komplexify! » Math musings http://komplexify.com/blog Self referencing and self contradictory Fri, 25 Jun 2010 06:22:09 +0000 http://wordpress.org/?v=2.8.4 en hourly 1 Quickies http://komplexify.com/blog/2010/06/13/quickies-2/ http://komplexify.com/blog/2010/06/13/quickies-2/#comments Sun, 13 Jun 2010 19:54:39 +0000 Travis http://komplexify.com/blog/?p=1730 Attention all idiots with babies:

The movie theater is not a daycare center.

That is all.

As you might have guessed, we went to the movies the other day, where we saw the new, Jackie-Chain-infused Karate Kid.  With its emphasis on Chinese culture and locales, should have more appropriately be renamed the Kung Fu Kid, but I digress.  One of the first trailers before the movie started was for The Last Airbender, which despite still being helmed by M. Night Shamadingdong still appears to KICK. ASS.

The Ladybug is similarly excited about the movie, and in fact went so far as to design her own movie poster for it:

In case you’re missing some of the subtle details, the Ladybug offers this explanation:

Speaking of the Karate Kid, which by the way was awesome itself, I just about died watching Jackie Chan Hates Karate Kids.

Last Sunday, the Ladybug, Queen B, and I went on the annual Crazy Horse Volksmarch, which I apparently only undertake on even-numbered years.  Its a 10K hike (that’s 6.2 miles for the metric-impaired) that goes up to the face of the ever-imcomplete Crazy Horse Monument.  Early on, we passed another family, where I overheard the following:

Brother: Ugh, this is tiring.

Sister: We only just started.  We’re not even a mile in.

Brother: I wish I was a bird, so I could fly to the end.

Sister: With your luck, you’d end up a penguin and still have to walk.

Brother: [Stops]

Brother: You just broke my dream.

On June 3, torrential rain caused a massive, 66-foot-diameter sinkhole to form in the middle of Guatemala City, devouring a 3-story building in the process.  As yet, scientists do not know what caused it, although I have a theory.

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Joke time! http://komplexify.com/blog/2010/06/07/joke-time-9/ http://komplexify.com/blog/2010/06/07/joke-time-9/#comments Tue, 08 Jun 2010 03:02:02 +0000 Travis http://komplexify.com/blog/?p=1714 Each semester, I offer students a last chance for extra credit by writing their favorite joke or riddle on their crib sheet, with extra credit assigned based purely on how funny I think it is. Here are some of the better ones.

Mathy contributions

Q: What did the acorn say when it grew up?
A: Gee-I’m-a-tree.

Q: Why couldn’t the identity \sin(2r) = 2 \sin(r) get a loan?
A: It needed a cosigner.

Q: How trigonometric functions do farmers use?
A: Swine and cow-sine.

Q: What do you get when you cross a rooster and a duck?
A: A bird that gets up at the quack of dawn.

Q: What do you get when you cross a rooster and a duck?
A: A vector orthogonal to the cow and the chicken, determined by the right-hand rule.

Q: What’s a polar bear?
A: A rectangular bear after a change of coordinates.

Q: What kind of toilet paper do mathematicians prefer?
A: Multi-ply.

Q: What does a mathematician do when constipated?
A: He works it out with a pencil.

Q: What does Einstein do on the toilet?
A: Brownian motion.

Q: What is the most erotic number?
A: 2110593.
Q: Why?
A: When 2 are 1 and they don’t pay at-10-tion, they’ll know within 5 weeks whether or not, after 9 months, they’ll be 3.

Want some more mathematical pick-up lines?

Did you hear about the largest prime number yet discovered?
According to CNN, it’s four times bigger than the previous record.

I will derive!

One day, Jesus said to his disciples: “The Kingdom of Heaven is like y = 3x^2 + 2x - 7.” A man who had just joined the disciples looked very confused and asked Peter: “What on Earth does he mean by that?” Peter smiled. “Don’t worry. It’s just another one of his parabolas.”

A woman in a bar tries to pick up a mathematician. “How old do you think I am?” she asks coyly. “Well,” he says, “18, by the fire in your eyes. 19, by the color of your cheeks. 20, by the radiance of your face. Now, if we add those up…”

George W. Bush to mathematicians: “It’s come to my attention that y’all are teaching algebra classes in which students learn to sove equations with the help of radicals. I can’t say I approve of that…”

An engineer, a physicist, and a mathematician went to the races one Saturday and laid their money down. Commiserating in the bar after the race, the engineer says, “I don’t understand why I lost all my money. I measured all the horses and calculated their strength and mechanical advantage and figured out how fast they could run…” The physicist interrupted him: “But you didn’t take individual variations into account. I did a statistical analysis of their previous performances and bet on the horses with the highest probability of winning…” “So if you’re so hot why are you broke?” asked the engineer. But before the argument can grow, the mathematician takes out his pipe and they get a glimpse of his well-fattened wallet. Obviously here was a man who knows something about horses. They both demanded to know his secret. “Well,” he says, between puffs on the pipe, “”first I assumed all the horses were identical and spherical…”

As an experiment, an engineer, a physicist and a mathematician are placed in separate rooms and left with a can of food but no can-opener. A day later, the rooms are opened one by one. In the first room, the engineer is snoring, with a battered, opened and emptied can. When asked, he explains that when he got hungry, he beat the can to its failure point. In the second room, the physicist is seen mouthing equations, with a can popped open beside him. When asked, he explains that when he got hungry, he examined the stress points of the can, applied pressure, and ‘pop’! In the third room, the mathematician is found sweating, and mumbling to himself, “Assume the can is open, assume the can is open…”

A mathematician, a physicist and an engineer were undergoing a thought-process experiment. As part of the experiment, they were seated at a table, given 3 metal spheres, and left alone for a while. After an hour or so, the experimenter returned to each of the three professionals. He checks in on the mathematician first, and finds the balls neatly arranged in a triangle at the center of the table. He checks in on the physicist next, and finds the balls stacked precariously, one on top of the other, in the center of the table. He then checks in on the engineer, and finds one of the balls is broken, one is missing, and the third being carried out in the engineer’s lunchbox.

