In studying abstract algebra, the process of experimentation, conjecture, and proof is strongly inhibited by a lack of data. While it is true that a good textbook will contain many well-known examples, those examples are usually introduced in the context of a single specific topic. Exploring an example in more depth or in a different context typically requires a prohibitive amount of computation.
GAP Primer --
A supplemental resource and reading assignment for the class.
Project 1. -- An Introduction to GAP
Illustrates the basics of GAP in the context of the group of rotations of a cube; Assumes no prior knowledge of GAP
Project 2. -- Subgroups Generated by Subsets
Discusses subgroups generated by a subset from two viewpoints: the "top-down" approach using intersections, and the "bottom-up" approach using group closure
Project 3. -- Exploring Rubik's Cube with GAP
Investigates the transformation group of Rubik's cube.
Project 4. -- Conjugation in Permutation Groups
Explores the relationship between the cycle structure of a permutation and cycle structure of its conjugate; Revisits permutations of the Rubik's cube.
Project 5. -- Exploring Normal Subgroups and Quotient Groups.
Project 6. -- The Number of Groups of a Given Order
Explores the number of possible group structures for any given order; the class will need hints and encouragement on the last problem!
Questions or Comments?
E-mail: firstname.lastname@example.org or email@example.com
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