Terence Tao Proposes Fluid New Path in Navier-Stokes ProblemComputers made purely of water. ..
- (We’re taking a calculus final. The TA is a well-known Lord of the Rings fan, and we’ve had running LotR jokes all semester.)
- TA: “Okay, guys, everyone look at me. We’ve been over the rules, but just in case: no notes, pencil your answers in on the scantron sheet, and graphing calculators only – no more ‘can I just used my cell phone’ nonsense.”
- Student: “[TA's name], my calculator batteries just died! What should I do?”
- TA: “Here, I’ve got a big box of spares.”
- Student: *struggling* “I can’t get this packaging open…”
- Student 2: “Here, I’ve got a pocket knife.”
- TA: “And I’ve got a pair of scissors if you need them.”
- Student 3: *from the back of the room* “OR MY AXE!”
- (Everyone starts laughing.)
- TA: “The only axes allowed on the exam are in the graph section.”
- (Everyone groans.)
- TA: “Oh, come on, you’re in a math class. Deal with the math jokes.”
- (The professor enters with a stack of exams. With him are two exam proctors.)
- Professor: “Tolkien jokes already, [TA's name]?”
- TA: “Hey, I didn’t start it.”
- (The professor starts handing stacks of exams to the TA and proctors.)
- Professor: “But I’m about to finish it. [TA], take these exams down the left flank. [Proctor 1], follow the desks down the center. [Proctor 2], take your exams right, along the wall.”
- (At this point, many of the students have realized where this is going: Theoden’s lines from ‘Return of the King.’)
- Professor: “Forth, and fear no problems! Solve! Solve, students of calculus! Points shall be taken, scores shall be splintered! A pencil day! A red-ink day! Until three thirty!”
- (The professor pulls out a pencil, holding it out like a sword, and runs down the first row holding it out. Students hold up their pencils, hitting his as he passes.)
- Professor: “Solve now! Solve now! Solve to good grades and the class ending! MAAATH!”
- Entire Class: “MAAATH!”
- Professor: “MAAAAATH!”
- Entire Class: “MAAAAAATH!”
- Professor: “Forth, exam-takers!”
- (The entire class rises to their feet and gives him a standing ovation. A week later, we get an email from the professor.)
- Professor: *at the end of the email* “PS: I appreciate all of you who wrote in their evaluations that I was the one professor to rule them all, but the best one yet was the student who called me ‘Mathrandir.’”
At my college, I am a student-athlete tutor, so each semester I get assigned kids to tutor in math and statistics. I’ve been tutoring a lot of Intro to Statistics students this semester and we’ve hit the dreaded section of the course: probability.
A lot of people struggle with probability. It’s probably one of the hardest parts of any intro to statistics course. And so I’ve had a lot of my kids say things to me like “I would never have figured that out” or “How do you remember all of this?” and the like. And the thing is, when I was taking into to statistics, I had the exact same issues.
When do you add probabilites? When do you multiply them? What’s the difference between mutually exclusive and independent? What does a random variable even mean?
The first time I saw any serious treatment of probability was in my high school precalculus class. I got an 80 on the test we had on it. The same thing happened when I took AP Statistics the next year. I got an 85 on the test on it. Each time these came as a blow to me because I usually did very well on tests and it was tough to see students who usually do worse than me excel in probability. It was just not my branch of math.
Going into college, I was an actuarial science major (insurance math). So naturally, I had to take a course purely on probability. Things went better. Part of it due to the fact I had seen the course material before. After that, I took a course called Elementary Stochastic Processes (which had varying amounts of success) and I’m currently in mathematical statistics which also deals with a lot of probability.
POINT BEING: I have seen probability in 5 separate courses, and it has taken that many courses for me to finally understand the little quirks that probability has to offer.
I could have very easily backed out of taking any probability after graduating high school, but I did stick with it, and I think that this persistence is something that is crucial as a math major. There will be some math course at some point in your academic career that trips you up. You will not get it as well as everything else. You will struggle. You will feel frustrated with the material and yourself.
But what matters is that you keep going at it regardless of how poorly it may go the first time through. The more you see the material, the more you work through it, the more you dive right into it, the better it is for you. Eventually you will get it. Eventually it will click. Eventually it will come together.
Good luck my fellow math and non-math peepz.
As my high school teacher once said, probability is hard to teach until the student gets a feel for it.
