What is “Mathematics”

[PatJParticipant @patj87806]

I am starting a new chat thread, so we don't polute the other one with mathematics.

A little history of me and mathematics:

I recall mathematics in 1st grade distinctly, with the bundles of sticks.

"No problem" I said, very obviious where they are going with these sticks and bundles.

By 3rd grade I recall getting behind in math, and was unable to follow it.

I asked for assistance, but none was forthcoming, and so I ignored math up until I took geometry in high school, which I liked very much.

I tried Trig in high school, but to no avail; I could not grasp it.

I got to college and I told my advisor "I want to take courses that are technical, but NO math ! ". LOL, young people can be stupid, and I fell into that category perfectly.

After 3 years of technology, I found the courses too watered down for even my "anti-math" liking.

I went back to the same advisor, and said "I want to change from Technology to Electrical Engineering. She looked shocked, and said "Well NOBODY does that".

My response was "Well I guess I will be the first then".

EE was hell, but I got through it 4 years later, with a lot of help from my math-genius girlfriend (now wife).

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[PatJParticipant @patj87806]

[PatJParticipant @patj87806]

When I started in Electrical Engineering, I had to basically learn math from scratch (I did know geometry, but that was the extent of my math knowledge).

I started with a Trig class, and then moved on through four semesters of calculus.

Along the way, I often asked myself "what the heck is Math exactly?".

Everyone taught it, but nobody seemed to be able to explain in layman's terms exactly what it was.

I finally came up with my own definition of math, which is "Math is a foreign language, uses as a shorthand method to describe the relationship between things in the universe, both in a static and dynamic way".

If you write out E=m c sq, it is a very long winded thing, such as: Energy equal the mass times the speed of light squared. Very cumbersome to use words, but both the written words and the shorthand mean the same thing, and describe relationships between things in an exact way.

Another analogy I used was the shell game.

You have a series of cups that are turned upside down, and you have math under each cup.

You can side the cups all around in any sort of confusing fashion, but when you raise the cups, you still have the same things under them, but just rearranged.

[PatJParticipant @patj87806]

For complex numbers, I used the analogy of a two-line phone, that has buttons for Line 1 and Line 2.

You can answer Line 1, or answer Line 2, and use either one, but you cannot answer Line 1 and Line 2 at the same time (using the old 2-button phone).

So you keep vectors stored as Line 1, Line 2 information, and all is well.

Don't mix your Lines.

Calculus was extremely intimidating at first, but eventually the simplicity of much of calculus became apparent.

Calculus is very useful in many ways, with respect to rate of change of variables, velocity, acceleration, stability, natural frequency, etc.

Took me a while to get a feel for Calculus, but again, it boiled down to treating it like a foreign language.

When I would see a strange formula, with all sorts of exotic symbols, I had to learn to read it and understand what the symbols meant; ie: summation "S" symbol, rate of change per time (dV/dT), etc.

The language of math not only describes what we see in the world around us, ie: 10 bushels of wheat, but it goes much deeper than that.

Math can be used as a "magic" (its not really magic, but it seems that way to those who do not understand it), and it can be used as a crystal ball, to predict what will happen in the future.

You can use math to predict whether an airplane control will operate correctly, or whether the airplane will fall uncontrollably out of the sky. Ditto with about anything, if your mathematical model is sufficiently accurate.

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[PatJParticipant @patj87806]

The math that we use operates within a somewhat narrow range of constraints, ie: we don't really use math equations such as "you are in the center of a massive black hole, where even light cannot escape".

We limit our math to a range of things we can understand.

What is the math for a black hole? I am not sure.

People often aske me "You took all that math in school, but do you really ever use it ?".

The answer is "No, I don't use anything other than addition, subtraction, multiplication, and division, on a daily basis".

But………and this is a big BUT………..I can crack open any handbook about any topic, and regardless of how gory the math may be, I can generally read the equations, and get a pretty good feel for what the equation means.

This is important if you are trying to design something, and you need to know how it will function, such as a power transformer, with induced currents, eddy losses, iron core saturation, hysteresis, etc.

The forumlas lay out the critical variable, and allow you to make things that work pretty much as intended, with good efficiency.

So I repeat, "What is math ?".

My answer "A foreign language".

It is akin to describing relationships, such as John is your second cousin, twice removed.

You get the idea. Very useful stuff, mathematics.

Was mathematics invented? Most definitley, just like the alphabets, which are used to describe physical objects or ideas.

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[Frances IoMParticipant @francesiom58905]

try reading Ian Stewart “the problems of Mathematics” published 1987 so well mature by now – might save significant time – his 1st chapter definition is that mathematics is about ideas – the following 19 chapters develop on this.

