Learning Abstract Algebra With Isetl
DOWNLOAD
Download Learning Abstract Algebra With Isetl PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Learning Abstract Algebra With Isetl book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Learning Abstract Algebra With Isetl
DOWNLOAD
Author : Ed Dubinsky
language : de
Publisher: Springer-Verlag
Release Date : 2019-06-12
Learning Abstract Algebra With Isetl written by Ed Dubinsky and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-12 with Mathematics categories.
Learning Abstract Algebra With Isetl
DOWNLOAD
Author : Ed Dubinsky
language : en
Publisher: Springer
Release Date : 1993-12-14
Learning Abstract Algebra With Isetl written by Ed Dubinsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-12-14 with Mathematics categories.
This book is based on the belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities that will establish an experiential base for any future verbal explanations and to have the opportunity to reflect on their activities. This approach is based on extensive theoretical and empirical studies, as well as on the substantial experience of the authors in teaching Abstract Algebra. The main source of activities in this course is computer constructions, specifically, small programs written in the math-like programming language ISETL; the main tool for reflection is work in teams of two to four students, where the activities are discussed and debated. Because of the similarity of ISETL expressions to standard written mathematics, there is very little programming overhead: learning to program is inseparable from learning the mathematics. Each topic is first introduced through computer activities, which are then followed by a text section and exercises. The text section is written in an informal, discursive style, closely relating definitions and proofs to the constructions in the activities. Notions such as cosets and quotient groups become much more meaningful to the students than when they are presented in a lecture.
Learning Abstract Algebra With Isetl
DOWNLOAD
Author : Ed Dubinsky
language : en
Publisher: Springer
Release Date : 2014-09-12
Learning Abstract Algebra With Isetl written by Ed Dubinsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-12 with Mathematics categories.
This book is based on the belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities that will establish an experiential base for any future verbal explanations and to have the opportunity to reflect on their activities. This approach is based on extensive theoretical and empirical studies, as well as on the substantial experience of the authors in teaching Abstract Algebra. The main source of activities in this course is computer constructions, specifically, small programs written in the math-like programming language ISETL; the main tool for reflection is work in teams of two to four students, where the activities are discussed and debated. Because of the similarity of ISETL expressions to standard written mathematics, there is very little programming overhead: learning to program is inseparable from learning the mathematics. Each topic is first introduced through computer activities, which are then followed by a text section and exercises. The text section is written in an informal, discursive style, closely relating definitions and proofs to the constructions in the activities. Notions such as cosets and quotient groups become much more meaningful to the students than when they are presented in a lecture.
Learning Abstract Algebra With Isetl
DOWNLOAD
Author : Ed Dubinsky
language : en
Publisher: Springer Science & Business Media
Release Date : 1994
Learning Abstract Algebra With Isetl written by Ed Dubinsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Education categories.
Most students in abstract algebra classes have great difficulty making sense of what the instructor is saying. Moreover, this seems to remain true almost independently of the quality of the lecture. This book is based on the constructivist belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities which will establish an experiential base for any future verbal explanation. No less, they need to have the opportunity to reflect on their activities. This approach is based on extensive theoretical and empirical studies as well as on the substantial experience of the authors in teaching astract algebra. The main source of activities in this course is computer constructions, specifically, small programs written in the mathlike programming language ISETL; the main tool for reflections is work in teams of 2-4 students, where the activities are discussed and debated. Because of the similarity of ISETL expressions to standard written mathematics, there is very little programming overhead: learning to program is inseparable from learning the mathematics. Each topic is first introduced through computer activities, which are then followed by a text section and exercises. This text section is written in an informed, discusive style, closely relating definitions and proofs to the constructions in the activities. Notions such as cosets and quotient groups become much more meaningful to the students than when they are preseted in a lecture.
Innovations In Teaching Abstract Algebra
DOWNLOAD
Author : Allen C. Hibbard
language : en
Publisher: Mathematical Association of America (MAA)
Release Date : 2002
Innovations In Teaching Abstract Algebra written by Allen C. Hibbard and has been published by Mathematical Association of America (MAA) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
How To Think About Abstract Algebra
DOWNLOAD
Author : Lara Alcock
language : en
Publisher: Oxford University Press, USA
Release Date : 2021
How To Think About Abstract Algebra written by Lara Alcock and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Mathematics categories.
How to Think about Abstract Algebra provides an engaging and readable introduction to its subject, which encompasses group theory and ring theory. Abstract Algebra is central in most undergraduate mathematics degrees, and it captures regularities that appear across diverse mathematical structures - many people find it beautiful for this reason. But its abstraction can make its central ideas hard to grasp, and even the best students might find that they can follow some of the reasoning without really understanding what it is all about. This book aims to solve that problem. It is not like other Abstract Algebra texts and is not a textbook containing standard content. Rather, it is designed to be read before starting an Abstract Algebra course, or as a companion text once a course has begun. It builds up key information on five topics: binary operations, groups, quotient groups, isomorphisms and homomorphisms, and rings. It provides numerous examples, tables and diagrams, and its explanations are informed by research in mathematics education. The book also provides study advice focused on the skills that students need in order to learn successfully in their own Abstract Algebra courses. It explains how to interact productively with axioms, definitions, theorems and proofs, and how research in psychology should inform our beliefs about effective learning.
