MATH 204 - Fall 2018 Linear Algebra

Professor: Erika L.C. King
Email: eking@hws.edu
Office: Lansing 304
Phone: (315) 781-3355

Office Hours: M: 11:15am-12:15pm, W: 3:00-4:30pm, Th: 2:15-3:45pm, F: 3:00-4:00pm, and by appointment
Class Schedule: held MWF 1:55-2:50pm in Eaton 110
Course Syllabus

An online book for reviewing/learning about logic and proofs: Book of Proof by Richard Hammack
Proof Writing and Presentation Tips

WEEK 9: October 22 - October 26

Homework for class Monday, October 22:

• Finish preparing for Exam 2!
• You should have a copy of the Exam 2 Preparation sheet. Here is another copy. Note that you can find the full statements of all the Theorems and Facts in boxes in your text. Note that these are all things you should know and you should use. They will not be given to you with the exam.
• Feel free to email me with questions any time over the weekend!!! Remember that I also have office hours on Monday morning.
• REMEMBER TO BE AT THE EXAM IN EATON 110 AT 1:25!!! Also, as it says on the syllabus, seats will be randomized for the exam. So don't get too settled before the names are set out.

WEEK 8: October 15 - October 19

Quiz 5 will take place on Monday at the beginning of class. It will cover Sections 2.1 and 2.2. Be prepared to state definitions and theorems, give examples with explanations, and complete short exercises.

Homework for class Monday, October 15:

• Review your class notes from Friday's class.
• Complete these practice problems from Section 2.2 (pages 111-113): 9, 11 ($X$ is a matrix. This is good practice in proving uniqueness: first prove that it is a solution and then assume two solutions exist and show they must be the same. See our work in class or the proof of Theorem 5 in the text for examples.), 13, 15 (this is generalizing the Shoes and Socks Theorem!), 17 and 21. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• If you did not finish the reading worksheet that was due on Friday, do it now! Be ready to discuss this and put solutions on the board!
• Reread Section 2.3 in your text (pages 113-116).
• Complete this worksheet. Bring your work to class to discuss and present! Note there is a place on the worksheet to write down your questions!

BONUS ASSIGNMENT due Wednesday, October 17 at 1:55pm:

You may rewrite the proof of the second problem from the homework for Week 5 to win points toward your homework score. This is a chance to practice proof writing. Here are the rules:
• No collaboration allowed. You may not discuss these rewrites with anyone but Professor King. You are highly encouraged to discuss them with Professor King!
• No outside resources allowed. You may only use your notes and the textbook.
• If you earned full credit on this problem, you must talk to me about redoing a different problem!
• Since this is for bonus points, I will be looking for even more detail and precision than on a regular assignment, but it should be concise.
• You can earn up to four points no matter how many you lost on your original submission (and even if you did not turn in the assignment originally!). Be sure to read my comments on your graded work!
• No bonus assignments will be accepted after 1:55. No exceptions!

Homework for class Wednesday, October 11:

• Review your notes from Monday's class. In particular, review the group work problems and make sure they all make sense.
• Practice material on Elementary Matrices with the WeBWorK assignment here. Many of these should be a quick check of your understanding. Be sure to read the directions and hints to help you understand what is being asked. This is due Wednesday at 1:00pm.
• If you did not finish the reading worksheet that was due on Monday, do it now! Be ready to discuss this and put solutions on the board!
• Reread Section 2.3 in your text (pages 113-116). Particularly work through the details of the proof of Theorem 2.9 using the text as a guide, but making sure to fill in details the text left out. Do you have any questions?
• Complete the Practice Problems for Section 2.3 on page 116 of the text. This will not be collected, and you should check your answers on pages 118-119.
• We know how to find the determinate of a $2\times 2$ matrix. Now we will learn how to find determinants of larger matrices. Read pages 166-167 of Section 3.1 in your text. Yes, we are skipping ahead! This is technical so I am only asking you to read the first two pages so that you can work on understanding the notation.
• Complete this short(!) worksheet. Bring your work to class to discuss and present! Note there is a place on the worksheet to write down your questions!

Collected Homework (Due Friday, October 19 at 1:55pm):

• Note that these assignments are due right at the beginning of class! You must be on time and be ready to turn in your work - already stapled, etc. If you turn it in after 1:55 it is late and you will have to use your free late or lose points.
• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the problems on this worksheet.
• The above assignment was originally posted on Monday afternoon. It was finalized on Tuesday afternoon!

