The Mathematics Thread

[ellen10]

Yes
No
No

 

[cove]

All I remember was using Sum of an annuity and Rule of 78. Yes I had a slide rule and then a good maths calculator.
Then it was hello computers after I had worked out how to add numbers five across down a page to save time.

 

[markis10]

How many people here could and used to use a slide rule and/or mathematical lookup tables (book of tables)

Still use one

 

[tgh]

Yes
Yes
Yes ( caveat is that it might take a while …..you did not set a time limit..)

add: I recently put new batteries in the HP11c, works perfectly and has outlived all the fancy come afters..Google tells me it is 45 years old…

 

[Pushka]

Alright, because the Mathematics thread is dead, a quick off-hand poll:

How many people here could and used to use a slide rule and/or mathematical lookup tables (book of tables)?

Of those of you who answered in the affirmative, do you think you could still use one or both today?

Yes to tables

No to slide rule (brother four years older used one but gone by the time I got there). I was bummed. I was fascinated by it.

Yes I think so, but why would I?

 

[VPS]

Alright, because the Mathematics thread is dead, a quick off-hand poll:

How many people here could and used to use a slide rule and/or mathematical lookup tables (book of tables)?

Of those of you who answered in the affirmative, do you think you could still use one or both today?

Yes
Yes
Mmmmm probably not

My friends were just moving house and found an old slide drawer that they were going throw in the bin so I rescued it and gave it to a friend who was ecstatic

 

[love_the_life]

Yes
No to slide rule,
Yes to log tables.
.....

Ditto

 

[Quickstatus]

How many people here could and used to use a slide rule and/or mathematical lookup tables (book of tables)?

Of those of you who answered in the affirmative, do you think you could still use one or both today?

Never used a slide rule/, log tables yes
I can use the Abacus though

Cant say that calculus has ever been of any use to me outside of school/uni.

Maybe not obvious but:

Im sure you have pressed on the accelerator in a car.
a(t) = dV/dt
a(t) = d²S/dt²

And compound interest especially the continuous compounding type is an exercise in calculus.
lets say you put $2500 in the bank and after 5 years the bank says you will get $3015.58.
what is the interest rate?
or you could do similar and ask how much will I get after 5 yearsif I know the interest rate

dM/dt = r.M
M = money in bank
t = time
r = interest rate

dM/M = r dt
∫dm/M = ∫r dt
ln(M) = rt +C

At time 0 (initial deposit)
ln(2500) = r0 +C
ln(2500) = C

ln(M) = rt + ln(2500)
M = eʳᵗ x e ᴸᴺ⁽²⁵⁰⁰⁾
M = 2500eʳᵗ

After 5 years M = 3015.38
t = 5
3015.38 = 2500eʳ⁵
r = ln(3015.38/2500) ∻ 5 = 0.037487 or about 3.75%

Its there , we just dont use it
we just remember the compound interest rate formula which is M(t) = M(0) x eʳᵗ
if we forget the formula just go back to basic calculus to get it from first principles

If you dont want continuously compounding, change eʳᵗ to (1+ r/n)ⁿᵗ
where n is the number of compounding periods per year. and r = annual interest rate

 

[Aeryn]

I have a spreadsheet that i use to calculate compound interest and verify i am not over charged interest on my mortgage without needing to use any calculus. I just plug in balance of my offset account, interest rate etc per each day.

I didnt say no one uses it, but ive never used it since a university exam that seemed to have no relationship to anything else.

All the maths I still use regualrly i had learnt by 8th grade when they covered compound interst without calculus.

YMMV.

 

[Quickstatus]

I have a spreadsheet

yes these days Excel is magic but the embedded formulas in Excel use calculus when compounding is in play

Its a pity that most people dont realise that compounding interest is fundamentally calculus

 

[Aeryn]

I dont use an embedded formula, i wrote my own. Compound interest is essentially simple interest calculated more often and added up.

