GUIDE FOR LECTURERS
Proof by vigorous handwaving:
Works well in a classroom or seminar setting.
Proof by omission:
"The reader may easily supply the details" or "The other 253 cases are analogous"
Proof by deferral:
"We'll prove this later in the course".
Proof by intimidation:
"Trivial."
Proof by adverb:
"As is quite clear, the elementary aforementioned statement is obviously valid."
Proof by seduction:
"Convince yourself that this is true! "
Proof by cumbersome notation:
Best done with access to at least four alphabets and special symbols (must include greek symbols,).
Proof by obfuscation:
A long plotless sequence of true and/or meaningless syntactically related statements.
Proof by wishful citation:
The author cites the negation, converse, or generalization of a theorem from the literature to support his claims.
Proof by reference to inaccessible literature:
The author cites a simple corollary of a theorem to be found in a privately circulated memoir of the Slovenian Philological Society, 1883.
Proof by cosmology:
The negation of the proposition is unimaginable or meaningless. Popular for proofs of the existence of God.
Proof by mutual reference:
In reference A, Theorem 5 is said to follow from Theorem 3 in reference B, which is shown to follow from Corollary 6.2 in reference C, which is an easy consequence of Theorem 5 in reference A.
Wednesday, July 16, 2008
math jargon
INSTEAD OF: THEY USE:
========== ===========
truth: tautology.
criteria: rubric.
example: substantive
similar structure: homomorphic.
very similar structure: isomorphic.
same area: isometric.
arithmetic: number theory.
count: enumerate.
one: unity.
generally/specifically: globally/locally.
constant: invariant.
bonus result: corollary.
distance: metric measure.
several: a plurality.
function/argument: operator/operand.
separation/joining: bifurcation/confluence.
random: stochastic.
tends to zero: vanishes.
tip-top point: apex.
perpendicular (adj.): orthogonal.
perpendicular (n.): normal.
path: trajectory.
shift: rectilinear translation.
similar: homologous.
very similar: congruent.
change direction: perturb.
join: concatenate.
approximate to two or more places: accurate.
clever scheme: algorithm.
alphabetical order: lexical order.
========== ===========
truth: tautology.
criteria: rubric.
example: substantive
similar structure: homomorphic.
very similar structure: isomorphic.
same area: isometric.
arithmetic: number theory.
count: enumerate.
one: unity.
generally/specifically: globally/locally.
constant: invariant.
bonus result: corollary.
distance: metric measure.
several: a plurality.
function/argument: operator/operand.
separation/joining: bifurcation/confluence.
random: stochastic.
tends to zero: vanishes.
tip-top point: apex.
perpendicular (adj.): orthogonal.
perpendicular (n.): normal.
path: trajectory.
shift: rectilinear translation.
similar: homologous.
very similar: congruent.
change direction: perturb.
join: concatenate.
approximate to two or more places: accurate.
clever scheme: algorithm.
alphabetical order: lexical order.
Theorems and Proofs
1.
Premise I: Knowledge is power.
Premise II: Power corrupts.
Conclusion: Therefore, knowledge corrupts.
2.
Theorem: Women are absolutely evil
Proof:
Women are the product of time and money: women = time × money
Time is money: time = money
So women are money squared: women = money2
Money is the root of all evil: money = √evil
So women are absolutely evil: women = (√evil)2 = abs(evil)
3.Salary Theorem : The less you know, the more you make.
Proof:
Postulate 1: Knowledge is Power.
Postulate 2: Time is Money.
As every engineer knows: Power = Work / Time
And since Knowledge = Power and Time = Money
It is therefore true that Knowledge = Work / Money .
Solving for Money, we get:
Money = Work / Knowledge
Thus, as Knowledge approaches zero, Money approaches infinity, regardless of the amount of Work done.
4. Love
"Do you love your math more than me?"
"Of course not, dear - I love you much more."
"Then prove it!"
"OK... Let R be the set of all lovable objects..."
5.
Theorem. A cat has nine tails.
Proof. No cat has eight tails. Since one cat has one more tail than no cat, it must have nine tails.
Premise I: Knowledge is power.
Premise II: Power corrupts.
Conclusion: Therefore, knowledge corrupts.
2.
Theorem: Women are absolutely evil
Proof:
Women are the product of time and money: women = time × money
Time is money: time = money
So women are money squared: women = money2
Money is the root of all evil: money = √evil
So women are absolutely evil: women = (√evil)2 = abs(evil)
3.Salary Theorem : The less you know, the more you make.