Homework for class Friday, October 19:

• Review your notes from Wednesday's class. We worked through the one part of the proof of Theorem 2.9; now make sure the rest of the proof makes sense too. Write down any questions you still have and ask them either in class or in office hours or through email! Do not let any question, no matter how small, go unanswered!
• Make sure you have worked through the worksheet that was due on Wednesday.
• Look back at the proof of Theorem 7 on page 109. Carefully study how Theorem 6 was vital to the result.
• Complete the ONE Practice Problem for Section 3.1 on page 169 of the text. This will not be collected, and you should check your answers on page 171.
• Complete these practice problems from Section 2.3 (pages 117-118): 11, 15, 17, 21, 27 and 31. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems (or even - these are GREAT QUESTIONS!!!) if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Read Section 3.2 in your text (pages 171-176).
• Complete this worksheet on Section 3.1 and 3.2. Bring your work to class to discuss and present! Note there is a place on the worksheet to write down your questions!

WEEK 7: October 10 - October 12

Have a Great Fall Break!!!

Since we have fall break this week, we will NOT have a quiz this week!

Homework for class Wednesday, October 11:

• Review your notes from class. In particular, review the group work problems and make sure they all make sense.
• Write up a short proof for 2(g) from the group work. (This is proving Theorem 3(d)!) Try looking at the $(i,j)$-entry of each matrix. Use your notation! Be ready to put your proof on the board!
• Complete these practice problems from Section 2.1 (pages 102-103): 5, 7, 8, 9, 10, 23 and 25 (this is a great problem!). These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• If you did not finish the reading worksheet that was due on Friday, do it now! Be ready to discuss this and put solutions on the board!
• Read Section 2.2 in your text (pages 104-111). As you read, take notes, record questions and work on your list (or a set of flashcards!) of definitions. You should also fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete this worksheet. Bring your work to class to discuss and present! Note there is a place on the worksheet to write down your questions!

Collected Homework (Due Friday, October 12 at 1:55pm):

• Note that these assignments are due right at the beginning of class! You must be on time and be ready to turn in your work - already stapled, etc. If you turn it in after 1:55 it is late and you will have to use your free late or lose points.
• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the problems on this worksheet.
• The above assignment was originally posted on Friday afternoon. It was finalized on Wednesday afternoon!

Homework for class Friday, October 12:

• Carefully read through your Exam 1 and rework any questions on which you lost points. Come to office hours to go over any questions you have. Everyone should do this no matter how few points you missed! We will start class on Friday by going over a few of the questions. As I said in class, I would like the following people to put their solutions for the corresponding questions on the board as soon as you arrive in class: Edgar (2c), Andy (4), Alex (6a), Lindsey (6b), Anna (6c) and Hamdan (6d). Note that I have asked you to rework question 5 for your collected homework due on Friday.
• Review your notes from class. Write down any questions you still have and ask them either in class or in office hours or through email! Do not let any question, no matter how small, go unanswered!
• If you did not finish the last two pages of the reading worksheet that was due on Monday, do it now! Be ready to discuss this and put solutions on the board!
• Reread Section 2.2 in your text (pages 104-111).
• Complete the Practice Problems for Section 2.2 on page 111 of the text. This will not be collected, and you should check your answers on page 113.
• Complete this worksheet. Bring your work to class to discuss and present! Note there is a place on the worksheet to write down your questions!
• Read Section 2.3 in your text (pages 113-116). This is really only three pages!

WEEK 6: October 1 - October 5

Quiz 4 will take place on Monday at the beginning of class. It will cover Sections 1.8 and the beginning of 1.9. Be prepared to state definitions and theorems, give examples with explanations, and complete short exercises.

Homework for class Monday, October 1:

• Reread Section 1.8 in your text (pages 63-69), and review your class notes from Friday's class. Do you have any questions?
• Reread Section 1.9 in your text (pages 71-78). If you did not complete the worksheet that was due on Friday, do it now.
• Review Theorem 10 and work through the proof of existence. Follow the text and fill in any missing parts.
• Complete this worksheet on the end of Section 1.9 and bring your work to class to discuss and present!
• Read the motivation for Chapter 2 on pages 93-94. Aircraft Design!!!
• Read pages 94-98 of Section 2.1. Take notes and write down any questions you have. This section is about Matrix Operations. Now we will look at operations with not only a matrix and a vector, but with two matrices (where the second is more than just an $n \times 1$ matrix)! See how these operations work similarly to real numbers, and how they are different.

