The Danger of Lying in Bed

I was listening to Mark Twain's satirical essay, The Danger of Lying in Bed the other day.

You can read it at The Complete Works of Mark Twain, or listen to it at Librivox.

This is how it begins:

The man in the ticket-office said:

"Have an accident insurance ticket, also?"

"No," I said, after studying the matter over a little. "No, I
believe not; I am going to be traveling by rail all day today.
However, tomorrow I don't travel. Give me one for tomorrow."

The man looked puzzled. He said:

"But it is for accident insurance, and if you are going to travel
by rail--"

"If I am going to travel by rail I sha'n't need it. Lying at home
in bed is the thing _I_ am afraid of."

From there, the speaker goes on to explain mathematically the number of deaths due to train accidents is insignificant next the number of deaths that occur while lying in bed (for any number of reasons). The satire is great. Which means that, to a degree, the criticism has grounds. We, as humans, do tend to become fascinated beyond reason with preventing a certain minority of misfortunes. One could object that we care how we die as well as if we die. One could also say that, pragmatically speaking, some deaths are more preventable than others, so strictly comparing numbers is naive. These points are well taken, but our instincts are so strong in the other direction, I wish we consulted the numerical severity of the problem more often. A quick check of the numbers before spending tons of time and money would be lovely.

Geek of the Week: Sue

Sue released her inner geek in an all out effort to win this year's Halloween costume contest. This is our best chance ever. I know she'll bring top prize back to the department. Great job squared, Sue!

I know a story that is sad but true
about a geek that I once knew.
She took my calculator and ran around
with every single theorem in town.

Feeling Incomplete

This problem comes from an exercise in Enderton's Intro to Mathematical logic, which I'm currently working through. This problem tripped me up yesterday. Thought it might be fun for any logic lovers. Here goes...

Consider the ternary connective #, defined by the following truth table

A B C #(A,B,C)
T T T T
T T F T
T F T T
F T T T
T F F F
F T F F
F F T F
F F F F

# is nicknamed the majority function because it always returns T if the majority of the arguments are T, and F if the majority of the arguments are F.

The task is to prove that {#} is incomplete. What this means is that there exists some well formed expression that can't be written tautologically with only #. If you've had a little logic you know that {negation, and, or} are complete. Any expression can be written tautologically with those three connectives in what is call "disjunctive normal form". Proving that a set of connectives is complete is easy. Proving that a set of connectives is incomplete is tougher. You have to be able to figure out some peculiar property of the connective and show there is some other connective that doesn't have it. The example I think Enderton gives is proving "or" is not complete. Note that if all the sentences are T in a formula built up with "or", then the entire formula has to be true. However, -A (read, not A) is an expression that when all of its sentences are T it is not itself T. Therefore there is no way for any expression built up with "or"'s to be equivalent to -A in the row of the truth table that assigns T to all the sentences.

Okay, a long setup, but a fun problem. See if you can find special property of # that distinguishes it from at least one other formula.

Found Math: In-flight Mag

A couple of weeks ago I flew to Chicago for my cousin's wedding. I found some very provocative scribbling in my in-flight magazine. The first one is particularly striking. The visual in the Westin add seems to harmonize with the pleasures of working problems for fun.

Geeks Gone Wild!

I had a great time at the Matyconn conference Friday night. We talked math, we geeked out, and ate Greek food.

There were two presentations:
"Functional Approach to Intermediate Algebra" by Marlene Megos Lovanio, who is a Mathematics Consultant for the Connecticut State Department of Education.

"Math in the Movies, Part 2" by Barbara Caserta, Math Professor at Naugatuck Valley Community College

The first provoked a lot of debate. The second was pure fun. Here are a couple of pics. Much to my chagrin, Sandy walked away with the massive chocolate door prize.

It is a great group. Check out their website.

Geek of the Week-Charles Hartman

Pi mnemonics have been around forever to help people remember the irrational number pi to a desired number of places. Here's an example:
"How I wish I could calculate pi."
The first word has three letters, the second, one, the third, four...giving us the digits of pi 3.141592 to 6 decimal places. The idea has been appropriated as a poetic form by Conn College professor/poet Charles Hartman, who starts his collection Island off with a pi mnemonic, possibly the longest in the world. Island is available from Ahsahta Press for the curious.

Math Courseware Part 3-ModuMath

Continuing Steve Krevisky's reviews of CMS's...

ModuMath

Instruction:
• Offers Basic Math (Prealgebra), Algebra I and Algebra II
• Has 51 video lessons and study guide
• Test for grade, or drill and practice
• Test is not adaptive
• Has diagnostic for students
• Can keep student records
• Will store last test with questions
• Interactive – student can get feedback right away
• Will reinforce by presenting 2nd similar question
• Will prompt student to see if they want to review
• Will prompt student to get help if 4 similar questions are wrong
• Each test is 12 questions
• Graphics: Uses color, but not animation
• Background sometimes consists of paintings (one was by Georges Seurat)

Technical:
• 4 DVDs, or 51 CDs
• Can order study guide
• Has to be installed on hard drive or network – 30 gigabytes
• Not web-based for home use – not for distance learning

Cost: $1300.00 one time charge for each set for 2 – 5 sets. The number of students who can access ModuMath concurrently is equal to the number of licenses purchased.
Study guide extra
Free technical support for 12 months
Free upgrades

Strengths:
• Easy for student to use
• Interactive
• Student gets immediate feedback
• Easy for instructor to customize

Weaknesses
• Dark background so it is difficult to read
• Examples on the videos are difficult to read
• Cost is high
• No animation and graphics could be better.
• Must purchase Basic Math (Prealgebra) and Algebra I and II separately.

This looks cool!

This looks like a very promising platform for education. Anyone tried WizIQ out? I'd love a review or any commments.

