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 : 34. 50 MB
Format : PDF
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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.

Invitation To Linear Algebra

Author : David C. Mello
ISBN : 9781498779586
Genre : Mathematics
File Size : 41. 53 MB
Format : PDF
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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 : 46. 18 MB
Format : PDF, Mobi
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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.

Applied Abstract Algebra With Mapletm And Matlab Third Edition

Author : Richard Klima
ISBN : 9781482248258
Genre : Mathematics
File Size : 43. 96 MB
Format : PDF, Docs
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Applied Abstract Algebra with MapleTM and MATLAB® provides an in-depth introduction to real-world abstract algebraic problems. This popular textbook covers a variety of topics including block designs, coding theory, cryptography, and counting techniques, including Pólya's and Burnside's theorems. The book also includes a concise review of all prerequisite advanced mathematics. The use of sophisticated mathematical software packages such as MapleTM and MATLAB® allows students to work though realistic examples without having to struggle with extensive computations. Notable additions to the third edition include expanded contemporary applications, coverage of the two-message problem, and a full chapter on symmetry in Western music. Several other parts of the book were also updated, including some MATLAB sections due to their adoption of the MuPAD computer algebra system since the last edition. This edition also contains more than 100 new exercises. This new edition includes the two most widely used mathematical software packages. It builds upon the successful previous editions, favored by instructors and students alike.

How To Teach Mathematics Third Edition

Author : Steven G. Krantz
ISBN : 9781470425524
Genre : MATHEMATICS
File Size : 57. 46 MB
Format : PDF
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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.

The Moore Method

Author : Charles Arthur Coppin
ISBN : 0883851857
Genre : Mathematics
File Size : 85. 27 MB
Format : PDF, Docs
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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.

Cooperative Learning In Mathematics

Author : Neil Davidson
ISBN : UOM:39015029742072
Genre : Mathematics
File Size : 85. 41 MB
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Grade level: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, p, e, i, s, t.

Enhancing University Mathematics

Author : Ki-hyŏng Ko
ISBN : 0821841947
Genre : Mathematics
File Size : 57. 85 MB
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The book deals with teaching mathematics, a core activity of the contemporary university. It is suitable for the library of every university and mathematician. It features a broad range of topics (technology, pedagogy, philosophy, course content) of interest and value to all who teach university mathematics. This is one of the few books dealing with this essential subject.

Constructing Numbers A Creative And Connected Approach

Author : Mark Daniels
ISBN : 1631894595
Genre :
File Size : 67. 32 MB
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"The discovery-based "Constructing Numbers: An Inquiry-Based Capstone Mathematics Course" helps students synthesize material from elementary analysis, linear algebra, algebraic structures, and geometry while providing perspective on how mathematical thought has developed. The book opens with the history of numbers. It moves on to cover axiomatic systems, real, complex, and constructible numbers, and an algebraic formulation of field construction. The final chapters are devoted to finite fields, probability, and permutation groups. By actively participating in the exercises and proofs, students learn how the material progresses in a logical way. They master the content by doing the work and presenting their results. Working through "Constructing Numbers" gives students a deeper understanding of the discipline of mathematics. They understand the importance of moving beyond a strictly mechanical approach to doing mathematics and to instead ask why mathematical processes are as they are. Intended for one-semester upper-division classes, "Constructing Numbers" can be used in capstone courses in the major, or classes for pre-service secondary mathematics teachers. Mark L. Daniels is a clinical professor of mathematics in the UTeach Natural Sciences Program at the University of Texas, Austin. Professor Daniels mathematical interests include discrete deterministic chaos, inquiry-based instruction in undergraduate mathematics, and the development of secondary mathematics teachers. Efraim P. Armendariz (1938 2013) was an algebraist and professor of mathematics at the University of Texas, Austin. Professor Armendariz devoted much of his career to enhancing the content knowledge of undergraduate and graduate mathematics students as well as both pre-service and in-service mathematics teachers."

Monge S Legacy Of Descriptive And Differential Geometry

Author : Kristen R. Schreck
ISBN : 1942795920
Genre : Mathematics
File Size : 85. 6 MB
Format : PDF, ePub
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A gifted mathematician and expert geometer, Gaspard Monge (1746--1818) was an inspiring educator with an innate ability to spark a fire within his students. Outside of mathematics, he was adept at cultivating political alliances with highly influential friends. Monge's everlasting contributions to mathematics were the development of descriptive geometry and the founding of the field ofdifferential geometry. Created during his early years while he was attending military school at the École Royale du Génie de Mézierès. It was based on the pure geometric methods of projection, perspective, and cross section. These methods originated from the functional requirements of designers and draftsmen to represent three-dimensional objects on a two-dimensional plane when constructing plans of fortifications.

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