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Punchline Algebra

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Abstract Algebra

Abstract Algebra Book
Author : Joseph H. Silverman
Publisher : American Mathematical Society
Release : 2022-03-07
ISBN : 1470468603
File Size : 31,5 Mb
Language : En, Es, Fr and De

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Book Summary :

This abstract algebra textbook takes an integrated approach that highlights the similarities of fundamental algebraic structures among a number of topics. The book begins by introducing groups, rings, vector spaces, and fields, emphasizing examples, definitions, homomorphisms, and proofs. The goal is to explain how all of the constructions fit into an axiomatic framework and to emphasize the importance of studying those maps that preserve the underlying algebraic structure. This fast-paced introduction is followed by chapters in which each of the four main topics is revisited and deeper results are proven. The second half of the book contains material of a more advanced nature. It includes a thorough development of Galois theory, a chapter on modules, and short surveys of additional algebraic topics designed to whet the reader's appetite for further study. This book is intended for a first introduction to abstract algebra and requires only a course in linear algebra as a prerequisite. The more advanced material could be used in an introductory graduate-level course.

Algebra I

Algebra I Book
Author : Sara Freeman
Publisher : Milliken Publishing Company
Release : 2002-09-01
ISBN : 1773445472
File Size : 48,8 Mb
Language : En, Es, Fr and De

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Book Summary :

Motivate Your Students! This easy-to-use workbook is chock full of stimulating activities that will jumpstart your students' interest in algebra while reinforcing the major algebra concepts. A variety of puzzles, mazes, and games will challenge students to think creatively as they sharpen their algebra skills. A special assessment section is also included to help prepare students for standardized tests.

Algebra I eBook

Algebra I  eBook  Book
Author : Sara Freeman
Publisher : Lorenz Educational Press
Release : 2002-09-01
ISBN : 0787781681
File Size : 24,7 Mb
Language : En, Es, Fr and De

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Book Summary :

Give your students all the essential tools for a solid introduction to algebra! The skills required to master basic algebra are introduced in Algebra I and developed further in the more advanced Algebra II. A variety of rules, theorems, and processes are presented along with easy-to-follow examples. Games and puzzles use answers to practice problems to reinforce learning and make algebra fun. 48 pages

Algebra 1

Algebra 1 Book
Author : Sara Freeman
Publisher : Lorenz Educational Press
Release : 2002-09-01
ISBN : 078770508X
File Size : 21,5 Mb
Language : En, Es, Fr and De

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Book Summary :

Give your students all the essential tools for a solid introduction to algebra! The skills required to master basic algebra are introduced in Algebra I and developed further in the more advanced Algebra II. A variety of rules, theorems, and processes are presented along with easy-to-follow examples. Games and puzzles use answers to practice problems to reinforce learning and make algebra fun. 48 pages

Future Curricular Trends in School Algebra And Geometry

Future Curricular Trends in School Algebra And Geometry Book
Author : Zalman Usiskin,Kathleen Andersen,Nicole Zotto
Publisher : IAP
Release : 2010-06-01
ISBN : 1617350087
File Size : 24,5 Mb
Language : En, Es, Fr and De

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Book Summary :

This volume contains papers from the Second International Curriculum Conference sponsored by the Center for the Study of Mathematics Curriculum (CSMC). The intended audience includes policy makers, curriculum developers, researchers, teachers, teacher trainers, and anyone else interested in school mathematics curricula.

Abstract Algebra

Abstract Algebra Book
Author : Jonathan K. Hodge,Steven Schlicker,Ted Sundstrom
Publisher : CRC Press
Release : 2013-12-21
ISBN : 1466567082
File Size : 32,7 Mb
Language : En, Es, Fr and De

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Book Summary :

To learn and understand mathematics, students must engage in the process of doing mathematics. Emphasizing active learning, Abstract Algebra: An Inquiry-Based Approach not only teaches abstract algebra but also provides a deeper understanding of what mathematics is, how it is done, and how mathematicians think. The book can be used in both rings-first and groups-first abstract algebra courses. Numerous activities, examples, and exercises illustrate the definitions, theorems, and concepts. Through this engaging learning process, students discover new ideas and develop the necessary communication skills and rigor to understand and apply concepts from abstract algebra. In addition to the activities and exercises, each chapter includes a short discussion of the connections among topics in ring theory and group theory. These discussions help students see the relationships between the two main types of algebraic objects studied throughout the text. Encouraging students to do mathematics and be more than passive learners, this text shows students that the way mathematics is developed is often different than how it is presented; that definitions, theorems, and proofs do not simply appear fully formed in the minds of mathematicians; that mathematical ideas are highly interconnected; and that even in a field like abstract algebra, there is a considerable amount of intuition to be found.

