#### Abstract Algebra

When doing your homework, I encourage you to use the Elements of Style for Proofs (see Appendix A of the course notes) as a reference. **Note:** On each homework assignment, please write (i) your name, (ii) name of course, and (iii) Daily/Weekly Homework number.

## Daily Homework

The following assignments are to be turned in at the end of the indicated class period. I reserve the right to modify the assignment if the need arises. These exercises will form the basis of the student-led presentations each day. Daily assignments will be graded on a $\checkmark$-system. Exercises marked with $\star$ are eligible for the formal Weekly Homework assignments. During class, **you are only allowed to annotate your homework using the felt-tip pens that I will provide**.

**Daily Homework 1:**Read the syllabus and Chapter 1: Introduction of the course notes. In addition, complete 2.12$\star$, 2.16(1)$\star$, 2.22, 2.23, 2.27, 2.28, 2.29, 2.34, 2.36, 2.37, 2.39, 2.40 from the course notes. For this homework assignment and the next, you can rely on external resources as much as you want. (Due Friday, August 30)**Daily Homework 2:**Read Appendix A: Elements of Style of Proof. Also, complete 2.43, 2.49$\star$, 2.50, 2.61, 2.62, 2.63, 2.68, 2.74, 2.76$\star$, 2.80. (Due Wednesday, September 4)**Daily Homework 3:**Read Appendix B: Fancy Mathematical Terms and Appendix C: Definitions in Mathematics. Also, complete 2.89, as well as, any outstanding problems from Daily Homework assignments 1 and 3. (Due Friday, September 6)**Daily Homework 4:**Read Chapter 3: An Intuitive Approach to Groups and complete 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 3.11, 3.12, 3.13. (Due Monday, September 9)**Daily Homework 5:**If necessary, re-read Chapter 3: An Intuitive Approach to Groups. In addition, read Chapter 4: Cayley Diagrams and complete 3.14, 3.15, 3.16, 3.17, 3.18, 3.19, 3.20, 3.21, 4.1, 4.2, 4.3, 4.4, 4.5. (Due Wednesday, September 11)**Daily Homework 6:**If necessary re-read Chapter 4: Cayley Diagrams and complete 4.6, 4.7, 4.8, 4.9, 4.10, 4.11. (Due Friday, September 13)**Daily Homework 7:**Finish reading Chapter 4: Cayley Diagrams and start reading Chapter 5: An Introduction to Subgroups and Isomorphisms. In addition, complete 4.12, 4.13, 4.14, 4.15, 4.16, 5.1. (Due Monday, September 16)**Daily Homework 8:**Read Chapter 5: An Introduction to Subgroups and Isomorphisms and complete 5.2, 5.3, 5.5$\star$, 5.6, 5.7, 5.8, 5.10, 5.11, 5.12, 5.13. (Due Wednesday, September 18)**Daily Homework 9:**Re-read Chapter 5: An Introduction to Subgroups and Isomorphisms and complete 5.14, 5.17, 5.18$\star$. (Due Friday, September 20)**Daily Homework 10:**Re-read Chapter 5: An Introduction to Subgroups and Isomorphisms and complete 5.19, 5.20, 5.22, 5.23, 5.24, 5.25. (Due Monday, September 23)**Daily Homework 11:**Read Chapter 6: A Formal Approach to Groups and complete 6.8, 6.9, 6.10, 6.11, 6.13, 6.14$\star$, 6.16, 6.17, 6.20, 6.21, 6.22, 6.23. (Due Wednesday, September 25)**Daily Homework 12:**Re-read Chapter 6: A Formal Approach to Groups and complete 6.36-6.42. I updated the notes, so if you printed them out a couple days ago, the numbering will be off. Also, be sure to read the paragraphs after 6.44 as they set the stage for things that come later. (Due Friday, October 4)**Daily Homework 13:**Re-read Chapter 6: A Formal Approach to Groups and complete 6.43-6.50, 6.52$\star$, 6.53. (Due Monday, October 7)**Daily Homework 14:**Re-read