Allen C. Hibbard, Kenneth M. Levasseur

Exploring Abstract Algebra With Mathematica® (eBook, PDF)

• Format: PDF

Produktbeschreibung

"Exploring Abstract Algebra with Mathematica" provides both students and instructors working in the area of abstract algebra with a heretofore not available set of powerful computational tools and visual aids to readily deal with these very complex mathematical concepts.

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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.