gap between mathematics and the basic fundamental laws of physics. With supplemental material such as graphs and equations, Mathematical Methods for Physics creates a strong, solid anchor of learning. The text has three parts: Part I focuses on the use of special functions in solving the homogeneous partial differential equations of physics, and emphasizes applications to topics such as electrostatics, wave guides, and resonant cavities, vibrations of membranes, heat flow, potential flow in fluids, plane and spherical waves. Part II deals with the solution of inhomogeneous differential equations with particular emphasis on problems in electromagnetism, Green's functions for Poisson's equation, the wave equation and the diffusion equation, and the solution of integral equations by iteration, eigenfunction expansion and the Fredholm series. Finally, Part II explores complex variable techniques, including evalution of itegrals, dispersion relations, special functions in the complex plane, one-sided Fourier transforms, and Laplace transforms.
Math for Scientists by Natasha Maurits,Branislava Ćurčić-Blake Pdf
This book reviews math topics relevant to non-mathematics students and scientists, but which they may not have seen or studied for a while. These math issues can range from reading mathematical symbols, to using complex numbers, dealing with equations involved in calculating medication equivalents, the General Linear Model (GLM) used in e.g. neuroimaging analysis, finding the minimum of a function, independent component analysis, or filtering approaches. Almost every student or scientist, will at some point run into mathematical formulas or ideas in scientific papers that may be hard to understand, given that formal math education may be some years ago. In this book we will explain the theory behind many of these mathematical ideas and expressions and provide readers with the tools to better understand them. We will revisit high school mathematics and extend and relate this to the mathematics you need to understand the math you may encounter in the course of your research. This book will help you understand the math and formulas in the scientific papers you read. To achieve this goal, each chapter mixes theory with practical pen-and-paper exercises such that you (re)gain experience with solving math problems yourself. Mnemonics will be taught whenever possible. To clarify the math and help readers apply it, each chapter provides real-world and scientific examples. In this new edition, two new chapters covering statistics and differential equations have been added, which have been workshopped in the 'authors' popular lecture series in order to maximize the benefit for readers.
Towards Higher Mathematics: A Companion by Richard Earl Pdf
Containing a large and varied set of problems, this rich resource will allow students to stretch their mathematical abilities beyond the school syllabus, and bridge the gap to university-level mathematics. Many proofs are provided to better equip students for the transition to university. The author covers substantial extension material using the language of sixth form mathematics, thus enabling students to understand the more complex material. Exercises are carefully chosen to introduce students to some central ideas, without building up large amounts of abstract technology. There are over 1500 carefully graded exercises, with hints included in the text, and solutions available online. Historical and contextual asides highlight each area of mathematics and show how it has developed over time.
Bridging the Achievement Gap by John E. Chubb,Tom Loveless Pdf
The achievement gap between white students and African American and Hispanic students has been debated by scholars and lamented by policymakers since it was first documented in 1966. The average black or Hispanic secondary school student currently achieves at about the same level as the average white student in the lowest quartile of white achievement. Black and Hispanic students are much less likely than white students to graduate from high school, acquire a college or advanced degree, or earn a middle-class living. They are also much more likely than whites to suffer social problems that often accompany low income. While educators have gained an understanding of the causes and effects of the education achievement gap, they have been less successful in finding ways to eliminate it—until now. This book provides, for the first time in one place, evidence that the achievement gap can be bridged. A variety of schools and school reforms are boosting the achievement of black and Hispanic students to levels nearing those of whites. Bridging the Achievement Gap brings together the findings of renowned education scholars who show how various states, school districts, and individual schools have lifted the achievement levels of poor and minority students. The most promising strategies include focusing on core academic skills, reducing class size, enrolling students in more challenging courses, administering annual achievement assessment tests, creating schools with a culture of competition and success, and offering vouchers in big-city school districts. While implementing new educational programs on a large scale is fraught with difficulties, these successful reform efforts offer what could be the start of widespread effective solutions for bridging the achievement gap.
Bridging the Gap Between Arithmetic & Algebra by Bradley S. Witzel Pdf
Although two federal panels have concluded that all students can learn mathematics and most can succeed through Algebra 2, the abstractness of algebra and missing precursor understandings may be overwhelming to many students … and their teachers. Bridging the Gap Between Arithmetic & Algebra responds to this need for instruction and interventions that go beyond typical math lesson plans. Providing a review of evidence-based practices, the book is an essential reference for mathematics teachers and special education teachers when teaching mathematics to students who struggle with the critical concepts and skills necessary for success in algebra. Audiences: General education (mathematics) teachers, special education teachers, administrators, teacher educators.
Bridging the gap between procedural mathematics that emphasizes calculations and conceptual mathematics that focuses on ideas, Mathematics: A Minimal Introduction presents an undergraduate-level introduction to pure mathematics and basic concepts of logic. The author builds logic and mathematics from scratch using essentially no background except natural language. He also carefully avoids circularities that are often encountered in related books and places special emphasis on separating the language of mathematics from metalanguage and eliminating semantics from set theory. The first part of the text focuses on pre-mathematical logic, including syntax, semantics, and inference. The author develops these topics entirely outside the mathematical paradigm. In the second part, the discussion of mathematics starts with axiomatic set theory and ends with advanced topics, such as the geometry of cubics, real and p-adic analysis, and the quadratic reciprocity law. The final part covers mathematical logic and offers a brief introduction to model theory and incompleteness. Taking a formalist approach to the subject, this text shows students how to reconstruct mathematics from language itself. It helps them understand the mathematical discourse needed to advance in the field.
A Classical Introduction to Modern Number Theory by K. Ireland,M. Rosen Pdf
This book is a revised and greatly expanded version of our book Elements of Number Theory published in 1972. As with the first book the primary audience we envisage consists of upper level undergraduate mathematics majors and graduate students. We have assumed some familiarity with the material in a standard undergraduate course in abstract algebra. A large portion of Chapters 1-11 can be read even without such background with the aid of a small amount of supplementary reading. The later chapters assume some knowledge of Galois theory, and in Chapters 16 and 18 an acquaintance with the theory of complex variables is necessary. Number theory is an ancient subject and its content is vast. Any intro ductory book must, of necessity, make a very limited selection from the fascinat ing array of possible topics. Our focus is on topics which point in the direction of algebraic number theory and arithmetic algebraic geometry. By a careful selection of subject matter we have found it possible to exposit some rather advanced material without requiring very much in the way oftechnical background. Most of this material is classical in the sense that is was dis covered during the nineteenth century and earlier, but it is also modern because it is intimately related to important research going on at the present time.