[derek hall 1Participant @derekhall1]

Ok so someone please clear this up for me.

Mathematics has an "s" at the end

I always shorten it to maths……which is logical, like the subject !

So why do some call it "math"……it cannot be short for mathematic……….?

One of lifes conundrums I suppose……

I hated maths at skool, I was hopeless. Managed to get an apprenticeship and suddenly with the right lecturers I began to grasp maths. Just goes to show the importance of a good lecturer or teacher…

Regards to all

[CalumParticipant @calumgalleitch87969]

The trick is that 'mathematics' is itself an abbreviation: there is no such thing as a mathematic, but there are mathematical arts, which was long ago abbreviated to 'mathematics'. In America, they had lost the adjectival sense of the word, so when 'mathematics' was felt to be a bit of a mouthful, it became 'math'. In the UK, 'maths'.

One of the big issues with maths is that we have practically no trained mathematicians in our schools. A century ago most Oxbridge mathematicians found jobs as school teachers and trained the next generation. Nowadays anyone with any mathematical competence can earn far higher salaries doing almost anything other than teaching, and the result is that most maths in British schools is taught by English and PE teachers (who do the very best they can, in fairness). It's hardly surprising people struggle with maths when their teachers barely understand the subject.

[not done it yetParticipant @notdoneityet]

Math or maths? ‘Math’ denotes only one part of the whole?

I still have a school exercise book from about 1961/2 where I had already mastered the means of only doing ‘simple maths’. I never actually worked out anything until I had to – we used log tables back then, so a simple arithmetic error could introduce horrendous errors in calculated results. Most complex expressions usually cancelled out quite a lot, to provide an easy final single calculation using log tables (before slide rules were introduced to us).

Imaginary numbers, if you get that far, definitely need something, in the sequence, to actually get rid of them! The square root of minus one will easily be dealt with (removed) if it can either be multiplied or divided by itself.

I don’t particularly like pure maths, but do enjoy the applied side.

Algebra is a very useful tool, but can often scare youngsters. Manipulating simultaneous equations is yet another useful means of solving problems. Geometry often needs the trig to calculate the answers. Statistics is useful, but only when used properly. Lies, damn lies and statistics is very true when results are ‘cherry-picked’!

The expression I like to demonstrate (and often use) is (a+b)(a–b) for calculating squares of numbers.

I mostly avoid internet calculators – preferring to check the maths myself.

Americans must find science so much more difficult than those using SI units? I grew up with £sd, Lbs and ounces, feet and inches. I’m glad we used metric, at school, for science subjects.

[Mick B1Participant @mickb1]

Mathematics can manifest as an art form.

I remember a lecturer explaining how to solve (I think) compound angles in a Computer Assisted Manufacturing course in the 80s.

It was like a Bach fugue – he started with a formula, then progressively expanded it until he had 2 blackboards completely covered in equations. Then he worked through them with algebra until he had a single division sum to punch into a calculator.

It was beautiful, and I understood every step of it.

At the time.

[peak4Participant @peak4]

It's a topic which came reasonably naturally to me, and I went on to study, Maths, Further Maths and Physics (+General Studies) as my A levels.

A few days ago I was reading a tale (apocryphal??) of someone on a plane who'd been reported to the flight crew as a potential terrorist, as he was writing in a "strange language"

It turned out he was working on differential equations, so I guess it's a language as well as an art form.

Bill

[EmgeeParticipant @emgee]

I believe these days mathematic calculations are made in spreadsheets containing the required formula, you just enter the variables and hit Enter.

I am not saying you don't need the same level of learning to understand any changes needed to fine tune but the result is more simple to achieve.

Emgee

[Martin ConnellyParticipant @martinconnelly55370]

Bill, my 4 A level subjects were exactly the same as you did.

Martin C

[PatJParticipant @patj87806]

Posted by not done it yet on 28/05/2022 21:45:51:

Americans must find science so much more difficult than those using SI units? I grew up with £sd, Lbs and ounces, feet and inches. I’m glad we used metric, at school, for science subjects.

Americans don't have problems with science, since they don't take it anymore.

Sad but true.

I do recall getting a multitude of units thrown at me in school, and it was used to try and trick students into getting the wrong answer, which tricked me for a while, until I caught onto the old "units switch" hat trick.

The way I finally started working problems was to work out the units first, and if the units all cancelled out to give me the unit I was looking for, then I plugged in the numbers. I still use this method.

I scratched my head when I first saw "maths". How many of them are there anyway? I said.