Homework due Wednesday, October 3:

• Review your notes from class on Monday and the worksheets we discussed. Review the three standard matrices we discussed at the end of class, and make sure you see how we were able to determine whether or not they correlated to one-to-one or onto linear transformations. Can you come up with a specific example that shows why $A_1$ correlates to a linear transformation that is not one-to-one? Be ready to share your example with the class.
• See if you can come up with a standard matrix that correlates to a linear transformation that is one-to-one but not onto. Justify that your example works or show that none can be found. Be ready to share your example with the class.
• Practice material on Linear Transformations with the WeBWorK assignment here. Many of these should be a quick check of your understanding. This is due Wednesday at 1:00pm.
• Complete the Practice Problems for Section 1.9 on page 78 of the text. This will not be collected, and you should check your answers on pages 80-81.
• Complete these practice problems from Section 1.9 (pages 69-70): 3, 9, 17, 19, 21, 23, 25, 27, 29, 31 and 35. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Reread/read Section 2.1 in your text (pages 94-102). As you read, take notes, record questions and start a list (or a set of flashcards!) of definitions. You should also fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete this worksheet on Section 2.1 and bring your work to class to discuss and present! This is meant to help to guide and direct you through the reading and beginning to comprehend the new material. Note questions you have as you are working through these!

Collected Homework (Due Friday, October 5 at 1:55pm):

• Note that these assignments are due right at the beginning of class! You must be on time and be ready to turn in your work - already stapled, etc. If you turn it in after 1:55 it is late and you will have to use your free late or lose points.
• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the problems on this worksheet.
• The above assignment was originally posted on Friday afternoon. It was updated on Tuesday afternoon at 3:50, and finalized on Wednesday!

Homework for class Friday, October 5:

• Review your notes from class particularly the proof of Theorem 11. Write down any questions that you have.
• Read the proof of Theorem 12 on page 78 in your text. Fill in any blanks and make sure it makes sense to you. Notice how this proof uses theorems and facts!
• Reread Section 2.1 in your text (pages 94-102).
• Complete the Practice Problems for Section 2.1 on page 102 of the text. This will not be collected, and you should check your answers on page 104.
• If you did not finish the reading worksheet that was due on Wednesday, do it now! Be ready to put your solutions on the board when you arrive in class on Friday!
• Complete this worksheet. As with the worksheet that was due on Wednesday, bring your work to class to discuss and present!

WEEK 5: September 24 - September 28

Homework for class Monday, September 24:

• Finish preparing for Exam 1!
• You should have a copy of the Exam 1 Preparation sheet. Here is another copy. Also, here is the Chapter 1 Theorems and Facts sheet. Note that you can find the full statements of all the Theorems and Facts in boxes in your text except for Facts 2 a and b. Those we have used multiple times, but they are not explicitly stated in the text. I included them so that you could use them without having to justify them. Note that these are all things you should know and you should use. They will not be given to you with the exam.
• Feel free to email me with questions any time over the weekend!!! Remember that I also have office hours on Monday morning.
• REMEMBER TO BE AT THE EXAM IN EATON 110 AT 1:25!!! Also, as it says on the syllabus, seats will be randomized for the exam. So don't get too settled before the names are set out.

Homework for class Wednesday, September 26:

• Read Section 1.8 in your text (pages 63-69). As you read, take notes, record questions and start a list (or a set of flashcards!) of definitions.
• Complete the Practice Problems on page 69 of the text. This will not be collected, and you should check your answers on page 71.
• Complete this worksheet on Section 1.8 and bring your work to class to discuss and present! Do the best you can with each part. Some parts of the reading assignment will be easier to complete than others. You should at least have all the definitions and attempt the other questions.

