Introduction to Algebra.
Title:
Introduction to Algebra.
Author:
Cameron, Peter J.
ISBN:
9780191566226
Personal Author:
Edition:
2nd ed.
Physical Description:
1 online resource (353 pages)
Contents:
Contents -- 1. Introduction -- What is mathematics? -- Numbers -- Elementary algebra -- Sets -- Modular Arithmetic -- Matrices -- Appendix: Logic -- 2. Rings -- Rings and subrings -- Homomorphisms and ideals -- Factorisation -- Fields -- Appendix: Miscellany -- 3. Groups -- Groups and subgroups -- Subgroups and cosets -- Homomorphisms and normal subgroups -- Some special groups -- Appendix: How many groups? -- 4. Vector spaces -- Vector spaces and subspaces -- Linear transformations and matrices -- 5. Modules -- Introduction -- Modules over a Euclidean domain -- Applications -- 6. The number systems -- To the complex numbers -- Algebraic and transcendental numbers -- More about sets -- 7. Further topics -- Further group theory -- Further ring theory -- Further field theory -- Other structures -- 8. Applications -- Coding theory -- Galois Theory -- Further reading -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z.
Abstract:
This Second Edition of a classic algebra text includes updated and comprehensive introductory chapters,. new material on axiom of Choice, p-groups and local rings, discussion of theory and applications, and over 300 exercises. It is an ideal introductory text for all Year 1 and 2 undergraduate students in mathematics. - ;Developed to meet the needs of modern students, this Second Edition of the classic algebra text by Peter Cameron covers all the abstract algebra an undergraduate student is likely to need. Starting with an introductory overview of numbers, sets and functions, matrices, polynomials, and modular arithmetic, the text then introduces the most important algebraic structures: groups, rings and fields, and their properties. This is followed by coverage of vector spaces and modules with. applications to abelian groups and canonical forms before returning to the construction of the number systems, including the existence of transcendental numbers. The final chapters take the reader further into the theory of groups, rings and fields, coding theory, and Galois theory. With over 300. exercises, and web-based solutions, this is an ideal introductory text for Year 1 and 2 undergraduate students in mathematics. -.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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