Tuesday, September 30, 2008

A Classic from Logic

If you ever studied logic, you have definitely seen this question. I found it in Enderton though I'm not sure that it is originally from there.

You are in a land inhabited by people who either always tell the truth or always tell falsehoods. You come to a fork in the road and you need to know which fork leads to the capital. There is a local resident there, but he has time only to reply to one yes-or-no question. What question should you ask so as to learn which fork to take?

An easier question is: if you just wanted to figure out whether the resident was a liar or not, what would you ask?

Monday, September 29, 2008

"I love math and extra credit"

Here are the best to test doodle from my last math test. Enjoy.


Friday, September 26, 2008

Geek of the Week: Danica McKellar



Bringing glam back (or maybe "to") math. Not only does she have geek cred with the The Chayes-McKellar-Winn Theorem, but she is spreading the math love with her book, Math Doesn't Suck. I couldn't agree more.

Thursday, September 25, 2008

Math Courseware Part 1--Hawkes Homework System

The math department, like most departments here at Tunxis, is eager to find ways that technology can help better serve our students. Our two main ventures are the use of MyMathLab in developmental courses and the pilot of two hybrid courses beginning Sping 09. We are not moving at blazing speed, but we want to make sure that we're not falling in the trap of tech for tech's sake. The following will begin a series evaluating different course management systems. It was put together by Steve Krevisky and Cora Preibis over at Middlesex Community College. Nice work guys!

Hawkes Homework System

Instruction:
• Has video lesson with audio. Lesson is mostly text
• Different levels of difficulty can be chosen by student to practice
• During practice, the student can ask for hint or step-by-step explanation
• Has mastery test after completing practice
• There are no hints during mastery, but student gets immediate feedback on question
• Textbook included, and can be used as a stand-alone product
• Interactive
• Drag and drop feature
• Has online grade book
• Has online test generator; tests can be downloaded

Technical:
• CD based – can be installed on home computer or network
• Lifetime license – need access code
• Has online grade book

Cost: Prealgebra – courseware and textbook $72 each.
Introductory and Intermediate Algebra $67 each
Combination Introductory and Intermediate Algebra $85 each

Strengths:
• Interactive and self-paced, but instructor can set due dates
• The student can have unlimited practice. He/she can choose to have a hint or see the problem worked step-by-step
• Instructor can create a diagnostics test online, and then download
• Can upload supplementary materials, such as course syllabus
• Has online grade book and progress report for student
• Focus is on mastery. The level of mastery can be changed by instructor
• There is a test generator available that can be exported into Word

Weaknesses
• Partly web-based and partly CD based. This may be a plus for some students without computers, but would probably create some difficulties for an online course
• The student must go online to submit grade for mastery test, while all of work is done offline
• The videos are mostly text, graphics are minimal
• Perhaps mathematics not rigorous enough (did not use parentheses with multiplication of a negative number)

LOOK FOR MORE SOON...

Wednesday, September 24, 2008

Going Up/Down

Here is a fun one to chew on.

Escalator Problem
Adrian is at the top of descending escalator, and his son Brad is at the bottom.
Adrian starts walking down the escalator, and counts 40 steps when he reaches the bottom. Brad starts running up the escalator, at three times the speed his father is walking down, and counts 72 steps when he reaches the top.
How many steps are visible when the escalator is stopped?

Post your answer when you get it. First correct answer gets 50 units of geek cred.

Tuesday, September 23, 2008

Seven, Seven, Seven

Rob sent me an email with a fun problem taken from a game show. Here it is

There are 7 girls in a bus.
Each girl has 7 backpacks.
In each backpack, there are 7 big cats.
For every big cat there are 7 little cats.

Question: How many legs are there in the bus?
We are warned: This is a real math problem so don't say that a bus has no legs.

It reminds me of the famous riddle (which actually made into a Die Hard movie) about the man going to St. Ives.

As I was going to St Ives
I met a man with seven wives
Seven wives with seven sacks
Seven sacks with seven cats
Seven cats with seven kits
Kits, cats, sacks, wives
How many were going to St Ives?

Thanks, Rob, for the problem. Everybody else keep them coming.

Monday, September 22, 2008

Slide Rule Sue Rides Again!


Sue brought her grandfather's slide rule in this morning. He was an engineer trained at MIT. Just being around it was seriously good math karma. Now if I could only figure out how to work it?

Friday, September 19, 2008

Math Survey Continued

Helen in Financial Aid responds to the question, 'What would you do if you saw a polynomial on the side of the road?' by saying "the safety issue is a variable…" The ellipsis at the end of that kind of scares me. It is kind of like the spooky music in a horror movie. I start thinking why, why is the safety issue variabe, what's she gonna do to the polynomial, don't go upstairs, that is where Helen the polnomial killer is, Ahhhh!

Sorry. Yes, where were we... and pay attention (my students), Helen also said, "And yes, I used math to plot out a perfect baseball diamond for a whiffle ball game for my cub scouts.. they were duly impressed…"

Not many know this, but Helen is also a movie star thanks to John Timmons and his students. Check out her video below.

Thursday, September 18, 2008

Geek of the Week: Carianne and Steve


This week's geek is 1/2 Carianne and 1/2 Steve for the incredible gallery opening of Windfall. These two used their fractional powers to couple 100 of Carianne's images with 100 of Steve's poems. That is some serious artistic stamina. For those too remote or lazy to visit the gallery, they have the images up online at Steve's MediaPlay site or Carianne's blog. Visit, look, and later buy. They have a book in the works. Carianne has a beautiful desk copy in her office. Your coffee table is drooling and you don't even know it.

