商品簡介
A Discovery-Based Approach to Learning about Algebraic Structures
Abstract Algebra: Structures and Applications helps students understand the abstraction of modern algebra. It emphasizes the more general concept of an algebraic structure while simultaneously covering applications. The text can be used in a variety of courses, from a one-semester introductory course to a full two-semester sequence.
The book presents the core topics of structures in a consistent order:
- Definition of structure
- Motivation
- Examples
- General properties
- Important objects
- Description
- Subobjects
- Morphisms
- Subclasses
- Quotient objects
- Action structures
- Applications
The text uses the general concept of an algebraic structure as a unifying principle and introduces other algebraic structures besides the three standard ones (groups, rings, and fields). Examples, exercises, investigative projects, and entire sections illustrate how abstract algebra is applied to areas of science and other branches of mathematics.
作者簡介
Stephen Lovett is an associate professor of mathematics at Wheaton College. He is a member of the Mathematical Association of America, American Mathematical Society, and Association of Christians in the Mathematical Sciences. He earned a PhD from Northeastern University. His research interests include commutative algebra, algebraic geometry, differential geometry, cryptography, and discrete dynamical systems.
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