# Homework

When doing your homework, I encourage you to use the Elements of Style of Proofs as a reference.

## 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 * are eligible for the formal Weekly Write-ups.

*Note:* On each Daily Homework, please write (i) your name, (ii) name of course, and (iii) Daily Homework number.

**Daily Homework 1:**Read all of Chapter 1 and complete Problem 1 (Due Friday, September 9).*Note:*Those of you that haven't had linear algebra shouldn't panic when you look at the sixth example of a binary operation.**Daily Homework 2:**Re-read all of Chapter 1 and complete Problems 2, 3, 4, 5, 6* (Due Monday, September 12).**Daily Homework 3:**Read Chapter 2 up to and including the hint immediately following Theorem 10. In addition, complete Theorem 7, Theorem 8*, Corollary 9*, and Theorem 10* (Due Wednesday, September 14).**Daily Homework 4:**Read Chapter 2 up to and including Theorem 12. In addition, re-do Theorem 10* (unless you are confident in your original write-up) and complete Corollary 11 and Theorem 12* (Due Friday, September 16).**Daily Homework 5:**Read Chapter 2 up to and including Theorem 14. In addition, complete Problem 13, Theorem 14* (Due Monday, September 19).**Daily Homework 6:**Read Chapter 2 up to and including Theorem 16. In addition, complete Theorem 15* and Theorem 16* (Due Wednesday, September 21).**Daily Homework 7:**Read the rest of Chapter 2. In addition, complete Lemma 18* and Theorem 19* (Due Friday, September 23).*Note:*I have not asked you to prove Theorem 17, but you should read and understand it.**Daily Homework 8:**Read Chapter 3 up to and including Problem 23. In addition, complete Lemma 20*, Lemma 21*, Lemma 22, Problem 23 (Due Monday, September 26).**Daily Homework 9:**Read Chapter 3 up to and including Problem 27. In addition, complete Problem 24, Problem 25, Lemma 26*, Problem 27 (Due Friday, September 30).**Daily Homework 10:**Read Chapter 3 up to and including Corollary 29. In addition, complete Theorem 28* and Corollary 29* (Due Monday, October 3).**Daily Homework 11:**Read Chapter 3 up to and including Theorem 31. In addition, complete Lemma 30* and Theorem 31* (Due Wednesday, October 5).**Daily Homework 12:**Finish reading Chapter 3. In addition, complete Theorem 32*, Lemma 33*, Theorem 34* (Due Friday, October 7).**Daily Homework 13:**Read Chapter 4 up to and including Theorem 38. In addition, complete Theorem 38* (Due Monday, October 17).**Daily Homework 14:**Read Chapter 4 up to and including Lemma 42. In addition, complete Problem 39, Problem 40, Lemma 41*, Lemma 42* (Due Wednesday, October 19).**Daily Homework 15:**Read Chapter 4 up to and including Lagrange's Theorem. In addition, complete Lemma 43* and Theorem 44* (Due Friday, October 21).**Daily Homework 16:**Finish reading Chapter 4. In addition, complete Corollary 45*, Corollary 46*, and Theorem 47* (Due Monday, October 24).**Daily Homework 17:**Read Chapter 5 starting with paragraph before Theorem 56. In addition, complete Theorem 56* and Lemma 57* (Due Wednesday, October 26).**Daily Homework 18:**Finish reading Chapter 5. In addition, complete Theorem 58* (you may assume that function composition is associative) (Due Friday, October 28).**Daily Homework 19:**Start reading Chapter 6 up to and including Lemma 61. In addition, complete Lemma 60* and Lemma 61* (Due Monday, October 31).**Daily Homework 20:**Complete Theorem 63* (Due Wednesday, November 2).**Daily Homework 21:**Complete Lemma 64* and Theorem 65* (Due Friday, November 4).**Daily Homework 22:**Complete Theorem 68* and Lemma 69* (Due Monday, November 7).**Daily Homework 23:**Complete Theorem 70* (Due Wednesday, November 9).**Daily Homework 24:**Read Chapter 6 up to and including Theorem 72. In addition, complete Theorem 71* and Theorem 72* (Due Monday, November 14).**Daily Homework 25:**Read Chapter 6 up to and including Lemma 73. In addition, finish up Theorem 71* and Theorem 72*, and then complete Theorem 73* (Due Wednesday, November 16).**Daily Homework 26:**Read Chapter 6 up to and including Lemma 77. In addition, complete Lemma 75*, Lemma 76*, and Lemma 77* (Due Wednesday, November 30).**Daily Homework 27:**Read the rest of Chapter 6. In addition, finish up Lemma 77* if you haven't already and complete Lemma 78* and Lemma 79* (Due Friday, December 2).**Daily Homework 28:**Complete Theorem 80* and any outstanding problems. (Due Monday, December 5).**Daily Homework 29:**Complete Theorem "86" (just (i) iff (ii)), Problem 85, Problem 83, and Corollary 88 (Due Wednesday, December 7).**Daily Homework 30:**Read and understand Corollary 90 and Theorem 95. Also, complete Lemma 96 and Theorem 97. (Due Friday, December 9).

