Groups For Undergraduates

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Groups for Undergraduates

Author : John Atwell Moody
Publisher : World Scientific
ISBN 13 : 9789810221058
Total Pages : 184 pages
Book Rating : 4.2/5 (21 download)

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Book Synopsis Groups for Undergraduates by : John Atwell Moody

Download or read book Groups for Undergraduates written by John Atwell Moody and published by World Scientific. This book was released on 1994 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these lecture notes the student learns basic theorems of the subject (due to Sylow, Burnside, Schur and Frobenius). More importantly, the student learns to use the theorems in various combinations, to discover for himself the groups of reasonably small order. In examples, presentations of the groups of order 1?31 and 33?42 are constructed.Once the groups are presented abstractly, the problem is not done: one needs to know how each abstract group may arise as a group of permutations or matrices. Theorems and techniques of representation theory are given which can do this for any group the student may have constructed in the earlier chapters ? and the student ends up building the actual representations (not only the characters). In a series of examples, which the student may carry further, all the matrix representations are constructed for the groups of order less than 13.For students who are already familiar with homomorphisms, cosets, Lagrange's theorem, and finite abelian groups, the text may be used alone. For any group theory course, at least one text such as this one, containing lots of examples, is strongly recommended.The book is written in a lucid, straightforward style. The subject matter is presented from a student's perspective and constantly demands the student's involvement. Both these strategies are highly appropriate for a book of lecture notes and guarantee the student's understanding of the mathematical concepts.

Matrix Groups for Undergraduates

Author : Kristopher Tapp
Publisher : American Mathematical Soc.
ISBN 13 : 1470427222
Total Pages : 250 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Matrix Groups for Undergraduates by : Kristopher Tapp

Download or read book Matrix Groups for Undergraduates written by Kristopher Tapp and published by American Mathematical Soc.. This book was released on 2016-04-07 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe the basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, maximal tori, homogeneous spaces, and roots. This second edition includes two new chapters that allow for an easier transition to the general theory of Lie groups.

Groups and Symmetry

Author : Mark A. Armstrong
Publisher : Springer Science & Business Media
ISBN 13 : 1475740344
Total Pages : 197 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Groups and Symmetry by : Mark A. Armstrong

Download or read book Groups and Symmetry written by Mark A. Armstrong and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a gentle introduction to the vocabulary and many of the highlights of elementary group theory. Written in an informal style, the material is divided into short sections, each of which deals with an important result or a new idea. Includes more than 300 exercises and approximately 60 illustrations.

Topics in Group Theory

Author : Geoff Smith
Publisher : Springer Science & Business Media
ISBN 13 : 1447104617
Total Pages : 266 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Topics in Group Theory by : Geoff Smith

Download or read book Topics in Group Theory written by Geoff Smith and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of groups is simultaneously a branch of abstract algebra and the study of symmetry. Designed for readers approaching the subject for the first time, this book reviews all the essentials. It recaps the basic definitions and results, including Lagranges Theorem, the isomorphism theorems and group actions. Later chapters include material on chain conditions and finiteness conditions, free groups and the theory of presentations. In addition, a novel chapter of "entertainments" demonstrates an assortment of results that can be achieved with the theoretical machinery.

Visual Group Theory

Author : Nathan Carter
Publisher : American Mathematical Soc.
ISBN 13 : 1470464330
Total Pages : 295 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Visual Group Theory by : Nathan Carter

Download or read book Visual Group Theory written by Nathan Carter and published by American Mathematical Soc.. This book was released on 2021-06-08 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.

Algebra in Action

Author : Shahriar Shahriari
Publisher :
ISBN 13 : 9781470436612
Total Pages : 675 pages
Book Rating : 4.4/5 (366 download)

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Book Synopsis Algebra in Action by : Shahriar Shahriari

Download or read book Algebra in Action written by Shahriar Shahriari and published by . This book was released on 2017 with total page 675 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text—based on the author's popular courses at Pomona College—provides a readable, student-friendly, and somewhat sophisticated introduction to abstract algebra. It is aimed at sophomore or junior undergraduates who are seeing the material for the first time. In addition to the usual definitions and theorems, there is ample discussion to help students build intuition and learn how to think about the abstract concepts. The book has over 1300 exercises and mini-projects of varying degrees of difficulty, and, to facilitate active learning and self-study, hints and short answers for many of the problems are provided. There are full solutions to over 100 problems in order to augment the text and to model the writing of solutions. Lattice diagrams are used throughout to visually demonstrate results and proof techniques. The book covers groups, rings, and fields. In group theory, group actions are the unifying theme and are introduced early. Ring theory is motivated by what is needed for solving Diophantine equations, and, in field theory, Galois theory and the solvability of polynomials take center stage. In each area, the text goes deep enough to demonstrate the power of abstract thinking and to convince the reader that the subject is full of unexpected results.