A mathematician, a physicist, and an engineer are all given identical rubber balls and told to find the volume. They are given anything they want to measure it, and have all the time they need. The mathematician pulls out a measuring tape and records the circumference. He then divides by two times pi to get the radius, cubes that, multiplies by pi again, and then multiplies by four-thirds and thereby calculates the volume. The physicist gets a large bucket of water, places 3 gallons of water in the bucket, drops in the ball, and measures the displacement to six significant figures. The engineer writes down the serial number of the ball, and looks it up.

A mathematician and an engineer are sitting next to each other on a long flight. The mathematician leans over to the engineer and asks if he would like to play a fun game. The engineer just wants to take a nap, so he politely declines and rolls over to the window to catch a few winks. The mathematician persists and explains that the game is real easy and lots of fun. He explains, “I ask you a question, and if you don’t know the answer, you pay me $5. Then you ask me a question, and if I don’t know the answer, I’ll pay you $5.” Again, the engineer politely declines and tries to get to sleep. The mathematician, now somewhat agitated, says, “Okay, if you don’t know the answer, you pay me $5, and if I don’t know the answer, I’ll pay you $50!” This catches the engineer’s attention, and he sees no end to this torment unless he plays, so he agrees to the game. The mathematician asks the first question. “What’s the distance from the earth to the moon?” The engineer doesn’t say a word, but reaches into his wallet, pulls out a five-dollar bill and hands it to the mathematician Now, it’s the engineer’s turn. He asks the mathematician “What goes up a hill with three legs and comes down on four?” The mathematician looks up at him with a puzzled look. He takes out his laptop computer and searches all of his references. He taps into the air phone with his modem and searches the net and the Library of Congress. Frustrated, he sends e-mail to his co-workers all to no avail. After about an hour, he wakes the engineer and hands him $50. The engineer politely takes the $50 and turns away to try to get back to sleep. The mathematician then hits the engineer, saying, “What goes up a hill with three legs, and comes down on four?” The engineer calmly pulls out his wallet, hands the mathematician five bucks, and goes back to sleep.

Arguing with an engineer is a lot like wrestling with a pig in mud. After a few hours, you realize he likes it.

A pessimist will tell you the glass is half-empty. An optimist will tell you the glass is half-full. An engineer will tell you the glass is twice the size it needs to be.

Q: What’s the difference between a woman and a number.
A: A number can have a period and still be rational.

Q: What is 6.9?
A: Good sex interrupted by a period.

“What happened to your girlfriend, that really cute math student?”
“She no longer is my girlfriend. I caught her cheating on me.”
“I don’t believe that she cheated on you!”
“Well, a couple of nights ago I called her on the phone, and she told me that she was in bed wrestling with three unknowns…”

Weapons of math instruction:

At New York’s Kennedy airport today, an individual later discovered to be a public school teacher was arrested trying to board a flight while in possession of a ruler, a protractor, a setsquare, a slide rule, and a calculator.

At a morning press conference, Attorney general John Ashcroft said he believes the man is a member of the notorious al-gebra movement. He is being charged by the FBI with carrying weapons of math instruction.

“Al-gebra is a fearsome cult,”, Ashcroft said. “They desire average solutions by means and extremes, and sometimes go off on tangents in a search of absolute value. They use secret code names like “x” and “y” and refer to themselves as “unknowns”, but we have determined they belong to a common denominator of the axis of medieval with coordinates in every country.

“As the Greek philanderer Isosceles used to say, there are 3 sides to every triangle,” Ashcroft declared.

When asked to comment on the arrest, President Bush said, “If God had wanted us to have better weapons of math instruction, He would have given us more fingers and toes.

“I am gratified that our government has given us a sine that it is intent on protracting us from these math-dogs who are willing to disintegrate us with calculus disregard. Murky statisticians love to inflict plane on every sphere of influence,” the President said, adding: “Under the circumferences, we must differentiate their root, make our point, and draw the line.”

President Bush warned, “These weapons of math instruction have the potential to decimal everything in their math on a scalene never before seen unless we become exponents of a Higher Power and begin to factor-in random facts of vertex.”

Attorney General Ashcroft said, “As our Great Leader would say, read my ellipse. Here is one principle he is uncertainty of: though they continue to multiply, their days are numbered as the hypotenuse tightens around their necks.”

Upgrading to Wife 1.0:

Last year a friend of mine upgraded GirlFriend 1.0 to Wife 1.0 and found that it’s a memory hog, leaving very little system resource for other applications. He is only now noticing that Wife 1.0 also is spawning Child-Processes which are further consuming valuable resources. No mention of this particular phenomenon was included in the product brochure or the documentation, though other users have informed him that this is to be expected due to the nature of the application. Not only that, Wife 1.0 installs itself such that it is always lauched at system initialisation where it can monitor all other system activity.

He’s finding that some applications such as PokerNight 10.3, BeerBash 2.5, and PubNight 7.0 are no longer able to run in the system at all, crashing the system when selected (even though they always worked fine before). At installation, Wife 1.0 provides no option as to the installation of undesired Plug-Ins such as MotherInLaw 55.8 and BrotherInLaw Beta release. Also, system performance seems to diminish with each passing day.

Some features he’d like to see in the upcoming wife 2.0.:

  • A “Don’t remind me again” button
  • A minimize button
  • An install shield feature that allows Wife 2.0 to be installed with the option to uninstall at anytime without the loss of cache and other system resources.