Proof:
Postulate 1: Knowledge is Power.
Postulate 2: Time is Money.
As every engineer knows: Power = Work / Time
And since Knowledge = Power and Time = Money
It is therefore true that Knowledge = Work / Money .
Solving for Money, we get:
Money = Work / Knowledge
Thus, as Knowledge approaches zero, Money approaches infinity, regardless of the amount of Work done.
4. Love
"Do you love your math more than me?"
"Of course not, dear - I love you much more."
"Then prove it!"
"OK... Let R be the set of all lovable objects..."
5.
Theorem. A cat has nine tails.
Proof. No cat has eight tails. Since one cat has one more tail than no cat, it must have nine tails.
Monday, July 14, 2008
Math pick up
1. "I wish I were your derivative so I could lie Tangent to your curves! "
2. "In front of you, I feel like a constant in front of a differential operator"
3. "Please allow me to calculate the area under the curves! "
2. "In front of you, I feel like a constant in front of a differential operator"
3. "Please allow me to calculate the area under the curves! "
Mathematicians
1. ENGINEER, MATHEMATICIAN & PHYSICIST--"FIRE IN THE ROOM"
A physicist and engineer and a mathematician were sleeping in a hotel room when a fire broke out in one corner of the room. Only the engineer woke up he saw the fire, grabbed a bucket of water and threw it on the fire and the fire went out, then he filled up the bucket again and threw that bucketfull on the ashes as a safety factor, and he went back to sleep. A little later, another fire broke out in a different corner of the room and only the physicist woke up. He went over measured the intensity of the fire, saw what material was burning and went over and carefully measured out exactly 2/3 of a bucket of water and poured it on, putting out the fire perfectly; the physicist went back to sleep. A little later another fire broke out in a different corner of the room. Only the mathematician woke up. He went over looked at the fire, he saw that there was a bucket and he noticed that it had no holes in it; he turned on the faucet and saw that there was water available. He, thus, concluded that there was a solution to the fire problem and he went back to sleep.
2. WIFE OR MISTRESS
A doctor, a lawyer and a mathematician were discussing the relative merits of having a wife or a mistress.
The lawyer says: "For sure a mistress is better. If you have a wife and want a divorce, it causes all sorts of legal problems.
The doctor says: "It's better to have a wife because the sense of security lowers your stress and is good for your health.
The mathematician says: " You're both wrong. 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 do some mathematics.
3. SCOTTISH SHEEP
An astronomer, a physicist and a mathematician are on a train in Scotland. The astronomer looks out of the window, sees a black sheep standing in a field, and remarks, "How odd. Scottish sheep are black." "No, no, no!" says the physicist. "Only some Scottish sheep are black." The mathematician rolls his eyes at his companions' muddled thinking and says, "In Scotland, there is at least one field, containing at least one sheep, at least one side of which appears black from here."
4. AREA = OUTSIDE THE FENCE
A sociologist, a physicist and a mathematician are all given equal amounts of fencing, and are asked to enclose the greatest area. The sociologist pauses for a moment and decides to enclose a square area with his fence. The physicist, realizing he can fence off a greater amount of land with the same amount of fencing, promptly sets his fence in the form of a circle, and smiles. "I'd like to see you beat that!" he says to the mathematician. The mathematician, in response, takes a very small piece of his own fencing, and wraps it around himself, proclaiming, "I define my area to be that outside of the fence!"
5. REDUCING THE PROBLEM TO A PREVIOUSLY SOLVED ONE (aka simplification)
A physicist and a mathematician are sitting in a faculty lounge. Suddenly, the coffee machine catches on fire. The physicist grabs a bucket and leap towards the sink, filled the bucket with water and puts out the fire. Second day, the same two sit in the same lounge. Again, the coffee machine catches on fire. This time, the mathematician stands up, got a bucket, hands the bucket to the physicist, thus reducing the problem to a previously solved one!
(because it can be proven that a physicist can put off the fire!).
6. LET N BE WHATEVER U LIKE
A Mathematician (M) and an Engineer (E) attend a lecture by a Physicist. The topic concerns Kulza-Klein theories involving physical processes that occur in spaces with dimensions of 9, 12 and even higher. The M is sitting, clearly enjoying the lecture, while the E is frowning and looking generally confused and puzzled. By the end the E has a terrible headache. At the end, the M comments about the wonderful lecture.
E: "How do you understand this stuff?"
M: "I just visualize the process"
E: "How can you POSSIBLY visualize something that occurs in 9-dimensional space?"