Collected Homework (Due Friday, September 28 at 1:55pm):

• Note that these assignments are due right at the beginning of class! You must be on time and be ready to turn in your work - already stapled, etc. If you turn it in after 1:55 it is late and you will have to use your free late or lose points.
• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the problems on this worksheet.
• Note that some of these problems will be clearer after our class on Wednesday!
• FREE LATE! I will allow you to turn these in up to 1:00pm on Sunday. This is a free free late! You may want to finish the third question after our class on Friday. Note, I will NOT accept homework at the end of class. That is, you should not be working on it during class. You should either submit it by 1:55pm on Friday, or bring it to my office after you have completed it later that day or Saturday or Sunday by 1pm.

Homework for class Friday, September 28:

• Review your notes from class and the worksheets we discussed. Make sure you have worked through the last two problems on the reading worksheet that was due on Wednesday. We did half of question 7 and discussed approaches to solving question 8. See if you can solve question 8 in two ways!
• Complete these practice problems from Section 1.8 (pages 69-70): 1, 5, 9, 15, 17, 21 and 31. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Read Section 1.9 in your text (pages 71-78). As you read, take notes, record questions and expand your list (or a set of flashcards!) of definitions. For example, you should know the definitions of the standard matrix of a transformation, one-to-one, onto, etc. You should also feel free to fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete this worksheet on Section 1.9 and bring your work to class to discuss and present!

WEEK 4: September 17 - September 21

Quiz 3 will take place on Monday at the beginning of class. It will cover Sections 1.4 and 1.5. Be prepared to state definitions and theorems, give examples with explanations, and complete short exercises.

Homework for class Monday, September 17:

• If you are still having questions about row reduction, check out this video!
• Review your notes from Friday's class (including the proof of Theorem 4) and the worksheet we discussed. Bring your questions to office hours and class. Do you have any questions about the form or the logic of our proof?
• Complete these practice problems from Section 1.5 (pages 48-49): 17, 19, 31, 33 and 23.
• Read Section 1.7 in your text (pages 56-61). As you read, take notes, record questions and start a list (or a set of flashcards!) of definitions. You should also feel free to fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete this worksheet on Section 1.7 and bring your work to class to discuss.

Homework for class Wednesday, September 19:

• Review the problems we worked on in class on Monday as well as the material (especially Theorem 6!) we discussed from Section 1.5.
• Reread Section 1.7 in your text (pages 56-61). Review your flashcards and other notes! Write down questions to bring to class. If you have not finished the worksheet that was due for Monday, make sure you finish it now.
• Complete the Practice Problems for Section 1.7 on page 61 of the text. This will not be collected, and you should check your answers on page 63.
• Complete this worksheet on Section 1.7 and bring your work to class to discuss.

Collected Homework (Due Friday, September 21 at 1:55pm):

• Note that these assignments are due right at the beginning of class! You must be on time and be ready to turn in your work - already stapled, etc. If you turn it in after 1:55 it is late and you will have to use your free late or lose points.
• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the problems on this worksheet.
• The above worksheet has been finalized! The first two problems were posted Monday and the rest was posted on Tuesday.

Homework for class Friday, September 21:

• Remember to come to office hours with any questions you have! Review your class notes from our discussions and problem sets. Make a list of specific questions that you can ask in office hours. You can also ask some questions in class as well, but you should not save all of your questions for class as others may have some as well. The exam on Monday will cover Sections 1.1-1.5 and 1.7. I will provide a review sheet with a list of Theorems and Facts you should know on Friday.
• Practice material in Section 1.7 with the WeBWorK assignment here. The theorems from Section 1.7 will be very helpful here!!! In order to not have too much due on Friday, this is due Saturday at 6:00pm. These questions are a good review for the exam!
• Reread Section 1.7 in your text (pages 56-61). Review your flashcards and other notes! If you have not finished the worksheets that were due Monday and Wednesday, make sure you finish them now.
• Be sure you complete the practice problems we started in class on Wednesday from Section 1.7 (page 62): 11, 15, 17, 19, 21, 23, 27 and 31. Also try exercises 33 and 35. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.

WEEK 3: September 10 - September 14

Quiz 2 will take place on Monday at the beginning of class. It will cover Sections 1.2 and 1.3. Be prepared to state definitions and theorems, give examples with explanations, and complete short exercises.

Due to needing to visit another professor's class, I must cancel my Monday office hours. If you would like to meet with me before my Wednesday office hours, please email me and we will find another time to meet!

