Login

Welcome, Guest. Please login or register.

March 29, 2024, 04:34:29 pm

Author Topic: Think Maths is useless? Think again.  (Read 8101 times)  Share 

0 Members and 1 Guest are viewing this topic.

jakesilove

  • HSC Lecturer
  • Honorary Moderator
  • Part of the furniture
  • *******
  • Posts: 1941
  • "Synergising your ATAR potential"
  • Respect: +196
Think Maths is useless? Think again.
« on: September 15, 2016, 06:07:59 pm »
+5
Hey all! Just thought I'd start this thread for anyone wanting to share real-world examples of how Maths has helped them outside of the HSC. I'm particularly proud of the way I've employed Maths today; whilst fairly simplistic, it was still pretty cool.

As part of my Contract Law assignment, there is an individual (Kelvin) who is selling a fridge. Initially, they contract to sell it for $15,000. However, after noting that the 'cost of the fridge increased more than 30%', he asks for more money from the buyer. Initially, he asks for $18,000, then $17,000, then $16,000.

One of the elements in allowing this change in price is that it is not done for reasons of economic duress or pressure. However, how can you assess whether that is the case or not? A normal Law student probably couldn't; someone who remembers their simultaneous equations can though! I was able to figure out, depending on the asking price, the initial cost of the fridge required to ensure that Kelvin wasn't gaining any substantial profit from the new sale. From there, I could assess the reasonableness of the initial cost (eg. The fridge DEFINITELY didn't cost $3,333, that's way too cheep) to say definitively that there was no economic duress!



Pretty cool, right? I think so.
ATAR: 99.80

Mathematics Extension 2: 93
Physics: 93
Chemistry: 93
Modern History: 94
English Advanced: 95
Mathematics: 96
Mathematics Extension 1: 98

Studying a combined Advanced Science/Law degree at UNSW

Ali_Abbas

  • Trailblazer
  • *
  • Posts: 43
  • Respect: +4
Re: Think Maths is useless? Think again.
« Reply #1 on: September 15, 2016, 07:01:17 pm »
0
I have much respect for applied mathematics but at the same time, there is so much beauty and enlightenment when studying mathematics in its pure form. There is a sense of discovery, wisdom, wonder, and perfection all infused in one. Man's inquisitiveness for truth is catered for and allowed to flourish. The way vastly distinct topics somehow merge unexpectedly and offer a unified result. The fact that mathematical claims can be irrefutibly proven or disproven rings universal justice. This shear splendor and astute mastery of the real science underpinning mathematics should be acknowledged and appreciated by all. In the words of the world's greatest living mathematician:

"...but I just do maths 'cause it's fun" - Terence Tao

Ali_Abbas

  • Trailblazer
  • *
  • Posts: 43
  • Respect: +4
Re: Think Maths is useless? Think again.
« Reply #2 on: September 15, 2016, 07:53:36 pm »
0
I forgot to mention that incidently, there was a time that maths came in handy for me in real-life. It was when my dad had finished building a plane he had designed and was now up to test-flying it. It turned out that the tail was offering too much stability and was making it hard to turn the aircraft. So my dad thought of a new design and I helped him analyse it geometrically to see if the measurements he wanted to put in were even mathematically possible. We also used already-established formulas to calculate the new stability this different design would theoretically provide. So I guess that would be my personal anecdote of where maths was essential in solving a real-world problem that arose in my life.

P.S. we did not end up modifying the tail and kept it the way it was.

EmileeSmith

  • Forum Regular
  • **
  • Posts: 87
  • Respect: 0
Re: Think Maths is useless? Think again.
« Reply #3 on: September 15, 2016, 08:08:33 pm »
+2
wish I didn't drop maths

conic curve

  • Forum Leader
  • ****
  • Posts: 714
  • Respect: +2
Re: Think Maths is useless? Think again.
« Reply #4 on: September 15, 2016, 08:44:37 pm »
0
Oh my gosh...does this remind me of a HSC topic that you learn in school?