A Mathematician’s Practical Guide to Mentoring Undergraduate Research

Author : Michael Dorff
Publisher : American Mathematical Soc.
ISBN 13 : 147044934X
Total Pages : 211 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A Mathematician’s Practical Guide to Mentoring Undergraduate Research by : Michael Dorff

Download or read book A Mathematician’s Practical Guide to Mentoring Undergraduate Research written by Michael Dorff and published by American Mathematical Soc.. This book was released on 2019-09-16 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Mathematician's Practical Guide to Mentoring Undergraduate Research is a complete how-to manual on starting an undergraduate research program. Readers will find advice on setting appropriate problems, directing student progress, managing group dynamics, obtaining external funding, publishing student results, and a myriad of other relevant issues. The authors have decades of experience and have accumulated knowledge that other mathematicians will find extremely useful.

Groups and Representations

Author : J.L. Alperin
Publisher : Springer Science & Business Media
ISBN 13 : 1461207991
Total Pages : 200 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Groups and Representations by : J.L. Alperin

Download or read book Groups and Representations written by J.L. Alperin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise treatment of topics from group theory and representation theory for use in a one-term course. Focussing on the non-commutative side of the field, this advanced textbook emphasizes the general linear group as the most important group and example. Readers are expected to be familiar with groups, rings, and fields, and to have a solid knowledge of linear algebra. Close to 200 exercises of varying difficulty serve both to reinforce the main concept of the text and to introduce the reader to additional topics.

Foundations of Differentiable Manifolds and Lie Groups

Author : Frank W. Warner
Publisher : Springer Science & Business Media
ISBN 13 : 1475717997
Total Pages : 283 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Foundations of Differentiable Manifolds and Lie Groups by : Frank W. Warner

Download or read book Foundations of Differentiable Manifolds and Lie Groups written by Frank W. Warner and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. Coverage includes differentiable manifolds, tensors and differentiable forms, Lie groups and homogenous spaces, and integration on manifolds. The book also provides a proof of the de Rham theorem via sheaf cohomology theory and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem.

Naive Lie Theory

Author : John Stillwell
Publisher : Springer Science & Business Media
ISBN 13 : 038778215X
Total Pages : 230 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Naive Lie Theory by : John Stillwell

Download or read book Naive Lie Theory written by John Stillwell and published by Springer Science & Business Media. This book was released on 2008-12-15 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called "classical groups'' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra. This naive approach to Lie theory is originally due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics. To compensate for the limitations of the naive approach, end of chapter discussions introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history. John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).

Groups, Rings and Fields

Author : David A.R. Wallace
Publisher : Springer Science & Business Media
ISBN 13 : 1447104250
Total Pages : 256 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Groups, Rings and Fields by : David A.R. Wallace

Download or read book Groups, Rings and Fields written by David A.R. Wallace and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a basic introduction to modern algebra, providing a solid understanding of the axiomatic treatment of groups and then rings, aiming to promote a feeling for the evolutionary and historical development of the subject. It includes problems and fully worked solutions, enabling readers to master the subject rather than simply observing it.

Colleges That Change Lives

Author : Loren Pope
Publisher : Penguin
ISBN 13 : 1101221348
Total Pages : 404 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Colleges That Change Lives by : Loren Pope

Download or read book Colleges That Change Lives written by Loren Pope and published by Penguin. This book was released on 2006-07-25 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Prospective college students and their parents have been relying on Loren Pope's expertise since 1995, when he published the first edition of this indispensable guide. This new edition profiles 41 colleges—all of which outdo the Ivies and research universities in producing performers, not only among A students but also among those who get Bs and Cs. Contents include: Evaluations of each school's program and "personality" Candid assessments by students, professors, and deans Information on the progress of graduates This new edition not only revisits schools listed in previous volumes to give readers a comprehensive assessment, it also addresses such issues as homeschooling, learning disabilities, and single-sex education.

