Math musings « komplexify!

03.9.2010

Joke time!

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 $\lambda$ .”

Filed under: Funny business, Funny pics, Math musings —

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03.4.2010

How do you parametrize stupidity?

I have students submit an electronic homework problem every day in my Calc III class. Today’s problem was “Find a vector valued function $f(t)$ whose graph lies on the curve $\displaystyle x^2 + 4 y^2 = 16$ .

About 25 of the 60 responses I got back read exactly as follows:

$\displaystyle \frac{x}{4} = \mathrm{cosec}$

$\displaystyle \frac{y}{2} = \cot$

$\vec{f}(t) = 4 \, \mathrm{cosec} \, \vec{i} + 2 \cot \vec{j}$

The probability of 25 students writing exactly the same derivation on a particular problem (especially one like this with infinitely many solutions) is small, and the probability that they would further divine this particular parametrization on simple inspection is smaller still. But the probability of any of them also choosing on their own to write the function $\csc$ in the style of Leonard Euler as “ $\mathrm{cosec}$ ” is zero.

Clearly students are copying their answers from somewhere, which is bad enough… but $\vec{f}(t) = 4 \, \mathrm{cosec} \, \vec{i} + 2 \cot \vec{j}$ ? That doesn’t even make sense! Even assuming they connect “cosec” with cosecant, cosecant and cotangent are functions… they require arguments before they have any meaning.

Actually, there were a few students who recognized that the lack of arguments was a problem, but apparently couldn’t quite figure out that $\vec{f}(t)$ was a function of $t$ , and so they instead wrote

$\vec{f}(t) = 4 \, \mathrm{cosec}(\vec{i}) + 2 \cot (\vec{j})$ ,

which might be even worse.

I’m not sure what I’m more offended by from this: that so many students are cheating, or that they’re doing it in such a spectacularly dumbfuck manner.

Update

It turns out that a few students fessed up to the source of the common solution, which apparently comes from a website called Cramster, in which students pay a fee to access “complete” solutions to every problem in a given textbook.

I find this vaguely amusing: here I have students whose study skills are so poor they’ll pay money to plagiarize the online solutions of someone else who apparently has no better mastery of the subject than themselves… but is making money of it nonetheless.

Capitalism and karma… who’da thunk they‘d go hand-in-hand?

Filed under: Math musings, School daze —

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03.3.2010

Movie review: Next

The movie Next has been on TV a lot lately. To say it’s a bit repetitive might be an understatement. Here’s the movie summarized in psuedocode.

movie NEXT ()
{
  set audience-satisfaction = 0;
  set plot-points-resolved = 0;
  set creepy_factor = 0;

  do while (creepy_factor < 2) {
    for (i = 1 to 100) {
       show << the mall-escape sequence from
               the movie "Minority Report";
    }
    audience_satisfaction ++;
    plot_points_resolved ++;
    show << creepy scene with 40-something Nic Cage in bed
            with 20-something Jessica Biehl;
    creepy_factor ++;
  }

  show << previous movie events invalidated
          as an extended dream sequence;
  plot_points_resolved --;
  audience_satisfaction = 0;
  return 0;
}

Filed under: Math musings, Reel life —

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03.2.2010

Fundamental theorem, part II

After Calc III, student C pulled me aside.

“Dr K,” he said, “I think I finally figured out calculus. Check this out.”

C grabbed a piece of chalk.

“At first you think math is all about functions and curves. Functions are like ‘I can do anything I want.’”

He drew a plane curve meandering across the board, strutting its stuff.

“But then calculus comes along and gives the derivative, the velocity right? And the derivative’s all like: Dude, I control you. Once you pick a starting point, I force you to go where I want you to go.”

C drew several velocity vectors along the curve’s periphery, including one at the end, effectively forcing the curve on.

“See? This function is the derivative’s bitch.”

“…..” I said.

“But then the second derivative is all like ‘Velocity, I control you! I decide where you go! You’re my bitch!’”

C sketched some acceleration vectors along the curve as well, to illustrate the point.

“And it keeps going,” C said. “Each derivative makes the derivative that came before him his bitch.”

“That’s calculus,” C concluded.

Filed under: Math musings, School daze —

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03.1.2010

Fundamental theorem

After a lecture introducing the cross product of vectors in $\mathbb{R}^3$ , student R countered me thus: “Dr. K, I’m a little worried about this cross product stuff.”

“How so?” I asked.

“Well, check this out,” R said. He then proceeded to diagram the determinant expansion formula for the cross product:

$\mathbf{u} \times \mathbf{v} = \left| \begin{array}{ccc} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ u_1 & u_2 & u_3 \\ v_1 & v_2 & v_3 \end{array} \right| = \left| \begin{array}{cc} u_2 & u_3 \\ v_2 & v_3 \end{array} \right| \mathbf{i} - \left| \begin{array}{cc} u_1 & u_3 \\ v_1 & v_3 \end{array} \right| \mathbf{j} + \left| \begin{array}{cc} u_1 & u_2 \\ v_1 & v_2 \end{array} \right| \mathbf{k}$ .

H continued: “When we work it out, we have to work out each of these little boxes of numbers–”

“2 x 2 determinants,” I offered helpfully.

“Right, each of these determinants by multiplying these two together and then subtracting these two multiplied together, like so.” He indicated each with a swooshing motion:

“Is it just me,” R said ,”or does that look just like a Jesus fish?”

“Er,” I said. The terms coincidence and conspiracy nut briefly flashed in my mind.

“And you get the cross product,” R continued, ” by computing three of these little things. And you said that any two perpendicular vectors can be crossed to get a third vector to form a ‘local frame of reference.’ So the cross product is one of three things that together form your frame of reference. Doesn’t that sound just like the Holy Trinity?”

“Huh,” I replied. I hadn’t really ever thought of that.

“And even the name of thing — the cross product? The symbol of Christianity?”

I was speechless.

“So,” R concluded, “isn’t all this vector stuff really just a plug for Christianity? And if so, shouldn’t I be excused from being forced to take calculus on First Amendment grounds?”

The next day in class, I pulled R aside.

“You raise an interesting point yesterday,” I admitted. “However, your fears are entirely unfounded. If you go on a little further in mathematics and take a course in Advanced Calculus, you’ll discover first that all the basic operations of calculus are justified using so-called $\epsilon$ - $\delta$ proofs, which are more or less arguments built up by comparing things to almost nothing. Go a little further, and you’ll even discover that all of the numbers we use in calculus are built from the empty set, which is quite literally nothing. Hence, calculus is really teaching you that one of the most effective ways to understand the world around you is to accept that it’s inherently based on nothingness.”

R considered this a moment.

“So,” I concluded, “I’m actually apparently plugging Buddhism instead.”

Filed under: Math musings, School daze —

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