Post Modern Algebra

Post Modern Algebra Book
Author : Jonathan D. H. Smith,Anna B. Romanowska
Publisher : John Wiley & Sons
Release : 2011-09-30
ISBN : 1118030834
File Size : 31,6 Mb
Language : En, Es, Fr and De

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Book Summary :

Advanced algebra in the service of contemporary mathematicalresearch-- a unique introduction. This volume takes an altogether new approach to advanced algebra.Its intriguing title, inspired by the term postmodernism, denotes adeparture from van der Waerden's Modern Algebra--a book that hasdominated the field for nearly seventy years. Post-Modern Algebraoffers a truly up-to-date alternative to the standard approach,explaining topics from an applications-based perspective ratherthan by abstract principles alone. The book broadens the field ofstudy to include algebraic structures and methods used in currentand emerging mathematical research, and describes the powerful yetsubtle techniques of universal algebra and category theory.Classical algebraic areas of groups, rings, fields, and vectorspaces are bolstered by such topics as ordered sets, monoids,monoid actions, quasigroups, loops, lattices, Boolean algebras,categories, and Heyting algebras. The text features: * A clear and concise treatment at an introductory level, tested inuniversity courses. * A wealth of exercises illustrating concepts and their practicalapplication. * Effective techniques for solving research problems in the realworld. * Flexibility of presentation, making it easy to tailor material tospecific needs. * Help with elementary proofs and algebraic notations for studentsof varying abilities. Post-Modern Algebra is an excellent primary or supplementary textfor graduate-level algebra courses. It is also an extremely usefulresource for professionals and researchers in many areas who musttackle abstract, linear, or universal algebra in the course oftheir work.

Learning Modern Algebra

Learning Modern Algebra Book
Author : Al Cuoco,Joseph Rotman
Publisher : MAA
Release : 2013
ISBN : 1939512018
File Size : 38,5 Mb
Language : En, Es, Fr and De

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Book Summary :

Learning Modern Algebra aligns with the CBMS Mathematical Education of Teachers II recommendations, in both content and practice. It emphasizes rings and fields over groups, and it makes explicit connections between the ideas of abstract algebra and the mathematics used by high school teachers. It provides opportunities for prospective and practicing teachers to experience mathematics for themselves, before the formalities are developed, and it is explicit about the mathematical habits of mind that lie beneath the definitions and theorems. This book is designed for prospective and practicing high school mathematics teachers, but it can serve as a text for standard abstract algebra courses as well. The presentation is organized historically: the Babylonians introduced Pythagorean triples to teach the Pythagorean theorem; these were classified by Diophantus, and eventually this led Fermat to conjecture his Last Theorem. The text shows how much of modern algebra arose in attempts to prove this; it also shows how other important themes in algebra arose from questions related to teaching. Indeed, modern algebra is a very useful tool for teachers, with deep connections to the actual content of high school mathematics, as well as to the mathematics teachers use in their profession that doesn't necessarily ""end up on the blackboard."" The focus is on number theory, polynomials, and commutative rings. Group theory is introduced near the end of the text to explain why generalizations of the quadratic formula do not exist for polynomials of high degree, allowing the reader to appreciate the more general work of Galois and Abel on roots of polynomials. Results and proofs are motivated with specific examples whenever possible, so that abstractions emerge from concrete experience. Applications range from the theory of repeating decimals to the use of imaginary quadratic fields to construct problems with rational solutions. While such applications are integrated throughout, each chapter also contains a section giving explicit connections between the content of the chapter and high school teaching.