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Geometry In Modules
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Book Synopsis Geometry by Its History by : Alexander Ostermann
Download or read book Geometry by Its History written by Alexander Ostermann and published by Springer Science & Business Media. This book was released on 2012-04-10 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications, while more recent findings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry, vector algebra and matrices are treated in chapters 9 and 10. The last chapter offers an introduction to projective geometry, which emerged in the 19thcentury. Complemented by numerous examples, exercises, figures and pictures, the book offers both motivation and insightful explanations, and provides stimulating and enjoyable reading for students and teachers alike.
Book Synopsis Eureka Math, A Story of Functions: Geometry, Module 1 by : Great Minds
Download or read book Eureka Math, A Story of Functions: Geometry, Module 1 written by Great Minds and published by Jossey-Bass. This book was released on 2013-11-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Common Core Mathematics is the most comprehensive Common Core State Standards-based mathematics curriculum available today. The modules are sequenced and paced to support the teaching of mathematics as an unfolding story that follows the logic of mathematics itself. They embody the instructional “shifts” and the standards for mathematical practice that are fundamental to the CCSS. Each module contains a sequence of lessons that combine conceptual understanding, fluency, and application to meet the demands of each topic in the module. Formative assessments are included to support data-driven instruction. The modules are written by teams of master teachers and mathematicians. In Common Core Mathematics, Geometry students explore more complex geometric situations and deepen their explanations of geometric relationships, moving towards formal mathematical arguments. Important differences exist between this Geometry course and the historical approach taken in Geometry classes. For example, transformations are emphasized early in this course. Close attention should be paid to the introductory content for the Geometry conceptual category found in the high school CCSS. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. Common Core Learning Standards Addressed in Geometry, Module 1: G-CO.1, G-CO.2, G-CO.3, G-CO.4, G-CO.5, G-CO.6, G-CO.7, G-CO.8, G-CO.9, G-CO.10, G-CO.11, G-CO.12, G-CO.13 SEQUENCE OF GEOMETRY MODULES Module 1: Congruence, Proof, and Constructions Module 2: Similarity, Proof, and Trigonometry Module 3: Extending to Three Dimensions Module 4: Connecting Algebra and Geometry through Coordinates Module 5: Circles With and Without Coordinates Common Core (www.commoncore.org) is a non-profit organization formed in 2007 to advocate for a content-rich liberal arts education in America’s K-12 schools. To improve education in America, Common Core creates curriculum materials and also promotes programs, policies, and initiatives at the local, state, and federal levels that provide students with challenging, rigorous instruction in the full range of liberal arts and sciences. Common Core is not affiliated with the Common Core State Standards Initiative. GRADE OVERVIEWS, GUIDANCE ON HOW TO IMPLEMENT COMMON CORE MATHEMATICS, MATH TOOLS, AND MORE, CAN BE FOUND AT www.commoncore.org
Book Synopsis Helping Children Learn Mathematics by : National Research Council
Download or read book Helping Children Learn Mathematics written by National Research Council and published by National Academies Press. This book was released on 2002-07-31 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.
Download or read book Turtle Geometry written by Harold Abelson and published by MIT Press. This book was released on 1986-07-09 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: Turtle Geometry presents an innovative program of mathematical discovery that demonstrates how the effective use of personal computers can profoundly change the nature of a student's contact with mathematics. Using this book and a few simple computer programs, students can explore the properties of space by following an imaginary turtle across the screen. The concept of turtle geometry grew out of the Logo Group at MIT. Directed by Seymour Papert, author of Mindstorms, this group has done extensive work with preschool children, high school students and university undergraduates.
Book Synopsis Algebraic D-modules by : Armand Borel
Download or read book Algebraic D-modules written by Armand Borel and published by . This book was released on 1987 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presented here are recent developments in the algebraic theory of D-modules. The book contains an exposition of the basic notions and operations of D-modules, of special features of coherent, holonomic, and regular holonomic D-modules, and of the Riemann-Hilbert correspondence. The theory of Algebraic D-modules has found remarkable applications outside of analysis proper, in particular to infinite dimensional representations of semisimple Lie groups, to representations of Weyl groups, and to algebraic geometry.
Book Synopsis Linear Geometry by : K. W. Gruenberg
Download or read book Linear Geometry written by K. W. Gruenberg and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is essentially a book on linear algebra. But the approach is somewhat unusual in that we emphasise throughout the geometric aspect of the subject. The material is suitable for a course on linear algebra for mathe matics majors at North American Universities in their junior or senior year and at British Universities in their second or third year. However, in view of the structure of undergraduate courses in the United States, it is very possible that, at many institutions, the text may be found more suitable at the beginning graduate level. The book has two aims: to provide a basic course in linear algebra up to, and including, modules over a principal ideal domain; and to explain in rigorous language the intuitively familiar concepts of euclidean, affine, and projective geometry and the relations between them. It is increasingly recognised that linear algebra should be approached from a geometric point of VIew. This applies not only to mathematics majors but also to mathematically-oriented natural scientists and engineers.