I have 1 row for every day of my mortgage which factors in the interest rate on that day, balance of account, balance of offtset account, annual fees etc. Interest rates dont change often, as most of my spend is on CC offset account also only changes 5 or so times a month. I have a tab for each year of mortgage and where it was each day.

Could it be done with calculus sure, but that would assume constant interest rate and non changing repayments - nice for an estimate but not reality. Banks calculate interest daily (end of day) so i have all the variables. I just update once a month and extrapolate for future, knowing it will change again next month.

Noting banks has made the odd error over the yaears and always refunded interest that should have been charged.

 

[anat0l]

Its a pity that most people dont realise that compounding interest is fundamentally calculus

It is quite easy to develop the compound interest formula / relationship without needing to resort to calculus.

In the current Australian Curriculum, compound interest is normally introduced to year 9 students (with no calculus, of course) but usually later in the year after they have learned simple interest. The derivation is quite easy, but of course hardly any student is interested in reading the derivation of formulas.

Even annuities, which model loans more realistically, can be derived without needing to understand calculus, though by that time someone who can understand that derivation should probably be apt enough to understand calculus too.

 

[Denali]

Alright, because the Mathematics thread is dead, a quick off-hand poll:

How many people here could and used to use a slide rule and/or mathematical lookup tables (book of tables)?

Of those of you who answered in the affirmative, do you think you could still use one or both today?

Mr Denali says yes and yes, he still has a slide rule in his office desk

 

[Aeryn]

Simple interest was taught in 5th Grade, Compound Interest without Calculus in 8th grade in Avanced Maths (maybe later if you only did intermediate or lower level).

Calculus wasnt taught until 11th grade and then only if you do higher levels of maths that was known as 2/3/4 unit in the 90s. What was MIS and MIP didnt learn calculus at all.

I had to relearn calculus in 4th year uni after forgetting it all the second hsc exam was over, only to purge it from brain as soon as that exam was passed. If i dont use knowledge, then my brain purges it to makes room for something more useful.

 

[Quickstatus]

but of course hardly any student is interested in reading the derivation of formulas.

That is part of the issue. rote learning formulas is meaningless without knowing the the principles behind it.
While interest and compound interest can be derived without knowing calculus, it is much simpler and intuitive to derive using calculus.

For example, why is the area of a circle 𝛑r?
The easy way to understand this is to cut the circle into infinitesimally small "pizza" pieces and stack them opposite side to side to form a rectangle and knowing the axiom that C=𝛑d
(There is a more difficult method that involves the formula of a circle )

If i dont use knowledge, then my brain purges it to makes room for something more useful.

Unfortunately true, but once learnt, re-learning is a lot easier.
It is interesting though that once people learn to ride a bike, that skill usually does not go away.

 

[Aeryn]

I rember 8th grade maths teacher using a woodern circle prop made up of thin pie shaped segements, that could be unrolled to give flat edge triangles to explain how pii was derived.

But i dont think you actaully need that background to use formulars which include pii effectively. Just like i dont need to know how a combustion engine works to drive a car or how electricty is generated to turn a light on.

 

[Quickstatus]

But i dont think you actaully need that background to use formulars which include pii effectively. Just like i dont need to know how a combustion engine works to drive a car or how electricty is generated to turn a light on.

That is true but that assumes that superficial knowledge is all that is required.
The problem arises when a deeper understanding is required.

These days no knowledge is required - only how to ask google or facebook

Excel knowledge these days can be a powerful tool for lots of things in everyday life.

 

[Hvr]

Excel knowledge these days can be a powerful tool for lots of things in everyday life.

That's the word.

But if you don't actually understand what outcome you're trying to achieve and how to use it then you're just a human version of AI slop.

 

[drron]

Alright, because the Mathematics thread is dead, a quick off-hand poll:

How many people here could and used to use a slide rule and/or mathematical lookup tables (book of tables)?

Of those of you who answered in the affirmative, do you think you could still use one or both today?

Yes

No

 

[RooFlyer]

Calculus OK. But Complex Numbers - or at least the ‘imaginary’ part, was the work of the devil.