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Several students were asked the following problem:

Prove that all odd integers are prime.

Well, the first student to try to do this was a math student. He says "Hmmm... Well, 1 is prime, 3 is prime, 5 is prime, and by induction, we have that all the odd integers are prime."

Of course, there are some jeers from some of his friends. The physics student then said, "I'm not sure of the validity of your proof, but I think I'll try to prove it by experiment." He continues, "Well, 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is ... uh, 9 is an experimental error, 11 is prime, 13 is prime... Well, it seems that you're right."

The third student to try it was the engineering student, who responded, "Well, actually, I'm not sure of your answer either. Let's see... 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is ..., 9 is ..., well if you approximate, 9 is prime, 11 is prime, 13 is prime... Well, it does seem right."

Not to be outdone, the computer science student comes along and says "Well, you two sort've got the right idea, but you'd end up taking too long doing it. I've just whipped up a program to REALLY go and prove it..." He goes over to his terminal and runs his program. Reading the output on the screen he says, "1 is prime, 1 is prime, 1 is prime, 1 is prime...."

and here's another version of the same joke:

Mathematician: 3 is a prime, 5 is a prime, 7 is a prime, 9 is not a prime - counter-example - claim is false.

Physicist: 3 is a prime, 5 is a prime, 7 is a prime, 9 is an experimental error, 11 is a prime, ...

Engineer: 3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime, 11 is a prime, ...

Computer scientist: 3's a prime, 5's a prime, 7's a prime, 7's a prime, 7's a prime, ...

Computer scientist using Unix: 3's a prime, 5's a prime, 7's a prime, segmentation fault

Theorem: a cat has nine tails.

Proof:

No cat has eight tails. A cat has one tail more than no cat. Therefore, a cat has nine tails.

An assemblage of the most gifted minds in the world were all posed the following question:

"What is 2 * 2 ?"

The engineer whips out his slide rule (so it's old) and shuffles it back and forth, and finally announces "3.99".

The physicist consults his technical references, sets up the problem on his computer, and announces "it lies between 3.98 and 4.02".

The mathematician cogitates for a while, oblivious to the rest of the world, then announces: "I don't what the answer is, but I can tell you, an answer exists!".

Philosopher: "But what do you _mean_ by 2 * 2 ?"

Logician: "Please define 2 * 2 more precisely."

Accountant: Closes all the doors and windows, looks around carefully, then asks "What do you _want_ the answer to be?"

Computer Hacker: Breaks into the NSA super-computer and gives the answer.

Three men are in a hot-air balloon. Soon, they find themselves lost in a canyon somewhere. One of the three men says, "I've got an idea. We can call for help in this canyon and the echo will carry our voices far."

So he leans over the basket and yells out, "Helllloooooo! Where are we?" (They hear the echo several times.)

15 minutes later, they hear this echoing voice: "Helllloooooo! You're lost!!"

One of the men says, "That must have been a mathematician."

Puzzled, one of the other men asks, "Why do you say that?"

The reply: "For three reasons. (1) he took a long time to answer, (2) he was absolutely correct, and (3) his answer was absolutely useless."

There are three kinds of people in the world; those who can count and those who can't.

And the related:

There are two groups of people in the world; those who believe that the world can be divided into two groups of people, and those who don't.

And then:

There are two groups of people in the world: Those who can be categorized into one of two groups of people, and those who can't.

And also:

The world is divided into two classes: people who say "The world is divided into two classes", and people who say The world is divided into two classes: people who say: "The world is divided into two classes", and people who say: The world is divided into two classes: people who say ...

97.3% of all statistics are made up.

TOP TEN EXCUSES FOR NOT DOING THE MATH HOMEWORK

1. I accidentally divided by zero and my paper burst into flames.

2. Isaac Newton's birthday.

3. I could only get arbitrarily close to my textbook. I couldn't actually reach it.

4. I have the proof, but there isn't room to write it in this margin.

5. I was watching the World Series and got tied up trying to prove that it converged.

6. I have a solar powered calculator and it was cloudy.

7. I locked the paper in my trunk but a four-dimensional dog got in and ate it.

8. I couldn't figure out whether i am the square of negative one or i is the square root of negative one.

9. I took time out to snack on a doughnut and a cup of coffee. I spent the rest of the night trying to figure which one to dunk.

