Homework
Math 300.001
Spring 2021
Prof. Girardi

Instructions: All homework is to be turned in
on Blackboard as one legible PDF file.		 Study Guide
HW Instructions 		Exercise
HW Instructions 		Writing
Guidelines		 Symbolically Write
Guidelines
Book's Resources: PDF of Book Book Homepage Section Study Guides Screencasts  

Each hanoutout is also posted on the course handout page.
section note to yourself of
due date 		variant
of

Homework.
SG = Study Guide Homework. ER = Exercise Homework.
Homework from Chapter 1 and Chapter 2
3.1 Th 2/11 (2pm) Study Guide Homework for this section.
3.2 Th 2/18 (2pm) Study Guide Homework for this section.
3.1 Mon 2/22 (9AM) §3.1 Congruence Group Work   (Direct Proofs) For Texing help: a LaTex file of this handout.
  • Write your PIN number on your AWW board (so that your team member submitting your group work knows your PIN).
  • One person from each group should submit their Group's proof on Blackboard. The paper should contain the PINs of each group member (remember, pins are on the Student Contact Info sheet posted on Blackboard).
  • Everyone else in the group must, on Blackboard, in the comment box (under "Add Comment"), indicate your group number.
    You can just type "I was in Group n" (filling in for n either 1, 2, or 3).
  • Your group number is the same as your Theorem number.
  • This simple trick will have Blackboard open up a box where I can enter your grade so if you do not do this, I cannot enter your grade.
3.1 Tue 2/23 (2pm) Print off and bring to class the below (not graded) §3.1 Congruence Group Work. We will discuss these solutions in class as so to learn how to improve our own proofs. Group 1 ,  Group 2 ,  Group 3 . For our discussion, it would be helpful to have on hand the following Handouts (posted on our Handout page): List of Writing Guidelines and Writing Guidelines (with further comments).
3.1 Sat 2/27 (11pm) 3.1.101 ER 20. A LaTeX file and the corresponding PDF file.
3.1 3.1.3c ER 21. A LaTeX file and the corresponding PDF file.
3.1 3.1.3h ER 22. A LaTeX file and the corresponding PDF file.
3.1 3.1.6b ER 23. A LaTeX file and the corresponding PDF file.
3.1 Tue 3/2 (2pm) Before class read §3.1 Exersice 19b (along with the general instructions for such a Evaluation of proofs problem). Be prepared to make comments on the presented proof when you are called upon in class on 3/2 to do so.
3.1 Thu 3/4 (2pm) Since several students are struggling with writting proof, here are student solutions to the last homework set: ER 20,  ER 21,  ER 22,  ER 23. Read over these solutions. The grader overall freeback was: "I did notice that a lot of students were not explaining their steps, formatting their equations, and clearly stating where they are getting their information from. Students also frequently used symbolic notation in their proofs". Make sure you are not making these error.
3.1 Sat 3/6 (11pm) 3.1.6c ER 24. A LaTeX file and the corresponding PDF file.
3.1 3.1.9b ER 25. A LaTeX file and the corresponding PDF file.
3.1 3.1.16c ER 26. A LaTeX file and the corresponding PDF file.
3.1 3.1.21a ER 27. A LaTeX file and the corresponding PDF file.
3.1 Tue 3/9 (2pm) Since several students are struggling with writting proof, which will be Exam 1 this week, here are student solutions to the last homework set: ER 24,  ER 25,  ER 26 (particulary nice),  ER 27 (particulary nice). Read over these solutions. The grader overall freeback was: "I did notice that a lot of students submitted incomplete assignments, and on exercise 27 a lot of students proved the theorem backwards (used what they wanted to show as the assumption to prove what should have been the assumption)." Make sure you are not making these error.
3.3 Tue 3/9 (2pm) Study Guide Homework for this section.
Ch3 Thu 3/18 (2pm) Read Symbolically Write Guidelines, which is posted on the homework and handout pages for your convenience.
3.2 Sat 3/20 (11pm) 3.2.1cd ER 28 A LaTeX file and the corresponding PDF file.
3.2 3.2.5 ER 29. A LaTeX file and the corresponding PDF file.
Grader feedback on ER 28 and ER 29. There were a couple students who did not prove both sides of the biconditional statement and a few very creative proofs that found alternative routes other than the simpler proof by contradiction/contrapositive.
3.4 Tue 3/23 (2pm) Study Guide Homework for this section.
3.2 Sat 3/27 (11pm) 3.2.7 ER 30 A LaTeX file and the corresponding PDF file.
3.2 3.2.14bc ER 31. A LaTeX file and the corresponding PDF file.
3.2 3.2.16 ER 32. A LaTeX file and the corresponding PDF file.
Grader feedback on ERs 30-32. The latest exercises were pretty well done overall. The proofs did look a lot better than they have all semester formatting and logic wise. Some students had difficulty with when they need to show one example. The grader also said some had troubles with ER 32 so a student solution to ER 32 with a few added comments.
3.6 Mon 4/5 (2pm)

and

Tue 4/6 (before class)

§3.6 Group Work   (Review Proof Methods). For Texing help: a LaTex file of this handout.
The designated group submitter should submit thier group's proof over Bb. On Bb, so that I may enter your grade, everone is to leave a comment in the comment box with their Group number (e.g., I am in Group 17).

(1) We will go over these Student Solution proofs in class on Tue 4/6 so please print them off and look over them before class: Group 1 ,  Group 2 ,  Group 3 .

