Algebra In Action A Course In Groups Rings And Fields PDF Download
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| Author | : Shahriar Shahriar |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 675 |
| Release | : 2017-08-16 |
| Genre | : Algebra |
| ISBN | : 1470428490 |
Download Algebra in Action: A Course in Groups, Rings, and Fields Book in PDF, ePub and Kindle
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.
| Author | : Marlow Anderson |
| Publisher | : CRC Press |
| Total Pages | : 684 |
| Release | : 2005-01-27 |
| Genre | : Mathematics |
| ISBN | : 1420057111 |
Download A First Course in Abstract Algebra Book in PDF, ePub and Kindle
Most abstract algebra texts begin with groups, then proceed to rings and fields. While groups are the logically simplest of the structures, the motivation for studying groups can be somewhat lost on students approaching abstract algebra for the first time. To engage and motivate them, starting with something students know and abstracting from there
| Author | : R. B. J. T. Allenby |
| Publisher | : Hodder Education |
| Total Pages | : 422 |
| Release | : 1983 |
| Genre | : Mathematics |
| ISBN | : |
Download Rings, Fields and Groups Book in PDF, ePub and Kindle
This book provides a stimulating and unusiual introduction to the results, methods and ideas which are now commonly studied in abstract algebra courses in universities and polytechnics. The mixture of informal and formal presentation generates the enthusiasm of the reader without neglecting the axiomatic approach necessary for the serious study.
| Author | : Marlow Anderson |
| Publisher | : CRC Press |
| Total Pages | : 547 |
| Release | : 2014-11-07 |
| Genre | : Mathematics |
| ISBN | : 1482245531 |
Download A First Course in Abstract Algebra Book in PDF, ePub and Kindle
Like its popular predecessors, this text develops ring theory first by drawing on students' familiarity with integers and polynomials. This unique approach motivates students in studying abstract algebra and helps them understand the power of abstraction. This edition makes it easier to teach unique factorization as an optional topic and reorganizes the core material on rings, integral domains, and fields. Along with new exercises on Galois theory, it also includes a more detailed treatment of permutations as well as new chapters on Sylow theorems.
| Author | : Marlow Anderson |
| Publisher | : Brooks/Cole |
| Total Pages | : 488 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : |
Download A First Course in Abstract Algebra Book in PDF, ePub and Kindle
| Author | : Jonathan D. H. Smith |
| Publisher | : CRC Press |
| Total Pages | : 330 |
| Release | : 2016-04-19 |
| Genre | : Mathematics |
| ISBN | : 1420063723 |
Download Introduction to Abstract Algebra Book in PDF, ePub and Kindle
Taking a slightly different approach from similar texts, Introduction to Abstract Algebra presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It helps students fully understand groups, rings, semigroups, and monoids by rigorously building concepts from first principles. A Quick Introduction to Algebra The first three chapters of the book show how functional composition, cycle notation for permutations, and matrix notation for linear functions provide techniques for practical computation. The author also uses equivalence relations to introduce rational numbers and modular arithmetic as well as to present the first isomorphism theorem at the set level. The Basics of Abstract Algebra for a First-Semester Course Subsequent chapters cover orthogonal groups, stochastic matrices, Lagrange’s theorem, and groups of units of monoids. The text also deals with homomorphisms, which lead to Cayley’s theorem of reducing abstract groups to concrete groups of permutations. It then explores rings, integral domains, and fields. Advanced Topics for a Second-Semester Course The final, mostly self-contained chapters delve deeper into the theory of rings, fields, and groups. They discuss modules (such as vector spaces and abelian groups), group theory, and quasigroups.
| Author | : Nathan Carter |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 295 |
| Release | : 2021-06-08 |
| Genre | : Education |
| ISBN | : 1470464330 |
Download Visual Group Theory Book in PDF, ePub and Kindle
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.
| Author | : Louis Rowen |
| Publisher | : CRC Press |
| Total Pages | : 264 |
| Release | : 2018-10-08 |
| Genre | : Mathematics |
| ISBN | : 1439863520 |
Download Algebra Book in PDF, ePub and Kindle
This text presents the concepts of higher algebra in a comprehensive and modern way for self-study and as a basis for a high-level undergraduate course. The author is one of the preeminent researchers in this field and brings the reader up to the recent frontiers of research including never-before-published material. From the table of contents: - Groups: Monoids and Groups - Cauchyís Theorem - Normal Subgroups - Classifying Groups - Finite Abelian Groups - Generators and Relations - When Is a Group a Group? (Cayley's Theorem) - Sylow Subgroups - Solvable Groups - Rings and Polynomials: An Introduction to Rings - The Structure Theory of Rings - The Field of Fractions - Polynomials and Euclidean Domains - Principal Ideal Domains - Famous Results from Number Theory - I Fields: Field Extensions - Finite Fields - The Galois Correspondence - Applications of the Galois Correspondence - Solving Equations by Radicals - Transcendental Numbers: e and p - Skew Field Theory - Each chapter includes a set of exercises
| Author | : John B. Fraleigh |
| Publisher | : Addison Wesley Publishing Company |
| Total Pages | : 0 |
| Release | : 1999 |
| Genre | : Algebra, Abstract |
| ISBN | : 9780201335965 |
Download A First Course in Abstract Algebra Book in PDF, ePub and Kindle
A First Course in Abstract Algebra is an in-depth, introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. The sixth edition of this text continues the tradition of teaching in a classical manner while integrating field theory and a revised Chapter Zero. New exercises were written, and previous exercises were revised and modified.
| Author | : Jeffrey Humpherys |
| Publisher | : SIAM |
| Total Pages | : 710 |
| Release | : 2017-07-07 |
| Genre | : Mathematics |
| ISBN | : 1611974895 |
Download Foundations of Applied Mathematics, Volume I Book in PDF, ePub and Kindle
This book provides the essential foundations of both linear and nonlinear analysis necessary for understanding and working in twenty-first century applied and computational mathematics. In addition to the standard topics, this text includes several key concepts of modern applied mathematical analysis that should be, but are not typically, included in advanced undergraduate and beginning graduate mathematics curricula. This material is the introductory foundation upon which algorithm analysis, optimization, probability, statistics, differential equations, machine learning, and control theory are built. When used in concert with the free supplemental lab materials, this text teaches students both the theory and the computational practice of modern mathematical analysis. Foundations of Applied Mathematics, Volume 1: Mathematical Analysis includes several key topics not usually treated in courses at this level, such as uniform contraction mappings, the continuous linear extension theorem, Daniell?Lebesgue integration, resolvents, spectral resolution theory, and pseudospectra. Ideas are developed in a mathematically rigorous way and students are provided with powerful tools and beautiful ideas that yield a number of nice proofs, all of which contribute to a deep understanding of advanced analysis and linear algebra. Carefully thought out exercises and examples are built on each other to reinforce and retain concepts and ideas and to achieve greater depth. Associated lab materials are available that expose students to applications and numerical computation and reinforce the theoretical ideas taught in the text. The text and labs combine to make students technically proficient and to answer the age-old question, "When am I going to use this?
