Allen C. Hibbard, Kenneth M. Levasseur

Exploring Abstract Algebra With Mathematica® (eBook, PDF)

• Format: PDF

Produktbeschreibung

This upper-division laboratory supplement for courses in abstract algebra consists of several Mathematica packages programmed as a foundation for group and ring theory. Additionally, the "user's guide" illustrates the functionality of the underlying code, while the lab portion of the book reflects the contents of the Mathematica-based electronic notebooks. Students interact with both the printed and electronic versions of the material in the laboratory, and can look up details and reference information in the user's guide. Exercises occur in the stream of the text of the lab, which provides a context within which to answer, and the questions are designed to be either written into the electronic notebook, or on paper. The notebooks are available in both 2.2 and 3.0 versions of Mathematica, and run across all platforms for which Mathematica exits. A very timely and unique addition to the undergraduate abstract algebra curriculum, filling a tremendous void in the literature.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 467
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461215301
• Artikelnr.: 44179720

Inhaltsangabe

I Group Labs.- 1 Using Symmetry to Uncover a Group.- 2 Determining the Symmetry Group of a Given Figure.- 3 Is This a Group?.- 4 Let's Get These Orders Straight.- 5 Subversively Grouping Our Elements.- 6 Cycling Through the Groups.- 7 Permutations.- 8 Isomorphisms.- 9 Automorphisms.- 10 Direct Products.- 11 Cosets.- 12 Normality and Factor Groups.- 13 Group Homomorphisms.- 14 Rotational Groups of Regular Polyhedra.- II Ring Labs.- 1 Introduction to Rings and Ringoids.- 2 Introduction to Rings, Part 2.- 3 An Ideal Part of Rings.- 4 What Does ?[i](a + b i) Look Like?.- 5 Ring Homomorphisms.- 6 Polynomial Rings.- 7 Factoring and Irreducibility.- 8 Roots of Unity.- 9 Cyclotomic Polynomials.- 10 Quotient Rings of Polynomials.- 11 Quadratic Field Extensions.- 12 Factoring in ?[?d].- 13 Finite Fields.- III User's Guide.- 1 Introduction to Abstract Algebra.- 2 Groupolds.- 3 Ringoids.- 4 Morphoids.- 5 Additional Functionality.