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Bridging The Gap Between Arithmetic Algebra
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Book Synopsis Bridging the Gap Between Arithmetic & Algebra by : Bradley S. Witzel
Download or read book Bridging the Gap Between Arithmetic & Algebra written by Bradley S. Witzel and published by . This book was released on 2016 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although two federal panels have concluded that all students can learn mathematics and most 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, this book is an essential reference for mathematics teaches and special education teachers when teaching mathematics to students who struggle with the critical concepts and skills necessary for success in algebra.
Book Synopsis Bridging the Gap Between Arithmetic & Algebra by : Bradley S. Witzel
Download or read book Bridging the Gap Between Arithmetic & Algebra written by Bradley S. Witzel and published by Council For Exceptional Children. This book was released on 2015-11-15 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Bridging the Gap to University Mathematics by : Edward Hurst
Download or read book Bridging the Gap to University Mathematics written by Edward Hurst and published by Springer Science & Business Media. This book was released on 2009-01-08 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Bridge Between Arithmetic and Algebra by : Rosemarie Bezerra-Nader
Download or read book The Bridge Between Arithmetic and Algebra written by Rosemarie Bezerra-Nader and published by . This book was released on 2013-07-25 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Understanding Algebra by : Terri Husted
Download or read book Understanding Algebra written by Terri Husted and published by . This book was released on 2015-01-15 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear Algebra as an Introduction to Abstract Mathematics by : Isaiah Lankham
Download or read book Linear Algebra as an Introduction to Abstract Mathematics written by Isaiah Lankham and published by World Scientific Publishing Company. This book was released on 2015-11-30 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory textbook designed for undergraduate mathematics majors with an emphasis on abstraction and in particular, the concept of proofs in the setting of linear algebra. Typically such a student would have taken calculus, though the only prerequisite is suitable mathematical grounding. The purpose of this book is to bridge the gap between the more conceptual and computational oriented undergraduate classes to the more abstract oriented classes. The book begins with systems of linear equations and complex numbers, then relates these to the abstract notion of linear maps on finite-dimensional vector spaces, and covers diagonalization, eigenspaces, determinants, and the Spectral Theorem. Each chapter concludes with both proof-writing and computational exercises.
Download or read book The Math Myth written by Andrew Hacker and published by New Press, The. This book was released on 2010-05-25 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: A New York Times–bestselling author looks at mathematics education in America—when it’s worthwhile, and when it’s not. Why do we inflict a full menu of mathematics—algebra, geometry, trigonometry, even calculus—on all young Americans, regardless of their interests or aptitudes? While Andrew Hacker has been a professor of mathematics himself, and extols the glories of the subject, he also questions some widely held assumptions in this thought-provoking and practical-minded book. Does advanced math really broaden our minds? Is mastery of azimuths and asymptotes needed for success in most jobs? Should the entire Common Core syllabus be required of every student? Hacker worries that our nation’s current frenzied emphasis on STEM is diverting attention from other pursuits and even subverting the spirit of the country. Here, he shows how mandating math for everyone prevents other talents from being developed and acts as an irrational barrier to graduation and careers. He proposes alternatives, including teaching facility with figures, quantitative reasoning, and understanding statistics. Expanding upon the author’s viral New York Times op-ed, The Math Myth is sure to spark a heated and needed national conversation—not just about mathematics but about the kind of people and society we want to be. “Hacker’s accessible arguments offer plenty to think about and should serve as a clarion call to students, parents, and educators who decry the one-size-fits-all approach to schooling.” —Publishers Weekly, starred review
Book Synopsis Mathematical Reasoning Level B (B/W) by : Doug Brumbaugh
Download or read book Mathematical Reasoning Level B (B/W) written by Doug Brumbaugh and published by . This book was released on 2008-03-11 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Towards Higher Mathematics: A Companion by : Richard Earl
Download or read book Towards Higher Mathematics: A Companion written by Richard Earl and published by Cambridge University Press. This book was released on 2017-09-07 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Linear Algebra and Matrix Theory by : Robert R. Stoll
Download or read book Linear Algebra and Matrix Theory written by Robert R. Stoll and published by Courier Corporation. This book was released on 2012-10-17 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced undergraduate and first-year graduate students have long regarded this text as one of the best available works on matrix theory in the context of modern algebra. Teachers and students will find it particularly suited to bridging the gap between ordinary undergraduate mathematics and completely abstract mathematics. The first five chapters treat topics important to economics, psychology, statistics, physics, and mathematics. Subjects include equivalence relations for matrixes, postulational approaches to determinants, and bilinear, quadratic, and Hermitian forms in their natural settings. The final chapters apply chiefly to students of engineering, physics, and advanced mathematics. They explore groups and rings, canonical forms for matrixes with respect to similarity via representations of linear transformations, and unitary and Euclidean vector spaces. Numerous examples appear throughout the text.
