Suitable for advanced undergraduate courses in abstract algebra, each chapter in this text consists of definitions, therorem, proofs and collaries. Worked-out exercises after each section provide techniques of problem solving. Comments are included throughout the text dealing with the historical development of abstract algebra as well as profiles of notable mathematicians.
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THEORY VS. APPLICATIONS:
Within the discipline, there are those instructors in the minority that teach this strictly as a theory course. Most of the market is looking for a more meaningful approach whereby theory and applications are blended. The emphasis on applications does not take away from the mathematical integrity and historical perspective but helps to enhance it. Students are then able to grasp concepts more easily. This text takes the blended theory/applications approach.
Primary Course: Prealgebra
Course: Introduction to Algebra
Integrates the elementary concepts of algebra with fundamental concepts of arithmetic.
Involves the student in the development of mathematical concepts using a sequence of explicit detailed examples.
Applications emphasized throughout.
Also includes equations,geometry, rate & motion measurement.
Emphasis on applications enhances the mathematical integrity and historical perspective, allowing students to more easily grasp concepts.
Worked-out exercises at the end of each section provide students with problem-solving techniques.
Computational techniques are provided throughout the text to help illustrate abstract concepts.
Special topics, such as algebraic varieties, matrix rings, and Noetherian and Artinian rings are unique to this text.
APPLICATIONS: Special topics showing applications of abstract algebra to other areas of mathematics as well as real world applications are included.
WORKED-OUT EXERCISES: These exercises appear at the end of each section and give students a model they can use to solve other exercises.
COMPUTATIONAL TECHNIQUES: These techniques are provided throughout the text to help illustrate abstract concepts. For example, how to find the subgroups of a group, find the Sylow subgroups, find different finite Abelian groups of a given order, etc.
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