10. I could have sworn I put the homework inside a Klein bottle, but this morning I couldn't find it.

Definitions of Terms Commonly Used in Higher Math

The following is a guide to the weary student of mathematics who is often confronted with terms which are commonly used but rarely defined. In the search for proper definitions for these terms we found no authoritative, nor even recognized, source. Thus, we followed the advice of mathematicians handed down from time immortal: "Wing It."

CLEARLY: I don't want to write down all the "in- between" steps.

TRIVIAL: If I have to show you how to do this, you're in the wrong class.

OBVIOUSLY: I hope you weren't sleeping when we discussed this earlier, because I refuse to repeat it.

RECALL: I shouldn't have to tell you this, but for those of you who erase your memory tapes after every test...

WLOG (Without Loss Of Generality): I'm not about to do all the possible cases, so I'll do one and let you figure out the rest.

IT CAN EASILY BE SHOWN: Even you, in your finite wisdom, should be able to prove this without me holding your hand.

CHECK or CHECK FOR YOURSELF: This is the boring part of the proof, so you can do it on your own time.

SKETCH OF A PROOF: I couldn't verify all the details, so I'll break it down into the parts I couldn't prove.

HINT: The hardest of several possible ways to do a proof.

BRUTE FORCE (AND IGNORANCE): Four special cases, three counting arguments, two long inductions, "and a partridge in a pair tree."

SOFT PROOF: One third less filling (of the page) than your regular proof, but it requires two extra years of course work just to understand the terms.

ELEGANT PROOF: Requires no previous knowledge of the subject matter and is less than ten lines long.

SIMILARLY: At least one line of the proof of this case is the same as before.

CANONICAL FORM: 4 out of 5 mathematicians surveyed recommended this as the final form for their students who choose to finish.

TFAE (The Following Are Equivalent): If I say this it means that, and if I say that it means the other thing, and if I say the other thing...

BY A PREVIOUS THEOREM: I don't remember how it goes (come to think of it I'm not really sure we did this at all), but if I stated it right (or at all), then the rest of this follows.

TWO LINE PROOF: I'll leave out everything but the conclusion, you can't question 'em if you can't see 'em.

BRIEFLY: I'm running out of time, so I'll just write and talk faster.

LET'S TALK THROUGH IT: I don't want to write it on the board lest I make a mistake.

PROCEED FORMALLY: Manipulate symbols by the rules without any hint of their true meaning (popular in pure math courses).

QUANTIFY: I can't find anything wrong with your proof except that it won't work if x is a moon of Jupiter (Popular in applied math courses).

PROOF OMITTED: Trust me, It's true.

Some famous mathematician was to give a keynote speech at a conference. Asked for an advance summary, he said he would present a proof of Fermat's Last Theorem -- but they should keep it under their hats. When he arrived, though, he spoke on a much more prosaic topic. Afterwards the conference organizers asked why he said he'd talk about the theorem and then didn't. He replied this was his standard practice, just in case he was killed on the way to the conference.

What do you call a young eigensheep?

A lamb, duh!!!

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 made a long, straight line and proclaimed 'We can assume the length is infinite...' and 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 thinks that his equations are an approximation to reality. A physicist thinks reality is an approximation to his equations. A mathematician doesn't care.

Why is the number 10 afraid of seven? -- because seven ate nine.

A group of scientists were doing an investigation into problem-solving techniques, and constructed an experiment involving a physicist, an engineer, and a mathematician.

The experimental apparatus consisted of a water spigot and two identical pails, one of which was fastened to the ground ten feet from the spigot.

Each of the subjects was given the second pail, empty, and told to fill the pail on the ground.

The physicist was the first subject: he carried his pail to the spigot, filled it there, carried it full of water to the pail on the ground, and poured the water into it. Standing back, he declared, "There: I have solved the problem."

The engineer and the mathematician each approached the problem similarly. Upon finishing, the engineer noted that the solution was exact, since the volumes of the pails were equal. The mathematician merely noted that he had proven that a solution exists.

Now, the experimenters altered the parameters of the task a bit: the pail on the ground was still empty, but the subjects were presented with a pail that was already half-filled with water.

The physicist immediately carried his pail over to the one on the ground, emptied the water into it, went back to the spigot, *filled* the pail, and finally emptied the entire contents into the pail on the ground, overflowing it and spilling some of the water. Upon finishing, he commented that the problem should have been better stated.