I myself decided to avoid all of the headaches associated with Wife 1.0 by sticking with Girlfriend 2.0. Even here, however, I found many problems. Apparently you cannot install Girlfriend 2.0 on top of Girlfriend 1.0. You must uninstall Girlfriend 1.0 first. Other users say this is a long standing bug which I should have been aware of. Apparently the versions of Girlfriend have conficts over shared use of the I/O port. You’d think they would have fixed such a stupid bug by now. To make matters worse, the uninstall program for Girlfriend 1.0 doesn’t work very well, leaving undesirable traces of the application in the system.

Another thing that sucks — all versions of Girlfriend continually popup little annoying messages about the advantages of upgrading to Wife 1.0.

BUG WARNING!

Wife 1.0 has an undocumented bug. If you try to install Mistress 1.1 before uninstalling Wife 1.0, Wife 1.0 will delete MSMoney files before doing the uninstall itself. Then Mistress 1.1 will refuse to install, claiming insufficient resources.

To avoid the above bug, try installing Mistress 1.1 on a different system and never run any file transfer applications such as Laplink 6.0. Another solution would be to run Mistress 1.0 via a UseNet provider under an anonymous name.

There are in fact two versions of this bug, and it seems to be a matter of luck which one you get afflicted with. The version described is the milder of the two. With the worse version, before uninstalling itself Wife 1.0 uses the Divorce protocol to install Lawyer 1.0 (and sometimes also Lawyer 1.1, Lawyer 1.2 and Lawyer 1.3 as well).

Lawyer (any version) will run for an indeterminate but lengthy period constantly consuming all resources. When it eventually ends it automatically installs Alimony 26.5, which removes MSMoney and any other financial application as soon as you install it. The core of Lawyer 1.0 remains as a TSR during this time, crashing the system as soon as any attempt is made to stop Alimony 26.5 or to interfere with its operation. This sometimes leads to fatal breakdown of the entire system.

As always, some pics:

Ever wonder where cursors come from?

Division by zero was a common theme, too.

In class I’ve tried to instill an appreciation for correct function notation, especially when in comes to the trigonometric functions. In particular, from time to time in class I’ve been known to say things like “Every time you write sin2 x instead of sin(x)2, God kicks a puppy.” Apparently, however, I didn’t specificy which god:

Other good ones

Did you hear about the agnostic dyslexic insomniac?
He stayed up all night wondering if there really was a dog.

Q: What do Americans do when they has an eight-thousand foot deep hole in the ground?
A: They drop a DUSEL in it.

In America, you pretend to work and your boss pays you. In Soviet Russia, you work and your boss pretends to pay you.

Light a man a fire, and you warm him for a night. Light a man on fire, and you warm him for the rest of his life.

Two cannibals are eating a clown. One of them says, “Does this taste funny to you?”

Two cannibals are eating. One says “Your wife makes a really delicious dinner.” The other says “I know. I’m going to miss her.”

A fireman is at the station house working outside on the fire truck when he notices a little boy next door. The little boy is in a little red wagon with little ladders hung off the side. He is wearing a fireman’s hat and has the wagon tied to a dog. The fireman says “Hey little boy. What are you doing?” The little boy says “I’m pretending to be a fireman and this is my fire truck!” The fireman walks over to take a closer look. “Little boy that sure is a nice fire truck!” the fireman says. “Thanks mister”, says the little boy. The fireman looks a little closer and notices the little boy has tied the dog to the wagon by its testicles. “Little boy”, says the fireman, “I don’t want to tell you how to run your fire truck, but if you were to tie that rope around the dog’s neck I think you could go faster.” The little boy says, “You’re probably right mister, but then I wouldn’t have a siren!”

A young boy enters a barber shop and the barber whispers to his customer,”This is the dumbest kid in the world. Watch while I prove it to you.” The barber puts a dollar bill in one hand and two quarters in the other, then calls the boy over and asks, “Which do you want, son?” The boy takes the quarters and leaves. “What did I tell you?” said the barber. “Every single time… That kid never learns!” Later, when the customer leaves, he sees the same young boy coming out of the ice cream store. “Hey, son! May I ask you a question? Why did you take the quarters instead of the dollar bill?” The boy licked his cone and replied, “Because the day I take the dollar the game’s over!”

A little boy’s first day in school and a teacher was going to play a “guessing” game. She passed out items to each of the students and proceeded to ask each student what item they received. When it was the new boy, Jimmy’s turn, the teacher gave him a candy kiss. She asked “Do you know what it is?” Jimmy replied “No.” The teacher said, ” Go ahead and open it up and taste it.” Little Jimmy did so. The teacher then asked, “Now do you know what it is?” Little Jimmy said “Sill no.” The teacher said, “I’ll give you a hint… it is something your daddy wants from your mommy every morning before he goes to work.” A little girl in the back of the class jumps up and screams “Jimmy, spit it out! It’s a piece of ass!!”

The young Indian boy had spent most of his life in a quandary. He felt different yet couldn’t figure why he was just so depressed. He went to the Chief for answers. He asked the chief how his brother Red Deer Running had gotten his name. The chief answered in his typically poetic way. “When Red Deer Running was born, at the moment of his birth, the first thing his mother saw was a beautiful deer running off into the forest… and so Running Deer was named. It is the custom of our tribe to name the offspring according to the spirits in nature visiting upon the birth.” Then, the boy said to the Chief “How did my sister Thundering Bird get her name?” The chief described again, how at the moment of her birth Thundering Bird’s mother had heard a roar of thunder and looking up, saw a bird flying in the sky…” The boy asked again, how his cousin “White Crouching Bear” had been given such a name. And the chief, looking down once more at the boy, explaining the traditions of their tribe. White Bear’s mother had seen a rare white bear crouched over a stream at the moment her baby’s birth. Then he asked the boy “Why do you ask, Two Dogs Fucking?”

