Back in 2012, I took an Approximate Number System aptitude test that I found online.
Then, in 2014, I took it again to see if my score had changed (since I’d done so much more math between 2012 and 2014 than I had prior to 2012). My score didn’t change at all.
So it’s 2016 now…wanna guess what I did?
I took it again!
And my score is still the same!
Yeah. I guess the amount of math/numbers I deal with doesn’t affect how good I am at this test. Pretty cool result, though, nonetheless.
Today I had to go invigilate a MATH 277 final as part of my TA requirements (we each have to invigilate/proctor two final exams; sometimes we get ones we’ve actually been TAs for and sometimes we don’t. This was a case of the latter). It turns out that MATT 277 is University of Calgary’s version of MATH 275, or multivariate calculus. The test involved about 20 or so questions.
Our job as TAs, apart from making everybody sign in on the little attendance sheet, was mainly to just walk around in order to discourage cheating and to help anybody out who raised their hand.
So let me just quickly set the scene for you: a large gym full of 250+ students, a 2-hour exam, and lots and lots of calculus.
I bet you can guess what I was thinking about.
I was thinking about Leibniz!
I was wondering, as I walked down the aisles of seats, watching students write the elongated “s” for integration and the dx/dy (or variations of that) for differentiation, what Leibniz would think if he saw a roomful of people, in 2016, still using some of his original symbols. Like, how ridiculous is that? Calculus has been studied, expanded upon, and extended to a ton of different fields/uses since it was first developed, but we’re still using some of Leibniz’ original symbols.
And what would he think about calculus being taught as basically standard curriculum at universities? What would he think about the tons of different uses of calculus today?
I know I kind of talked about this in a previous post, but I actually think about this quite a bit. Especially today.
Yay calculus! Yay Leibniz!
GUYS I HAVE PURCHASED A SLIDE RULE
Story: Okay, so it’s been like four days since I’ve gone walking, which is four days too many, so I decided to walk down to Chinook Centre (about 13 miles round trip). However, once I got down there, I changed my mind and decided to check out the Value Village close to the mall instead. I was just going to look around since I have practically no money at the moment, but when I was digging through the miscellaneous baskets on one of the shelves I came upon THIS:
And since it was only $2, I had to get it. So I did.
It didn’t have a manual or anything with it and I’ve never used a slide rule before in my life, so I went to teh internetz to see if I could figure out how it works. And it’s super cool! Let me show you a few basic things.
Multiplication: Say I wanted to multiply 1.2 by 3. What I’d do is find 1.2 on the “D” scale and slide my “C” scale so that its 1 is right above 1.2.
Then I would find 3 on my “C” scale. Whatever number on the “D” scale is right below the 3 on the “C” scale is the product of 1.2 times 3: 3.6!
Division: Let’s do 6 divided by 4. You take the divisor, 4, on the “C” scale and set it above the dividend, 6, on the “D” scale like so:
The quotient is whatever number is on the “D” scale right below the 1 on the “C” scale: 1.5!
Finding a square root: Say I wanted to find the square root of 5. I would find 5 on the “A” scale. Whatever number on the “D” scale that is below that 5 is the square root: approximately 2.23!
Super cool. You can also do things like cubes/cube roots, proportions, logarithms, and sines and tangents of angles, but I’m still learning.
Alright fools, sit your butts down. Today’s blog post is an important one.
I’ll start this whole thing off with a confession. You’ve all heard me say that I can’t do math in my head, right? Well, that’s a lie. I am perfectly capable of doing math in my head.
I just can’t do it when others expect me to be able to do math in my head.
Elaboration: like a lot of people, I’ve always equated math ability with intelligence. I know that’s a narrow and inaccurate way to define intelligence, but for the longest time, math was my go-to smarts-o-meter. That’s probably because I used to be hella afraid of it and thus considered anyone who wasn’t hella afraid of it to be way smarter than I was.
I’ve long since redefined how I view intelligence. Namely, it’s very obvious to me now that people can easily be “intelligent” in a wide variety of things (think Gardner’s theory of multiple intelligences). A dude who’s fantastic at painting but horrible with numbers, for example, can be just as intelligent as a dude who’s amazing with numbers but not so much with paint. And people who are not “book smart” (or “school smart” or whatever) can be ridiculously intelligent in other aspects of existence that just aren’t captured by that book smartness/school smartness.
