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I was a chem major bison

Chemists I've known have always been good at math.

For instance, my friend's dad is a retired chemistry professor and he was writing papers on things like statistical mechanics and Brownian Motion and co-wrote an undergraduate math textbook with a super-famous mathematician, well famous in the field, anyway.

plus I didn't always like the Eloi vs. Morlocks setup of formal grad school,

what does this mean?

― flopson, Saturday, November 9, 2013 5:52 PM (1 hour ago)

http://en.wikipedia.org/wiki/The_Time_Machine

i'm good at math but i've never taken like hardcore college classes, i can just do stuff in my head pretty well and am good at algebra, that's basically the math i need or will ever need

I was trying to teach a student synthetic division today and I kept fucking up! So frustrating! Somehow stressing that you don't actually use that in real life isn't a satisfactory explanation!

Fuck you rational root theorem!!!

i actually kinda think hs math should be less about like, finding roots of polynomials or learning division algorithms, and more, like, elementary/discrete probability theory, basic combinatorics & graph theory, just the really easy stuff you can do with elementary methods

ne x86 math topics aside from khaninstitute? trying to set up equasions on x11 in darwin

Isn't that what computer science freshman learn in their Discrete Math course, flopson, iirc?

well how does that help high schoolers?

besides logic, teaching a critical thinking course now that's heavy on inductive logic and probability, for the first time ever, and already (not being super deep into the material) i'm struck by how useful it could be if more people learned this stuff early on. i had a science-heavy math education, and i've spent some time thinking about how science works, but i can see that there's a lot about it that's overly opaque to me because my knowledge of probability/statistics is shallow. especially when it comes to the social sciences.

Yeah, obviously doesn't help high schoolers, you are right.

you know what helps high schoolers DAILY BEATINGS that's what

j/k

the question of what type of math to teach in school is so contentious and political that it makes my brain boil every time the subject comes up, that's why i made the lame joke

isn't the typical college-prep math track basically set up to produce calculus students (then engineers, and the few others who need calculus, like physicists)?

sorry, don't mean to incense you, v, obv. you do the lord's work

There are certain problems about way math is taught-even if you major in it and are good at it!-my old math team coach is still big in education wrote an article about his take on it, maybe I can find it. One thing is overemphasis on proofs- "it was good enough for Euclid"- rather than other kinds of mathematical thinking to develop intuition and visualize or in some other way organize mathematical structures. Another think I've talked to people about, at least as far as applied math, is not enough discussion about the subtleties of units. Little kids learn that if they are given a problem about the perimeter of a triangle with the sides given in feet, they should give the answer in feet and they figure units must be trivial but in fact a better understanding of units can really help you solve a problem more quickly and, more importantly, accurately, even if it ultimately requires calculus. See the book Street Fighting Math, freely downloadable, for a good presentation.

xpost

you are correct j, which is sad because the 95% of kids who don't want to be engineers and physicists just end up getting turned off of the subject by the end of high school, if they're not already turned off by 9th grade (i would estimate about half are by that age)

http://mitpress.mit.edu/sites/default/files/titles/content/9780262514293_Creative_Commons_Edition.pdf

^ this one?

When I was in high school basically they were leading up to teaching Calculus senior year, when you could take it only if you were in the AP class, in which it was gingerly taught at an extremely leisurely pace, as if we had to slooow ourselves down time-lapse style in order to observe the delta-epsilon proofs.

Yeah, that one.

my thinking matured a lot, esp. my proofs, once i took a logic course, which suggests that maybe mathematicians in my hood were not as plain about what we were doing as they could have been.

but abstract algebra was always more elusive for me (even though really interesting), despite having lots of proof-theoretic niceties in its usual u.g. presentation, because i didn't have so many of those intuitions and had trouble learning how to visualize it or play with the structures. never had much of a feel for numbers, compared to many math majors, when younger, which i think would have made a difference. number theory as a gentleman's pastime, say, still has mostly zero attraction for me.

sometimes i wish i could just chill and enjoy math instead of stressing about mathematically illiteracy

let's just like, do some problems

"A farmer has some rabbits and some cages. When he puts 2 rabbits in each cage, there are 2 rabbits left over. When he puts 3 rabbits in each cage, there are 16 cages (but no rabbits) left over. How many rabbits and how many cages are there?"

