Math 392

Winter 2021

• Syllabus.
• Lecture 1: Welcome back; ℤ[√-5] continued.
  notes, worksheet.
• Lecture 2: Intersections, sums, and products of ideals.
  notes, worksheet.
• Homework 1 (due 1/8): pdf, tex. Solutions: pdf, tex.
• Lecture 3: Ideal operations continued.
  notes, worksheet.
• Lecture 4: Quotient rings.
  notes, worksheet.
• Lecture 5: Quotients of polynomial rings.
  notes, worksheet.
• Homework 2 (due 1/15): pdf, tex. Solutions: pdf, tex.
• Lecture 6: Prime ideals.
  notes, worksheet.
• Reading 1 (due 1/17): §4.2. The material after Example 6 is not crucial but still interesting.
• Lecture 7: Noether's first isomorphism theorem.
  notes, worksheet.
• Homework 3 (due 1/22): pdf, tex. Solutions: pdf, tex.
• Lecture 8: First isomorphism theorem continued.
  notes, continue previous worksheet.
• Reading 2 (due 1/24): §4.3.
• Lecture 9: More on primes, Chinese Remainder Theorem.
  notes, no worksheet.
• Lecture 10: The Gaussian integers.
  notes, worksheet.
• Homework 4 (due 1/29): pdf, tex. Solutions: pdf, tex.
• Lecture 11: Gaussian integers continued.
  notes, continue previous worksheet.
• Lecture 12: Toward Fermat’s Christmas Theorem.
  notes, worksheet.
• Lecture 13: Fermat’s Christmas Theorem.
  notes, worksheet.
• Homework 5 (due 2/5): pdf, tex. Solutions: pdf, tex.
• Lecture 14: Ring theory wrap-up.
  notes, no worksheet but some pictures of quotient rings.
• Reading 3 (due 2/7): §6.1 and §6.2.
• Lecture 15: Groups.
  notes, worksheet.
• Lecture 16: Order of a group, order of an element.
  notes, worksheet.
• Homework 6 (due 2/12):
  §6.1 #1, 4 (but skip the part about subgroups), 18.
  Solutions: pdf, tex.
• Lecture 17: Additive group, group of units.
  notes, worksheet.
• Lecture 18: More on orders, cyclic subgroups, dihedral groups.
  notes, worksheet.
• Lecture 19: Groups acting on sets.
  notes, worksheet.
• Homework 7 (due 2/19): pdf, tex. Solutions: pdf, tex.
• Lecture 20: The orbit-stabilizer theorem.
  notes, worksheet.
• Reading 4 (due 2/21): §6.3.
• Lecture 21: Cosets.
  notes, no worksheet.
• Lecture 22: Groups acting on themselves.
  notes, worksheet.
• Homework 8 (due 2/26): pdf, tex. Solutions: pdf, tex.
• Lecture 23: More on conjugation.
  notes, worksheet.
• Reading 5 (due 2/29): §7.1.
• Lecture 24: More on actions, normal subgroups.
  notes, no worksheet.
• Lecture 25: Cycles and transpositions.
  notes, worksheet.
• Homework 9 (due 3/5): pdf, tex. Solutions: pdf, tex.
• Lecture 26: Sign of a permutation.
  notes, worksheet.
• Lecture 27: Classifying groups of small order.
  notes, worksheet.
• Lecture 28: Quotient groups.
  notes, worksheet.
• Homework 10 (due 3/12, no peer review or revision):
  §6.3 #2, 25.
  Solutions: pdf, tex.
• Lecture 29: The first isomorphism theorem and an application.
  notes, no worksheet.