Book Synopsis The Development of Arabic Mathematics: Between Arithmetic and Algebra by : R. Rashed
Download or read book The Development of Arabic Mathematics: Between Arithmetic and Algebra written by R. Rashed and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: An understanding of developments in Arabic mathematics between the IXth and XVth century is vital to a full appreciation of the history of classical mathematics. This book draws together more than ten studies to highlight one of the major developments in Arabic mathematical thinking, provoked by the double fecondation between arithmetic and the algebra of al-Khwarizmi, which led to the foundation of diverse chapters of mathematics: polynomial algebra, combinatorial analysis, algebraic geometry, algebraic theory of numbers, diophantine analysis and numerical calculus. Thanks to epistemological analysis, and the discovery of hitherto unknown material, the author has brought these chapters into the light, proposes another periodization for classical mathematics, and questions current ideology in writing its history. Since the publication of the French version of these studies and of this book, its main results have been admitted by historians of Arabic mathematics, and integrated into their recent publications. This book is already a vital reference for anyone seeking to understand history of Arabic mathematics, and its contribution to Latin as well as to later mathematics. The English translation will be of particular value to historians and philosophers of mathematics and of science.
Book Synopsis Bridging the Gap: Philosophy, Mathematics, and Physics by : G. Corsi
Download or read book Bridging the Gap: Philosophy, Mathematics, and Physics written by G. Corsi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Bridging the Gap: Philosophy, Mathematics, and Physics by : Giovanna Corsi
Download or read book Bridging the Gap: Philosophy, Mathematics, and Physics written by Giovanna Corsi and published by Springer Science & Business Media. This book was released on 1993 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Approaches to Algebra by : N. Bednarz
Download or read book Approaches to Algebra written by N. Bednarz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an "arithmetic" of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano.
Book Synopsis Quality Instruction and Intervention Strategies for Secondary Educators by : Brittany L. Hott
Download or read book Quality Instruction and Intervention Strategies for Secondary Educators written by Brittany L. Hott and published by Rowman & Littlefield. This book was released on 2023-03-17 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book equips educators with an introduction to quality general education instruction and the most up to date evidence-based academic and behavioral interventions, including instruction and intervention practices. Author teams of content area and strategy experts bridge the gap between effective instruction and quality intervention"--
Book Synopsis How Not to Be Wrong by : Jordan Ellenberg
Download or read book How Not to Be Wrong written by Jordan Ellenberg and published by Penguin. This book was released on 2015-05-26 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Witty, compelling, and just plain fun to read . . ." —Evelyn Lamb, Scientific American The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it. Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer? How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God. Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.
Book Synopsis The First Seven Days by : Richard Poulo
Download or read book The First Seven Days written by Richard Poulo and published by Richard Poulo. This book was released on 2018-06-17 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calculus is often called Infinitesimal Calculus, even when it is developed using limits and there are no infinitesimals. The historical confusion between the two formulations is finally untangled. These seven chapters can be covered in seven lectures in a formal course or in seven sessions for self-instruction. The opening chapter "All the Preliminaries" lays the groundwork for the rest of the book. The next chapters. "What is the Problem?" and "Developing a New Intuition," make plain the mathematical obstacles that caused a two- century delay between the invention of calculus and the first rigorous formulation of the subject. The succeeding chapters, "Limits: A First Attempt at Rigor" and "Limits: Rigor That Works" show why the more obvious definition does not work and why the modern definition solves that problem. The final chapters, "Continuity: The Key to Everything" and "Derivatives: Putting It All Together," launch the student into calculus with the most solid foundation possible.