And the winner is…

Q: If all the Tea-Partiers were at a convention, and the convention center caught on fire, and the fire department only had time to save one person, who would be saved?
A: America.

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I didn’t fail the test, I just found 100 ways to do it wrong http://komplexify.com/blog/2010/06/04/i-didnt-fail-the-test-i-just-found-100-ways-to-do-it-wrong/ http://komplexify.com/blog/2010/06/04/i-didnt-fail-the-test-i-just-found-100-ways-to-do-it-wrong/#comments Sat, 05 Jun 2010 04:52:13 +0000 Travis http://komplexify.com/blog/?p=1700 The spirit of blog 0 out of 5 is summed up as follows: even if you have no clue about how to answer a test question, write down something… anything… in the hopes of partial credit.  Here are 0/5 insights that I can give to you, dear student, based on my test grading experience over the years.

If you’re completely at a loss, go for exotic fauna.  Strive for accuracy now!

I think some Extra Credit is in order due to my beautiful giraffe.

Remember, detail counts.

I.d.k., this is a complete shot in the dark.  As an apology, here is a crude drawing of a whale (up there).

Failing that, sci-fi is always another option.

If I had time, I would have found the vector between (1,0,-1) & (0,2,1).  Then I would have found the cross product between that vector and the vector I found in part a.  I would then plug in the point and the cross product of the vectors into

a(x-x_0)+b(y-y_0)+c(z-z_0)=0

but enjoy my pic & I’m sorry for stabbing you with my pencil.

Once again, detail counts.

Of course, if you can’t draw a cool picture, you can still demonstrate your creativity other ways.  For example, through the written arts:

I’d certainly caution you against endless ranting on an exam.  Not only will you not get points for the problem, but you’ll also piss away any good will the professor might have had for you.

And above all, if you do choose to write something down, for the sake of the Flying Spaghetti Monster, make sure it makes an iota of sense.  I knew a professor who failed a student for turning in the following work on a final exam…

…and then demanding partial credit for the work since he got the answer correct.  Be ye not so foolish.

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The moment you cheat for the sake of beauty, you know you’re an artist http://komplexify.com/blog/2010/06/03/the-moment-you-cheat-for-the-sake-of-beauty-you-know-youre-an-artist/ http://komplexify.com/blog/2010/06/03/the-moment-you-cheat-for-the-sake-of-beauty-you-know-youre-an-artist/#comments Thu, 03 Jun 2010 06:54:49 +0000 Travis http://komplexify.com/blog/?p=1695 Cheat sheets are paradoxical things when I was a student: the more thought I put into making one, the less likely I actually needed to use it during the test.  For me, designing a cheat sheet was one of the best ways to study for a test, and I often found that I would make one even for exams on which they were not allowed just to help me organize my thoughts for the exam.  As a result, as a semester proceeds I often allow students to make their own cheat sheets, in the hope that they might find them similarly useful.

Many do, but probably just as many make something like this:

Not only does this 3×5 card have a boatload of formulas and a complete duplicate solutions guide to a practice exam crammed onto it in miniscule 4 point Arial font, but if you rotate it clockwise ninety degrees you’ll see additional integration formulas written over them in pencil.  The student said that it took him something like six hours to typeset the card the night before the exam, but in the end we only got a 40% on the exam, largely because (a) he couldn’t find anything on the card and (b) since he spent all his time copying formulas onto his cheat sheet rather than, say, attempting to comprehend what any of them meant, he didn’t even know what he was supposed to look for even if he could find it.

I use this as an example in class when I tell students about cheat sheets, and encourage them to not just perform a “formula dump” on a smallish piece of paper, but to spend time thinking about what things might actually help them, and how to organize those things to make it easy to find.

This semester, many students seemed to take this to heart, and I got a number of unique and clever cheat sheets.

For example, some students don’t need lots of formulas, they just need a little bit of encouragement.  By Batman, for example:

(In case you can’t read it, Batman says Good luck on your test, TJ!  Gothan City depends on it!)

Or Darth Vader:

Other students spent time organizing their cheat sheets various ways.  If your work can be subdivided into, say, six major topics, don’t just partition your cheat sheet into six subregions. That’s soooo 2D.  Buck up and add the extra dimension:

Another version was to anthropomorphize the subject matter as, well, me:

(Apparently, this is a common theme for me.)

Speaking of cheating, albeit tangentially, I thought my students’ plagiarizing crappy solutions to two-point calculus problems (summarized here and here) was a bad enough… but plagiarizing your valedictory speech?

At Columbia University?

By stealing from a web-savvy comedian whose job is, in part, to destroy hecklers?

Sucks to be this guy.

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Yojimbo http://komplexify.com/blog/2010/05/14/yojimbo/ http://komplexify.com/blog/2010/05/14/yojimbo/#comments Fri, 14 May 2010 21:52:30 +0000 Travis http://komplexify.com/blog/?p=1617 Let’s wrap up the end of the semester in Sergio Leone fashion.

The good

Some cool stuff happened this semester.  First off, I was an invited panelist for a Section NExT discussion at our annual sectional meeting of the MAA.  It was cool round-table talk about the hows and whys of integrating twenty-first century technology into the mathematics classroom.  I also won a R2OPE Award, which is a student award given by the Residence Hall Council “to a professor that has been a positive influence in their careers” at Komplexify U.  Thanks, guys.

This site has also apparently been making the rounds this month, which is paradoxical in that I haven’t updated it at all over said time frame.  Apparently my letter to cheating students made it briefly to the front page of Reddit, and my defense of j also had a brief stab of Reddit popularity.  Perhaps for these reasons, komplexify somehow managed to get included on to this list of the Top 50 Blogs for Math Majors.  Sure, it’s at Number 50, but it’s included with the likes of of real math blogs like Division by Zero or y of x or God plays dice.