M: "Easy, first visualize it in N-dimensional space, then let N be 9"
7. MATHEMATICIANS (as abstract as always) !!
A graduate student of mathematics who used to come to the University on foot every day arrives one day on a fancy new bicycle. "Where did you get the bike from?" his friends asked. "It's a `thank you' present", he explains, "from that freshman girl I've been tutoring. 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 at me, and said: `You can get from me whatever you desire!'" One of his friends remarks: "You made a really smart choice when you took the bicycle." "Yeah", another friend adds, "just imagine how silly you would have looked in a girl's clothes - and they wouldn't have fit you anyway!"
8.
A physicist and engineer and a mathematician were sleeping in a hotel room when a fire broke out in one corner of the room. Only the engineer woke up he saw the fire, grabbed a bucket of water and threw it on the fire and the fire went out, then he filled up the bucket again and threw that bucketfull on the ashes as a safety factor, and he went back to sleep. A little later, another fire broke out in a different corner of the room and only the physicist woke up. He went over measured the intensity of the fire, saw what material was burning and went over and carefully measured out exactly 2/3 of a bucket of water and poured it on, putting out the fire perfectly; the physicist went back to sleep. A little later another fire broke out in a different corner of the room. Only the mathematician woke up. He went over looked at the fire, he saw that there was a bucket and he noticed that it had no holes in it; he turned on the faucet and saw that there was water available. He, thus, concluded that there was a solution to the fire problem and he went back to sleep.
2. WIFE OR MISTRESS
A doctor, a lawyer and a mathematician were discussing the relative merits of having a wife or a mistress.
The lawyer says: "For sure a mistress is better. If you have a wife and want a divorce, it causes all sorts of legal problems.
The doctor says: "It's better to have a wife because the sense of security lowers your stress and is good for your health.
The mathematician says: " You're both wrong. 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 do some mathematics.
3. SCOTTISH SHEEP
An astronomer, a physicist and a mathematician are on a train in Scotland. The astronomer looks out of the window, sees a black sheep standing in a field, and remarks, "How odd. Scottish sheep are black." "No, no, no!" says the physicist. "Only some Scottish sheep are black." The mathematician rolls his eyes at his companions' muddled thinking and says, "In Scotland, there is at least one field, containing at least one sheep, at least one side of which appears black from here."
4. AREA = OUTSIDE THE FENCE
A sociologist, a physicist and a mathematician are all given equal amounts of fencing, and are asked to enclose the greatest area. The sociologist pauses for a moment and decides to enclose a square area with his fence. The physicist, realizing he can fence off a greater amount of land with the same amount of fencing, promptly sets his fence in the form of a circle, and smiles. "I'd like to see you beat that!" he says to the mathematician. The mathematician, in response, takes a very small piece of his own fencing, and wraps it around himself, proclaiming, "I define my area to be that outside of the fence!"
5. REDUCING THE PROBLEM TO A PREVIOUSLY SOLVED ONE (aka simplification)
A physicist and a mathematician are sitting in a faculty lounge. Suddenly, the coffee machine catches on fire. The physicist grabs a bucket and leap towards the sink, filled the bucket with water and puts out the fire. Second day, the same two sit in the same lounge. Again, the coffee machine catches on fire. This time, the mathematician stands up, got a bucket, hands the bucket to the physicist, thus reducing the problem to a previously solved one!
(because it can be proven that a physicist can put off the fire!).
6. LET N BE WHATEVER U LIKE
A Mathematician (M) and an Engineer (E) attend a lecture by a Physicist. The topic concerns Kulza-Klein theories involving physical processes that occur in spaces with dimensions of 9, 12 and even higher. The M is sitting, clearly enjoying the lecture, while the E is frowning and looking generally confused and puzzled. By the end the E has a terrible headache. At the end, the M comments about the wonderful lecture.
E: "How do you understand this stuff?"
M: "I just visualize the process"
E: "How can you POSSIBLY visualize something that occurs in 9-dimensional space?"
M: "Easy, first visualize it in N-dimensional space, then let N be 9"
7. MATHEMATICIANS (as abstract as always) !!
A graduate student of mathematics who used to come to the University on foot every day arrives one day on a fancy new bicycle. "Where did you get the bike from?" his friends asked. "It's a `thank you' present", he explains, "from that freshman girl I've been tutoring. 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 at me, and said: `You can get from me whatever you desire!'" One of his friends remarks: "You made a really smart choice when you took the bicycle." "Yeah", another friend adds, "just imagine how silly you would have looked in a girl's clothes - and they wouldn't have fit you anyway!"