There is only one topic of mathematics; and so there is just "math"; just my slant on the nomenclature.

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[PatJParticipant @patj87806]

Posted by peak4 on 28/05/2022 21:59:01:

It's a topic which came reasonably naturally to me, and I went on to study, Maths, Further Maths and Physics (+General Studies) as my A levels.

A few days ago I was reading a tale (apocryphal??) of someone on a plane who'd been reported to the flight crew as a potential terrorist, as he was writing in a "strange language"

It turned out he was working on differential equations, so I guess it's a language as well as an art form.

Bill

LOL, I can hear it now………."miss, miss, somebody is writing in that voodoo language in aisle 5, we must DO something to stop this….".

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[PatJParticipant @patj87806]

I see it as like "feet".

You may have two feet, but that does not mean you have "feets".

I don't know, I guess it is what you grow up hearing others say.

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[PatJParticipant @patj87806]

I worked with a young woman who had a masters in mathematics.

I use to quiz her about what she did with that knowledge, and what it meant to her.

Apparently she had no concept of how any of it related to the real world; none whatsoever.

However, she was a superb mathematician, and very talented in that respect.

So I guess it is like training someone to make a very precise part on a lathe, but they don't know what the part is for, and they don't know how to design the machine upon which the part fits.

Just a tool in the toolbag I guess; it is all in what you do with that tool.

My wife is a math genius. She got straight A's in every math class, including but not limited to Field Theory, Statics, Dynamics, Thermodynamics, 4 semesters of Calculus, Transforms, Differential Equations, etc.

It was so easy for her that she went on to get a Masters in EE, graduating with honors.

So I had a case study to observe and compare with, since math was anything but easy for me.

I asked her more than once "How do you do it ?".

She said "I just think about the problem, and the answer appears in my head".

LOL, I always wished I had that gift, but unfortunately there is very little in my head.

For her, it was a matter of thriving; for me is was a matter of surviving (school).

Math was brutal for me during school. I have made peace with it these days.

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Edited By PatJ on 29/05/2022 00:49:17

[derek hall 1Participant @derekhall1]

Hi PatJ,

Yeah maths was horrible for me as well at school. In the late 1960's we had to do something called "modern maths " which was the in trendy thing at the time. Set me back years.

Every maths school teacher I had was awful.

I was fortunate to get a marine engineering apprenticeship and went to technical college where the lecturers were vastly better qualified and had the ability to explain clearly.

I went on to complete an HND in mechanical engineering and then also in electronics. I even studied maths with the open university.

I dont pretend to be good at it, just see it as a tool. I must admit in the latter stages of the ou courses in pure maths, the maths got a bit …..well…..weird!!!!

[PatJParticipant @patj87806]

Derek-

Your post reminds me of some of the tricks I had to use in order to get through school.

At the beginning of the semester, I would attend every session of a given calculus class that I needed.

They were all the same class, but taught by different professors.

I would pick the best professor, and then transfer into his/her class.

Having a good professor (for me) was the difference between understanding the material to a great extent and passing the class, and not comprehending the material and failing.

Some professors were gifted in that they could break down a complex subject into something that was understandable and approachable for a beginner.

The professors who bragged about getting through their doctorate with a 4.0 (+) gradepoint average were absolutely the worst at teaching any subject. I quickly figured out who those folks were and avoided them like the plague.

I had an oriental fellow for my first FORTAN class, and I recall distinctly what he said on the first day, which was (in a broken english with a heavy accent) "Computer is like man eating hamburger………….cannot put whole hamburger in mouth at once………must take bites…..".

I failed his class, but retook it with another instructor and a better book, and made an "A".

I still have my FORTRAN compiler.

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Edit: I recall some of those senior level classes getting rather "spacy" towards the end, and I recall the instructor struggling to explain it in any rational way.

I also recall the senior level classes getting so rough that I seriously wanted to just walk away from it all and never see another equation in my life.

The only reason I did not quit school was because I was so heavily invested in it by the time I got to my senior year, that it would have been too much to give up.

My motto in my senior year was "graduate engineering school or die trying".

Many days I did not know which way it would go, but I finally got through it, with much rejoicing.

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Edited By PatJ on 29/05/2022 04:47:10

[not done it yetParticipant @notdoneityet]

The way I finally started working problems was to work out the units first, and if the units all cancelled out to give me the unit I was looking for, then I plugged in the numbers. I still use this method.

Ahh, the main difference between pure and applied maths? Maths, with units, applies to real situations, while Sines, Cosines and Tangents are just (pure) numbers.

