## Exam 2 Review UPDATE

Hi everyone,

Two things about the review sheet:

1.  There is a typo in problem #5c — it should read |X|=3, instead of |A|=3.

2. As I told a number of you in my office today, I will NOT put a problem like #12 (There is no largest prime number) on the exam.

Best of luck with your studying,

Mr. Reitz

## Homework Week 9

Homework Week 9
Written work – Chapter 7: One odd-numbered problem and one even-numbered problem of your choice from Chapter 7, p127.
WeBWorK – none
OpenLab – (reminder: OpenLab #3, assigned last week,  is due Tuesday 10/29).

## Office hours Tuesday 1-2 by request

Hi everyone,

If you have questions for me BEFORE the exam on Thursday, I can be available tomorrow (Tuesday) between 1 and 2 pm, BUT only if you notify me ahead of time (by email, or by leaving a comment here, or by telling me in class tomorrow).

Best of luck with your studying,
Prof. Reitz

## Exam Review 2 UPDATE – review of division and remainders

Hi everyone,

First, the answer key for the Exam 2 review is now complete (it follows the questions in the Review document).  Second, you will notice that there are a few places (especially in problems 8 and 12) that I use basic facts about remainders when one number is divided by another.  These are facts that you understand intuitively from working with dividing numbers, but it might help to have them stated explicitly.  This is the basic fact about dividing and remainders:

Fact (The Division Algorithm).  Given two integers a and b with $b>0$, there exist unique integers q and r for which $a=qb+r$ and $0\leq r .

What does this mean?  It expresses the fact that when we divide one integer a by another integer b, and it will go in some number of times q with a remainder of r.  The remainder r must be less than the number b that we are dividing by.  If the remainder is zero, then b divides a (because $r=0$ means $a=qb$), and if the remainder is not zero, then b does not divide a.

-Prof. Reitz

## OpenLab #3: The MIU puzzle

We are going to play a game with strings of symbols.  This game was invented by a man named Douglas Hofstadter and found in his book Gödel, Escher, Bach. Here are the rules:

Suppose there are the symbols ‘M’, ‘I’, and ‘U’, which can be combined to produce strings of symbols called “words”, like MUI or MIUUU. The MIU game asks one to start with the “axiomatic” word MI and transform it using the following four rules, to obtain some “goal” word.  The rules state that you may:

1. Add a U to the end of any string ending in I. For example: MI to MIU, or MUUII to MUUIIU.
2. Double any string after the M (that is, change Mx, to Mxx, where ‘x’ represents any string of symbols). For example: MIU to MIUIU
3. Replace any III with a U. For example: MUIIIU to MUUU
4. Remove any UU. For example: MUUU to MU

WARM UP.  In each example, start with the axiomatic word MI and show, step-by-step, how to obtain the goal word (in each step, state which of the rules you used). These are just for practice (you do NOT need to submit your answers).

Example 1: Goal word MIU
Example 2: Goal word MIIU
Example 3: Goal word MIIUIIU
Example 4: Goal word MUUII
Example 5: Goal word MUUIIUIIU

Here is a sample solution to Example 2:
MI to MII (rule 1)
MII to MIIU (rule 2)

Assignment (due Tuesday, 10/29): Your assignment has three parts.

PART 1.  First, create an MIU puzzle — that is, make up a goal word, and post it in the comments.  Try to create a goal word that balances the following two requirements:

1. The goal word should not be too long – definitely not more than 10 letters (but the shorter the better).
2. The goal word should be tricky to reach, requiring at least four steps to reach (but the more the better).  See if you can find a clever use of the rules!

PART 2.  The second part of your assignment is to solve someone else’s puzzle.   Type your solution step-by-step, indicating which rule you used at each step.  Leave your comment as a response to their puzzle.  Only one solution per puzzle!

PART 3.  The third part of your assignment is to write a short paragraph (at least 3 sentences) responding to the following prompt.  Be sure to respond to each part:

Writing Prompt, MIU puzzle:  Did you enjoy this assignment? Why or why not?  Describe a connection between this assignment and our work in the class.  (If you don’t believe there is a connection, try to imagine why we are doing this).  Leave your response in the comments.

## Homework Week 8

Homework Week 8
Written work – Chapter 6 p. 116 #5, 8 (due next Tuesday, 10/22)
WeBWorK – none
OpenLab – OpenLab #3, due Tuesday 10/29.

NOTE: Exam #2 will take place on Thursday, 10/24.

## Exam 2 Review is posted

Find it on the “Exam Reviews” page (link in the menu above the shark).  Answers to the review will be added to the document sometime this week.  If you have any questions or notice any errors please let me know.

-Prof. Reitz

## Office hours tomorrow (Thursday 10/10)

Hi everyone,

My office hours tomorrow will not be at the regularly scheduled time, but instead:

• 9:00am – 10:00am (before class), in N707 – moving to the classroom around 9:45.
• 1:45pm-2:30pm, in N707

As always, I’m happy to make individual arrangements to meet at other times – just send me an email.

Take care,
Prof. Reitz

## Followup on Today’s Lecture (Tues 10/8)

Hi everyone,

In the homework from today, the final two problems (#15, 16) use an idea called “Proof by cases” (considering different possible situations within your proof).    To complete these two problems, read Page 96 (starting with “4.4 Cases” and ending at the end of the first proof, at the bottom of the page).  Bring your questions on Thursday!

-Prof. Reitz

## Homework Week 7

Homework Week 7
Written work – Chapter 4 p.98 #1, 6, 15, 16,  Chapter 5 p.108 #1, 4, 20 (due next Thursday, 10/17 – NOTE that Tuesday 10/15 is a Monday schedule, so our class does not meet)
WeBWorK – none
OpenLab – none

KEEP IN MIND: For written work, the odd-numbered problems have complete solutions in the back of the book.  USE THIS RESOURCE.  You should try the problem on your own first, but when you are done read the solution carefully, and adjust your answer accordingly!  Let these examples be your guide on how to approach a proof.