A pastor, a doctor, and a mathematician were stuck behind a slow foursome while playing golf. The greenskeeper noticed their frustration and explained to them, “The slow group ahead of you is a bunch of blind firemen. They lost their sight saving our clubhouse from a fire last year, so we always let them play for free.”
The pastor responded, “That’s terrible! I’ll say a prayer for them.”
The doctor said, “I’ll contact my ophthalmologist friends and see if there isn’t something that can be done for them.”
And the mathematician asked, “Why can’t these guys play at night?”
I love a good math limerick. And, no, “Nantucket” is never a destination for some mathematician in a good math limerick. Here’s a new one I discovered online:
For the laymen,
The integral sec y dy -> (read as “seek y dee y”)
From zero to one-sixth of pi
Is the log to base e
Of the square-root of three
Times the sixty fourth power of i.
This rivals my favorite limerick of all time. And I can’t talk about limericks without repeating it for you:
Again, for the unconverted,
The integral z-squared dz
From one to the cube root of 3
Times the cosine
Of three pi over nine
Is the log of the cube root of e.
“It’s gold, Jerry! Gold!”
Ok, so I know that several of the readers of this blog will enjoy this, several others will groan as they read, and many others will just roll their eyes at the lack of humor below. I’m posting anyways.
And for the record, at one time, I have laughed out loud at every one of these. There, I confessed.
Q: How does a mathematician induce good behavior in his children?
A: `I've told you n times, I've told you n+1 times...'
A mathematician and his best friend, an engineer, attend a public lecture on geometry in thirteen-dimensional space.
"How did you like it?" the mathematician wants to know after the talk.
"My head's spinning", the engineer confesses. "How can you develop any intuition for thirteen-dimensional space?"
"Well, it's not even difficult. All I do is visualize the situation in arbitrary N-dimensional space and then set N = 13."
One day, Jesus said to his disciples: "The Kingdom of Heaven is like 3x squared plus 8x minus 9."
A man who had just joined the disciples looked very confused and asked Peter: "What, on Earth, does he mean by that?"
Peter replied: "Don't worry - it's just another one of his parabolas."
[I’ve heard the ones about the Abelian Grape and Zorn’s Lemon, but this one was new to me]
Q: What is normed, complete, and yellow?
A: A Bananach space...
A mathematician has spent years trying to prove the Riemann hypothesis - without success. Finally, he decides to sell his soul to the devil in exchange for a proof. The devil promises to deliver a proof within four weeks.
Four weeks pass, but nothing happens. Half a year later, the devil shows up again - in a rather gloomy mood.
"I'm sorry", he says. "I couldn't prove the Riemann hypothesis either. But" - and his face lightens up - "I think I found a really interesting lemma..."
That’s enough for now. Are you smiling yet or just confused?
Following in the vein of my earlier post, here’s another oldie, but goodie:
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, here it is again.
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.
ONE MAY SHOW: One did, his name was Gauss.
IT IS WELL KNOWN: See “Mathematische Zeitschrift”, vol XXXVI, 1892.
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 the details, so I’ll break it down into parts I couldn’t prove.
HINT: The hardest of several possible ways to do a proof.
BRUTE FORCE: 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, 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 the answer.
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, then the rest of this follows.
TWO LINE PROOF: I’ll leave out everything but the conclusion.
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 because I’ll make a mistake.
PROCEED FORMALLY: Manipulate symbols by the rules without any hint of their true meaning.
QUANTIFY: I can’t find anything wrong with your proof except that it won’t work if x is 0.
FINALLY: Only ten more steps to go…
Q.E.D. : T.G.I.F.
PROOF OMITTED: Trust me, it’s true.
If you ask an average person on the street what is the highest level of mathematics, the most common answer would probably be Calculus. There might even be a few throwing College Algebra out there as fairly advance. However, if you ask a math major or engineering student the question of what is the lowest level of mathematics, the foundation of the mathematics they use, the most common answer would likely be Calculus. Why the disparity?
The mathematics that is taught from kindergarten through secondary is often limited to procedural techniques to solve specific problem types without recognizing that advanced mathematics is all about recognizing patterns and using axioms, definitions, and theorems to formalize those patterns thereby leading to new patterns.
So, of course, in upper level mathematics we spend a great deal of time moving from procedural mathematics, to proving theorems, to developing new theorems. Unfortunately, the rigor is sometimes lost in the classroom for many reasons. I’m sure I’ve used just about every one of the following invalid proof techniques.