Thanks Carianne and Steve! You are always making us look good.

Wednesday, September 17, 2008

my all time favorite problem


Fill in the following sentence to make the sentence true:

There is ___ 0's, ___ 1's, ___ 2's, ___ 3's, ___ 4's, ___ 5's, ___ 6's, ___ 7's, ___ 8's, and ___ 9's in this sentence.

Note: First, there are two solutions. Second, this is one of my favorite all time problems. I found it in a Doug Hofstadter book, Metamagical Themas. Aparently Abraham Robinson, inventor of non-standard analysis, came up with the problem. I've had students look this up online for the answer. One even found a site that treated this as the base 10 version of a larger set of problems. He was able to generalize a solution. Very cool! Make sure to try it first though.

Monday, September 15, 2008

The Polygon Song



As hypnotic as the thong song, but with shapes. If you have ever felt like 'just a boring square', watch this movie. Thanks Marguerite!

Thursday, September 11, 2008

Geek of the Week: Matty Sallin



An alarm clock that wakes you up by cooking a strip of bacon. I have no words for this. The geekieness shines through. Thanks Matty Sallin.

Math Survey


In order to test the mathematical pulse of the nation, the following questions were emailed to a highly selective target population.

1. What is your favorite math problem?
2. Has a math problem ever kept you up at night?
3. On a logarithmic scale, from 0 to 1, describe how positive you feel towards math?
4. If a polynomial was to breakdown on the side of the road, would you stop?
5. Have you ever used math in real life?
6. What is one question you wish math could answer?

I was underwhelmed by the number of responses. But the two emails I got were excellent. Jeff, a former student, has this to say.

1. What is your favorite math problem?
Less of a problem, and more of a belief. There's a religion (I really wish I could remember which, or where I even heard this before), a secular Jewish religion I think, that believes the true name of god is revealed by the answer when a number is divided by zero
2. Has a math problem ever kept you up at night?
Surely you must by joking, Mr. Milward
3. On a logarithmic scale, from 0 to 1, describe how positive you feel towards math?
Is zero even a positive number? Is this a trick question?
4. If a polynomial was to breakdown on the side of the road, would you stop?
No, I'd keep on factoring by....
5. Have you ever used math in real life?
Real life? That's so limiting. I prefer to live in the square root of a negative world.
6. What is one question you wish math could answer?
Why are there two consecutive e's at the end of Hendree's name?

Well done, Jeff. I pat myself on the back for having taught you so well. The only other response was from a colleague, who will remain nameless (but is directly across from me and has a Hello Kitty fetish). She answered "yuck-o-rama" when asked to pick a number between 0 and 1 to describe her feelings toward math. Don't worry. Sue and I are working on the situation right now. By early next week, we'll have her down to 'yuck'. By the end of the month, she'll be turning cartwheels for polynomials.

(pic from Kate Austin)

Wednesday, September 10, 2008

What does estimation have to do with the perfect world of numbers?

Steve sent me an interesting story in Science News about new research done on the correlation between the ability to estimate quantity and skill in algebra. Knowing very little about the study design, it is hard to argue for (or against) such a correlation. It does, however, seem quite counter intuitive to me. Algebra is primarily about symbol manipulation. Those that have trouble in it, tend to have trouble manipulating symbols in the correct way. To me, the figures of music seem to have more in common with algebra than the ability to guess the number of jelly beans in a jar. Be that as it may, math does teach us that some of the best results are counter intuitive.

Tuesday, September 9, 2008

Diagram Diaries Photo Group



I was starring at this photostream my whole lunch break. I'm a sucker for any kind of information visualization. My favorite diagram was some guy who plotted his weight against the frequency of his sexual activity. Anything can be studied!

Monday, September 8, 2008

The Lit Course I've Always Dreamed Of




Courtesy of colleagues Jesse and Steve, I've been tipped off on a new book Graphs, Maps, and Trees (F. Moretti). This is definitely going on the read-next shelf. It advocates a quantitative, model based approach to studying literature. I've added a couple of cool graphs from the book. (You might have to blow them up to see decently.) Literature might make sense now.

Friday, September 5, 2008

Wednesday, September 3, 2008

Geek of the Week: Hendree Milward


I sent emails out to the department, letting them know about yofx, and asking for nominations for a new series called 'Geek of the Week'. Here are some quotes.




Rob says, "I nominate you as geek of the week for starting the math blog!"

Lori says, "I think that you earn the 'geek of the week' just by starting this blog!"

So you see, yours truly was the top nominee. While I'm not sure my colleagues meant to flatter me, I'll gladly accept the honor. I also predict that in a month they will be begging me for 'Geek of the Week' status.

Also, kudos to Lori, who vanquished yesterday's challenging cube root equation. If you're in her College Algebra class, live in fear. She threatened to put it on the next quiz. (Just Kidding)

photo: pillowhead designs

Tuesday, September 2, 2008

Happy First Day of Class!


I was plenty nervous. Every year I forget I can teach. There were plenty of familiar faces in class though. It was great seeing everyone. One guy even stopped by the office and dropped off a copy of an Algebra text from 1841. It had a ton of stuff that I'd never even learned, like root extraction (settle down dental people--it's not what you think). Thanks, Jon.