Also what is "calculus", especially when they say things like Actuarial maths is calculus (not integration and differentiation)

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: Think Maths is useless? Think again.
« Reply #5 on: September 15, 2016, 08:47:47 pm »
0
Oh my gosh...does this remind me of a HSC topic that you learn in school?

Also what is "calculus", especially when they say things like Actuarial maths is calculus (not integration and differentiation)
Meh. It's more statistics than calculus.

Calculus is mainly the study of how things change or how things accumulate. First year university calculus concepts include (but is not limited to)
- Formalising definition of limits
- Continuity based theorems
- Differentiation based theorems
- Improper integrals
- Integration based theorems
- Error in quadrature (trapezoidal rule etc.)
- Calculus proofs

In addition, it also starts dealing with calculus not restricted to just one variable x. 3D graphs and several variable calculus is different to single variable calculus.

If you want to inquire more about maths at uni, feel free to make a post in the university section of the forum. I can provide a comprehensive description of my maths courses thus far for your interest. Or just PM me specific questions.

Dragomistress

  • Trendsetter
  • **
  • Posts: 162
  • Respect: 0
  • School: James Ruse Agricultural High School
  • School Grad Year: 2018
Re: Think Maths is useless? Think again.
« Reply #6 on: November 06, 2016, 09:19:58 pm »
0
Hmm, you have a point with some things but isn't mathematics (especially the higher level ones) rather obsolete? Like, when will one use the quadratic formula or even a simple find the angle. Even if you do use mathematics for your job, won't it be few (relatively speaking).

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: Think Maths is useless? Think again.
« Reply #7 on: November 06, 2016, 09:22:27 pm »
0
Hmm, you have a point with some things but isn't mathematics (especially the higher level ones) rather obsolete? Like, when will one use the quadratic formula or even a simple find the angle. Even if you do use mathematics for your job, won't it be few (relatively speaking).
Only if what you choose to do as a job falls under that umbrella.

Heaps of people are tending to jobs that require it these days. Imagine doing engineering without maths.

The only thing that can be said is that not every job requires every single element of mathematics.

keltingmeith

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 5493
  • he/him - they is also fine
  • Respect: +1292
Re: Think Maths is useless? Think again.
« Reply #8 on: November 06, 2016, 10:03:44 pm »
+1
Meh. It's more statistics than calculus.

I mean, try doing actuarial statistics without calculus. :P

Hmm, you have a point with some things but isn't mathematics (especially the higher level ones) rather obsolete? Like, when will one use the quadratic formula or even a simple find the angle. Even if you do use mathematics for your job, won't it be few (relatively speaking).

This is actually one I found rather interesting recently. See, I study statistics, and so I do a lot of maths which is regularly applied to lots of situations. The question was actually quite simple: we wanted to find out how long it would take for a last name to "die out". That is, assuming a traditional society where each person takes the last name of their father, then you know a name will die out if a family gives birth to no sons, or their sons don't have children. Each enough.

The trick ends up being to find a probability distribution that models the birth of each family. When we did this, we had to solve a quadratic along the way. After you have the distribution, there's lots of things you can do (mainly, find the probability of the last name dying out), but that's beside the point for this argument.

Now, this type of process, called a branching process, happens a lot in society - in fact, it's one of the BEST models for tracking genetic mutations. However, to solve the model and find a solution, we needed to know how to solve quadratics.


Okay, so let's look a bit more commercey now - you can very easily define a business in terms of the amount of money that it spends (consumption, C) to give some amount of output (x). You can show that the demand (d) of a business is given by the equation d=(1-C)^(-1)*x.

So, this is where it gets interesting - you know your consumption and your output, the question is, are you meeting your demand? Logical thinking says that if (1-C)^(-1) exists AND is non-negative, then your business is sustainable (or usually it's said to be feasible).

Okay, cool, so what does this have to do with quadratics and angles? Well, this problem and solution I've just told you about is actually useless in its entirety unless you think about it in terms of vectors. So, you need to define vectors. However, you cannot use vectors unless you first understand how to define angles between them, their magnitude, etc. So, you need to have some method of working with those - say, sine, cosine, and tangent. Just like the case of the branching process - it's incredibly relevant, and the question and answer themselves don't directly use the stuff you learn in high school. But without using the stuff from high school, this more interesting stuff wouldn't exist in the first place.

