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Exploring Abstract Algebra with Mathematica
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| Organization: | Central College |
| Department: | Mathematics and Computer Science |
| Organization: | University of Massachusetts Lowell |
| Department: | Mathematical Sciences |
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| Publisher: | Springer-Verlag |
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PART I: Group Labs | Using Symmetry to Uncover a Group | Determining the Symmetry Group of a Given Figure | Is This a Group? | Let's Get These Orders Straight | Subversively Grouping Our Elements | Cycling Through the Groups | Permutations | Isomorphisms | Automorphisms | Direct Products | Cosets | Normality and Factor Groups | Group Homomorphisms | Rotational Groups of Regular Polyhedra | PART II: Ring Labs | Introduction to Rings and Ringoids | Introduction to Rings, Part 2 | An Ideal Part of Rings | What Does \[DoubleStruckCapitalZ][i]/\[LeftAngleBracket]a+bi\[RightAngleBracket] Look Like? | Ring Homomorphisms | Polynomial Rings | Factoring and Irreducibility | Roots of Unity | Cyclotomic Polynomials | Quotient Rings of Polynomials | Quadratic Field Extensions | Factoring in \[DoubleStruckCapitalZ][\[Sqrt]d] | Finite Fields | PART III: User's Guide | Introduction to AbstractAlgebra | Groupoids | Ringoids | Morphoids | Additional Functionality | Appendices | Index
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Upper-level laboratory supplement consisting of two collections of labs forgroup theory and ring theory built around a suite of Mathematica packagescalled AbstractAlgebra. The Mathematica labs allow students to bothvisualize and explore algebraic ideas while providing an interactivity thatenhances the learning process. Accompanying multi-platform CD-ROM containsboth Mathematica Version 2.2 and Version 3 notebooks of all the labs alongwith additional resources
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