Monthly Archives: September 2013

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!

The review sheet is too darn long

This review sheet is rather long – because of this, I’ve marked certain problems ¬†as optional (denoted with a double asterisk **). ¬†If you have only a limited time for review, do the other problems first. ¬†If you have a little extra time, the ** problems are good practice.

Optional Problems:  1b, 2d, 4bf, 5efij, 6ae, 7c, 8d, 10a, 12b

Homework Week 4

Homework Week 4
Written work Рnone
WeBWorK РAssignment3-Sec2.1-2.6 (Due Tuesday, 9/24, at midnight)
OpenLab Рnone

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.

 

Office hours today are all messed up

Hi everyone,

Due to several meetings (the curse of a big institution), my regularly scheduled office hours will be all messed up today. ¬†I’ll be available:
– Directly after class for about 12 minutes (until 11:27)
– From 12:30-1:00

If need more time with me, please let me know either at the end of class or by email, and I’ll do my best to find a time that works

.Apologies for the late notice,
Prof. Reitz

Homework Week 3

Homework Week 3
Written work¬†–¬†Sec 1.8: 3, 5, 6, 8
WeBWorK РAssignment2-Sec1.4-1.7 (Due Tuesday, 9/17, at midnight)
OpenLab Рnone

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.

Getting Started with WeBWorK

WeBWorK is accessible from on and off campus (anywhere you have access to the internet).  Your first WeBWorK assignment is due on Tuesday, September 10th, at midnight, and will cover the material from the first two weeks of class (primarily from the second week).  Here’s what you have to do:

Assignment.  To get started on your first assignment, you must complete the following three steps.

Step 1.  Log in to WeBWorK here:  http://mathww.citytech.cuny.edu/webwork2/MAT2070/.  I have created Usernames and Passwords for each student registered for my class.

Username. ¬†Your username for WeBWorK consists of your first initial plus your last name, all lowercase (for example, John Smith would have username ‚Äėjsmith‚Äô).

Password. ¬†Your temporary password is the same as your username (if your username is ‘jsmith’, your password is currently ‘jsmith’).

Step 2. ¬†Change your password and update your email address. ¬†To do this, select ‚ÄúPassword/Email‚ÄĚ from the main menu on the left. ¬†Use whatever email address you like (I suggest using one that you check often).

Step 3.  Complete the first assignment, titled Assignment1-Sec1.2-1.3, by clicking on it in the main screen.

If you have¬†any trouble¬†‚Äď either with logging in, or with completing the assignment, post a comment here or send me an email and I will get back to you.

WeBWorK Tips:

  1. Click on a problem to see the details (the list of problems appears in the menu on the left). ¬†Enter an answer and hit ‚ÄúSubmit Answers‚ÄĚ. ¬†Don‚Äôt worry, if you get it wrong you can try it again.
  2. You can work on the problems in any order you wish.  You can do some problems now, and come back and do the rest another day (your work will be saved, as long as you submit your answers).
  3. If you want to print out a copy of the assignment, click on the assignment name in the main menu on the left, and then click the link in the main screen area that reads ‚ÄúDownload a hardcopy of this homework set.‚ÄĚ

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.

Homework Week 2

Homework Week 2
Written work Рnone
WeBWorK РAssignment1-Sec1.2-1.3 (Due Tuesday, 9/10, at midnight)
OpenLab РOpenLab 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).