The engineer, in turn, thought for some time before going into action. He then took his half-filled pail to the spigot, filled it to the brim, and filled the pail on the ground from it. Again he noted that the problem had an exact solution, which of course he had found.

The mathematician thought for a long time before stirring. At last he stood up, emptied his pail onto the ground, and declared, "The problem has been reduced to one already solved."

Three Laws of Thermodynamics (paraphrased):

First Law: You can't get anything without working for it.

Second Law: The most you can accomplish by work is to break even.

Third Law: You can't break even.

The upgrade path to the most powerful and satisfying computer:

* Pocket calculator

* Commodore Pet / Apple II / TRS 80 / Commodore 64 / Timex Sinclair (Choose any of the above)

* IBM PC

* Fastest workstation of the time (HP, DEC, IBM, SGI: your choice)

* Minicomputer (HP, DEC, IBM, SGI: your choice)

* Mainframe (IBM, Cray, DEC: your choice)

And then you reach the pinnacle of modern computing facilities:

********************************************************* ******* G R A D U A T E S T U D E N T S ******** *********************************************************

Yes, you just sit back and do all of your computing through lowly graduate students. Imagine the advantages:

* Multi-processing, with as many processes as you have students. You can easily add more power by promising more desperate undergrads that they can indeed escape college through your guidance. Special student units can even handle several tasks *on*their*own*!

* Full voice recognition interface. Never touch a keyboard or mouse again. Just mumble commands and they *will* be understood (or else!).

* No hardware upgrades and no installation required. Every student comes complete with all hardware necessary. Never again fry a chip or $10,000 board by improper installation! Just sit that sniveling student at a desk, give it writing utensils (making sure to point out which is the dangerous end) and off it goes.

* Low maintenance. Remember when that hard disk crashed in your Beta 9900, causing all of your work to go the great bit bucket in the sky? This won't happen with grad. students. All that is required is that you give them a good *whack!* upside the head when they are acting up, and they will run good as new.

* Abuse module. Imagine yelling expletives at your computer. Doesn't work too well, because your machine just sits there and ignores you. Through the grad student abuse module you can put the fear of god in them, and get results to boot!

* Built-in lifetime. Remember that awful feeling two years after you bought your GigaPlutz mainframe when the new faculty member on the block sneered at you because his FeelyWup workstation could compute rings around your dinosaur? This doesn't happen with grad. students. When they start wearing and losing productivity, simply give them the PhD and boot them out onto the street to fend for themselves. Out of sight, out of mind!

* Cheap fuel: students run on Coca Cola (or the high-octane equivalent -- Jolt Cola) and typically consume hot spicy chinese dishes, cheap taco substitutes, or completely synthetic macaroni replacements. It is entirely unnecessary to plug the student into the wall socket (although this does get them going a little faster from time to time).

* Expansion options. If your grad. students don't seem to be performing too well, consider adding a handy system manager or software engineer upgrade. These guys are guaranteed to require even less than a student, and typically establish permanent residence in the computer room. You'll never know they are around! (Which you certainly can't say for an AXZ3000-69 150gigahertz space-heater sitting on your desk with its ten noisy fans....) [Note however that the engineering department still hasn't worked out some of the idiosyncratic bugs in these expansion options, such as incessant muttering at nobody in particular, occasionaly screaming at your grad. students, and posting ridiculous messages on world-wide bulletin boards.]

So forget your Babbage Engines and abacuses (abaci?) and PortaBooks and DEK 666-3D's and all that other silicon garbage. The wave of the future is in wetware, so invest in graduate students today! You'll never go back!

Dean, to the physics department. "Why do I always have to give you guys so much money, for laboratories and expensive equipment and stuff. Why couldn't you be like the math department - all they need is money for pencils, paper and waste-paper baskets. Or even better, like the philosophy department. All they need are pencils and paper."

A mathematician, a physicist, and an engineer were travelling through Scotland when they saw a black sheep through the window of the train.

"Aha," says the engineer, "I see that Scottish sheep are black."

"Hmm," says the physicist, "You mean that some Scottish sheep are black."

"No," says the mathematician, "All we know is that there is at least one sheep in Scotland, and that at least one side of that one sheep is black!"

What is "pi"?

Mathematician: Pi is the number expressing the relationship between the circumference of a circle and its diameter.

Physicist: Pi is 3.1415927 plus or minus 0.00000005

Engineer: Pi is about 3.