Chapter 6: A Formal Approach to Groups and complete 6.54, 6.55, 6.56, 6.57 (could skip since it was on exam), 6.58, 6.59$\star$, 6.61$\star$. (Due Wednesday, October 9)**Daily Homework 15:**Re-read Chapter 6: A Formal Approach to Groups and complete 6.62, 6.63$\star$, 6.64-6.66. (Due Friday, October 11)**Daily Homework 16:**Re-read Chapter 6: A Formal Approach to Groups and complete 6.67-6.72, 6.74-6.77. (Due Monday, October 14)**Daily Homework 17:**Re-read Chapter 6: A Formal Approach to Groups and complete 6.78$\star$, 6.79$\star$, 6.80$\star$, 6.81$\star$, 6.82. (Due Wednesday, October 16)**Daily Homework 18:**Re-read Chapter 6: A Formal Approach to Groups and start reading Chapter 7: Families of Groups. Also, complete 6.83$\star$, 6.85, 7.1, 7.2, 7.4, 7.5, 7.6, 7.7. You don’t have to do 6.84, but read it. (Due Friday, October 18)**Daily Homework 19:**Read Chapter 7: Families of Groups and complete 7.8$\star$, 7.9$\star$, 7.10, 7.12, 7.13, 7.14$\star$, 7.15, 7.16. (Due Wednesday, October 23)**Daily Homework 20:**Re-read Chapter 7: Families of Groups and complete 7.18$\star$, 7.19$\star$, 7.20$\star$, 7.21$\star$, 7.22$\star$, 7.23.*Note:*We are skipping 7.17, but feel free to use the result if you need it. (Due Friday, October 25)**Daily Homework 21:**Read Section 7.3 and complete 7.25, 7.26, 7.28-7.37, 7.38$\star$. (Due Monday, November 4)**Daily Homework 22:**Re-read Section 7.3 and complete 7.39$\star$, 7.41-7.46, 7.49, 7.50. I’ve omitted 7.40 and 7.48, but be sure to digest these theorems. (Due Wednesday, November 6)**Daily Homework 23:**Read Section 7.4 and complete 7.53, 7.54, 7.61, 7.62, 7.67, 7.68. I’ve omitted several problems from notes for this assignment. However, to be able to do some of the ones that I have included, you’ll need to digest the ones I omitted. (Due Friday, November 8)**Daily Homework 24:**Read Chapter 8: Cosets, Lagrange’s Theorem, and Normal Subgroups and complete 8.2, 8.3, 8.4(a)(b), 8.5, 8.7, 8.8(b)$\star$, 8.10, 8.12$\star$, 8.14, 8.15, 8.18$\star$, 8.19. You are responsible for digesting the content of the problems that were omitted, but you do not have to formally complete them. (Due Wednesday, November 13)**Daily Homework 25:**Re-read Chapter 8: Cosets, Lagrange’s Theorem, and Normal Subgroups and complete 8.21, 8.24, 8.25, 8.27, 8.29$\star$, 8.30, 8.33$\star$, 8.35, 8.36. You are responsible for digesting the content of the problems that were omitted, but you do not have to formally complete them. (Due Friday, November 15)**Daily Homework 26:**Read Chapter 9: Products and Quotients of Groups and complete 9.6, 9.10$\star$, 9.13, 9.15$\star$, 9.16, 9.17, 9.18, 9.19$\star$, 9.20, 9.24, 9.25. You are responsible for digesting the content of the problems that were omitted, but you do not have to formally complete them. (Due Monday, November 18)**Daily Homework 27:**Re-read Chapter 9: Products and Quotients of Groups and complete 9.26, 9.27, 9.29, 9.32 (any 2), 9.33 (any 4), 9.36$\star$, 9.37, 9.38, 9.39$\star$, 9.40. You are responsible for digesting the content of the problems that were omitted, but you do not have to formally complete them. (Due Wednesday, November 20)**Daily Homework 28:**Complete the problems located here. (Due Wednesday, December 4)**Daily Homework 29:**Complete the problems located here. (Due Friday, December 6)**Daily Homework 30:**Complete the problems located here. (Due Monday, December 9)**Daily Homework 31:**Complete the problems located here. (Due Wednesday, December 11)

