Tag Archives: openlab

OpenLab #5: Advice for the Future

Assignment (due Tuesday, December 17).  Imagine that you are invited to speak on the first day of MAT 2070, to give advice to entering students.  Write at least three sentences responding to at least one of the following, describing what you would tell them.

  1. What do you wish that you had been told at the start of this class, to help you succeed?
  2. Choose one topic in the course that is especially challenging. Identify it, and give advice to students trying to master that topic.
  3. What is the most important prior knowledge (not taught in the class) that you need in order to succeed?  Why is it important?

Extra Credit.¬† Respond to someone else’s comment. ¬†Do you agree? disagree? Have anything to add?

OpenLab #4: The MIU puzzle, continued

UPDATE: See the “Assignment Version 2” added below.

This assignment is a continuation of OpenLab #3, on the MIU puzzle.  Your assignment this time is a little different.  Consider the following conjecture about the MIU puzzle:

Conjecture. ¬†Any goal word (any word with first letter M, followed by a combination of U’s and I’s) can be obtained from the starting word MI using the rules of the MIU puzzle.

Assignment (Due Thursday 11/14.  Submit your answer between Tuesday, 11/12 and Thursday, 11/14). Is the conjecture above true?  If so, prove this fact.  If not, provide an example of a goal word that cannot be obtained, and prove that it is impossible for your word to be obtained.

IMPORTANT: Because of the nature of this assignment, DO NOT SUBMIT YOUR ANSWER BEFORE  TUESDAY 11/12. However, I strongly recommend getting started on this problem well before that date!

ASSIGNMENT VERSION 2

If you wish, you can respond to the assignment below INSTEAD of completing the assignment above.  In the assignment below, you will be writing about your experience working on the MIU puzzle above.  Be sure to respond to EACH PART Рdetailed answers to part 2 and 3 below will gain the MOST credit.

  1. Write down what you think the answer is Рno proof necessary.
  2. Describe in as much detail as you can the process of working on the assignment.  What did you think in the beginning? What are the different things you tried in order to solve the problem?  Describe each one, in the order that you tried them.
  3. Give a detailed list of the resources you used, and how you used each one (these could include anything – your brain, pen & paper, a computer (what applications did you use), the internet, other people, and so on).
  4. What activity or resource do you feel was most effective for you in working on the assignment (what helped you the most in understanding the assignment and figuring out an answer)?

Extra Credit. ¬†Respond to one of your classmates’ submissions.

 

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.

Our OpenLab site is up and running again

Let me know if you have any further difficulties.  Barring future problems, the due date for the assignment is still midnight on Thursday 10/4 (tomorrow).

See you tomorrow,

Prof. Reitz

Problems with our OpenLab site

Hi everyone,

A number of you have pointed out that our site is having problems – I’ve submitted a bug report, and will keep you posted. ¬†Don’t worry – if it’s not resolved soon I’ll extend the deadline for OpenLab assignment #2.

Sorry for the trouble!

Prof. Reitz

Homework Week 6

Homework Week 6
Written work Рnone
WeBWorK РAssignment5-Sec3.1-3.4 (Due Tuesday, 10/8, at midnight)
OpenLab РOpenLab #2 due this Thursday

Homework Week 5

Homework Week 5
Written work Рnone
WeBWorK РAssignment4-Sec2.7-2.11 (Due Thursday 10/3, at midnight)
OpenLab РAssignment #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 Рa saying, a quote, a song lyric, or anything recognizable to most people Рand 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!

OpenLab Assignment 1: Sudden understanding

This assignment is due Thursday, September 12, at the start of class.

Assignment.  Choose ONE of the following two topics.  Write a reply to this post, responding to the topic.  Begin by telling us which topic you chose. (1-2 paragraphs).  Be sure to include your name in the post, and which section you are in (so I can give you credit).

Topics.¬†There is a common experience that ¬†many people describe having at various times when they are learning mathematics. ¬†It is the experience of suddenly understanding a concept for the first time – something that might have seemed confusing, or hard, or just didn’t make sense, ¬†all of a sudden becomes clear. ¬†This can happen in class, because of something a teacher says, or because a friend explained it to you in a new way. ¬†Sometimes it happens on your own, because you were thinking hard about a particular problem. ¬†Afterwards,¬†¬†the concept might even seem obvious, or simple – for some people it might even be hard to remember exactly why you found it so confusing.

  1. Choose an experience you had in which you suddenly understood a math concept (it could be any kind of math, from elementary school up through college).  Describe what happened.  What was the mathematical concept?  Who was involved? How did it happen?  Finally, do you think you could explain it to others in a way that they could have the same flash of understanding?
  2. If you have never had an experience like this, then talk about your own experiences in learning math.  Choose one mathematical concept that you feel you know well Рhow did you learn it?  What did your teachers/friends/parents/tutors/yourself/etc. do that helped you to learn it?  What was the most important factor that contributed to your understanding?

Extra Credit. ¬†For extra credit, write a response to one of your classmates’ comments. ¬†Do you feel the same, or different? ¬†Did you learn anything? ¬†Did you get any ideas about teaching, or about learning?

Why are we doing this, anyway?¬†¬†Having progressed this far in your school career, you are familiar with many of the tools for learning math:¬†¬†studying, practicing by doing problems, asking questions when you need help, and so on. ¬†I’d like to talk about two activities that may NOT seem related to learning math — but research shows that engaging in these activities can¬†dramatically¬†increase the amount that you learn, and change the way you learn it. ¬†The first is¬†writing¬†— something not typically associated with mathematics. ¬†When you express your ideas in words, it forces you to think them through very carefully, detail by detail. ¬†A great way to check and see if you really understand something is to try to explain it to someone else, either out loud or in writing. ¬†Example: if you know how to add fractions, try teaching it someone who doesn’t know how. ¬†The second is called¬†metacognition, or “thinking about thinking.” ¬†This happens when you think about what was going on in your head while you were working on a problem or trying to learn a new idea. ¬†What train of thought did you follow? ¬†Where did you get stuck, and what did you do next? ¬†What were you feeling at the time? and so on. ¬†Combining writing and metacognition can be a tremendously powerful tool in identifying the ways we learn best and the ways we make mistakes, and learning to improve. ¬†However, like any skill, it takes practice. ¬†That’s why we’re getting started by writing a little about our past experiences with learning mathematics.