lol i swear the cover of that book practically reads like 'the art of fucking shit up and guessing about things' to me

number theory is ridic ... as far as algebra goes i learned groups rings and fields to pass a test and promptly forgot everything. i know nothing about topology or real analysis.

this course was about as far as i got in math before i gave up (i passed!)

http://www.amazon.com/Foundations-Higher-Mathematics-Peter-Fletcher/dp/053495166X

i just tried to solve that rabbits and cages problem and got six cages and eighteen rabbits

hm

ahem

http://math.arizona.edu/~savitt/GTM.html

okay, fixed

apparently i am

You are William S. Massey's A Basic Course in Algebraic Topology.

You are intended to serve as a textbook for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unecessary definitions, terminology, and technical machinery. Wherever possible, the geometric motivation behind the various concepts is emphasized.

so this test has really revealed something about my self to me

Awesome. I have a copy of that book somewhere that I can give if you want, if I can find it and you are in NYC.

Tried to do that caged rabbit problem in my head but suspect it's broken meaning non-integral solutions. But maybe it's my brane that's broken will solve properly when I get home.

nah there's a simple integer answer

you can do it with just a system of linear equations but wording is so funny it took me a few tries to get the right expressions

The sides of triangle ABC have lengths 6, 8 and 10. A circle with center P and radius 1 rolls clockwise around the inside of triangle ABC, always remaining tangent to at least one side of the triangle. When P first returns to its original position, what distance has P traveled?

^^ this one is grate

and everyone saw this right?

http://sciencevsmagic.net/geo/

OK, took out a pen and the answer is obvious. Now to review why my mental meanderings failed and see if I learned something.

See the error of my ways too, which I may explain to y'all in a bit.

Here's where I went RONG
Wanted to do it without pencil and paper and without algebra, so I decided to
1) figure out what number rabbits had to be multiple of
2) what number cages had to be a multiple of
3) try various values of 1 and 2 until I was close and then
4) perturb to get exact answer

Got to 3,but then 4 wouldn't quite work. Thought it might be because I perturbed in wrong direction.bIt turned out I had mixed up 1 and 2. When I wrote down the two equations I was able to solve it immediately.

Now I remember the potential problem with word problems. For the "smart" kids, they see the same word problems over and over and just know immediately how to translate them into mathematical terms and solve it, it is too easy for them. For the other kids or the old geezers like some of us, the mathematical content is elusive. In my experiment I went into the transporter beam and was split into both smart kid and dumb kid, and hopefully learned something from it.

Can you get to that?

vahd33m's last problem reminds me of PSAT (or SAT?) controversy in the 80s in which one of the Jungreis brothers, must have been Doug, challenged the testing authorities on their wrong answer to a similar problem.

Somehow that is one of those rare bits of information from Ye Olden Times that has not been caught up in the meshes of the undiscriminating internet.

Here is a book of high school contest problems from way back when: http://www.math.nyu.edu/cmt/pdfs/NYCIML.ProblemBook.pdf

Another, related book: http://www.mathpropress.com/books/ARML/ You could also look at some of it in google books.

http://www.mathpropress.com/books/index.html

Looks like you can't really get it nowadays.

Isn't that what computer science freshman learn in their Discrete Math course, flopson, iirc?

― I Wanna Be Blecch (James Redd and the Blecchs), Saturday, November 9, 2013 9:21 PM (Yesterday) Bookmark Flag Post Permalink

well how does that help high schoolers?

besides logic, teaching a critical thinking course now that's heavy on inductive logic and probability, for the first time ever, and already (not being super deep into the material) i'm struck by how useful it could be if more people learned this stuff early on. i had a science-heavy math education, and i've spent some time thinking about how science works, but i can see that there's a lot about it that's overly opaque to me because my knowledge of probability/statistics is shallow. especially when it comes to the social sciences.

― j., Saturday, November 9, 2013 9:41 PM (Yesterday) Bookmark Flag Post Permalink

isn't the typical college-prep math track basically set up to produce calculus students (then engineers, and the few others who need calculus, like physicists)?