I stumbled across the website of Chuck Norris Facts not long ago. You know such treasured gems as
1. When Chuck Norris does a pushup, he isn’t lifting himself up, he’s pushing the Earth down.
2. There is no chin behind Chuck Norris’ beard. There is only another fist.
3. Chuck Norris can lead a horse to water AND make it drink.
and my personal favorite
4. Chuck Norris doesn't eat honey, he chews bees.
Well, I was quite impressed when I came across a similar list of facts about one of the greatest (some would say THE greatest) mathematicians of all time, Carl Friedrich Gauss.
From Matt Heath:
- Gauss didn't discover the normal distribution, nature conformed to his will.
- Gauss can construct transcendental numbers only using a compass.
- Parallel lines meet where Gauss tells them to.
- Some problems are NP because Gauss doesn't like computers.
- Gauss never runs out of room in the margin.
- Gauss can write irrationals as the ratio of 2 integers.
- Gauss never needs the axiom of choice.
- Gauss can square the circle and then transform it into the hyper-sphere.
- The location and momentum of a particle are what Gauss say they are.
- An elegant proof is one line long. Gauss' elegant proofs are one word long.
- Gauss doesn't look for roots of equations, they come to him.
- There are no theorems, just a list of propositions Gauss allows to be true.
- When Gauss integrates he doesn't need to add a constant.
- Hilbert put forward 23 unsolved problems because he hadn't properly read Gauss' notebooks.
- Gauss knows the topological difference between a doughnut and a coffee cup.
- Gauss can divide by zero.
- Gauss would never ever have a badbox error.
- Primes that aren't Gaussian primes get teased.
- If Gauss had to walk 100 metres, and half the remaining distance, then half the remaining distance again, and so on, he'd get there.
- Erdos believed God had a book of all perfect mathematical proofs. God believes Gauss has such a book.
- Gauss has Hilbert hotels on Mayfair and Park Lane.
- God does not play dice, unless Gauss promises to let him win once in a while.
My favorite has to be "Gauss doesn't look for roots of equations, they come to him."
One of the first comics I read on the XKCD website was this one:
So don't you think it would be a good idea to write a script that would factor every time throughout the day. Just to make it interesting you might factor the time as a 6 digit number, including the seconds. You could answer fascinating questions like what's the most number of factors a time can have, how many times are prime, how many twin prime's are there, etc...
Well, if you think it's a good idea, too late. It's already been done and not by me.
What's the largest number of factors a time can have?
How many times are prime, and what are they?
How many times form twin primes, and what are they?
I was finally catching up on some blog reading today (Yes, I should be finishing the grading of my Differential Equations tests, but I was kind of cranky this morning for no apparent reason. I'm sure my students would prefer me to be in a good mood before I start grading)
While reading the Carnival of Mathematics over at Walking Randomly, I was pointed in the direction of "Murphy's Laws for Mathematics". I'm sure just about everyone knows the fundamental principle called Murphy's Law:
Murphy's Law: If anything can go wrong, it will. Corollary 1: At the worst possible time Corollary 2: Causing the most damage
Over at the site, Murphy's Laws and Mathematics, we see how that works itself out in a mathematics course. Here are a few of my favorites:
- Every problem is harder than it looks and takes longer than you expected.
- Notes you understood perfectly in class transform themselves into hieroglyphics at home.
- The answers you need aren't in the back of the book.
- No matter how much you study for exams, it will never be enough.
- The problems you can work are never put on the exam.
- The problems you are certain won't be on the test will be.
- The answer to the problem you couldn't work on the exam will become obvious after you hand in your paper.
This page was linked to over at 360 and I found his additions worth quoting as well:
- That brilliant insight to the problem you’ve been working on for weeks will disappear the moment you find some paper to write it down.
- The set of GREAT exam questions from a teacher perspective and the set of GREAT exam questions from a student perspective are nearly disjoint.
- If you wait until the last minute to print/photocopy something, the printer/copier will most surely break down.
Now that I am using Office Live to store my PowerPoint slides for my Intermediate Algebra course and also teaching an online Algebra course as well, I have a technological addition:
- Any online tool essential for your curriculum will be unavailable from 30 minutes before class or an online exam, until roughly 2 seconds after other arrangements have been made.