Why maths matter, especially to liberal arts students

Yesterday morning I was listening to WNYC/NPR during my commute. The reporter was explaining De Beers’ claim of supply shortage of diamonds and there will be a price increase of 5% a year for the next 5 years. In closing of the story, the reporter said something about the effect of price hike of 25%, thus implying that 5% annual increase over 5 years equals to 25% increase in total!

Wrong!

Let’s take a look at the concept of compound interest. First let’s say we start with the price of a mythical diamond at $100. At the end of first year, we increase price by 5%. That is $100 + ($100 x 5%) = $105.

So at the beginning of second year, the price of the mythical diamond is now at $105. At the end second year, we increase price by 5% again. This time $105 + ($105 x 5%) = $110.25.

Repeat this for the next three years:

Year 3: $110.25 + ($110.25 x 5%) = $115.76

Year 4: $115.76 + ($115.76 x 5%) = $121.55

Year 5: $121.55 + ($121.55 x 5%) = $127.63

So at the beginning of fifth year, the last price increase puts the final price of our mythical diamond at $127.63.

But what about the 25% increase in 5 years? Ok, let’s see.

$100 + ($100 x 25%) = $125

Huh! That’s clearly not the same as $127.63!

So my message to liberal arts graduates who may (or may not) become a reporter who would work on story involves numbers: brush up your maths skill!

The beauty of maths

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Difference of Opinions

Now, please bear with me for a few mathematical facts before I show you this hilarious phone recording. I know being apt in mathematics since a young age means I don't have problem dealing with or visualising fractions and decimals. But I realise other people do so I want to lay out the fact first.

So, the last time I check this equation is true (as in factually true):

$1 = 100 cents

Let's introduce the decimal point just for the sake of it while keeping the same 'truth':

$1.00 = 100.00 cents

Then for argument sake, instead of a dollar on the left hand side of the equation I am going to make it one cent using dollar as the unit:

$0.01 = 1 cent

Still with me? Good. Now comes the crazy parts! Let's make the 1 cent a fifth smaller, like this:

$0.002 = 0.2 cents

Finally I hope if you have followed all of this so far you will agree that:

0.002 dollar is not the same as 0.002 cents

Ok, now listen to this phone conversation between a Verizon customer and the Customer Service representative. It's a bit long (nearly 23  minutes) but I think it's well worth your time.

The worst thing of this is that one of the CSR has the guts to say the difference between dollar  and cent is, and I quote,

"I mean it's obviously a difference of opinion…"

And do visit VerizonMath blog and read more.

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QotD: Teacher’s Pet

What was (or is) your favorite subject in school?

When I was at school in Hong Kong my favorite subject was science, with maths a close second. I despised Chinese while English came quite nature to me. Strange for a Chinese but it's true. Then when I emigrated to the UK and progressed to A-Level, maths and science had swapped and maths became my favorite subject with physics second. I liked computer studies too because it is hi tech but at that time my mind was in the clouds of abstract mathematics and so I was no good at writing programs in BASIC. I did learn Pascal on my own and managed to write a rudimentary algebraic graph drawing program. Really I was more interested in computer games than learning it as a skill.

Then I went to uni to study physics and I enjoyed that very much in the first year. The maths was easy (the double maths A-Level I took prepared me for it) and really not much work was needed to get good grades. Then in the second and final years we got into the heavy shit; thermodynamic, solid state physics, etc. that involves statistical maths. I hated them with a vengeance, but since they are a very important part of physics I ended up not doing well in exams. It was then that I realized while I love the concept of physics I am crap at actually applying the theory. Around the same time I found that computer programming came very easy to me and I started taking more and more computing courses as my optional units to boost my average. It worked and I managed to graduate with a degree!

And this is how a physics graduate ended up working as a software engineer/developer/programmer. The road isn't that windy, really…

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