I’m sure most if not all of my readers would agree with this.
However, if you’re someone who likes math and are around people who know you like math, they’re probably going to expect you to be good at mental calculations. That’s always been my experience, at least.
And that makes me panic like you wouldn’t believe.
Especially since going into the quantitative/statistics side of things, my ability to do math in my head—“on the fly”—has gotten worse. And I think that’s because if the people I’m around know I’m into stats, I suspect they automatically assume I’m some sort of human calculator. And if I can’t prove my amazing calculating abilities, then I’m too stupid to be studying something like stats. After all, who wants a statistician who can’t add 23 + 27 in their heads?
Here’s the thing. I can add 23 + 27 in my head. It’s super easy to do. But if you just ask me to do it, I will panic and not be able to because I’m too busy freaking out about being judged on if I’m doing the calculation quick enough or what would happen if I make an error.
That sounds really stupid and maybe a bit unclear. Let’s use pictures to clear it up a bit.
Here’s what I would suspect loosely happens in the head of a person without this “math on the fly” anxiety when they’re asked to add 146 + 279:
And here’s what happens to me and, I suspect, a good deal of others:
I’m not exaggerating. When someone poses a math question—even something simple like basic addition—I automatically lose focus on the numbers and start freaking out about how dumb they think I am if I don’t answer it right away.
And I can’t be the only one. However, most of my friends (based on just watching them answer impromptu math questions) don’t experience this, so I just wanted to show you how it is for me.
So there you go.
I FOUND SOMETHING ELSE I WANT.
IT IS A MATH STENCIL.
IT IS GLORIOUS.
Look at this. Look at those lower case Greek letter stencils. I’ve needed those so many times in the past.
(Image from Tumblr.) And the curly braces. THE CURLY BRACES, PEOPLE.
Edit: Okay, found the motherlode.
This is glorious.
Today we learned how to use complex analysis to solve real-values integrals that would otherwise be very difficult to solve.
No complex variables in sight in that integral, right (assuming x is real-valued, haha)? Well you can CONVERT THIS TO A COMPLEX-VALUED INTEGRAL AND HAVE AN EASIER TO SOLVE PROBLEM!
That freaking blew my mind this morning in class. I’d go through the details of how to do this, but I’m a lazyass and don’t want to use Word’s equation editor to make like 30 different equations showing the steps to solve. Instead, I’ll link to Dr. Datta’s notes from class. Go to page 10 in the PDF (the page labeled “161”) for this example.
Side note: if any of you ever end up going back to UI or know anyone who will be taking some upper-division math classes there, I highly recommend Dr. Datta. She’s very clear at explaining things, good at giving examples, gives reasonable homework, and is always willing to help.
Remember my post on John Napier awhile back?
Well check out the Genaille-Lucas rulers, a variant of Napier’s bones. They’re used to carry out multiplication and have a really snazzy way of visually representing the “carry” part of multiplication.
Check out this example on Wikipedia.
I’m totally printing out that PDF of the rulers at the bottom of the Wiki page. Snazzy!
HAHAHA, oh, Yale.
I read about the Conic Sections Rebellion quite some time ago, but I’d forgotten about it.
The rebellion refers to two incidents that occurred at Yale in 1825 and 1830. Both were students’ responses to having to draw out their own conic sections diagrams for exams rather than being able to refer to the diagrams in their textbooks.
A large number of students refused to take their final exams because of this, resulting in about 50% of the students in both the ’25 and ’30 incidents being expelled. That’s awesome.
I’m a really visual person. That’s how I learn best, by studying diagrams or remembering the processes of things. So seeing binary addition visually is really, really helpful to me. I wish I’d found this back when I first learned this—it probably would have been less confusing, haha.
How cool is that?
I am someone who has very little mathematical intuition. I mean, I think some people just have a knack for thinking about math and “math things” and for piecing bits of different types of math together. I don’t. Like, even at the most basic levels—simplifying factorial expressions, the logic behind summation rules, all that stuff. I mean, I know I’m a total idiot, but still. At least with other topics I have some degree of intuition.
And I’ve always wondered if others who actually have a more intuitive understanding of math—or at least have delved into it far enough—see advanced math (or math in general) in a different way.
Anyway. Interesting read, check it out.
Do you like math?
Do you like fiction?
DO YOU LIKE THEM BOTH??
