Ed Dubinsky, Uri Leron

Learning Abstract Algebra with ISETL (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book is based on the constructivist belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities which will establish an experiential base for any future verbal explanation. The main source of activities in this course is computer constructions, specifically, small programs written in the mathlike programming language ISETL; the main tool for reflections is work in teams of 2-4 students, where the activities are discussed and debated.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 248
• Erscheinungstermin: 1. Dezember 2013
• Englisch
• ISBN-13: 9781461226024
• Artikelnr.: 43986727

Inhaltsangabe

1 Mathematical Constructions in ISETL.- 1.1 Using ISETL.- 1.2 Compound objects and operations on them.- 1.3 Functions in ISETL.- 2 Groups.- 2.1 Getting acquainted with groups.- 2.2 The modular groups and the symmetric groups.- 2.3 Properties of groups.- 3 Subgroups.- 3.1 Definitions and examples.- 3.2 Cyclic groups and their subgroups.- 3.3 Lagrange's theorem.- 4 The Fundamental Homomorphism Theorem.- 4.1 Quotient groups.- 4.2 Homomorphisms.- 4.3 The homomorphism theorem.- 5 Rings.- 5.1 Rings.- 5.2 Ideals.- 5.3 Homomorphisms and isomorphisms.- 6 Factorization in Integral Domains.- 6.1 Divisibility properties of integers and polynomials.- 6.2 Euclidean domains and unique factorization.- 6.3 The ring of polynomials over a field.