This joke never gets old...

I found basically the same math joke in two different youtube clips. It would be interesting if there were more examples. The first is from Abbot and Costello. The second looks to be from a movie called Ma and Pa Kettle. I'm not sure which clip was first. I like Ma and Pa Kettle slightly better, only because I like to hear Ma Kettle say, "I'm surprised at yer learnin'". 075 students I want an explanation of the mistake.

NPR says girls just as geeky as guys

Check out the 7/24/08 NPR report on current research showing gender parity in math performance. Hopefully this is giant kiss off to the math Barbie fiasco. (photo from ianmacm on flickr). In looking for this photo, I found a website for the BLO--Barbie Liberation Organization. You may want to join.

Geek of the Week: Sam Loyd

It is really hard to come up with a good math problem. I'm not talking about the routine problems that constitute the homework questions in math classes. I mean the kind of puzzle that piques your curiosity/keeps you up at night/won't let you think about anything else. Sam Loyd didn't further mathematical theory and won't go down in history with names like Gauss, Cantor, and Newton, but he had a special talent for creating this type problem. Try the one above, his famous Donkey Puzzle. The instructions are

To solve it, cut out the three rectangles and reassemble the pieces so that the two jockeys are riding the two donkeys.


Care to try anymore: scans of Sam Loyd's Cyclopedia are available online.

More from Steve Krevisky...

Here is his review of the Aleks system.

Aleks Software

Instruction:
• Stand alone product – can be linked to text
• Has learning tutorial
• Practice with explanations
• Shows pie chart of mastery, and will deliver to student

Technical:
• Web-based online instruction
• Stand alone or can link to test

Cost: $40 per student (before markup)
MathZone, an online homework system with diagnostics, is free to the student only if associated with text. MathZone is not free to the instructor.

Strengths:
• Has diagnostic test of 20-30 questions
• Can be customized by instructor
• Instructor can generate quizzes
• Many texts can be associated with this product

Weaknesses
• Lacks overview
• Has video only if associated with text
• Graphics just ok.
• Not as user-friendly as some other software
• Doesn’t have online grade book. The grade book is available to the
instructor if linked to MathZone.

Friends and Enemies

I picked this one off the problem feed. Cool problem!

In Smallville, each man is either a friend or an enemy to every other man.

The mayor picks six men to serve on a committee.

Show that among those six men, there are either three men that are friends to each other, or three men that are enemies to each other.

The Holy Grail of Education

Christina sent us a NY Times article about success that middle school teachers are having with video games that teach math. Educators have been trying to work this for a long time. The idea is to make learning as fun as playing video games. Hopefully, we're getting closer. This article looks promising.

Lunch Break

Found this entertaining myself with flickr on lunch break. Check out tarotastic's page.

Problem Blog

Dr. Addy sent us this cool link. MAA has problem blog. Each day they post a problem from one of their contests. Here's a sample:

A positive number x has the property that x% of x is 4. What is x?

Another source of good problems. Enjoy.

Mathalicious

Think Fergie with specs. Thanks, Lori, for sending this over.

Geek of the Week: Christian

This smug young man holding the cup of coffee is our new geek of the week. Everybody wants to use shortcuts in math. The dilemma for math teachers is often short cuts are used improperly resulting in tons of errors. Christian had one such short cut picked out for finding the y-intercept of any line from the slope and a point on the line. I assured him the technique was sound, but warned him that he was likely to screw up if the numbers given weren't nice. He didn't look worried at all, which piqued me, so I threw up a difficult example on the board and bet him a cup of coffee he couldn't find the y-intercept. Of course, he did. This is a picture of him enjoying my humiliation. By the way, if any of you want to congratulate him on his geek eminence, he takes hazelnut, cream, and sugar.

Functional Cooking

This post is dedicated to Nicole who posed the question, "When will you ever use math in the real world?" My favorite response to that question is to ask, "What can you do with math in the real world?" Nicole is a good cook, and uses math all the time to adjust recipes for the number of people she is serving. I suggested to her the following mathematically informed notation for her recipes.

Shrimp Scampi(x)
x/5 lbs linguini
4x/5 tablespoons butter
4x/5 tablespoons of olive oil
x/5 large shallots
x cloves of garlic diced
x/5 pinches of red flakes
4x large shrimp, peeled
kosher salt and black pepper to taste
x/10 cups dry white wine
x/5 lemons, juiced
x/20 cups finely chopped parsley leaves

Serves about x people.

I'm hungry already!

Photo by: Eli Hodapp

What Would You Really Do To A Math Test?

Sometimes I give a fun quiz right before a big test. One of my favorites questions is "What are you going to do to the test?". I get the normal things a student thinks a teacher wants want to hear.
-study hard
-relax
-do my best
Sometimes, honest fatalism.
-bomb it

Of course, none of that is fun. I encourage them to get mean and violent. These are some of the best answers. The tub of acid is particulary chilling.

Geek of the Week: GIMPS

The mathematical news of the week is that a new Mersenne prime of over 10 million digits has been found. It was found by an organization called GIMPS (The Great Internet Mersenne Prime Search). It is really the collective effort of people donating spare computing power to search for primes. The hunt for large primes has been a long-time fascination of mathematicians, and recently has become important to government and commerce because of RSA public key encryption. There is no known algorithm for generating ever higher primes, so we have to keep checking numbers. This gets pretty tedious as numbers get large, but you can donate your spare computing power to help out. Just visit GIMPS and see how your computer can help.

Buying Books

THE PRICE OF A BOOK
A book costs $1 plus half its price. How much does it cost?

Guess My Number

Barb sent us a link to this really fun game. Follow the link, and be the first to explain how the computer guesses your number. Serious geek points are involved.

(And Barb thanks for sending us your picture for the blog.)