Homework for class Monday, September 10:

• Practice material in Sections 1.3 and 1.4 with the WeBWorK assignment here. It isn't as long as it looks! But be very careful about how many attempts you have for each question!!! This is due Monday at 1:00pm.
• Review your notes from class and the worksheet we discussed. Bring your questions to office hours and class.
• Reread Section 1.4 in your text (pages 35-40). Write down questions to bring to class.
• Complete the second side of the group work sheet we were working on in class on Friday. This is on Theorem 4 and matrix equations. Bring your work to class to share and discuss.
• Complete the Practice Problems on page 40 of the text. This will not be collected, and you should check your answers on pages 42-43.
• If you didn't complete the Section 1.3 practice problems assigned for Friday, do them now. Then try these practice problems from Section 1.3 (pages 32-33): 23 and 24. Be sure you can explain why the statements are true or false.

Homework for class Wednesday, September 12:

• We are going to back track a bit to make sure we all feel comfortable with this material. Reread Section 1.4 in your text (pages 35-40). Write down questions to bring to class.
• Complete this worksheet on Section 1.4 and bring your work to class to discuss. Some of these things we already discussed in class, but here is a chance to review it.
• Complete these practice problems from Section 1.4 (pages 40-42): 1, 5, 7, 9, 11, 13, 15, 17, 21, 23 and 25. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Start reading Section 1.5 in your text (pages 43-47). There will be a reading worksheet for this section due on Friday.

Collected Homework (Due Friday, September 14 at 1:55pm):

• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the problems on this worksheet.

Homework for class Friday, September 14:

• Review notes from class and work on expanding on the outline for the proof of part of Theorem 4: The Connections Theorem that we discussed in class. Can you see which facts, definitions and theorems we need to combine to fill in the details? Be ready to share your thoughts!
• Read Section 1.5 in your text (pages 43-47). Make flashcards! Write down questions to bring to class.
• Complete this worksheet on Section 1.5 and bring your work to class to discuss.
• Complete the Section 1.5 Practice Problems on page 47 of the text. This will not be collected, and you should check your answers on pages 49-50.

WEEK 2: September 3 - September 7

Quiz 1 will take place on Monday at the beginning of class. It will cover Sections 1.1 and 1.2. Be prepared to state definitions and theorems, give examples with explanations, and complete short exercises.

Homework for class Monday, September 3:

• Practice material in Sections 1.1 and 1.2 with the first real WeBWorK assignment here. It isn't as long as it looks! But be very careful about how many attempts you have for each question!!! For many of these you only have ONE or TWO attempts! This is due Monday at 1:00pm.
• Read pages 24-29 of Section 1.3 in your text.
• Complete this worksheet on Section 1.3 and bring your work to class to discuss. Also while you are reading, you are encouraged to take additional notes and record questions. You should also feel free to fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete these practice problems from Section 1.2 (pages 21-22): 1, 5, 11, 13, 15, 21, 23, 25. These will NOT be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.

Homework for class Wednesday, September 5:

• Remember to bring in your picture if you forgot to bring it to your appointment!
• If you didn't have it ready for Monday, complete this worksheet on Section 1.3 and bring your work to class to discuss. Also while you are reading, you are encouraged to take additional notes and record questions. You should also feel free to fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Also complete this worksheet on Section 1.3 and bring your work to class to discuss. Also while you are reading, you are encouraged to take additional notes and record questions. You should also feel free to fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete the Practice Problems on page 32 of the text. This will not be collected, and you should check your answers on pages 34-35.
• Complete these practice problems from Section 1.2 (pages 21-22): 27, 29 and 31 (Draw what is happening geometrically here!). These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.

Collected Homework (Due Friday, September 7 at 1:55pm):

• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the following problems:
1. Number 33 from Section 1.1, page 11. Show your work as was done for $T_1$ in the problem statement above the question.
2. Number 34 from Section 1.1, page 11. Use the hint!!! Remember to show each step separately!
3. Number 12 from Section 1.2, page 22. Be sure to show your work!
4. Number 20 from Section 1.2, page 22. Change the directions slightly to finding ALL possible $h$ and $k$ that fulfill the requirements for each part (not just one pair for each part). Be sure to show your work and explain your reasoning where appropriate! Don't forget to use Theorems in explanations!
5. For each of the following, decide whether or not it is possible for a system to satisfy the given description. If it is possible, give an augmented matrix (in row-echelon or reduced row-echelon form) that corresponds to such a system and prove that the corresponding system does in fact fulfill the requirements; if it is not possible, prove that it is not possible. (Hint: Theorems are helpful in proving!) (a) A system of 5 equations in 3 unknowns that has exactly 1 solution. (b) A system of 5 equations in 3 unknowns that has infinitely many solutions. (c) A system of 5 equations in 3 unknowns that has exactly 2 solutions.
6. Prove part (vii) of the Algebraic Properties of Vectors in $R^n$ Theorem (p. 27). See the solution to Practice Problem 1 of Section 1.3 for an example of how such a proof should go. Note that the sample proof on page 34 is really an outline for a proof. Be sure to include sentences and write your proof in paragraph form. You will quote definitions and properties of real numbers in your proof.