That being said it’s one of my favourite topics in math from day one pretty much, but alas the probability course I’m taking right now in third year isn’t as fun as I hoped it’d be. It’s not problem solving probability, and it’s not super rigorous probability like starting from measure spaces.
Engineer: Remember to tip 18%, everybody.
Mathematician: Is that 18% of the pre-tax total, or of the total with tax?
Physicist: You know, it’s simpler if we assume the system doesn’t have tax.
Computer Scientist: But it does have tax.
Physicist: Sure, but the numbers work out more cleanly if we don’t pay tax and tip. It’s a pretty small error term. Let’s not complicate things unnecessarily.
Engineer: What you call a “small error,” I call a “collapsed bridge.”
Economist: Forget it. Taxes are inefficient, anyway. They create deadweight loss.
Mathematician: There you go again…
Economist: I mean it! If there were no taxes, I would have ordered a second soda. But instead, the government intervened, and by increasing transaction costs, prevented an exchange that would have benefited both me and the restaurant.
Economist: In practice, yes. But my argument still holds in theory.
The computer scientist lays a smart phone on the table.
Computer Scientist: Okay, I’ve coded a program to help us compute the check.
Mathematician: Hmmph. Any idiot could do that. It’s a trivial problem.
Computer Scientist: Do you even know how to code?
Mathematician: Why bother? Learning to code is also a trivial problem.
Engineer: Uh… your program says we each owe $8400.
Computer Scientist: Well, I haven’t de-bugged it yet, if that’s what you’re getting at.
Economist: No! That’s so inefficient. Let’s each write down the amount we’re willing to put in, then auction off the remainder at some point on the contract curve.
Mathematician: Like most economics, that’s just gibberish with the word “auction” in it.
Engineer: Look, it’s simple. Total your items, add 8% tax, and 18% tip.
Mathematician: Sure. Does anybody know 12 plus 7?
Computer Scientist: You don’t?
Mathematician: What do I look like, a human calculator? Numbers are for children, half-wits, and bored cats.
The engineer looks at the cash they’ve gathered.
Engineer: Is everyone’s money in? It seems we’re a little short…
Physicist: How short?
Engineer: Well, the total was $104, not including tip… and so far we’ve got $31.07 and an old lottery ticket.
Physicist: Close enough, right? It’s a small error term.
Mathematician: Which of you idiots wasted your money on a lottery ticket?
Economist: I should mention that I’m not planning to eat here again. Are any of you?
Computer Scientist: What does that matter?
Economist: Well, in a non-iterated prisoner’s dilemma, the dominant strategy is to defect.
Economist: We should be tipping 0%, since we’ll never see that waiter again.
Computer Scientist: That’s awful.
Physicist: Will the waiter really care – 0%, 20%? Let’s not split hairs. It’s a small error term.
The engineer looks up from a graphing calculator.
Engineer: All right. I’ve computed the precise amount each of us should pay, using double integrals and partial derivatives. I triple-checked my work.
Mathematician: Didn’t we all order the same thing? You could have just divided the total by five.
Engineer: I could? I mean… of course I could! Shut up! You think you’re so clever!
Computer Scientist: Well… the waiter did only bring two orders of fries for the table.
Physicist: We only ordered two.
Computer Scientist: Exactly. We got the 1st order, and the 2nd, but never the 0th.
Economist: I’ll be frank. At this point, my self-interest lies in not paying. And the economy prospers when we each pursue our individual self-interest. See you later!
The economist dashes off. The engineer and computer scientist glance at one another, then follow.
Mathematician: Looks like it’s just me and you, now.
Physicist: Good. The two-body problem will be easier to solve.
Physicist: By reducing it to a one-body problem.
The physicist scampers away.
Mathematician: Wait! Come back here!
Waiter: I notice your friends have gone. Are you done with paying the check?
Mathematician: Well, I’ve got a proof that we can pay. But I warn you: it’s not constructive.
Finally, those intro courses in college finally paid off with a good laugh.
What’s purple and commutes?
An Abelian grape.
What’s yellow and is everywhere infinitely differentiable?
A bananalytic function.
What’s an anagram of Banach-Tarski?
What’s yellow, normed, linear, and complete?
A Bananach space.
What’s purple and all its offspring have been committed to institutions?
A simple grape; it has no normal subgrapes.
— Youtuber rlinfinity
— G. H. Hardy
-The Mathematics of Paul Erdos