## Weekly Write-ups

In addition to the Daily Homework, you will also be required to submit two formally written proofs each week. By 5PM on Tuesday of week $n$, you should submit the proofs of any two *theorems* that were *turned in* for Daily Homework during week $n-1$. Beginning with the second Weekly Write-up, you will be required to type your submission. You can either email me your Weekly Write-up as a PDF file, share them with me via PSU Google Docs, or submit a hard copy in person.

*Note:* On each Weekly Write-up, please write (i) your name, (ii) name of course, and (iii) Weekly Write-up number. You should type your Weekly Write-ups using $\LaTeX$, MS Word, OpenOffice/LibreOffice, or Google Docs. If you plan to email me your file, then you should send me a PDF (if you need help with this, please let me know). Furthermore, you should name your file using the following convention:

`WeeklyXLast-Name.pdf`

where you replace "X" with the assignment number and replace "Last-Name" with your actual last name. Please don't put any spaces in your file name.

**Weekly Write-up 1:**Choose any two *-problems from Daily Homework 2, 3, 4 (Due Tuesday, September 20 by 5PM).*Note:*This assignment does not need to be typed.**Weekly Write-up 2:**Choose any two *-problems from Daily Homework 5, 6, 7 (Due Friday, September 30 by 5PM).*Note:*Beginning with this assignment, your weekly write-ups should be typed (using $\LaTeX$, MS Word, Google Docs, etc.). Regardless of what you use to type up your assignment, if you email me your assignment, please email me a PDF file following the naming convention discussed above.**Weekly Write-up 3:**Choose any two *-problems from Daily Homework 8 and 9 (Due Tuesday, October 4 by 5PM).**Weekly Write-up 4:**Choose any two *-problems from Daily Homework 10, 11, 12 (Due Thursday, October 18 by 5PM).**Weekly Write-up 5:**Choose any two *-problems from Daily Homework 13, 14, 15 (Due Thursday, October 27 by 5PM).**Weekly Write-up 6:**Choose any two *-problems from Daily Homework 16, 17, 18 (Due Thursday, November 3 by 5PM).**Weekly Write-up 7:**Choose any two *-problems from Daily Homework 19, 20, 21, 22, 23 (Due Tuesday, November 15 by 5PM).**Weekly Write-up 8:**Choose any two *-problems from Daily Homework 24, 25, 26, 27, 28 (Due Thursday, December 8 by 5PM).

## LaTeX Template for Homework

You can find a $\LaTeX$ template for typing up your homework in my public ScribTeX folder. In this directory you will also find a help file for using $\LaTeX$ with ScribTeX. You can download the entire directory and then if you are using ScribTeX, you can upload the files you are interested in using. Alternatively, you can copy the content of the file and paste it into a new tex file.

For a rough overview of some of the basics of $\LaTeX$, you might find the Quick LaTeX Guide useful.