Welcome to Math 3230: Abstract Algebra I, this Fall 2019! Today is .

Actual Schedule

See also UConn Calendar for 2019-2020 for important deadlines and other dates.

Office hours Monday, Wednesday, or Friday

Final Exam (Mon, Dec 9 – Sun, Dec 15)

• Due Thursday, Dec 12 at 5pm You may submit up to two take-home problems. These are optional - it is possible to earn 100% on the final exam by completing only the problems given in-class.
  • For hand-written submission, hand in at the beginning of the final exam (if you finish by Tuesday), or slip under my door (if you submit after the final).
  • You can also create an Overleaf project and share it with me.

Policy for the take-home problems:

• You can reference any textbooks, websites, videos, etc
• You may only discuss the take-home problems with me or other students currently enrolled in this Abstract Algebra I’s section.

Final Exam Study guide:

• Reading 4 HW
• In-class Practice Problems A + key
• In-class Practice Problems B + key

Current: Week 15 (Dec 2 – Dec 6)

• Mon Finish Sec 5.3, Example 5 and 7, SET survey questions
• Wed Practice Problems + key
• Fri Practice Problems + key

Past: Week 14 (Thanksgiving break)

Thanksgiving recess is from Sun, Nov 24 to Sat, Nov 30

Past: Week 13 (Nov 18 – 22)

• Mon DUE at the beginning of class If you want the take-home extra credit and the last question to be part of your Exam 2, submit at the beginning of class
  • Sec 5.1 Groups acting on sets

• Wed Sec 5.2 Orbit-stabilizer theorem

• Friday Due Reading HW 4 Vocab and Reading 4 HW: vocabulary for group action from slides 5.1-5.2, pdf, .tex, by hand or via Overleaf
  • Sec 5.3 Covered up to Example 5a.

• Links:

  • Sec 5.1 Groups acting on sets, Slides 5.1, see lecture video 5.1 Groups acting on sets by M. Macauley
  • Sec 5.2 Orbit-stabilizer theorem, Slides 5.2, see lecture video 5.2 Orbit-Stabilizer theorem by M. Macauley
  • Sec 5.3 Examples of group actions, Slides 5.3, see lecture video 5.3 Examples of group actions by M. Macauley

Past: Week 12 (Nov 11 – 15)

• Mon Student presentations of the three isomorphism theorems

• Wed Student presentations of the three isomorphism theorems + Review for exam

• FRIDAY EXAM 2 (you can choose to arrive to class 10 minutes early and stay a few minutes late)
  • Practice questions for Exam 2, key last updated Thursday 7am
  • Fact sheet from Exam 1
  • HW5 and HW5 answer key (in HuskyCT)

Past: Week 11 (Nov 4 – 8)

• Mon Sec 4.3 The first isomorphism theorem
• Wed Due (not graded) Bring your notes (from watching the videos) for HW6, so that I can help you with your preparation
• Fri Team Edward, TJ, Yuchen presented most of Sec 1 then lecture on Sec 4.4
• Fri Due (collected) Fri, Nov 8
  1. Individual notes for HW6 (labeled Reading 3 in Gradebook): PDF and source code .tex - write in your own notebook or Overleaf. You will be graded based on completeness only.
  2. Team write up for HW6: PDF and source code .tex - do all bullet points of the sections your team is assigned to; submit only one copy per team, handwritten or via Overleaf. You will be graded based on correctness and clarity.
  3. Team presentations will be done on Friday and Monday. Instruction for team presentation: PDF and source code .tex. You will be graded on correctness and effort (trying to be clear and to get the audience to understand)
  4. Team assignments:
     • Team Alex, Thomas, Tianyu, Tommy: write up Sec 1 and Sec 2
     • Team Ashley, Christine, Paula: write up Sec 1 and Sec 2
     • Team Edward, TJ, Yuchen: write up Sec 1 and Sec 3
     • Team Claudia, Gelsey, Jacob, James: write up Sec 1 and Sec 3
• Links:
  • Handwritten notes for the proofs of the isomorphism theorems: 1st, 2nd, 3rd
  • Sec 4.3 The fundamental homomorphism theorem (or, first isomorphism theorem) slides 4.3, see lecture video Fundamental homomorphism theorem by M. Macauley
  • Sec 4.4 Finite and finitely generated abelian groups slides 4.4
  • Only 2nd and 3rd isomorphism theorems are covered, Sec 4.5 Other isomorphism theorems slides 4.5, see lecture video The isomorphism theorems by M. Macauley
  • Printout of Chapter 11 of Judson
  • Not covered, Sec 4.6 automorphisms slides 4.6