The bad

At aforementioned MAA meeting, we had a bona fide mathematical crank!  Not one of those Cantor-disproving goofballs I occasionally poke fun at; no, this guy had re-invented the whole of mathematics at an axiomatic level to a theory of “Systems and/or Sub Systems” capable of describing the properties not just to numbers and geometric constructs, but also of taxes, poetry, God, and horticulture.

Seriously:

I didn’t get to see his talk (I was the MC at an undergraduate paper session), but my friends who did see it were at a loss of words to describe anything about his rambling and incoherent presentation except for (1) a Cartesian plane coordinatized by faces of various degrees of hydrocephalusy, (2) an inordinate amount of fruit accepting numerical inputs, and (3) an equation whose solution at one point included dividing both sides by God. I did manage to snag a copy of his PowerPoints later, which include the following “God Test”

Interestingly enough, he sat with our group at the opening banquet that night.  Whereas during his presentation he was talkative to the point of tachylalia, he spent the entire time intently ignoring the other folks at the table and staring intently (and singularly) into his vegetable platter.  I can only assume he’d surmised the proof of the Riemann Hypothesis in it.

But apparently he has a website!  Go learn some Zim Mathematics and be on the cutting edge of… quantitative fruit analysis for deities, I guess.

The ugly

I’ve lost my faith. 

In the nostalgic, sepia-toned days of my youth… say, the start of this semester… I designed courses with a sizable percentage of the grade set aside for homework and projects and such.  I did so for two main reasons: (1) I set aside a lot of points for homework because I want students to do the homework and (2) it helps balance the grades against my notoriously unpleasant exams.  (I have heard it said that I honed my test-writing skills from having sold by soul to the Devil, but that’s just plain silly.  It was a low-level demon.)

My colleagues argued that this was a foolhardy approach, since (as one colleague said) “any homework assignment becomes a group assignment.”   I always argued that while cheating was inevitable among some students, it was not representative of the majority of them; moreover, those who couldn’t master the material on their own would still fail the exams (and, therefore, the class) anyway.

Unfortunately, Calculus III proved me wrong.

Don’t get me wrong… I had a number of really good Calc III students,both those who were innately quantitatively gifted, and those who struggled and worked hard to persevere.  Hell, I’d wager than most of Calc III students were honest, if not exactly hard-working.

It’s just the sheer volume and indifference displayed by the students this semester is infuriating and disheartening.  First there was the Cramster fiasco, which was followed two weeks later by the solutions manual blunder.  The former was committed by about 15% of the class, and the latter by about 20%, with 10% of the class being caught both times.  Some of the students were the expected under-performers looking for easy points, but many were talented and smart students who, surprisingly to me at least, claimed to have done the same thing all through high school.  I understand this mentality and could have even sympathized with it, except for the fact that  all of students, when I talked to them individually about it, be they good or bad, couldn’t have cared less about being caught, and brushed it off with a nonchalant “aw shucks, you caught me” attitude, which pissed… me… off.

(Of course, that apathy dissolved into professed sorrow and shame the moment I called each one of them into my office to sign their name on the Dean of Students’ official Academic Dishonesty Reporting Form.  I might have taken a moment’s bemusement from that if I wasn’t in anguish about labeling a tenth of class as cheaters on official paperwork.)

As a result, I killed the rest of the homework and labs, and let the rest of course be decided by exams and “podcast” assignments.  Students knew I was ticked, and seemed to take the Honor Code I established fairly seriously.  Finally.

So fast-forward to the last week.  One of my students — let’s call him Billy — asked if he could take the final exam early as the scheduled exam time conflicted with a military deployment.  Now our department has a no-early-finals policy, and I always stick to it on the grounds that the date of the final is clearly stated both in the syllabus and on the course website from the very the first day of class.   This  has caused me trouble before when students (or the parents) are too short-sighted to plan around it, but this didn’t seem to be the case, and so I acquiesced.

The exam was written to let students use Maple, and as a result had some strict rules governing its use, the two most paramount being (1) no online communication at all during the exam and (2) to ensure that, the manual disabling of the wireless adapter for the duration of the exam.  Long story short: whenever I wasn’t around, Billy would turn on the wireless and chat for clues (effectively sharing the exam online in the process), and then disable it before I returned.  I know this because I have it recorded using a program called Monitor.  So got to sign the form and fail the class and ruin my faith in student honesty all in one fell swoop.

Honestly… for fuck’s sake…

(And I’d sure be happy for any advice anyone has out there…)

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Apparently ambiguous times http://komplexify.com/blog/2010/04/08/apparently-ambiguous-times/ http://komplexify.com/blog/2010/04/08/apparently-ambiguous-times/#comments Thu, 08 Apr 2010 18:01:46 +0000 Travis http://komplexify.com/blog/?p=1589 My spring semester schedule is such that on certain days I have a four-hour break between my classes, which is an ideal time to get research done, although in practice most of that time is wasted on the web.  The other day I glanced up at my wall clock to gauge the time, and was surprised when I saw this:

I first I though the hour hand had fallen off the clock (which had happened to a wristwatch I owned) and was momentarily panicked at the prospect of missing my afternoon class (or rather, being 11 minutes late to it). However, a few seconds later the minute hand moved a smidge more to reveal that it had simply obscured the hour hand entirely, indicating a time of 2:11.

That got me to thinking… What are the other such “apparently ambiguous times,” times at which the hour hand and the minute hand both point in the same direction? Generalizing a bit, what are the “really apparently ambiguous times” at which the hour, minute, and second hands all point in the same direction?

It’s a little fun to figure out, and I won’t deprive you of it until after the jump.