Go here! It’s a pretty comprehensive list of math-related fiction. If you so desire, you can search by keyword, genre, topic (calculus, chaos, fractals, statistics, etc.), motif, or rating in terms of literary value or math involvement.
Just a quick little blog today!
So remember this Approximate Number System aptitude test I did back in 2012? I decided to try it again. I’ve been doing so much more math since then, I wondered if that would affect my performance at all.
HAHA, nope. My Weber fraction (w = .13) is exactly the same. That’s hilarious.
Though to be fair, it’s 4:30 in the morning and I’m kinda hyper, so maybe that’s affecting stuff.
But I’m always like that, so maybe not.
Alternate title: Claudia Makes Things Way More Complicated than They Need to Be Because She Sucks
We had this bonus question on our homework for Probability today:
Suppose X has a density defined by
Let FX(x) be the cumulative distribution of X. Find the area of the region bounded by the x-axis, the y-axis, the line y = 1, and the curve y = FX(x).
And I was like, “Aw, sweet! Areas of regions! CALCULUS!”
So first, I had to find the cumulative distribution function (cdf) of X. Easy. It’s just the integral of the density fX(x) from negative infinity to a constant b. In this case:
With 2 ≤ b ≤ 3. So that’s my curve y. The area I’m looking for, therefore, is this (the red part, not the purplish part):
Now anyone with half a brain would look at this and go, “oh yeah, that’s easy. I can find the area of the rectangle formed by the two axes, the line y = 1, and the line x = 3, then find the area of the region below the curve from 2 to 3, and subtract the latter from the former to get the correct area.”
Which works. Area of rectangle = 3, area of region below FX(x) = .25, area of region of
interest = 2.75.
Or they could remember the freaking formula that was explicitly taught last week. Such areas can be calculated using:
But did I see either of those? Nooooooope.
I looked at the graph and was like, “how the hell do you find that?” I tried a few things that didn’t work, then realized that it would be a lot easier to figure out if I changed the integral from being in terms of x (or b, rather) to being in terms of y.
So then I just had to integrate. This gave me the right answer: 2.75!
Moral of the story: don’t complicate things. But if you do complicate things, you might actually end up in a scenario where you’ll use something that you were taught back in calculus I but didn’t ever suspect you’d actually use. I had appreciated learning the handy-dandy technique of changing variables, but I didn’t think I’d be in a situation where I’d apply it. Shows what I know, eh?
It was a nice refresher, at least. I’ve missed calculus.
“WTF is a Curta?” you may be asking.
I’ll tell you!
The Curta is a little handheld mechanical calculator introduced in 1948 by Austrian engineer Curt Herzstark (so I guess “Curta” was an easier name than “Herzstarka”). Real-life ones look like THIS (source for pic)…
…and were considered the best portable calculators until the digital ones started coming out in the 1970s.
Its design is based in part off of…(wait for it)…Leibniz’ Step Reckoner. It is able to do addition, subtraction, multiplication, division, and also square roots. What made it different from contemporary calculators was, though it employed a stepped drum mechanism like most others, Herzstark was able to create and patent a single drum that did the work of 10+ drums, thus making the Curta super compact.
I wanted to get a real one, but they’re like $400 now, so this simulator was a cool find. If you want to get all up in the Curta’s business but are intimidated by all the arrows/dials (it’s like a slide rule on steroids!), check out this manual.
Holy crap dudes, this is the best discussion of imaginary numbers I’ve ever heard. Listen to this, it’s really cool.
“MAA MathFest 2013 will be held at the Connecticut Convention Center and Hartford Marriott Downtown in Hartford, Connecticut.”
WHAT THE CRAP IS THIS CONFERENCE AND WHY CAN’T I BE THERE?
There’s a minicourse entitled “Passion-Driven Statistics: A Supportive, Project-Based, Multidisciplinary Introductory Curriculum” and another one called “Mathematical Expeditions in Polar Science” in which “Participants will learn about many different areas of scientific research going on in the Arctic and in Antarctica, including sea ice, glaciers, ice cores, phenology, astronomy, biology, and satellite mapping.”
Math and Antarctica? Seriously?
AND DR. ARTHUR BENJAMIN (THIS GUY) IS GOING TO BE THERE?!?
Nooooooooo life is not fair, it’d cost like an entire semester’s tuition to get me to Connecticut.
I’m sad now.