Reading Assignments

Instructions

Each Reading Asssignment (RA) has three parts:

1. Read some material from the textbook. Feel free to supplement your reading with other resources.

2. Submit the “Comprehension Check” (CC) exercises through Gradescope.

   You’ll get credit for sincere attempts. You don’t need to get answers correct, and if you find yourself very stuck, it is okay to just write a few sentences explaining what you’ve tried, where you get stuck, etc. Conversely, you won’t get credit if your work doesn’t demonstrate a sincere attempt: leaving things blank or just drawing a giant question mark, transcribing solutions verbatim from the back of the book, etc.

   Speaking of solutions in the back of the book, you’re encouraged to use them, but use them critically. Attempt something yourself first. Only look in the back when you’re stuck, or after you’re done. Once you do look, think carefully about why you got stuck, or about how your solution was similar to or different from the solution in the back. Maybe even jot down a brief sentence or two reflecting on this next to your work!

3. Submit a “Reading Question” (RQ) using the Reading Question Form.

   Your question can be about something you found confusing or intriguing in the reading. You could also ask something specific about a CC question you struggled with. Do your best to formulate as precise a question as you can. If you really don’t have any questions, you can also share something about the reading that you found confusing at first but then managed to figure out, or something that you understand but you think other people in the class might find confusing — anything that you think will clearly demonstrate to me that you sincerely engaged with the reading.

I’ve also listed some “Further Practice” (FP) questions below. These are usually a little harder than the CC problems, so it might make sense to try them out after we’ve worked on the relevant topics in class. These are not collected, but it’s strongly recommended that you try them out (or at least look through and pick some that you find interesting). Exam problems might resemble some of these!

Week 1, Monday

• Read: Chapter 0, “Properties of Integers” and “Modular Arithmetic”
• CC: (Chapter 0) 1–4, 16
• FP: (Chapter 0) 6, 9, 11–12, 17, 19–21, 49

Week 1, Wednesday

• Read: Chapter 0, “Equivalence Relations” and “Functions”
• CC: (Chapter 0) 59, 61, 65

Week 1, Friday

• Read: Chapter 1
• CC: 1–4
• FP: (Chapter 1) 11, 13, 21, 23, 25

Week 2, Monday

• Read: Chapter 2, “Definition and Examples of Groups”
• CC: (Chapter 2) 1(a), 2(a), 3(a), 4(a), 5(a), 21
• FP: (Chapter 2) 1–9 (skip 5(d) and 6(a)), 12, 18, 29, 32, 45

Week 2, Wednesday

• Read: Chapter 2, “Elementary Properties of Groups” and “Historical Note”
• CC: (Chapter 2) 13, 14, 20, 25
• FP: (Chapter 2) 11, 15–16, 26, 28, 33, 40–44, 51

Week 2, Friday

• Read: Chapter 3, “Terminology and Notation” and “Subgroup Tests”
• CC: (Chapter 3) 11, 19, 65, 69
• FP: (Chapter 3) 1–4, 7–8, 16, 26, 34, 55–57, 68

Week 3, Wednesday

• Read: Chapter 3, “Examples of Subgroups”
• CC: (Chapter 3) 35, 41, 42(a), 73
• FP: (Chapter 3) 36–37, 42(b–e), 44

Week 3, Friday

• Read: Chapter 4, “Properties of Cyclic Groups”
• CC: (Chapter 4) 1, 3, 5, 19
• FP: (Chapter 4) 2, 4, 8, 22, 41–42, 70

Week 4, Friday

• Read: Chapter 4, “Classification of Subgroups of Cyclic Groups”
• CC: (Chapter 4) 9, 10, 33, 37, 53
• FP: (Chapter 4) 14, 30, 32, 50, 52, 55, 56, 67, 69

Week 5, Monday

• Read: Chapter 5
• CC: (Chapter 5) 1(a–b), 3(a–b), 5(a–b), 8(a–b), 49
  
• FP: (Chapter 5) 7, 14, 16, 17, 22, 39, 43, 67–68

Week 5, Wednesday

• Read: Chapter 6, “Motivation” and “Definition and Examples”
• CC: (Chapter 6) 1, 4, 5, 11
• FP: (Chapter 6) 7, 8, 21, 22, 30, 56, 66

Week 5, Friday

• Read: Chapter 6, “Cayley’s Theorem”
• CC: (Chapter 6) 9, 35, 61
• FP: (Chapter 6) 40, 43

Week 6, Monday

• Read: Chapter 6, “Properties of Isomorphisms”
• CC: (Chapter 6) 6, 10

Week 6, Wednesday

• Read: Chapter 6, “Automorphisms”
• CC: (Chapter 6) 3, 13, 15
• FP: (Chapter 6) 2, 14, 20

Week 6, Friday

• Read: Chapter 7, “Properties of Cosets”
• CC: (Chapter 7) 1, 2, 3, 5
• FP: (Chapter 7) 4, 6, 7, 11

Week 7, Monday

• Read: Chapter 7, “Lagrange’s Theorem and Consequences” onwards
• CC: (Chapter 7) 15, 17, 19, 21
• FP: (Chapter 7) 12, 28, 34, 35, 42, 45, 65

Week 7, Wednesday

• Read: Chapter 9, “Normal Subgroups”
• CC: (Chapter 9) 1, 3, 7
• FP: (Chapter 9) 2, 4, 6, 9, 10(a), 39, 55, 58

Week 8, Friday

• Read: Chapter 9, “Factor Groups” and “Applications of Factor Groups”
• CC: (Chapter 9) 8, 13, 15, 17
• FP: (Chapter 9) 14, 20, 32, 37, 38
• Note: The notation \(U_k(n)\) is introduced on p. 160.

Week 9, Monday

• Read: Chapter 8
• CC: (Chapter 8) 3, 9, 39, 41
• FP: (Chapter 8) 4, 6, 8, 10, 12, 16, 25

Week 9, Wednesday

• Read: Chapter 9, “Internal Direct Products”
• CC: (Chapter 9) 25, 69
• FP: (Chapter 9) 22, 24, 26, 28, 54
• Note: You may find it helpful to re-read the section “The Group of Units Modulo \(n\) as an External Direct Product” from Chapter 8.

Week 10, Monday

• Read: Chapter 10, “Definition and Examples” and “Properties of Homomorphisms”
• CC: (Chapter 10) 1, 5, 9, 19, 35
• FP: (Chapter 10) 2–4, 8, 15, 18, 36, 38, 44, 64, 66

Week 10, Wednesday

• Read: Chapter 10, “The First Isomorphism Theorem”
• CC: (Chapter 10) 13, 16, 21
• FP: (Chapter 10) 17, 42, 53