(*) Copies of our in class discussion of the Group Work: Group 1 ,  Group 2 ,  Group 3 .

(2) Print off and bring to class on Tue 4/6 the two handouts (which are also on the Handout page): Ch. 4: Induction (PMI summary) and Basic PMI example

(3) Everyone, please go into Bb and, under §3.6 Group Work Honework , put leave a comment with group number so that I can enter your grade into Bb. Thanks!

3.5 Tue 4/6 (2pm) Study Guide Homework for this section.
3.6 Tue 4/6 (2pm) Adjusted Study Guide Homework for this section. For Section 3.6, actively read the section and answer the Focus Quesions. There does not exist Screen Casts nor (starred) Exercises to do. Being honest with you, I find the §3.6 Exercises in the book to be a great source of exam problems.
3.7 Thur 4/8 (2pm) Read Section 3.7, the (short) last section of Chapter 3, which collects up the chapter's key ideas. Ask in class if you have any questions but there is nothing to turn in.
4.1 Thur 4/8 (2pm) Study Guide Homework for this section.
3.3 Sat 4/10 (11pm) 3.3.6a ER 33. A LaTeX file and the corresponding PDF file.
3.3 3.3.6c ER 34. A LaTeX file and the corresponding PDF file.
3.3 3.3.8a ER 35. A LaTeX file and the corresponding PDF file.
3.4 3.4.5a ER 36. A LaTeX file and the corresponding PDF file.
3.5 3.6.12a ER 37. A LaTeX file and the corresponding PDF file. (Covers §3.5.)
Feedback. Great jobs. The grader said:"The students did a really good job overvall".
3.6 Not to hand in Study Help For Exam Two Section 3.6 is called appropriately Review of Proof Methods. In each section of Ch. 3, you learned some methods of proofs. Now the book throws a whole bunch of exercises at are you and asks you to proof them (but does not indicate which Proof Method to use). So you have to choice which method to use and then execute the method properly. Sometimes several methods work but a certain method is much easier than the other methods. Sometimes only one method is do-able given what you know thus far in you math career.

§3.6 is a excellent source of exam problems. You should be able to do the following problems when you walk into Exam 2 (and also be able to write each one symbolically but you do not have to hand them in as of now):
3.6.1 ; 3.6.3 ; 3.6.4 ; 3.6.5 (see hint below) 3.6.7 (see hint below) ; 3.6.12 .
Hint on 3.6.5. You may use Thm 3.20 (pg. 124) which say 2 is irrational. Try cases (considering the square root of 2 raised to the power of the square root of 2, i.e, 22), which is either rational or irrational (who knows, but who cares since ...) Case 1: The 22 is rational. Case 2: The 22 is irrational.
Hint on 3.6.7. Try proof by contradiction. So assume there exists n∈ ℕ that is a solution. Then use with book's hint to help you factor n3 + 13.

4.2 Tue 4/13 (2pm) Study Guide Homework for this section.
Ch 4. Tue 4/13 (2:30 pm) Bring to class copies of the 2 new handouts
  1. Strong PMI example   (recurively defined sequences)
  2. Strong PMI example   (n=2k m)
as well as the older handouts
  1. Ch. 4: Induction (PMI summary)
  2. Basic PMI example
  3. Generalized PMI example   (with some writing guidelines for induction proofs)
Bb Fri 4/16 (11 pm) Go into Blackboard. On the left side bar, link to "Exam 1 and 2". For Exam 2, in the litlle white box, just type your PIN number, e.g., 317. This will open up a window for me to return your graded exams. Thanks.
4.1 Sat 4/17 (11pm) 4.1.19 ER 38 A LaTeX file and the corresponding PDF file.
This Exercise's LaTeX file will be helpful with LaTeXing up other induction Exercises.
4.1 4.1.3c ER 39. A LaTeX file and the corresponding PDF file.
- Solutions to: ER 38 and ER 39. For class on Tue (4/20), for ER 39, look at the comments to students (between brackets < and >) for hints on to simplify your algebra in such induction proofs. This will greatly help in the group work on Tue.
4.3 Tue 4/20 (2pm) Study Guide Homework for this section.
4.4 Tue 4/20 (2pm) Read this section, the (short) last section of Chapter 4, which collects up the chapter's key ideas. Ask in class if you have any questions but there is nothing to turn in.
Tue 4/20 and Thur 4/22: Current game plan - do group work on Tue and go over your group work on Thursday.
4.PMI Thur 4/22 (noon) Group Work over (generalized) PMI. Will start in class on Tue 4/20.

For the AWW boards:

For Overleaf:   (without instructions)

  1. Group 1's LaTeX file and the corresponding PDF file.
  2. Group 2's LaTeX file and the corresponding PDF file.
  3. Group 3's LaTeX file and the corresponding PDF file.
Group Solutions: From Students, without comments:
Group 1  ,  Group 2  ,  Group 3  .

Group Solutions: From Students, with comments from class a copy of the Ipad scrren
Group 1  ,  Group 2  ,  Group 3  .

Group Solutions: Student's solutions corrected after class.
Group 1  ,  Group 2  ,  Group 3  .

4.3 Sat 4/24 (11pm) 4.3.11 ER 40. A LaTeX file and the corresponding PDF file.
4.2 4.2.101 ER 41. A LaTeX file and the corresponding PDF file.
- Feedback.

Findable from URL: http://people.math.sc.edu/girardi/w300.html