Course - Groups and Group Actions HT23

Created: January 14, 2023 | Updated: September 30, 2025 | Read markdown | About these notes | View in context | Study these flashcards

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This course introduced the idea of a group, which is a fundamental mathematical structure that can be thought of as the way of encoding all of the symmetries of something. It’s also the first time seeing the idea of a quotient, which shows up in lots of other courses. This means you can give precise meaning to statements like “the complex numbers without (‘mod’) the real numbers are just angles” ($\mathbb C / \mathbb R \cong S^1$).

• Course Webpage
• Lecture Notes
• Predecessor to: Course - Groups and Group Actions TT23^U
• Other courses this term: Courses HT22^U
• Related books:
  • The Fascination of Groups^N

Notes

• Notes - Groups HT23, Group axioms^U
• Notes - Groups HT23, Cayley tables^U
• Notes - Groups HT23, Homomorphisms^U
• Notes - Groups HT23, Subgroups^U
• Notes - Groups HT23, Permutations^U
• Notes - Groups HT23, Cyclic groups^U
• Notes - Groups HT23, Modular arithmetic^U
• Notes - Groups HT23, HCF and LCM^U
• Notes - Groups HT23, Lagrange’s theorem^U
• Notes - Groups HT23, Equivalence relations^U
• Notes - Groups HT23, Cosets^U
• Notes - Groups HT23, Normal subgroups^U
• Notes - Groups HT23, Special groups^U

Problem Sheets

• Sheet 1
• Sheet 2
• Sheet 3
• Sheet 4

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