## Weekly Homework

In addition to the Daily Homework, we will also have Weekly Homework assignments. For most of these assignments, you will be required to submit two formally written proofs. In general, you may choose any two problems marked with $\star$ that were *turned in* during a given week to submit the following week (due dates to be announced). For example, you may choose any two problems marked with a $\star$ that were turned in during week 2 for the second Weekly Homework. These problems are due during week 3.

Beginning with the second Weekly Homework, you will be required to type your submission. You should type your Weekly Homework assignments using $\LaTeX$ (see below for more on this). I will walk you through how to do this.

**Weekly Homework 1:**Choose any two $\star$-problems from Daily Homework 1-3. For this first Weekly Homework, you do not need to type up your proofs. (Due Thursday, September 12 by 5PM)**Weekly Homework 2:**For this assignment, complete a single $\star$-problem from Daily Homework 1-6. You must choose one that is different from the problems you did for Weekly Homework 1. Also, you are required to type your homework using LaTeX. If you are unfamiliar with LaTeX, see below for some helpful links, including some introductory videos. (Due Thursday, September 19 by 5PM)**Weekly Homework 3:**Choose any two $\star$-problems from Daily Homework 7-9. Use LaTeX to type your homework. Either print out your assignment or email me the corresponding PDF. (Due Thursday, September 26 by 5PM)**Weekly Homework 4:**Choose any two $\star$-problems from Daily Homework 10-13. Use LaTeX to type your homework. Either print out your assignment or email me the corresponding PDF. (Due Thursday, October 10 by 5PM)**Weekly Homework 5:**Choose any two $\star$-problems from Daily Homework 14-15. Use LaTeX to type your homework. Either print out your assignment or email me the corresponding PDF. (Due Thursday, October 17 by 5PM)**Weekly Homework 6:**Choose any two $\star$-problems from Daily Homework 16-17. Use LaTeX to type your homework. Either print out your assignment or email me the corresponding PDF. (Due Thursday, October 24 by 5PM)**Weekly Homework 7:**Choose any two $\star$-problems from Daily Homework 19-23. Use LaTeX to type your homework. Either print out your assignment or email me the corresponding PDF. (Due Friday, November 15 by 5PM)**Weekly Homework 8:**Choose any two $\star$-problems from Daily Homework 24-25. Use LaTeX to type your homework. Either print out your assignment or email me the corresponding PDF. (Due Thursday, November 21 by 5PM)**Weekly Homework 9:**Choose any two $\star$-problems from Daily Homework 26-27. Use LaTeX to type your homework. Either print out your assignment or email me the corresponding PDF. (Due Thursday, December 5 by 5PM)**Weekly Homework 10:**(Optional) Choose any two proof-type from Daily Homework 28-29. Use LaTeX to type your homework. Either print out your assignment or email me the corresponding PDF. (Due Thursday, December 12 by 5PM)

## Using LaTeX for Weekly Homework

You are required to use $\LaTeX$ to type up your Weekly Homework assignments. To do this, I suggest that you use my LaTeX Homework Template. The easiest way to get started with $\LaTeX$ is to use an online editor. I recommend using writeLaTeX, but there are other options. The good folks over at writeLaTeX have preloaded my template, so to get started, all you need to do is click the link below.

For a rough overview of some of the basics of $\LaTeX$, you might find my Quick LaTeX Guide useful. Also, I’ve created a couple videos that explain how to get started with my LaTeX Homework Template using writeLaTeX. The first video is here and the second one is here. I ran my mouth too much, but this is what you get when you wing it. **Note:** The first video walks you through copying the contents of the template from GitHub, but this is unnecessary now that you can just click the button above. If you need any help with LaTeX, please ask.