Let’s deal with the hour and minute hand question first. Let h(t) and m(t) denote the clockwise angles (in degrees) the hour-hand and the minute-hand, respectively, make with “high noon” at hour t. In particular, the minute hand completes a full revolution in one hour, so

m(t) = 360 \cdot t,

while the hour hand only makes one-twelfth a revolution, so

\displaystyle h(t) = 360 \cdot \frac{t}{12} = 30 \cdot t.

The two hands will point in the same direction whenever there respective angle functions differ by a multiple of 360, so we need only solve the equation m(t) = h(t) + 360 k. Solving this yields

\displaystyle t = \frac{12}{11} k,

which means the two hands point in the same direction every 1 \frac{1}{11} hours. Note that one-eleventh of an hour is 5 \frac{5}{11} minutes, or five minutes and 27 \frac{3}{11} seconds.

Hence, starting from 12 o’clock, the two hands will realign every 1 hour, 5 minutes, and 27.2727… seconds, doing this a grand total of eleven times before reaching 12 o’clock again. To the nearest second, these times are:

12:00:00

1:05:27

2:10:55

3:16:22

4:21:49

5:27:16

6:32:44

7:38:11

8:43:38

9:49:05

10:54:33

How about the issue of all three hands (hour, minute, second)  in agreement?

Well, given the solution above, this is easy.  If all three hands agree, then the first two agree, so it must be at one of the 11 times indicated above.  It’s pretty easy to now sketch the appropriate second hand to determine that it’s only at high noon or the stroke of midnight that this event occurs.

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Pun-ishment http://komplexify.com/blog/2010/04/01/pun-ishment/ http://komplexify.com/blog/2010/04/01/pun-ishment/#comments Fri, 02 Apr 2010 04:33:59 +0000 Travis http://komplexify.com/blog/?p=1581

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A letter to cheating students http://komplexify.com/blog/2010/03/29/and-the-stupidity-continues-on/ http://komplexify.com/blog/2010/03/29/and-the-stupidity-continues-on/#comments Mon, 29 Mar 2010 23:59:45 +0000 Travis http://komplexify.com/blog/?p=1544 To all students  planning on copying their math solutions straight out of the solutions manual:

Please first consider the following story.

Billy needed to compute the general antiderivative of the function 1/x. Stumped, he glanced around the class, and saw that Amy, who always got things right, had written “log x”, so he copied the answer from her.  Of course, Billy was a sharp tack himself, so in order to prevent himself from being caught copying, he rewrote the answer as “timber x!”.

Now, if you happen to be a student planning on copying his or her answers from some outside source, let me be frank with you.

You are as dumb as Billy.

As proof, did you realize that Amy’s answer is wrong?

Did you realize it’s wrong for two different reasons?

No?

You are as dumb as Billy.

Fortunately, this is easy to rectify:

Seriously.  You are not smart enough to get away with cheating.

If  you cannot do a problem on your own, and you are not smart enough to seek help from the professor or a tutor or a peer, then you are not smart enough to get away with cheating.

I’ve tried to explain this to you before, but apparently it hasn’t sunk in.

Let me try again.  I’ll stick to three reasons.

Reason # 1: if you are dumb enough to plan on copying down a problem wholesale, so too are a bunch of your equally dumb classmates.  As a result, a sizable portion of the class will turn in exactly the same solution, down to the freaking formatting.  On a scale of 0 to 100, the chance of that occurring naturally is 0.  Now, whether or not you have any experience with basic probability, your math professor sure as hell does.

Don’t be a Billy!

Reason #2: if you are dumb enough to copy down an entire problem wholesale, you’re dumb enough to have no idea when the thing you’re copying is total garbage.  Earlier in the month I gave an example of the sheer stupidity of which you are capable when you attempt to cheat.  To return to the probabilistic statement, on a scale of 0 to 100, the chance of a sizable portion of the class naturally turning in exactly the same batshit-insanely stupid solution, down to the freaking formatting, is -100.

Don’t be a Billy!

Reason #3: if you are dumb enough to copy down an entire problem wholesale, you’re also dumb enough to be unable to cover your tracks should you decide to “pull a Billy.”  To wit, just a few weeks after the “cot/cosec” debacle alluded to above,  I had students turn the following problem: compute the arclength of the plane surve x = t^3, \, y = t^2 over the interval [0,2].  A quarter of them handed in the following, word for word:

There is absolutely no way to get the second equality from the first one: what did you do — cancel some of the powers of t under the radical, but nothing else? Nor is there any way to get the third equality from the second one: neither integration by parts nor substitution works, and in any case, the expression in parentheses in the fourth line is not the same thing as the expression in parentheses from the third line.  The final equality does follow from the third one, but at this point if you’re clueless enough to have bought the previous two lines, there’s no way your professor is going to believe you can track fractional powers of large integers in your head.

Of course, if you look to the answer in the back of the book, it reads

If you haven’t found the flaw yet, let me just put in in terms you’ll understand:

It’s one thing to cheat.  It’s another thing to cheat badly.  It pisses off your professors to no end, and if they’re like me, they’ll make you sign a letter of Academic Dishonesty that gets submitted with the Dean of Students and appears in big ol’ letters on your transcripts as a punishment for EPIC STUPIDITY.

Don’t be a Billy!

Sincerely,

– Every math professor you’ve ever had.

