abstract algebra an inquiry based approach textbooks in mathematics

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Abstract Algebra

Author : Jonathan K. Hodge
ISBN : 9781466567061
Genre : Mathematics
File Size : 88. 55 MB
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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.

Abstract Algebra

Author : William Paulsen
ISBN : 9781498719797
Genre : Mathematics
File Size : 24. 95 MB
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The new edition of Abstract Algebra: An Interactive Approach presents a hands-on and traditional approach to learning groups, rings, and fields. It then goes further to offer optional technology use to create opportunities for interactive learning and computer use. This new edition offers a more traditional approach offering additional topics to the primary syllabus placed after primary topics are covered. This creates a more natural flow to the order of the subjects presented. This edition is transformed by historical notes and better explanations of why topics are covered. This innovative textbook shows how students can better grasp difficult algebraic concepts through the use of computer programs. It encourages students to experiment with various applications of abstract algebra, thereby obtaining a real-world perspective of this area. Each chapter includes, corresponding Sage notebooks, traditional exercises, and several interactive computer problems that utilize Sage and Mathematica® to explore groups, rings, fields and additional topics. This text does not sacrifice mathematical rigor. It covers classical proofs, such as Abel’s theorem, as well as many topics not found in most standard introductory texts. The author explores semi-direct products, polycyclic groups, Rubik’s Cube®-like puzzles, and Wedderburn’s theorem. The author also incorporates problem sequences that allow students to delve into interesting topics, including Fermat’s two square theorem.

Invitation To Linear Algebra

Author : David C. Mello
ISBN : 9781498779586
Genre : Mathematics
File Size : 23. 45 MB
Format : PDF, ePub
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Unlike most books of this type, the book has been organized into “lessons” rather than chapters. This has been done to limit the size of the mathematical morsels that students must digest during each class, and to make it easier for instructors to budget class time. The book contains considerably more material than normally appears in a first course. For example, several advanced topics such as the Jordan canonical form and matrix power series have been included. This was done to make the book more flexible than most books presently available, and to allow instructors to choose enrichment material which may reflect their interests, and those of their students.

Advanced Linear Algebra

Author : Hugo Woerdeman
ISBN : 9781498754040
Genre : Mathematics
File Size : 60. 40 MB
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Advanced Linear Algebra features a student-friendly approach to the theory of linear algebra. The author’s emphasis on vector spaces over general fields, with corresponding current applications, sets the book apart. He focuses on finite fields and complex numbers, and discusses matrix algebra over these fields. The text then proceeds to cover vector spaces in depth. Also discussed are standard topics in linear algebra including linear transformations, Jordan canonical form, inner product spaces, spectral theory, and, as supplementary topics, dual spaces, quotient spaces, and tensor products. Written in clear and concise language, the text sticks to the development of linear algebra without excessively addressing applications. A unique chapter on "How to Use Linear Algebra" is offered after the theory is presented. In addition, students are given pointers on how to start a research project. The proofs are clear and complete and the exercises are well designed. In addition, full solutions are included for almost all exercises.

Cooperative Learning In Mathematics

Author : Neil Davidson
ISBN : UOM:39015029742072
Genre : Mathematics
File Size : 41. 21 MB
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Grade level: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, p, e, i, s, t.

How To Teach Mathematics Third Edition

Author : Steven G. Krantz
ISBN : 9781470425524
Genre : MATHEMATICS
File Size : 56. 96 MB
Format : PDF, Mobi
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This third edition is a lively and provocative tract on how to teach mathematics in today's new world of online learning tools and innovative teaching devices. The author guides the reader through the joys and pitfalls of interacting with modern undergraduates--telling you very explicitly what to do and what not to do. This third edition has been streamlined from the second edition, but still includes the nuts and bolts of good teaching, discussing material related to new developments in teaching methodology and technique, as well as adding an entire new chapter on online teaching methods.

Challenges And Strategies In Teaching Linear Algebra

Author : Sepideh Stewart
ISBN : 9783319668116
Genre : Education
File Size : 26. 14 MB
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This book originated from a Discussion Group (Teaching Linear Algebra) that was held at the 13th International Conference on Mathematics Education (ICME-13). The aim was to consider and highlight current efforts regarding research and instruction on teaching and learning linear algebra from around the world, and to spark new collaborations. As the outcome of the two-day discussion at ICME-13, this book focuses on the pedagogy of linear algebra with a particular emphasis on tasks that are productive for learning. The main themes addressed include: theoretical perspectives on the teaching and learning of linear algebra; empirical analyses related to learning particular content in linear algebra; the use of technology and dynamic geometry software; and pedagogical discussions of challenging linear algebra tasks. Drawing on the expertise of mathematics education researchers and research mathematicians with experience in teaching linear algebra, this book gathers work from nine countries: Austria, Germany, Israel, Ireland, Mexico, Slovenia, Turkey, the USA and Zimbabwe.

The Moore Method

Author : Charles Arthur Coppin
ISBN : 0883851857
Genre : Mathematics
File Size : 47. 4 MB
Format : PDF
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The Moore Method: A Pathway to Learner-Centered Instruction offers a practical overview of the method as practiced by the four co-authors, serving as both a "how to" manual for implementing the method and an answer to the question, "what is the Moore method?". Moore is well known as creator of The Moore Method (no textbooks, no lectures, no conferring) in which there is a current and growing revival of interest and modified application under inquiry-based learning projects. Beginning with Moore's Method as practiced by Moore himself, the authors proceed to present their own broader definitions of the method before addressing specific details and mechanics of their individual implementations. Each chapter consists of four essays, one by each author, introduced with the commonality of the authors' writings.Topics include the culture the authors strive to establish in the classroom, their grading methods, the development of materials and typical days in the classroom. Appendices include sample tests, sample notes, and diaries of individual courses. With more than 130 references supporting the themes of the book the work provides ample additional reading supporting the transition to learner-centered methods of instruction.

Die 5 Elemente Effektiven Denkens

Author : Edward B. Burger
ISBN : 3933689139
Genre :
File Size : 56. 61 MB
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Was Ist Mathematik

Author : Richard Courant
ISBN : 9783642137013
Genre : Mathematics
File Size : 69. 48 MB
Format : PDF
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"Was ist Mathematik?" lädt jeden ein, das Reich der Mathematik zu betreten, der neugierig genug ist, sich auf ein Abenteuer einzulassen. Das Buch richtet sich an Leser jeden Alters und jeder Vorbildung. Gymnasiallehrer erhalten eine Fülle von Beispielen, Studenten bietet es Orientierung, und Dozenten werden sich an den Feinheiten der Darstellung zweier Meister ihres Faches erfreuen.

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