Info
Grading:
- attendance: 5%
- tutorials: 5%
- quizzes: 15%
- midterm: 25%
- endsem: 50%
Lecture Notes
These notes have been reorganized because I lost count of the lectures at some point, and do not reflect the exact sequence or breadth of topics covered in class.
- ALG2_L1 ✅
- Groups, examples of groups, subgroups
- ALG2_L2 ✅
- Symmetric groups, homomorphisms
- ALG2_L3 ✅
- Cosets, Lagrange’s theorem, quotient groups, normal subgroups
- ALG2_L4 ✅
- Isomorphisms, automorphisms and conjugation, first isomorphism theorem
- ALG2_L5 ✅
- Correspondence Theorem
- ALG2_L6 ✅
- Product of groups, third isomorphism theorem, Chinese remainder theorem
- ALG2_L7 ✅
- Double cosets, group actions
- ALG2_L8 ✅
- Orbit, stabilizer, kernel, groups acting on themselves, centralizer, normalizer, second isomorphism theorem
- ALG2_L9 ✅
- Orbit-stabilizer theorem, the class equation, p-groups, conjugacy in , more on automorphisms
- ALG2_L10
- Semidirect product
- ALG2_L11
- Sylow’s theorems, proofs from Herstein
- ALG2_L12
- Simplicity of
- ALG2_L13 ✅
- Free groups
- ALG2_L14
- Free abelian groups
- ALG2_L15
- Linear operators
- ALG2_L16
- Symmetries
Other notes
Normalizers and Conjugacy
Finding all subgroups of S4
Group of units mod n is cyclic
Dummit and Foote Solutions
Assessments
Tutorials
to do
Review midsem- Review all tuts
- Review all notes
- Solve Sunaina’s PS
Ask Titan for probs (proof using Cayley)- Dummit: CHapter 4 and 5
- Artin: relevant stuff from chapter 5, 6
- past endsems
???
- midsem 10