A Course On Abstract Algebra
DOWNLOAD
Author : Minking Eie
language : en
Publisher: World Scientific Publishing Company
Release Date : 2010-02-26
A Course On Abstract Algebra written by Minking Eie and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-26 with Mathematics categories.
This textbook provides an introduction to abstract algebra for advanced undergraduate students. Based on the authors' lecture notes at the Department of Mathematics, National Chung Cheng University of Taiwan, it begins with a description of the algebraic structures of the ring and field of rational numbers. Abstract groups are then introduced. Technical results such as Lagrange's Theorem and Sylow's Theorems follow as applications of group theory. Ring theory forms the second part of abstract algebra, with the ring of polynomials and the matrix ring as basic examples. The general theory of ideals as well as maximal ideals in the rings of polynomials over the rational numbers are also discussed. The final part of the book focuses on field theory, field extensions and then Galois theory to illustrate the correspondence between the Galois groups and field extensions. This textbook is more accessible and less ambitious than most existing books covering the same subject. Readers will also find the pedagogical material very useful in enhancing the teaching and learning of abstract algebra.
Connecting Abstract Algebra To Secondary Mathematics For Secondary Mathematics Teachers
DOWNLOAD
Author : Nicholas H. Wasserman
language : en
Publisher: Springer
Release Date : 2018-12-12
Connecting Abstract Algebra To Secondary Mathematics For Secondary Mathematics Teachers written by Nicholas H. Wasserman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-12 with Education categories.
Secondary mathematics teachers are frequently required to take a large number of mathematics courses – including advanced mathematics courses such as abstract algebra – as part of their initial teacher preparation program and/or their continuing professional development. The content areas of advanced and secondary mathematics are closely connected. Yet, despite this connection many secondary teachers insist that such advanced mathematics is unrelated to their future professional work in the classroom. This edited volume elaborates on some of the connections between abstract algebra and secondary mathematics, including why and in what ways they may be important for secondary teachers. Notably, the volume disseminates research findings about how secondary teachers engage with, and make sense of, abstract algebra ideas, both in general and in relation to their own teaching, as well as offers itself as a place to share practical ideas and resources for secondary mathematics teacher preparation and professional development. Contributors to the book are scholars who have both experience in the mathematical preparation of secondary teachers, especially in relation to abstract algebra, as well as those who have engaged in related educational research. The volume addresses some of the persistent issues in secondary mathematics teacher education in connection to advanced mathematics courses, as well as situates and conceptualizes different ways in which abstract algebra might be influential for teachers of algebra. Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers is a productive resource for mathematics teacher educators who teach capstone courses or content-focused methods courses, as well as for abstract algebra instructors interested in making connections to secondary mathematics.
A Friendly Introduction To Abstract Algebra
DOWNLOAD
Author : Ryota Matsuura
language : en
Publisher: American Mathematical Society
Release Date : 2022-07-06
A Friendly Introduction To Abstract Algebra written by Ryota Matsuura and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-06 with Mathematics categories.
A Friendly Introduction to Abstract Algebra offers a new approach to laying a foundation for abstract mathematics. Prior experience with proofs is not assumed, and the book takes time to build proof-writing skills in ways that will serve students through a lifetime of learning and creating mathematics. The author's pedagogical philosophy is that when students abstract from a wide range of examples, they are better equipped to conjecture, formalize, and prove new ideas in abstract algebra. Thus, students thoroughly explore all concepts through illuminating examples before formal definitions are introduced. The instruction in proof writing is similarly grounded in student exploration and experience. Throughout the book, the author carefully explains where the ideas in a given proof come from, along with hints and tips on how students can derive those proofs on their own. Readers of this text are not just consumers of mathematical knowledge. Rather, they are learning mathematics by creating mathematics. The author's gentle, helpful writing voice makes this text a particularly appealing choice for instructors and students alike. The book's website has companion materials that support the active-learning approaches in the book, including in-class modules designed to facilitate student exploration.
Abstract Algebra
DOWNLOAD
Author : Claudia Menini
language : en
Publisher: CRC Press
Release Date : 2017-11-22
Abstract Algebra written by Claudia Menini and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
In one exceptional volume, Abstract Algebra covers subject matter typically taught over the course of two or three years and offers a self-contained presentation, detailed definitions, and excellent chapter-matched exercises to smooth the trajectory of learning algebra from zero to one. Field-tested through advance use in the ERASMUS educational project in Europe, this ambitious, comprehensive book includes an original treatment of representation of finite groups that avoids the use of semisimple ring theory and explains sets, maps, posets, lattices, and other essentials of the algebraic language; Peano's axioms and cardinality; groupoids, semigroups, monoids, groups; and normal subgroups.