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.
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