Homework for class Friday, September 7:

• Reread Section 1.3 in your text! Then complete any parts of the group work sheet we were working on in class that you did not finish. Bring your work to class to share and discuss.
• Try these practice problems from Section 1.3 (pages 32-33): 1, 5, 9, 11, 15, 21 and 25. These will not be collected, but you should do as many as you need to in order to feel comfortable with the material. In fact, you should do more odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Read Section 1.4 in your text (pages 35-40).
• Complete this worksheet on Section 1.4 and bring your work to class to discuss. Also while you are reading, you are encouraged to take additional notes and record questions. You should also feel free to fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Continue reading/reviewing the Book of Proof by Richard Hammack. For this week, read Chapter 4: Direct Proof. Pay special attention to Section 4.3 that starts on page 92 (page 6 of the pdf). The answers to the odd exercises are found in the Solutions section of the text. At a minimum, complete the exercises 3, 5 and 11 on page 100 (page 14 of the pdf), and as with all practice sets, do as many odd problems as you need to in order to feel comfortable with the material. You should be sure to work through this chapter by Wednesday. Note that there is a link to this text at the top of this page. I encourage you to ask me any questions you have on this material in office hours.

WEEK 1: August 27 - August 31

Welcome to Linear Algebra!!!

Homework due Tuesday, August 28:

Although I will not normally assign homework to be due on non-class days, this week we will need to in order to get started and refresh our memories. Please complete the following:

Homework for class Wednesday, August 29:

• Read the syllabus! In fact, read it at least two times. You should be sure you have read all of it and understand what is expected. Please ask if you have questions. Note the paper copy I gave you is blue so that you can easily find it. Refer to it often. (There is also a link to the syllabus at the top of this page.)
• Put the exam dates from the syllabus on your calendar. Note that the midterm exams begin at 1:25, a half hour before our usual class time. Let me know ASAP if you have any issues with this.
• Although it is not required, it is recommended that you take MATH 135 before you take this course. If you have not yet taken MATH 135 or if you feel rusty, you should do additional outside reading on logic and proof writing as you will need those skills from time to time in this course. Although we will review a bit along the way, you will benefit highly from having a firm foundation on these concepts. There is a free online text, Book of Proof by Richard Hammack, that I recommend you review. For this first week, read Chapter 2: Logic. Pay special attention to Section 2.10 on Negation that starts on page 57 (page 25 of the pdf). The answers to the odd exercises are found in the Solutions section of the text. At a minimum, complete the odd exercises in Section 2.10 on pages 60-61 (pages 28-29 of the pdf). You should be sure to work through this chapter by Monday. Note that there is a link to this text at the top of this page.
• I put together a website for my MATH 135 classes to help with proof writing and presentations. Read the Proof Writing and Presentation Tips website. Use this as a reference when you are preparing your homework and presentations for class. Note there is a link to this site at the top of this web page as well.
• Read the Introduction to Chapter 1 and Section 1.1 in your text. This covers pages 1-9. We started discussing some of this in class.
• Complete this worksheet on Section 1.1 and bring your work to class to discuss. Also while you are reading, you are encouraged to take additional notes and record questions. You should also feel free to fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Read pages 12-15 of Section 1.2 in your text.
• Complete this worksheet on Section 1.2 and bring your work to class to discuss. Also while you are reading, you are encouraged to take additional notes and record questions. You should also feel free to fill in the blanks for any skipped steps in the reading by working through calculations yourself!

Collected Homework (Due Friday, August 31 at 1:55pm):

• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the problems on this worksheet.

Homework for class Friday, August 31:

• Reread Section 1.1 in your text!