MATH417

  1. Lecture 01: Groups and Symmetries

  2. Lecture 02: Rotations in Space

  3. Lecture 03/04: Permutation Groups and Cycle Decomposition
  4. Book Notes: [1.5] Permutations (Representing Symmetries)

  5. Lecture 04: Integers, Primes
  6. Book Notes: [1.6] Z (1.6.1 - 1.6.2)

  7. Lecture 05: Greatest Common Divisor
  8. Book Notes: [1.6] Alternative Greatest Common Divisor Proof
  9. Book Notes: [1.6] Prime Factorization is Unique

  10. Lecture 06: Least Common Multiple

  11. Lecture 06/07: Modular Arithmetic

  12. Lecture 08: Groups and Isomorphism

  13. Lecture 09/10: Subgroups
  14. Book Notes: [2.2] Subgroup and Cyclic Groups

  15. Lecture 11: Dihedral Groups

  16. Lecture 12: Homomorphism
  17. Book Notes: [2.4] Homomorphisms

  18. Lecture 13: Cosets
  19. Book Notes: [2.5] Cosets

  20. Lecture 14: Lagrange's Theorem, Order Theorem & Equivalence Relations

  21. Lecture 15: Quotient Groups

  22. Lecture 16: Theorems: Homomorphism and Isomorphism
  23. Study Notes: Isomorphism Theorem Examples

  24. Lecture 17: Correspondence Theorem

  25. Lecture 18: Groups and the Chinese Remainder Theorem

  26. Lecture 19: Direct Product Group

  27. Lecture 20: Semi-direct Products
  28. Study Notes: Semi-direct Products

  29. Lecture 21/22: Finite Abelian Groups

  30. Lecture 23/24: Invariant Factor Decompositions

  31. Lecture 25: Symmetry Groups of the Regular Polyhedra

  32. Lecture 26/27: Group Actions and Orbits

  33. Lecture 28: Group Actions

  34. Lecture 29: Burnside Formula

  35. Lecture 30: Finite Subgroups of \(SO(3)\)

  36. Lecture 31: Fixed Point Theorem and Cauchy Theorem

  37. Lecture 32: Rings

  38. Lecture 33: Polynomial Rings

  39. Lecture 34: Homomorphisms of Rings and the Substitution Principle

  40. Lecture 35: Principle Ideal

  41. Study Notes: Extra Proofs ...