I insert the units when working through a calculation that is not a simple one, as a check system. I simply remember M = VD (Mass = Volume x Density) as my first triangle (although I hadn’t been introduced to ‘triangles’, for re-organising equations, back then). VD was memorable because it referred to human disease, in those days. There were other ‘naughty’ ways to remember equations using mnemonics.

Again, cancelling numerators with denominators simplifies the calculations. That anything divided by itself is unity is a great help when applying maths to real situations. If more did it they would,perhaps, not be spouting rubbish. For instance, power instead of energy – particularly where electricity is concerned.

Perhaps one reason why maths is either OK or hated is that it is likely the only examination where one can achieve a 100% result. No waffling, having an opinion on the matter (subjectivity) – the final answer is either right or wrong.

That gaining a maths exam ‘pass’ result can be achieved without getting any right answers can be a difficult concept for many school-age students – but achieving 100% needs all the right answers.

I like maths – as long as it is simple.

 

Edited By not done it yet on 29/05/2022 07:34:03

[derek hall 1Participant @derekhall1]

I recall many years ago doing calcs with fluid mechanics using a technique called "dimensional analysis", where alongside your numeric workings you had a similar working just using the units as a simple example multiplying 4 mm by 8 mm……..you would note ….. mm x mm = mm^2.

Useful to check that your expected answer was going to be in sensible units.

My dad used to have a saying "Calculate the follow consumption, if a bottle of ink cost 2/6d, to how many square yards will a chicken run?"

[derek hall 1Participant @derekhall1]

I don't mind maths to be honest – it is similar as learning a foreign language.

Hate and loathe statistics though I call it "maths for politicians".

I agree with Not Done It Yet – there is no subjectivity or personal opinion in maths, it's wrong or its right. Unlike statistics where you can make it show anything you want it to !

[PatJParticipant @patj87806]

One trick they used on the professional engineer's exam was to ask vague, open-ended questions.

The answer was highly subjective.

The approach to take was to state every assumption you made, and then work the problem based on your assumptions.

I did well with these types of questions, but was a bit shocked when I saw the first one.

When designing things in the real world, there is never one answer or one solution to anything.

For students who go through school with every question being multiple choice, they struggle when given infinite choices.

I generally ask a client the following, before proceeding with a solution to a problem:

1. How much money do you want to spend?

2. How long do you need it to last?

3. How easy of access to it do you need for maintenance?

4. Are there any limitations on the amount of space I can use?

5. Do you have a favorite vendor that you prefer?

6. Do you have adequate power available to feed the equipment? If not, do we need to expand the power source?

Then I start the layout, and start making calculations.

Some clients have basically infinite money (such as a large air freight company in town), and they want the very best money can buy ,and something that will last forever and never break.

Diddo for the local refinery, and large wastewater plants.

Other clients may be tight on money, and so they trade off things.

For big clients, who can't afford a shutdown for any reason, the cheapest overall long term design often has the highest initial expense.

As I have told some young students, don't crack walnuts with a locomotive.

But if you do have a big problem, don't hesitate to use a locomotive.

One student asked "How do I know when to use a locomotive, and when not to use a locomotive".

My response was "That is the art of engineering. There are often no simplistic solutions in the real world, and you have to learn when to use what."

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[PatJParticipant @patj87806]

Some clients have very knowledgeable staff, and some employ some very ignorant folks.

The worst clients are the ones who bring you in, and say "We are having this problem, and we want you do use this solution".

So many times, I have to tell them "That is not your problem, and that solution will not do anything to correct your problem".

People will say "I have a harmonics problem", or a thermal problem, or a voltage over or under from the utility company, and on and on.

In school, they spoonfeed you cookbook questions with exact answers.

In the real world, the real question is "What exactly is the problem?".

More often than not, the client is in left field about what his problem is.

Many engineers are this way too unfortunately, ie: they make a false assumption, and then spend a lot of money installing something that does not correct the problem.

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Edited By PatJ on 29/05/2022 09:03:42

[Clive SteerParticipant @clivesteer55943]

I think the infinite answer questions are a classic case of "show your working" where the answer isn't as important as the way you got there. How does one test the "creativity" of a candidate to use the stand building blocks of engineering that the maths and other analysis techniques tought in schools allow you to understand. The real indicator of creativity is the translation of a requirement into a solution. A well designed product can be likened to a jigsaw puzzle where every piece links intimately to the next to make an efficient homogenous design. The worst situation, having just completed the 100 piece puzzle, is when the salesman asks you for the must have feature that requires it to become a 101 piece puzzle.

CS

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