Modern Algebra

Modern Algebra

by Seth Warner, Warner
3.2 4


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Modern Algebra 3.3 out of 5 based on 0 ratings. 4 reviews.
Guest More than 1 year ago
One of the best introductory algebra textbooks around.It is aimed at undergraduate students but even postgrads can benefit from it.I won't give a list of contents because it can be found in the review at Mathscinet.But I should add that it also covers constructions using ruler and compass plus the unsolvability of the three famous geometrical problems of antiquity. There is a huge number of exercises which form an integral part of the book.Most of the exercises are really summaries of proofs of important theorems.For example the Sylow theorems for groups are mentioned in the exercises. The book does not simply teach algebra it also teaches rigorous mathematical thinking and it manages to be understandable as well as formal.A student who will work carefully through the detailed proofs and write detailed solutions for a large number of exercises will gain huge amounts of mathematical maturity as well as knowledge of the specific topic. Special mention should be made of the final chapter on the axiom of choice.If a student feels puzzled as to what the axiom of choice says or when it should be used then this chapter will make things a lot clearer for them.Also in just 4 pages it presents a detailed proof of the equivalence of the axiom of choice with Zorn's lemma , the well ordering principle and Hausdorff's maximal chain principle.These proofs use just elementary concepts from set theory without any mention of ordinals or transfinite induction.The chapter also presents the main applications of the axiom of choice in algebra like the proof that every vector space has a basis or that every field can be extended to an algebraically closed field. Thoroughly recommended !!
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