― j., Saturday, November 9, 2013 9:51 PM (Yesterday) Bookmark Flag Post Permalink

yeah i guess what i meant was that you spend most of high school math doing pre-cal + geometry, but don't even get to the punchline of the former unless you take calculus in university, by which point your relationship to math is already largely determined. i enjoyed geometry but that's not most people's experience, particularly due to the focus on tedious things like trigonometry. i think those topics i mentioned have some fun, big results that come very quickly and can be derived and made intuitive with elementary methods accessible to hs students, and broadening the amount of topics you see might make more people likely to realize that they like math, and would give people a better idea of what it's all about. i don't have very strong feelings about pedagogical approaches to math and i know that it's very hard to get people to learn even the simplest stuff. but i don't think my suggestion necessarily means students should learn more or harder material, if anything it's more about giving a practical layman's set of tools for people not continuing calculus

I’m fascinated by this debate. Excuse my rambling:

Calculus is an opportunity to survey mathematics. It’s possible that a student’s calculus sequence will be their first, and only exposure to foundations (e.g. proof by Riemann sums), abstract algebra (e.g. vectors and vector spaces), combinatorics (e.g. infinite series and sequences), geometry (e.g. differential and topology), and a variety of philosophical and applied areas of mathematics. If you care about mathematics as a subject of humanity, there’s no better introduction to the themes, relationships, and problems within mathematics. In a perfect world, we’d rename the courses “An Introduction to Mathematics.”

Nonetheless, I don’t think the typical calculus sequence is useful for non-hobbyists (e.g. “engineers”)—it’s far too comprehensive and not enough time is spent on useful knowledge (e.g. dynamics, differential equations, and numerical approximation). I also don’t think it’s useful for young mathematicians—too much time is spent on sharpening basic knowledge (e.g. algebra, counting, geometry, sentential calculus) rather than rigor. For example, my undergraduate track:

* Introduction to Calculus
* Intermediate Calculus
* Multivariable Calculus
* Functions of a Complex Variable (i.e. complex analysis)
* Introduction to Analysis
* Functions of a Real Variable (i.e. elementary real analysis)

I also took a differential equations and Fourier analysis course. I suspect most people had a similar experience.

In retrospect, I feel like the calculus sequence could’ve been reduced into one course—using Spivak—better preparing me for the jump into analysis and freeing my schedule to study non-analysis subjects.

Incidentally, I feel like algebra has the reverse problem. In my experience, most students enter Ph.D programs with two courses in algebra: linear and an abstract algebra course (covering groups, rings, fields). If you replaced a calculus course from the standard calculus sequence with an algebra course, you could then require an upper-level algebra course in the junior or senior year (e.g. commutative algebra) that’d better prepare everyone.

Also: I’ll join the interested in Homotopy Type Theory choir. While I’ve spent the past while working in compilers, I’ve been studying PLT topics wherever necessary (mostly semantics and types). I enjoyed Types and Programming Languages, but I’ve been looking for something a bit wilder. If there’s enough interest, maybe we can use this tread as an informal book club/Agda help desk.

My interest in mathematics is very much related to computer science. I didn't post here earlier, because I thought this thread would only be mathematics.

But I see some may appreciate these drawings that use Turing machines: http://maximecb.github.io/Turing-Drawings/

Also recently bought a copy of Best Writing on Mathematics 2012 which is very nice and pitched at a similar level, the article on Math and Music was very interesting, written by a guy who is both a practicing musician and research mathematician.

I haven’t read it in its entirety, but I’ve liked everything I’ve read from Paul Hudak’s Haskell School of Music:

http://www.cs.yale.edu/homes/hudak/Papers/HSoM.pdf

(However, I didn’t know anything about music theory. So, the relationship between music and, say, lazy evaluation and typing might be overwrought.)

Sort of agree on calc. Way over done on specific tricks, and not enough emphasis on intuitions and meaning. All the exercises that are just about remembering a zillion tricks and identities for symbolic manipulation and simplification are just really about rote memorization and speed. Calc is a pretty specialized subject and treating it as "genuine advanced math" is pretty maddening compared to what gets left out.

Math is really used due to the history of standards bodies and testing, etc. as much as a screen/weeder as actually taught to teach math, and the emphasis on calc is the biggest symptom of this (but all the trig identities actually similar -- I mean we should really start with the unit circle, euler's identity, etc. and build trig on that.

also hate the way linear algebra is taught, determinants first.

its all derived from teaching things you can test in a certain way.