Tag Archives: assignment

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.

 

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.  

Homework Week 6

Homework Week 6
Written work – none
WeBWorK – Assignment5-Sec3.1-3.4 (Due Tuesday, 10/8, at midnight)
OpenLab – OpenLab #2 due this Thursday

Homework Week 5

Homework Week 5
Written work – none
WeBWorK – Assignment4-Sec2.7-2.11 (Due Thursday 10/3, at midnight)
OpenLab – Assignment #2 (Due Thursday, 10/3)

OpenLab Assignment #2: Create a logical puzzle

Make a translation puzzle (Due Thursday, October 3).  Your assignment this week is to take a common phrase – a saying, a quote, a song lyric, or anything recognizable to most people – and translate it into logical notation.  You should break it up into individual parts (such as P, Q and R), and then combine them using logical notation to create your phrase.  This is meant to be a puzzle for your classmates, so do NOT include the original phrase.

Your submission should include: the individual parts P, Q, R etc. (written in English), and the puzzle itself (written in logical notation).

Extra Credit.  You can earn extra credit by responding to a classmate’s puzzle – either by being the first person to correctly guess the phrase, or by making suggestions, or by offering an alternative way of translating the phrase into logical notation.

Here are two examples:

1.

P: you're happy
Q: you know it
R: clap your hands

Puzzle:   ( P \wedge Q) \Rightarrow R

Answer: “If you’re happy and you know it, clap your hands”

2.

P(x,y): you can fool person x at time y

Puzzle:   \sim (\forall x,y P(x,y)) 

Answer: “You can’t fool all the people all the time”

How do I type logical notation on the OpenLab?  This is not too hard — BUT it takes a little getting used to.  Here’s an example. If you type this into a comment:

Here is a statement:  $latex P \wedge Q $

then (after you post the comment) you should see this:

Here is a statement:  P \wedge Q 

Each equation or expression begins with “$latex ” and ends with “$”.  In between “$latex ” and  “$” you type your math — many things you type just as they are, like letters and numbers, but each special symbol has a special code.  In the example above, we use the code “\wedge” to produce the upside-down vee which means “and”.

Here are a few more examples:

Type this: to get this result:
$latex P \vee Q$ P \vee Q
$latex P \Rightarrow Q$ P \Rightarrow Q
$latex \sim P$ \sim P
$latex \bar{P}$ \bar{P}
$latex P \Leftrightarrow Q$ P \Leftrightarrow Q
$latex \forall x, P(x)$ \forall x, P(x)
$latex \exists x, P(x)$ \exists x, P(x)
$latex \forall x \exists y ( P(x) \vee Q(y)) \implies R(x,y) $ \forall x \exists y ( P(x) \vee Q(y)) \implies R(x,y)

LaTeX tester.  Want to test out your LaTeX code before you post it in a comment?  There is a LaTeX tester here, where you can type in your formula, hit the button, and see how it looks: http://samples.geekality.net/latex/.
NOTE:  When you use the test, do NOT include the dollar signs or the word “latex” — just include the stuff in between.

Finally, if you submit a comment but you find it doesn’t look right, don’t hesitate to make corrections and submit it again – you will NOT be penalized for multiple submissions!

Homework Week 4

Homework Week 4
Written work – none
WeBWorK – Assignment3-Sec2.1-2.6 (Due Tuesday, 9/24, at midnight)
OpenLab – none

Heads up: Exam #1 is next week Thursday, 9/26.  Review sheet is posted on the OpenLab, answer key will be added within the week.

 

Homework Week 3

Homework Week 3
Written work – Sec 1.8: 3, 5, 6, 8
WeBWorK – Assignment2-Sec1.4-1.7 (Due Tuesday, 9/17, at midnight)
OpenLab – none

If you have questions on any of the assignments, feel free to ask them here (leave a comment in reply to this post).

Quick reminder – the grading policy for written work is as follows (from the Grading Details post):

  • Odd-numbered problems are worth 3 points unless otherwise indicated.  They will be graded for completion.  (Solutions appear in the back of the book)
  • Even-numbered problems are worth 5 points unless otherwise indicated.  They will be graded for correctness.

Homework Week 2

Homework Week 2
Written work – none
WeBWorK – Assignment1-Sec1.2-1.3 (Due Tuesday, 9/10, at midnight)
OpenLab – OpenLab Assignment 1: Sudden Understanding (Due Thursday, 9/12, at start of class)

If you have questions on any of the assignments, feel free to ask them here (leave a comment in reply to this post).

Homework Week 1

Hi everyone,

Your first homework assignment will be exclusively in the book (you do NOT have a WeBWorK assignment this week).  Don’t forget to register for the OpenLab and join this course.

Welcome back,
Prof. Reitz

Homework Week 1
Written work  due Tuesday Sept 3rd –  Sec 1.1: 1, 12, 19, 26, 29, 35
WeBWorK – none
OpenLab – Register for the OpenLab and join this course (instructions provided in a separate post)