8.
short math jokes
1. Q: What does the zero say to the the eight?
A: Nice belt!
2.
In Zimbabwe, due to inflation, pi has shot to 3,142,000 from 3.142 !!!
3. Q: How does a mathematician induce good behavior in her children?
A: I've told you n times, if i tell you n+1 times...
4. "Students nowadays are so clueless", the math professor complains to a colleague.
"Yesterday, a student came to my office hours and wanted to know if General
Calculus was a Roman war hero...
5. Q: What do you get if you cross an elephant with a zebra.
A: Elephant zebra sin theta
6.
A mathematician organizes a lottery in which the prize is an infinite amount of money. When the winning ticket is drawn, and the jubilant winner comes to claim his prize, the mathematician explains the mode of payment: "1 dollar now, 1/2 dollar next week, 1/3 dollar the week after that..."
7.
When a statistician passes the airport security check, they discover a bomb in his bag. He explains. "Statistics shows that the probability of a bomb being on an airplane is 1/1000. However, the chance that there are two bombs at one plane is 1/1000000. So, I am much safer..."
8.
A constant function and e^x are walking on Broadway. Then suddenly the constant function sees a differential operator approaching and runs away. So e^x follows him and asks why the hurry. "Well, you see, there's this differential operator coming this way, and when we meet, he'll differentiate me and nothing will be left of me...!" "Ah," says e^x, "he won't bother ME, I'm e to the x!" and he walks on. Of course he meets the differential operator after a short distance.
Exponent x : "Hi, I'm e^x"
differrential operator: "Too bad, I'm d/dy"
9.
"The number you have dialed is imaginary. Please rotate your phone 90 degrees and try again."
10.
The limit as 3 tends to 4 of 3^2 is 16.
11.
A woman in a bar tries to pick up a mathematician.
"How old, do you think, am I?" she asks coyly.
"Well - 18 by that fire in your eyes, 19 by that glow on your cheeks, 20 by that radiance of your face, and adding that up is something you can probably do for yourself..."
12.
"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..."
13.
TWO sodium atoms are walking from a VCT. All of a sudden, one stops and turns to its friend looking worried:
Na(1)- "Oh No... I think I've lost an Electron!"
Na(2)- "What... are you sure?"
Na(1)- "Yes, I'm Positive!"
A: Nice belt!
2.
In Zimbabwe, due to inflation, pi has shot to 3,142,000 from 3.142 !!!
3. Q: How does a mathematician induce good behavior in her children?
A: I've told you n times, if i tell you n+1 times...
4. "Students nowadays are so clueless", the math professor complains to a colleague.
"Yesterday, a student came to my office hours and wanted to know if General
Calculus was a Roman war hero...
5. Q: What do you get if you cross an elephant with a zebra.
A: Elephant zebra sin theta
6.
A mathematician organizes a lottery in which the prize is an infinite amount of money. When the winning ticket is drawn, and the jubilant winner comes to claim his prize, the mathematician explains the mode of payment: "1 dollar now, 1/2 dollar next week, 1/3 dollar the week after that..."
7.
When a statistician passes the airport security check, they discover a bomb in his bag. He explains. "Statistics shows that the probability of a bomb being on an airplane is 1/1000. However, the chance that there are two bombs at one plane is 1/1000000. So, I am much safer..."
8.
A constant function and e^x are walking on Broadway. Then suddenly the constant function sees a differential operator approaching and runs away. So e^x follows him and asks why the hurry. "Well, you see, there's this differential operator coming this way, and when we meet, he'll differentiate me and nothing will be left of me...!" "Ah," says e^x, "he won't bother ME, I'm e to the x!" and he walks on. Of course he meets the differential operator after a short distance.
Exponent x : "Hi, I'm e^x"
differrential operator: "Too bad, I'm d/dy"
9.
"The number you have dialed is imaginary. Please rotate your phone 90 degrees and try again."
10.
The limit as 3 tends to 4 of 3^2 is 16.
11.
A woman in a bar tries to pick up a mathematician.
"How old, do you think, am I?" she asks coyly.
"Well - 18 by that fire in your eyes, 19 by that glow on your cheeks, 20 by that radiance of your face, and adding that up is something you can probably do for yourself..."
12.
"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..."
13.
TWO sodium atoms are walking from a VCT. All of a sudden, one stops and turns to its friend looking worried:
Na(1)- "Oh No... I think I've lost an Electron!"
Na(2)- "What... are you sure?"
Na(1)- "Yes, I'm Positive!"
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