A First Course In Group Theory PDF Download
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Author | : Bijan Davvaz |
Publisher | : Springer Nature |
Total Pages | : 300 |
Release | : 2021-11-10 |
Genre | : Mathematics |
ISBN | : 9811663653 |
Download A First Course in Group Theory Book in PDF, ePub and Kindle
This textbook provides a readable account of the examples and fundamental results of groups from a theoretical and geometrical point of view. Topics on important examples of groups (like cyclic groups, permutation groups, group of arithmetical functions, matrix groups and linear groups), Lagrange’s theorem, normal subgroups, factor groups, derived subgroup, homomorphism, isomorphism and automorphism of groups have been discussed in depth. Covering all major topics, this book is targeted to undergraduate students of mathematics with no prerequisite knowledge of the discussed topics. Each section ends with a set of worked-out problems and supplementary exercises to challenge the knowledge and ability of the reader.
Author | : Cyril F. Gardiner |
Publisher | : Springer Science & Business Media |
Total Pages | : 236 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461381177 |
Download A First Course in Group Theory Book in PDF, ePub and Kindle
One of the difficulties in an introductory book is to communicate a sense of purpose. Only too easily to the beginner does the book become a sequence of definitions, concepts, and results which seem little more than curiousities leading nowhere in particular. In this book I have tried to overcome this problem by making my central aim the determination of all possible groups of orders 1 to 15, together with some study of their structure. By the time this aim is realised towards the end of the book, the reader should have acquired the basic ideas and methods of group theory. To make the book more useful to users of mathematics, in particular students of physics and chemistry, I have included some applications of permutation groups and a discussion of finite point groups. The latter are the simplest examples of groups of partic ular interest to scientists. They occur as symmetry groups of physical configurations such as molecules. Many ideas are discussed mainly in the exercises and the solutions at the end of the book. However, such ideas are used rarely in the body of the book. When they are, suitable references are given. Other exercises test and reinfol:'ce the text in the usual way. A final chapter gives some idea of the directions in which the interested reader may go after working through this book. References to help in this are listed after the outline solutions.
Author | : John S. Rose |
Publisher | : Courier Corporation |
Total Pages | : 322 |
Release | : 2013-05-27 |
Genre | : Mathematics |
ISBN | : 0486170667 |
Download A Course on Group Theory Book in PDF, ePub and Kindle
Text for advanced courses in group theory focuses on finite groups, with emphasis on group actions. Explores normal and arithmetical structures of groups as well as applications. 679 exercises. 1978 edition.
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 | : Derek J.S. Robinson |
Publisher | : Springer Science & Business Media |
Total Pages | : 498 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468401289 |
Download A Course in the Theory of Groups Book in PDF, ePub and Kindle
" A group is defined by means of the laws of combinations of its symbols," according to a celebrated dictum of Cayley. And this is probably still as good a one-line explanation as any. The concept of a group is surely one of the central ideas of mathematics. Certainly there are a few branches of that science in which groups are not employed implicitly or explicitly. Nor is the use of groups confined to pure mathematics. Quantum theory, molecular and atomic structure, and crystallography are just a few of the areas of science in which the idea of a group as a measure of symmetry has played an important part. The theory of groups is the oldest branch of modern algebra. Its origins are to be found in the work of Joseph Louis Lagrange (1736-1813), Paulo Ruffini (1765-1822), and Evariste Galois (1811-1832) on the theory of algebraic equations. Their groups consisted of permutations of the variables or of the roots of polynomials, and indeed for much of the nineteenth century all groups were finite permutation groups. Nevertheless many of the fundamental ideas of group theory were introduced by these early workers and their successors, Augustin Louis Cauchy (1789-1857), Ludwig Sylow (1832-1918), Camille Jordan (1838-1922) among others. The concept of an abstract group is clearly recognizable in the work of Arthur Cayley (1821-1895) but it did not really win widespread acceptance until Walther von Dyck (1856-1934) introduced presentations of groups.
Author | : W. R. Scott |
Publisher | : Courier Corporation |
Total Pages | : 512 |
Release | : 2012-05-23 |
Genre | : Mathematics |
ISBN | : 0486140164 |
Download Group Theory Book in PDF, ePub and Kindle
Here is clear, well-organized coverage of the most standard theorems, including isomorphism theorems, transformations and subgroups, direct sums, abelian groups, and more. This undergraduate-level text features more than 500 exercises.
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 | : John D. Dixon |
Publisher | : Courier Corporation |
Total Pages | : 194 |
Release | : 2007-01-01 |
Genre | : Mathematics |
ISBN | : 0486459160 |
Download Problems in Group Theory Book in PDF, ePub and Kindle
265 challenging problems in all phases of group theory, gathered for the most part from papers published since 1950, although some classics are included.
Author | : Tony Barnard |
Publisher | : CRC Press |
Total Pages | : 286 |
Release | : 2016-12-19 |
Genre | : Mathematics |
ISBN | : 1315405768 |
Download Discovering Group Theory Book in PDF, ePub and Kindle
Discovering Group Theory: A Transition to Advanced Mathematics presents the usual material that is found in a first course on groups and then does a bit more. The book is intended for students who find the kind of reasoning in abstract mathematics courses unfamiliar and need extra support in this transition to advanced mathematics. The book gives a number of examples of groups and subgroups, including permutation groups, dihedral groups, and groups of integer residue classes. The book goes on to study cosets and finishes with the first isomorphism theorem. Very little is assumed as background knowledge on the part of the reader. Some facility in algebraic manipulation is required, and a working knowledge of some of the properties of integers, such as knowing how to factorize integers into prime factors. The book aims to help students with the transition from concrete to abstract mathematical thinking.
Author | : Dan Saracino |
Publisher | : Waveland Press |
Total Pages | : 320 |
Release | : 2008-09-02 |
Genre | : Mathematics |
ISBN | : 1478610131 |
Download Abstract Algebra Book in PDF, ePub and Kindle
The Second Edition of this classic text maintains the clear exposition, logical organization, and accessible breadth of coverage that have been its hallmarks. It plunges directly into algebraic structures and incorporates an unusually large number of examples to clarify abstract concepts as they arise. Proofs of theorems do more than just prove the stated results; Saracino examines them so readers gain a better impression of where the proofs come from and why they proceed as they do. Most of the exercises range from easy to moderately difficult and ask for understanding of ideas rather than flashes of insight. The new edition introduces five new sections on field extensions and Galois theory, increasing its versatility by making it appropriate for a two-semester as well as a one-semester course.