19. RIDING THE HOT AIR WAVE/PARTICLES
Two Physicists were riding in a hot air balloon and were blown off course sailing over a mountain trail, and were completely lost. They spotted a jogger running on the trail and they shouted "Can you tell us where we are?" After a few minutes, the jogger yelled back "You're up in a balloon." One physicists said to the other, "Just our luck to run into a mathematician". "How do you know he was a mathematician?" asked the other. "Well, in the first place he took a long time to answer; second, his answer was 100% correct and third ,it was totally useless."
If a ham sandwich is better than nothing and Nothing is better than Life itself, does that mean that a ham sandwich is better than Life itself?
This scientist is doing some theoretical research, real heavy stuff, eventually he starts to lose it and he begins running around, screaming to everyone "i'm going to integrate you and differentiate you, i'm going to integrate you and differentiate you". He does this long enough for some authorities to notice, and they decide to lock him up in a nuthouse. Well, it turns out that, in another part of the world, another theorist has begun to do the same thing. Out of pure coincidence this researcher gets sent to the *same* nuthouse. At this nuthouse, these two researchers continue on their mad rantings, and it is only a matter of time before they run into each other. One says: "i'm going to integrate you and differentiate you. i'm going to integrate you and differentiate you". The other researcher pulls open his shirt, a la superman, and screams "that's okay, i'm e to-the x !"
When God created the world, the animals came up to Him, two by two. To each pair, God said "Go forth and multiply."
Eventually a pair of snakes came up to Him. "Go forth and multiply," said God.
"We can't," the snakes replied. "We're adders."
Unperturbed, God took a large block of wood, split it in half, and put legs on it. Laying it on the ground, He placed the adders on top of it. "Go forth and multiply," He repeated.
"We told you," protested the snakes. "We're adders."
God sighed. "Didn't anyone ever tell you that adders can multiply on a log table?"
Why did the function cross the road?
Because it was defined on both sides and continuous!
never say "N factorial", simply scream "N" at the top of your lungs.
"The number you have dialed is imaginary. Please rotate your phone 90 degrees and try again."
Definitions of Terms Commonly Used in Higher MathThe following is a guide to the weary student of mathematics who isoften confronted with terms which are commonly used but rarelydefined. In the search for proper definitions for these terms wefound 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 whoerase your memory tapes after every test...
WLOG (Without Loss Of Generality): I'm not about to do all thepossible 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 beable 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 itdown 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 regularproof, but it requires two extra years of course work just tounderstand the terms.
ELEGANT PROOF: Requires no previous knowledge of the subject matterand 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, andif I say that it means the other thing, and if I say the otherthing...
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, youcan'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 Imake a mistake.
PROCEED FORMALLY: Manipulate symbols by the rules without any hint oftheir 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 mathcourses).
PROOF OMITTED: Trust me, It's true.
"Psst, c'mere," said the shifty-eyed man wearing a long black trenchcoat, as he beckoned me off the rainy street into a damp darkalley. I followed."What are you selling?" I asked."Geometrical algebra drugs.""Huh!?""Geometry drugs. Ya got your uppers, your downers, your sidewaysers, yourinside-outers...""Stop right there," I interrupted. "I've never heard of inside-outers." "Oh, man, you'll love 'em. Makes you feel like M.C. ever-lovin'Escher on a particularly weird day.""Go on...""OK, your inside-outers, your arbitrary bilinear mappers, and here,heh, here are the best ones," he said, pulling out a large clearbottle of orange pills."What are those, then?" I asked."Givens transformers. They'll rotate you about more planes than youeven knew existed.""Sounds gross. What about those bilinear mappers?""There's a whole variety of them. Here's one you'll love -- they callit 'One Over Z' on the street. Take one of these little bad boys andyou'll be on speaking terms with the Point at Infinity."
The four branches of arithmetic - ambition, distraction, uglification and derision. (Lewis Caroll: "Alice in Wonderland")
: MATHEMATICS PURITY TEST Count the number of yes's, subtract from 60, and divide by 0.6.
1) Have you ever been excited about math?
2) Had an exciting dream about math?
3) Made a mathematical calculation?
4) Manipulated the numerator of an equation?
5) Manipulated the denominator of an equation?
6) On your first problem set?
7) Worked on a problem set past 3:00 a.m.?
8) Worked on a problem set all night?
9) Had a hard problem?
10) Worked on a problem continuously for more than 30 minutes?
11) Worked on a problem continuously for more than four hours?
12) Done more than one problem set on the same night (i.e. both started and finished them)?
13) Done more than three problem sets on the same night?
14) Taken a math course for a full year?
15) Taken two different math courses at the same time?
16) Done at least one problem set a week for more than four months?
17) Done at least one problem set a night for more than one month (weekends excluded)?
18) Done a problem set alone?
19) Done a problem set in a group of three or more?
20) Done a problem set in a group of 15 or more?
21) Was it mixed company?
22) Have you ever inadvertently walked in upon people doing a problem set?
23) And joined in afterwards?
24) Have you ever used food doing a problem set?
25) Did you eat it all?
26) Have you ever had a domesticated pet or animal walk over you while you were doing a problem set?
27) Done a problem set in a public place where you might be discovered?
28) Been discovered while doing a problem set?
29) Have you ever applied your math to a hard science?
30) Applied your math to a soft science?
31) Done an integration by parts?
32) Done two integration by parts in a single problem?
33) Bounded the domain and range of your function?
34) Used the domination test for improper integrals?
35) Done Newton's Method?
36) Done the Method of Frobenius?
37) Used the Sandwich Theorem?
38) Used the Mean Value Theorem?
39) Used a Gaussian surface?
40) Used a foreign object on a math problem (eg: calculator)?
41) Used a program to improve your mathematical technique (eg: MACSYMA)?
42) Not used brackets when you should have?
43) Integrated a function over its full period?
44) Done a calculation in three-dimensional space?
45) Done a calculation in n-dimensional space?
46) Done a change of bases?
47) Done a change of bases specifically in order to magnify your vector?
48) Worked through four complete bases in a single night (eg: using the Graham-Schmidt method)?
49) Inserted a number into an equation?
50) Calculated the residue of a pole?
51) Scored perfectly on a math test?
52) Swallowed everything your professor gave you?
53) Used explicit notation in your problem set?
54) Purposefully omitted important steps in your problem set?
55) Padded your own problem set?
56) Been blown away on a test?
57) Blown away your professor on a test?
58) Have you ever multiplied 23 by 3?
59) Have you ever bounded your Bessel function so that the membrane did not shoot to infinity?
60) Have you ever understood the following quote: "The relationship between Z^0 to C_0, B_0, and H_0 is an example of a general principle which we have encountered: the kernel of the adjoint of a linear transformation is both the annihilator space of the image of the transformation and also the dual space of the quotient of the space of which the image is a subspace by the image subspace." (Shlomo & Bamberg's _A "Course" in Mathematics for Students of Physics_)