Small Groups

Author : John M. Levine
Publisher : Psychology Press
ISBN 13 : 1135471401
Total Pages : 564 pages
Book Rating : 4.1/5 (354 download)

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Book Synopsis Small Groups by : John M. Levine

Download or read book Small Groups written by John M. Levine and published by Psychology Press. This book was released on 2008-02-19 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research on small groups is highly diverse because investigators who study such groups vary in their disciplinary identifications, theoretical interests, and methodological preferences. The goal of this volume is to capture that diversity, and thereby convey the breadth and excitement of small group research by acquainting students with work on five fundamental aspects of groups. The volume also includes an introductory chapter by the editors which provides an overview of the history of and current state-of-the-art in the field. Together with introductions to each section, discussion questions and suggestions for further reading, make the volume ideal reading for senior undergraduate and graduate students interested in group dynamics.

Learning in Groups

Author : David Jaques
Publisher : Psychology Press
ISBN 13 : 9780749430917
Total Pages : 324 pages
Book Rating : 4.4/5 (39 download)

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Book Synopsis Learning in Groups by : David Jaques

Download or read book Learning in Groups written by David Jaques and published by Psychology Press. This book was released on 2000 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book, rateher than a formal lectures or presentations, allows students to have greater scope ot negotiate meaning and express themselves and their own ideas. It also helps them to establish far more effective relationships, not only with their tutors and trainers but with each other. It can also play a central role in developing key profesional skills, such as listening, presenting ideas, persuasion ...

Groups, Matrices, and Vector Spaces

Author : James B. Carrell
Publisher : Springer
ISBN 13 : 038779428X
Total Pages : 415 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Groups, Matrices, and Vector Spaces by : James B. Carrell

Download or read book Groups, Matrices, and Vector Spaces written by James B. Carrell and published by Springer. This book was released on 2017-09-02 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory and cryptography are interwoven throughout. Each section ends with ample practice problems assisting the reader to better understand the material. Some of the applications are illustrated in the chapter appendices. The author's unique melding of topics evolved from a two semester course that he taught at the University of British Columbia consisting of an undergraduate honors course on abstract linear algebra and a similar course on the theory of groups. The combined content from both makes this rare text ideal for a year-long course, covering more material than most linear algebra texts. It is also optimal for independent study and as a supplementary text for various professional applications. Advanced undergraduate or graduate students in mathematics, physics, computer science and engineering will find this book both useful and enjoyable.

Undergraduates

Author : Richard Henry Edwards
Publisher :
ISBN 13 :
Total Pages : 392 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Undergraduates by : Richard Henry Edwards

Download or read book Undergraduates written by Richard Henry Edwards and published by . This book was released on 1928 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to Lie Groups and the Geometry of Homogeneous Spaces

Author : Andreas Arvanitogeōrgos
Publisher : American Mathematical Soc.
ISBN 13 : 0821827782
Total Pages : 162 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis An Introduction to Lie Groups and the Geometry of Homogeneous Spaces by : Andreas Arvanitogeōrgos

Download or read book An Introduction to Lie Groups and the Geometry of Homogeneous Spaces written by Andreas Arvanitogeōrgos and published by American Mathematical Soc.. This book was released on 2003 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is remarkable that so much about Lie groups could be packed into this small book. But after reading it, students will be well-prepared to continue with more advanced, graduate-level topics in differential geometry or the theory of Lie groups. The theory of Lie groups involves many areas of mathematics. In this book, Arvanitoyeorgos outlines enough of the prerequisites to get the reader started. He then chooses a path through this rich and diverse theory that aims for an understanding of the geometry of Lie groups and homogeneous spaces. In this way, he avoids the extra detail needed for a thorough discussion of other topics. Lie groups and homogeneous spaces are especially useful to study in geometry, as they provide excellent examples where quantities (such as curvature) are easier to compute. A good understanding of them provides lasting intuition, especially in differential geometry. The book is suitable for advanced undergraduates, graduate students, and research mathematicians interested in differential geometry and neighboring fields, such as topology, harmonic analysis, and mathematical physics.