Algebra (English Version)

Author: T.W. Hungerford W. Hungerford
Publisher:
Publish Date: 2003-01-01
Features: The guiding philosophical principle throughout the book is that the material should be presented in the maximum usable generality consistent with good pedagogy. The principle is relatively easy to apply to various technical questions. It is more difficult to apply to broader questions of conceptual organization. On the one hand, for example, the student must be made aware of relatively recent insights into the nature of algebra: the heart of the matter is the study of morphisms (maps); many deep and important concepts are best viewed as universal mapping properties. On the other hand, a high level of abstraction and generality is best appreciated and fully understood only by those who have a firm grounding in the special situations which motivated these abstractions. Consequently, concepts which can be characterized by a universal mapping property are not defined via this property if there is available a definition which is more familiar or easier to comprehend by the student.