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Eponymy http://komplexify.com/blog/2010/03/17/eponymy/ http://komplexify.com/blog/2010/03/17/eponymy/#comments Wed, 17 Mar 2010 18:53:13 +0000 Travis http://komplexify.com/blog/?p=1522 It has always amused me that,despite mathematicians’ twin loves of hero worship and precision, we’re just as bad about correctly naming things as anybody else.  For example,

  • Arabic numbers were invented in India.  By Hindus.
  • The Leibniz formula \displaystyle \frac{\pi}{4} = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots was discovered before Leibniz by his contemporary James Gregory, and 300 years before either of them by Madhava of Sangamagram.
  • Euler’s number e was discovered by Jacob Bernoulli, while Euler’s formula e^{i\theta} = \cos(\theta) + i \, \sin(\theta) was discovered by Cotes.
  • l’Hospital’s Rule was discovered by Johann Bernoulli.
  • Pell’s equation was solved by Lord Brouncher
  • The Gaussian distribution was introduced by de Moivre.
  • Cramer’s Rule was discovered by Maclaurin…
  • But Maclaurin series were discovered by Taylor.
  • Burnside’s Lemma was proved by Cauchy and Frobenius…
  • But Frobenius’ Theorem by proven by  Deahna.
  • Stoke’s Theorem was discovered by Lord Kelvin.
  • The Mandlebrot set was discovered by Fatou and Juila.

Interestingly enough, these are all examples of something called Stigler’s Law, which states that “No scientific discovery is named after its original discoverer.”  It was put forth in 1980 by statistician Stephen Stigler… and is based on work in the 1940s by sociologist Robert Merton.

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Joke time! http://komplexify.com/blog/2010/03/09/joke-time-8/ http://komplexify.com/blog/2010/03/09/joke-time-8/#comments Wed, 10 Mar 2010 05:52:49 +0000 Travis http://komplexify.com/blog/?p=1502 Each semester, I offer students a last chance for extra credit by writing their favorite joke or riddle on their crib sheet, with extra credit assigned based purely on how funny I think it is. Although it’s a little late this year (these are from Fall 2009!), here are some of the better ones.

Mathy contributions

Q: What did the zero say to the eight?
A: Nice belt!

Q: Why was ten afraid of seven?
A: 7 8 9!

Q: Why was 3 afraid of \pi?
A: He was being irrational.

Q: What did the circle say to the tangent line?
A: Stop touching me!

Q: Why do you rarely find mathematicians at the beach?
A: Because they can get a tan from sine and cosine. They don’t need the sun.

Q: Why are math books always sad?
A: They have so many problems.

Q: What do you get when you add three apples to two apples?
A: A liberal arts college math problem.

Q: Why was the student’s failed exam wet?
A: It was below C level.

Q: If the natural log is \displaystyle \int_1^x \frac{dt}{t}, what’s the unnatural log?
A: Duraflame.

Q: Did you here the joke about the empty set?
A: Don’t worry. It doesn’t have a point.

Q: What’s the worst part about math jokes?
A: If you get them, you probably don’t have friends.

“I heard the government wants to put a tax on the mathematically ignorant.”
“Funny… I thought that’s what the lottery was.”

Suppose we know that if you don’t study, then you’ll fail. It then follows that

\begin{array}{r@{\,=\,}l}  \mbox{no study} & \mbox{fail} \\+ \mbox{study} & \mbox{no fail} \\ \hline \mbox{study} + \mbox{no study} & \mbox{fail} + \mbox{no fail} \\ \mbox{study}(1 + \mbox{no}) & \mbox{fail}(1 + \mbox{no}) \\ \therefore \mbox{study} & \mbox{fail} \end{array}

That is, you’re gonna fail either way. Might as well play video games.

Happy face arithmetic:

Math puns:

  • What kind of undergarments does a mermaid wear?  An algebra!
  • What did the acorn say when it grew up?  Geometry!
  • What do you call a teapot boiling on Mt. Everest?  Hypotenuse!
  • What do you get when you divide the circumference of a pumpkin by its diameter?  Pi!

What is 2 x 2?

  • A junior mathematician: 4.
  • A tenured mathematician: I don’t know what the answer is, but I can prove it exists.
  • Physicist (after consulting technical references): Between 3.98 and 4.02.
  • An engineer (after consulting a slide rule): 3.99.
  • A logician: I think you need to define 2 x 2 more precisely.
  • A philosopher: What you do mean by 2 x 2?
  • A sociologist: I don’t know, but it was nice talking about it.
  • A behavioral ecologist: A polygamous mating system.
  • A college student: 4.  (The when asked by astonished colleagues how he knew, replies “I memorized it.”)

I thought it was a great idea to name my child after \pi… until the first time he misbehaved, and I had to call him by his full name.

Students nowadays are clueless about mathematics. Why, just the other day a student came into office hours asking if General Calculus was an ancient Roman war hero.

Mathematical pick-up lines:

  • If you were cos2x, then I’s be sin2x so that you and I could be 1.
  • I wish I was your second derivative so I could fill up your concavity.
  • It’s not the magnitude of the vector, it’s how you apply the force.
  • (Hacker’s pick-up line) Solve 2 u x = 106 x2 y for u.

The only arithmetic a man needs in life: add the girl, subtract the clothes, divide the legs, and pray to God you don’t multiply.

A physicist, a mathematician and a computer scientist were discussing the relative merits of having a wife or a girlfriend.  “For sure a girlfriend is better,” says the physicist. “You still have the freedom to experiment.”  “No, no, it’s better to have a wife,” says the mathematician, “because the sense of security you get.”  “No, no, you’re both wrong,” replies the computer scientist. “It’s best to have both so that when the wife thinks you’re with the mistress and the mistress thinks you’re with your wife, you can be with your computer without anyone disturbing you.”

A professor of mathematics sent a fax to his wife: “Dear Wife, You must realize that you are 54 years old, and I have certain needs which you are no longer able to satisfy. I am otherwise happy with you as a wife, and I sincerely hope you will not be hurt or offended to learn that by the time you receive this letter, I will be at the Grand Hotel with my 18-year-old teaching assistant. I’ll be home before midnight. Your Husband.”  When he arrived at the hotel, there was a faxed letter waiting for him that read as follows: “Dear Husband, You, too, are 54 years old, and by the time you receive this letter, I will be at the Breakwater Hotel with the 18-year-old pool boy. Since you are a mathematician, you will appreciate that 18 goes into 54 more times than 54 goes into 18. Therefore, don’t wait up.  Your Wife.”