Past: Week 10 (Oct 28 – Nov 1)

• Mon Sec 4.1 Homomorphism
  • No drop-in office hours after class this Monday, but available by appointment before class
• Wed Sec 4.1 Examples of homomorphism
• Fri Sec 4.2 Kernels
  • Due (collected) Fri, Nov 1 Complete ALL questions (including optional questions) from HW5: PDF and source code .tex. Complete by hand (or Overleaf).
• Links:
  • Sec 4.1 Homomorphisms and isomorphisms Slides 4.1
  • Sec 4.2 Kernels, handwritten lecture notes slides 4.2

Past: Week 9 (Oct 21 – 25)

• Mon Finish board lecture Sec 3.6 Normalizers. Guided group work for HW5
• Wed Board lecture Sec 3.7 Conjugacy classes def. Guided group work for HW5
• Fri Board lecture Sec 3.7 Conjugacy classes for permutations and partitioning the set of subgroups of G
  • HW 5 deadline is moved to next Friday, Oct 28
• Links:
  • Guide group work for HW5: handout
  • Sec 3.7 Conjugacy classes Handwritten lecture notes, Slides 3.7, see a lecture video Conjugacy classes by M. Macauley

Past: Week 8 (Oct 14 – 18)

• Mon Slides 3.4 Direct products

• Wed Board lecture Sec 3.5 Quotients

• Fri Board lecture Sec 3.6 Normalizers
  • Due (collected) Oct 18 Complete Vocab and Reading 2 HW (PDF) by hand. You can also submit via Overleaf, download the source code: .tex
  • Recommended Due Date Oct 18 (not collected) HW4: PDF and source code .tex
• Links:
  • Slides 3.4, two-page printout 3.4 Direct products, see a lecture video Direct products by M. Macauley
  • Sec 3.5 Quotients Handwritten lecture notes, Slides 3.5 Quotients, see a lecture video Quotients by M. Macauley
  • Sec 3.6 Normalizers Handwritten lecture notes, Slides 3.6 Normalizers, see a lecture video Normalizers by M. Macauley

Past: Week 7 (Oct 7 – 11)

• Mon Slides 3.3 normal subgroups
• Wed Practice problems in groups for exam 1: handout + key
• Fri In-class 50-minute EXAM 1 (you can choose to arrive to class 10 minutes early and stay a few minutes late)
  • Fact sheet from Exam 1
  • All materials up to Slides 3.2 (cosets)
  • Exam 1 study guide: HW1, HW2, HW3, HW4, Quiz1, Quiz1 Extra questions + key, Quiz2, Reading (vocab) 1, and additional practice questions + key
• Links:
  • Slides 3.3, two-page printout 3.3 Normal subgroups, see a lecture video Normal subgroups by M. Macauley

Past: Week 6 (Sept 30 – Oct 4)

• Mon In class: Finish whiteboard lecture on Sec 2.3 Part II: Alternating groups. In-class group work for HW3

• Wed In class: Slides 2.4 Cayley’s Theorem, Slides 3.1 subgroups
• Fri In class: Slides 3.2 cosets
  • Due (collected) Oct 4 Complete at least 8 questions from HW3: PDF and source code .tex. Complete by hand (or Overleaf).
• Links:
  • slides 2.4 Cayley’s Theorem, see a lecture video Cayley’s Theorem by M. Macauley
  • slides 3.1 Subgroups and lattice of subgroups, see a lecture video Subgroups by M. Macauley
  • Slides 3.2, two-page printout 3.2 Cosets, see a lecture video Cosets by M. Macauley

Past: Week 5 (Sept 23 – 27)

