Groups and Symmetry¶
Armstrong, M. A. (1988). Groups and Symmetry. Springer.
Cited by¶
1 citation across 1 artifact.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Group
- The reason a group is a prime, and not merely a piece of mathematics, is that the same skeleton organizes the analysis of physical systems (gauge symmetries and conservation laws), cryptosystems (discrete logarithms and elliptic-curve points), moves on combinatorial objects (a Rubik's cube, a shuffled deck), music-theoretic transformations (transposition and inversion), and role permutations in social structures.
This sourceDevelops group theory explicitly as the mathematics of symmetry, with group actions, orbits, stabilisers, Lagrange's theorem, and the wallpaper groups.
Supported in partVerified against the publisher's abstract
The abstract backs group theory as the mathematics of symmetry with geometrical examples, but says nothing of the cryptographic, combinatorial, musical or social applications.
“Groups are important because they measure symmetry. This text, designed for undergraduate mathematics students, provides a gentle introduction to the highlights of elementary group theory.”
- The reason a group is a prime, and not merely a piece of mathematics, is that the same skeleton organizes the analysis of physical systems (gauge symmetries and conservation laws), cryptosystems (discrete logarithms and elliptic-curve points), moves on combinatorial objects (a Rubik's cube, a shuffled deck), music-theoretic transformations (transposition and inversion), and role permutations in social structures.
Verification¶
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Registry ID ref:e82c94e33bf5 · see in the full table