This textbook presents modern algebra from the ground up using numbers and symmetry. 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 modulon, and is encouraged to take the time to explore and become familiar with those structures.
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If Birkhoff and Mac Lane is too intimidating for you...,
This review is from: Numbers and Symmetry: An Introduction to Algebra (Paperback)
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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Inside This Book
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First Sentence:
Algebra begins with the natural numbers {1,2,3,...}, which we can add and multiply. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
rational root test, frieze pattern, clock arithmetic, full symmetry group, isomorphism invariant, cyclic code, cycle notation, ordinary integers, plane groups, division algorithm, generator matrix, elementary row operations, rational primes, glide reflection, row space, generator polynomial, many symmetries, rational integers, common divisor, rectangular lattice New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Algebra begins with the natural numbers {1,2,3,...}, which we can add and multiply. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
rational root test, frieze pattern, clock arithmetic, full symmetry group, isomorphism invariant, cyclic code, cycle notation, ordinary integers, plane groups, division algorithm, generator matrix, elementary row operations, rational primes, glide reflection, row space, generator polynomial, many symmetries, rational integers, common divisor, rectangular lattice New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 8
books:
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3
books
cite this book:
- Topics in Algebra by I. N. Herstein in Front Matter, and page 185
- Geometries and Groups (Universitext) by Viacheslav V. Nikulin on page 124
- Introduction to the Theory of Error-Correcting Codes, 3rd Edition by Vera Pless on page 240
- The Theory of Error-Correcting Codes (North-Holland Mathematical Library) by F.J. MacWilliams on page 240
- Introduction to Finite Fields and their Applications by Rudolf Lidl on page 185
See all 8 books this book cites
- A Course in Modern Geometries by Judith N. Cederberg on page 116, and Back Matter
- Identification Numbers and Check Digit Schemes (Classroom Resource Materials) by Joseph Kirtland in Back Matter
- Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis on Rotation and Motion Groups by Gregory S. Chirikjian on page 237
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