Numbers and Symmetry: An Introduction to Algebra 1st Edition by Bernard L. Johnston (PDF)

Description

This textbook presents modern algebra from the ground up using numbers and symmetry. The idea of a ring and of a field are introduced in the context of concrete number systems. Groups arise from considering transformations of simple geometric objects. The analysis of symmetry provides the student with a visual introduction to the central algebraic notion of isomorphism.Designed for a typical one-semester undergraduate course in modern algebra, it provides a gentle introduction to the subject by allowing students to see the ideas at work in accessible examples, rather than plunging them immediately into a sea of formalism. The student is involved at once with interesting algebraic structures, such as the Gaussian integers and the various rings of integers modulo n, and is encouraged to take the time to explore and become familiar with those structures.In terms of classical algebraic structures, the text divides roughly into three parts:

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐on time, and even better than described

⭐I needed a textbook urgently. The deliver was earlier than estimated and the condition was very good. I am very happy with it. Thank you.

⭐The forward describes this book as a “trip to the modern algebra zoo”, and it’s a fit description. It shows many of the oddities that typical math courses don’t touch at the high school or junior college level courses, and makes them available to the high school or junior college student who loves math. I wouldn’t go so far as to say it’s a modern tabloid of math, but it’s close.

⭐I really enjoyed the delivery of the information and the basic problems that help build up your foundation. Great starting point.

⭐An easy-to-read self-study guide through the wonderful world of modern algebra. Excellent chapters on Z[sqrt(2)], and Q[sqrt(2)]. Symmetries, groups, tiling patterns, the 17 plane groups, fields. A whole chapter on error correcting codes. Written in the same friendly style as V. Bryant’s “Aspects of Combinatorics” and R.P Burn’s “A Pathway into Number Theory.” Each section has many practical, insightful examples and a good problem set.

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