No wonder the mathematician’s marriage is falling apart: he’s into scientific computing… and she’s incalculable!

A mathematician is a device for turning coffee into theorems.
A computer scientist is a device for turning coffee into code.
An engineer is a device for turning coffee into urine.

An engineer thinks his equations are an approximation of reality.
A physicist thinks that reality is an approximation of his equations.
A mathematician doesn’t care.

Billy needed to integrate the function 1/(1+x). Stumped, he glanced around the class, and saw that Amy, who always got things right, had written “log(1+x)”, so he copied the answer from her. Of course, Billy was a sharp tack himself, so in order to prevent himself from being caught copying, he rewrote the answer as “timber(1+x)”.

One day a farmer called up an engineer, a physicist, and a mathematician and asked them to fence of the largest possible area with the least amount of fence. The engineer made the fence in a circle and proclaimed that he had the most efficient design. The physicist pointed out that fencing off half of the Earth was certainly a more efficient way to do it. The mathematician just laughed at them. He built a tiny fence around himself and said “I declare myself to be on the outside.”

“An engineer, a physicist, and a mathematician are staying at a hotel. That night, the engineer awakes to smell smoke. He goes out into the hallway and sees a fire, so he fills the trash can from his room with water and douses the fire (and most of the hallway too) before going back to sleep. Later, the physicists awakes to smell smoke. He goes out into the hallway and sees a fire. After a few mental calculations involving the flame velocity, water pressure, ballistic trajectory, and so forth, he fills the trash can from his room with a minimal amount of water and effectively douses the fire before going back to sleep. Later, the mathematician awakes to smell smoke. He foes out into the hallway and sees a fire. He also sees the trash can in his room and the sink in his bathroom and concludes “A solution exists” before going back to sleep.

Sherlock Holmes and Dr. Watson went on a camping trip. After a good meal and a bottle of wine they laid down for the night and went to sleep. Some hours later, Holmes awoke and nudged his faithful friend. “Watson, look up at the sky and tell me what you see.”  Watson replied, “I see millions and millions of stars.”  “And,” Holmes asked, “what does that tell you?”  Said Watson, “Astronomically, it tells me that there are millions of galaxies and potentially billions of planets. Astrologically, I observe that Saturn is in Leo. Horologically, I deduce that the time is approximately a quarter past three. Theologically, I can see that God is all powerful and that we are but small and insignificant and finally, meteorologically, I suspect that that we will have a beautiful day for hiking tomorrow. What does it tell you, Holmes?”  Holmes was silent for a minute, then spoke.  “It tells me, dear Watson, that some bastard has stolen our tent.”

A mathematician is flying a 6-hour nonstop flight from California to Florida. Shortly after take-off, the pilot announces that one of the engines had to be turned off due to mechanical failure. “But don’t worry,” he adds, “we’re safe, and we’ve got three engines running perfectly. The only noticeable effect will be that our flight time will be 7 hours instead of 6.” A half-hour later, the pilot announces that a second engine had to be turned off due to mechanical failure. “But don’t worry,” he adds, “we’re safe, and we’ve still got two engines running perfectly. The only noticeable effect will be that our total flight time will be 9 hours instead of 6.” Another half-hour later, the pilot announces that a third engine had to be turned off due to mechanical failure. “But don’t worry,” he adds, “even with one engine we’re still perfectly safe. However, we’re now looking at a total flight time will of 13 hours instead of 6.” “Great,” grumbles the mathematician. “At this rate, when the next engine goes it’s going to take 19 hours to get there.”

A mathematics major is walking across campus when his classmate rides up to him on a new bicycle. “Where did you get the bike from?” he asks. “It’s a Thank you present from that freshman girl I’ve been tutoring,” the math major explains. “Yesterday she called me and told that she had passed her math final and wanted to drop by to thank me in person. She arrived at my place on her bicycle. When I had let her in, she took all her clothes off, smiled, and said to take anything I wanted!” His friend stares at him for a moment, and then replies, “Good choice. I doubt the clothes would’ve have fit.”

Black holes are where God divided by zero.

Math problems? Call \displaystyle 1-800-\big[(10x)(13i)^2 \big] - \frac{\sin(x)}{2.362x} \bigg|_{x=\sqrt{e}}.

The number you have dialed is imaginary. Please rotate your telephone 90 degrees and try again.

Typical student response to seeing the limit definition of the derivative for the first time:

I also got a lot of charts this time round:

Other good ones

Q: Where did the one-legged man work?
A: IHOP.

A cop was on his horse waiting to cross the street when a little girl rode up beside him on her shiny new bike. “Nice bike you got there,” said the cop, “did you get it for Christmas?” “Yes sir,” said the little girl. The cop looked the bike over, and then handed the girl a $5 ticket for a safety violation. “Next time,” he said, “tell Santa to put a reflector light on the back of it.” The girl looked at the ticket, and then at the cop. “Nice horse you got there,” said the girl, “did you get it for Christmas?” “Sure,” said the cop, humoring her. The girl looked the horse over. “Next time,” she said, “tell Santa that the dick goes underneath the horse, not on top.”

“Bob, how’d you get that black eye?” “Well, my wife came home yesterday after shopping for cars. She told me she wanted something that can go from 0 to 160 in 2 seconds. So I got her a bathroom scale

“Honey, I bought a new toilet brush!” “I know, dear, I know. I still prefer toilet paper, though.”

Three Chinese brothers, Bu, Chu, and Fu, came to live in the United States. They decided to change their names to acclimate to the nation. Bu changed his name to Buck, and Chu changed his name to Chuck, and Fu was deported back to China.

And the winner is…

You know you’ve been a physics major too long when someone asks you “What’s new?” and you reply, “That’s c divided by \lambda.”

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