Practical
This course will enable the students to -
- Numerical computation of group and its properties using Mathematica.
Course Outcomes (COs):
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Course |
Learning outcomes (at course level) |
Learning and teaching strategies |
Assessment Strategies |
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|---|---|---|---|---|
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Course Code |
Course Title |
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CMAT 512 |
Practical (Practical)
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The students will be able to –
CO81: Perform both simple and complicated mathematical calculations, which require no previous knowledge of or training in computer programming. CO82: use the skills about programming in software oriented toward advanced data analysis, which will cover such areas as econometrics in addition to the language of the software itself. Because it can be used for a variety of computational techniques, it can be useful for students in mathematics, the sciences, management, economics, finance, accounting, and information sciences. |
Approach in teaching:
Interactive Lectures, Discussion, Power Point Presentations, Informative videos
Learning activities for the students: Self learning assignments, Effective questions, presentations, Giving tasks |
Quiz, Poster Presentations, Power Point Presentations, Individual and group projects, Open Book Test, Semester End Examination
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CONTENTS
- A permutation group defined by two generators and representation of a group generated by multiplication of the permutations.
- An empty list of generators represents the identity (or trivial, or neutral) group and to find the order of a group generated by two permutations.
- Test the equality of permutation groups with the same support but possibly generated by different permutations and sample problems: The group of all rotations and reflections of a regular n-sided polygon, the dihedral group.
- To construct the octagon corresponding to each group element.
- The original polygon and its seven rotations. Numbers increase counterclockwise and the polygon reflected along the bisection 1–5 and its seven rotations. Numbers increase clockwise.
- Generate the alternating group of degree n using (n-2) generators.
- Representation of a permutation with disjoint cycles and a permutation with two cycles.
- Automatic evaluation to a canonical form and permutations can involve any positive integers, with cycles of any length.
- The identity permutation contains no cycles in its canonical form.
- Permutation applied to a single point and points not present in the cycles are mapped onto themselves.