Sure - you could just be lazy, not learn the stuff in high school, and then get a computer to do it all for you. Computers can do that nowadays. The problem is, that you don't have an appreciation for this stuff, and you'll never be able to do it yourself. The moment your program crashes because your problem has changed slightly and the usual method doesn't apply, you need someone else who knows this stuff to do it instead. However, if everyone takes the easy way out, nobody will know how to setup the computer, and we'll (in essence) lose the solution to these problems.

Later on, when you do get to answering these questions - you know what? You will probably use a computer, and never have an issue. BUT, someone will have to know how to do this stuff properly, and in high school, you have no way of knowing if that person is you. Just because you think you don't like maths, that doesn't mean you won't learn to love something that requires you know these basics. So that's what high school does - it teaches you the basics so that if you decide later that you do like it, you can do on and learn about it more.


Tl;dr - maths is super useful later in its educational life. However, often the more interesting problems, and ones that students will care about, can't be done until you can do the simple stuff first.

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: Think Maths is useless? Think again.
« Reply #9 on: November 06, 2016, 10:16:13 pm »
0
I mean, try doing actuarial statistics without calculus. :P
Hey I never claimed that calculus was useless ahaha

keltingmeith

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 5493
  • he/him - they is also fine
  • Respect: +1292
Re: Think Maths is useless? Think again.
« Reply #10 on: November 06, 2016, 10:20:05 pm »
0
Hahah, I meant more you saying it's not calculus, as opposed to suggested calculus isn't useful. ;)

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: Think Maths is useless? Think again.
« Reply #11 on: November 06, 2016, 10:23:53 pm »
0
Although I definitely need calculus to do statistics, the way I see calculus now is somewhere along the lines of this...

...or this...

jamonwindeyer

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 10150
  • The lurker from the north.
  • Respect: +3108
Re: Think Maths is useless? Think again.
« Reply #12 on: November 06, 2016, 10:25:18 pm »
0
INSERT FOURIER SERIES HERE  8) 8) 8) Your wish is my command 8)

« Last Edit: November 06, 2016, 10:28:42 pm by RuiAce »

keltingmeith

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 5493
  • he/him - they is also fine
  • Respect: +1292
Re: Think Maths is useless? Think again.
« Reply #13 on: November 06, 2016, 10:32:24 pm »
0
Although I definitely need calculus to do statistics, the way I see calculus now is somewhere along the lines of this...

...or this...


See, that's rather interesting! Because the first case, yeah, sure, I see a delta-epsilon proof. But the second one? I see a normal distribution, with mean zero, and variance 0.5.

It's all about your perspective. ;) At the end of the day, calculus isn't really studied anymore like it used to be - it's just a tool, used for statistics, engineering, the solving of differential equations, analysis, etc.

Or at least, that's just my two cents.

INSERT FOURIER SERIES HERE  8) 8) 8) Your wish is my command 8) (Image removed from quote.)

(Image removed from quote.)

Actually did fourier transforms for one of my statistics units (fun fact: electrical engineers took this unit for a bludge because the first half is legit just signals processing :P), and then fourier series for my applied unit. Not fun at all :'(

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: Think Maths is useless? Think again.
« Reply #14 on: November 06, 2016, 10:40:18 pm »
0
See, that's rather interesting! Because the first case, yeah, sure, I see a delta-epsilon proof. But the second one? I see a normal distribution, with mean zero, and variance 0.5.

It's all about your perspective. ;) At the end of the day, calculus isn't really studied anymore like it used to be - it's just a tool, used for statistics, engineering, the solving of differential equations, analysis, etc.

Or at least, that's just my two cents.

Actually did fourier transforms for one of my statistics units (fun fact: electrical engineers took this unit for a bludge because the first half is legit just signals processing :P), and then fourier series for my applied unit. Not fun at all :'(
Thing is in first year (and tbh probably in general because of the tables; nobody has time to do it via first principles) they just make you assume shit in the actl courses :P

Not too sure how many gaps are left in calculus at this point though.