000			03956nam a2200361 4500
001			OTLid0000217
003			MnU
005			20201105133307.0
006			m o d s
008			180907s2016 mnu o 0 0 eng d
020			_a9781944325022
040			_aMnU _beng _cMnU
050		4	_aQA1
050		4	_aQA37.3
100	1		_aJudson, Thomas W. _eauthor
245	0	0	_aAbstract Algebra _bTheory and Applications _cThomas Judson
264		2	_bOpen Textbook Library
264		1	_bUniversity of Puget Sound
300			_a1 online resource
490	0		_aOpen textbook library.
505	0		_aPreliminaries -- The Integers -- Groups -- Cyclic Groups -- Permutation Groups -- Cosets and Lagrange's Theorem -- Introduction to Cryptography -- Algebraic Coding Theory -- Isomorphisms -- Normal Subgroups and Factor Groups -- Homomorphisms -- Matrix Groups and Symmetry -- The Structure of Groups -- Group Actions -- The Sylow Theorems -- Rings -- Polynomials -- Integral Domains -- Lattices and Boolean Algebras -- Vector Spaces -- Fields -- Finite Fields -- Galois Theory
520	0		_aThis text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly. Until recently most abstract algebra texts included few if any applications. However, one of the major problems in teaching an abstract algebra course is that for many students it is their first encounter with an environment that requires them to do rigorous proofs. Such students often find it hard to see the use of learning to prove theorems and propositions; applied examples help the instructor provide motivation. This text contains more material than can possibly be covered in a single semester. Certainly there is adequate material for a two-semester course, and perhaps more; however, for a one-semester course it would be quite easy to omit selected chapters and still have a useful text. The order of presentation of topics is standard: groups, then rings, and finally fields. Emphasis can be placed either on theory or on applications. A typical one-semester course might cover groups and rings while briefly touching on field theory, using Chapters 1 through 6, 9, 10, 11, 13 (the first part), 16, 17, 18 (the first part), 20, and 21. Parts of these chapters could be deleted and applications substituted according to the interests of the students and the instructor. A two-semester course emphasizing theory might cover Chapters 1 through 6, 9, 10, 11, 13 through 18, 20, 21, 22 (the first part), and 23. On the other hand, if applications are to be emphasized, the course might cover Chapters 1 through 14, and 16 through 22. In an applied course, some of the more theoretical results could be assumed or omitted. A chapter dependency chart appears below. (A broken line indicates a partial dependency.)
542	1		_fFree Documentation License (GNU)
546			_aIn English.
588	0		_aDescription based on print resource
650		0	_aMathematics _vTextbooks
710	2		_aOpen Textbook Library _edistributor
856	4	0	_uhttps://open.umn.edu/opentextbooks/textbooks/217 _zAccess online version
999			_c19622 _d19622