• Mon In class: Whiteboard lecture Sec 2.3 Part I Symmetric groups and cycle notation, for lecture notes see the first half of Slides 2.3
• Wed In class:
• Fri In class: Whiteboard lecture Sec 2.3 Part II Parity and Alternating groups, for lecture notes see the second part of Slides 2.3
  • Due (collected) Sept 27 Vocab and Reading 1 HW (PDF), .tex
  • Quiz 2 Study guide: HW 2 (including question 0 and def of group) + def and computation of “order of a group”, “orbit of an element” and “order of an element”
  • Cayley’s Theorem (preview)
• Links:
  • Handwritten lecture notes Sec 2.3 part 1: symmetric groups and part 2: alternating groups
  • slides 2.3 Symmetric and alternating groups and cycle notation, see a lecture video Symmetric and alternating groups by M. Macauley

Past: Week 4 (Sept 16 – 20)

• Mon In class:
  • Work on HW2 (printout, last four pages of slides 1.5)
  • Lecture Slides 2.1 Cylic groups and abelian groups
• Wed In class:
  • Work on HW3 Orbits (print out, from slides 2.1)
  • Whiteboard lecture, for lecture notes see the second half of Slides 2.1: Orbits
  • Gave 10-minute overview of Slides 2.2 Dihedral groups
• Fri In class: Discuss HW2, question 9; Whiteboard lecture, see Slides 2.2 for notes
  • Bonus Name Quiz (Postponed to next week) Post on Piazza an introduction (e.g “Hi! I am [blank]!”). Match up the faces and first names of all your classmates.
  • Due (collected) Sept 20 HW2
    • Submit questions 1-5 on Overleaf using this template for HW2
    • Submit the rest of the questions by hand or via Overleaf
    • The hand-written portion is due at the beginning of class, the Overleaf portion can be submitted later.

• Links:
  • slides 2.1 Cyclic groups, abelian groups, orbits, see a lecture video Cyclic and abelian groups by M. Macauley
  • slides 2.2 Dihedral group, see a lecture video Dihedral groups by M. Macauley

Past: Week 3 (Sept 9 – 13)

• Mon In class: Start slides 1.3 inverses and group presentations
• Wed In class: Finish slides 1.3; Discuss Group Explorer software; Finish slides 1.4.
• Fri In class:
  • Quiz 1 Study guide: HW 1 + Extra questions with key
  • Whiteboard lecture (group definition); for lecture notes see slides 1.5
• Links:
  • slides 1.3 inverses and group presentations, see a similar lecture video Group presentations by M. Macauley
  • slides 1.4 multiplication tables
  • Board lecture notes slides 1.5 formal definition of group, examples and non-examples of groups
  • Group Explorer software

Past: Week 2 (Sept 2 – 6)

Sept 2 Labor Day - No classes

• Wed In class: Start slides 1.2 until frame 13 (basic THVRG symmetries in each frieze pattern)
• Fri In class: Work on the next homework: HW2 warmup, then finish slides 1.2
  • Due (collected) Sept 6 HW1: PDF, .tex
  • Submit the first question (on Francis Su’s article on mathematical writing) via Overleaf: template for question 1 of HW1
  • Submit the rest of the questions by hand or via Overleaf (the source code is available above)
  • The hand-written portion is due at the beginning of class, the Overleaf portion can be submitted later.
• Links: slides 1.2 Mostly frieze groups, but also groups in chemistry and braid groups, see a similar lecture video Groups in science, art, and math by M. Macauley

Past: Week 1 (Aug 26 – 30)

• Mon In class:
  • Introductory Examples Activity: worksheet, triangle cutout, answer key for the triangle symmetries
  • Intro to Overleaf:
    • First, create an account on Overleaf
    • Go to this read-only template for HW0 Overleaf template
    • Optional: Skim Learn LaTeX in 30 minutes
• Wed In class: Start slides 1.1, slides 2 to 10.
  • Due (collected) Aug 28 HW0: Survey and LaTeX practice, HW Overleaf template at 11:55pm
    • First, create an account on Overleaf
    • Go to the above link
    • Click on the upper-left button called ‘menu’
    • Click on ‘Copy Project’ and rename the project so that your name is on the project’s name
    • Make all the requested edits
    • To submit, click on the share button and share your project with me by entering my UConn email. Please give me a Read and Edit permission (so that I can write a comment directly on your project)
    • You may continue to edit your project even after your share it with me.

• Fri In class: Work on HW1 in groups - use polygon cutouts: from hexagon to triangle, finish slides 1.1.

• Links: slides 1.1 groups and Cayley diagram, watch YouTube lecture on Cayley graphs by M. Macauley