Book Synopsis Computing the Continuous Discretely by : Matthias Beck
Download or read book Computing the Continuous Discretely written by Matthias Beck and published by Springer. This book was released on 2015-11-14 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart’s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler–Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: “You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.” — MAA Reviews “The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.” — Zentralblatt MATH “This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.” — Mathematical Reviews “Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.” — CHOICE
Book Synopsis The Geometry of Schemes by : David Eisenbud
Download or read book The Geometry of Schemes written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
Book Synopsis Using Algebraic Geometry by : David A. Cox
Download or read book Using Algebraic Geometry written by David A. Cox and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: An illustration of the many uses of algebraic geometry, highlighting the more recent applications of Groebner bases and resultants. Along the way, the authors provide an introduction to some algebraic objects and techniques more advanced than typically encountered in a first course. The book is accessible to non-specialists and to readers with a diverse range of backgrounds, assuming readers know the material covered in standard undergraduate courses, including abstract algebra. But because the text is intended for beginning graduate students, it does not require graduate algebra, and in particular, does not assume that the reader is familiar with modules.
Book Synopsis Module Theory by : Thomas Scott Blyth
Download or read book Module Theory written by Thomas Scott Blyth and published by . This book was released on 1990 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a self-contained course on the basic properties of modules and their importance in the theory of linear algebra. The first 11 chapters introduce the central results and applications of the theory of modules. Subsequent chapters deal with advanced linear algebra, including multilinear and tensor algebra, and explore such topics as the exterior product approach to the determinants of matrices, a module-theoretic approach to the structure of finitely generated Abelian groups, canonical forms, and normal transformations. Suitable for undergraduate courses, the text now includes a proof of the celebrated Wedderburn-Artin theorem which determines the structure of simple Artinian rings.
Book Synopsis The Geometry of Moduli Spaces of Sheaves by : Daniel Huybrechts
Download or read book The Geometry of Moduli Spaces of Sheaves written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2010-05-27 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.
Book Synopsis Algebraic Geometry by : Robin Hartshorne
Download or read book Algebraic Geometry written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
Book Synopsis Topological Persistence in Geometry and Analysis by : Leonid Polterovich
Download or read book Topological Persistence in Geometry and Analysis written by Leonid Polterovich and published by American Mathematical Soc.. This book was released on 2020-05-11 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of persistence modules originated in topological data analysis and became an active area of research in algebraic topology. This book provides a concise and self-contained introduction to persistence modules and focuses on their interactions with pure mathematics, bringing the reader to the cutting edge of current research. In particular, the authors present applications of persistence to symplectic topology, including the geometry of symplectomorphism groups and embedding problems. Furthermore, they discuss topological function theory, which provides new insight into oscillation of functions. The book is accessible to readers with a basic background in algebraic and differential topology.
Book Synopsis Poisson Geometry in Mathematics and Physics by : Giuseppe Dito
Download or read book Poisson Geometry in Mathematics and Physics written by Giuseppe Dito and published by American Mathematical Soc.. This book was released on 2008 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of articles by speakers at the Poisson 2006 conference. The program for Poisson 2006 was an overlap of topics that included deformation quantization, generalized complex structures, differentiable stacks, normal forms, and group-valued moment maps and reduction.
Book Synopsis Lectures on Symplectic Geometry by : Ana Cannas da Silva
Download or read book Lectures on Symplectic Geometry written by Ana Cannas da Silva and published by Springer. This book was released on 2004-10-27 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
Book Synopsis Ring and Module Theory by : Toma Albu
Download or read book Ring and Module Theory written by Toma Albu and published by Springer Science & Business Media. This book was released on 2011-02-04 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of invited papers and articles, many presented at the 2008 International Conference on Ring and Module Theory. The papers explore the latest in various areas of algebra, including ring theory, module theory and commutative algebra.
Book Synopsis A Primer of Algebraic D-Modules by : S. C. Coutinho
Download or read book A Primer of Algebraic D-Modules written by S. C. Coutinho and published by Cambridge University Press. This book was released on 1995-09-07 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of D-modules is a rich area of study combining ideas from algebra and differential equations, and it has significant applications to diverse areas such as singularity theory and representation theory. This book introduces D-modules and their applications avoiding all unnecessary over-sophistication. It is aimed at beginning graduate students and the approach taken is algebraic, concentrating on the role of the Weyl algebra. Very few prerequisites are assumed, and the book is virtually self-contained. Exercises are included at the end of each chapter and the reader is given ample references to the more advanced literature. This is an excellent introduction to D-modules for all who are new to this area.
