Author Topic: Maths in Engineering  (Read 8015 times)

0 Members and 1 Guest are viewing this topic.

Offline JohnwiccTopic starter

  • Newbie
  • Posts: 8
  • Country: au
Re: Maths in Engineering
« Reply #25 on: December 30, 2019, 05:47:49 am »
I suck at math and I found most of that test to be very easy, I really hate to deliver bad news but I think you will really be struggling if you jump into an engineering program right now. Can you afford a private tutor? Are you self motivated? If the latter you could study intensely for a year on Khan Academy or take some classes elsewhere. You should be able to pretty much ace that exam you posted without too much trouble. You will certainly encounter much, much more advanced math on the way to a 4 year engineering degree.

Yes I'm self motivated to lean about circuits that make hardware work, but maths is my downfall. If I apply for a scholarship, I could get a tutor.

BTW the degree that I want to do is 3 years. And I have already aceped the offer, but I can pull out at any time I think before the census date

Do u think I would be able to handle the foundation maths class? https://www.griffith.edu.au/study/courses/foundation-mathematics-1017SCG#trimester-1-gold-coast-campus.
« Last Edit: December 30, 2019, 06:01:46 am by Johnwicc »
 

Offline Rick Law

  • Super Contributor
  • ***
  • Posts: 3490
  • Country: us
Re: Maths in Engineering
« Reply #26 on: December 30, 2019, 07:07:47 am »
I am with those who have been saying "go for it."  If the college already accepted you, it is the college telling you they think you can and they are giving you a go at it.  If there is any chance at all that you can push yourself to the finish line.  Go for it.  Every year you managed to finish is a strip earned.  If you finished with a degree, well, that is a mission accomplished.

You pointed to your math issues.  In my view, there are two distinct kind of "math-confidence" problems.  First is those who really can do it found it too intimidating.  Second is those who is bad at abstraction.

Solving the confidence problem is easy if you are of the first kind.  Just doing it until you are comfortable with it will overcome the problem.

Solving the second kind is a good bid harder.  One has to figure out if the lacking in abstraction is because of poor math foundation, or because of the mind not used to thinking in abstract terms.

Get an SAT practice test, do it - and apply all the applicable limits to the test (such as time limit, no calculators, etc.).  Do it with the intend of getting the best score you can.  Immediately after you finish, think about how you felt.   You may be able to identify your weakness and work on it.
Here is an SAT practice you can start with (and I am sure there are many others):
https://collegereadiness.collegeboard.org/sat/practice/full-length-practice-tests


From my experience as math tutor and as a TA when I was a graduation student (in Physics): Abstraction typically is the most likely problem that held students back.  Let me spend a moment on abstraction.  At the first year, you need merely algebra level of abstraction.  There is plenty of time during year 1 to get yourself in shape math-wise to be able to deal with year 2.  After that, you are on even rougher grounds but you would be experienced enough to handle it.  You probably have been doing abstractive thinking and you just didn't know it.  For example, when you watch a movie, you might have thought: "I wouldn't do it if I was her, instead I would have..."  That is thinking in abstract.  Anyone who have had fantasies was having a good moment living in abstraction.

Go for it, and make it count.

My best wishes to you - I hope you succeed in your pursuit of your goal.
« Last Edit: December 30, 2019, 07:10:15 am by Rick Law »
 

Offline coppice

  • Super Contributor
  • ***
  • Posts: 10035
  • Country: gb
Re: Maths in Engineering
« Reply #27 on: December 30, 2019, 10:48:56 am »
I am with those who have been saying "go for it."  If the college already accepted you, it is the college telling you they think you can and they are giving you a go at it.
That's a very naive view. In much of the world colleges will accept practically anyone, and expect a huge drop out rate at the end of the first year.
 

Offline james_s

  • Super Contributor
  • ***
  • Posts: 21611
  • Country: us
Re: Maths in Engineering
« Reply #28 on: December 30, 2019, 05:53:31 pm »
I'm very hesitant to tell anyone to do anything in the realm of not trying or giving up, but I hate to see someone dump a bunch of money into something and then fail.

I'd say if it's something that one is interested in doing, do what it takes to make it happen, but that test is very, very easy compared to what will be encountered earning an engineering degree. One can go through a whole career designing hardware without ever using math beyond basic algebra (which you will use constantly) but you still have to learn the more advanced math to get through school.

Then as someone else mentioned, the logic/deductive reasoning thing. This is something that cannot be escaped, it is one of the core parts of engineering and one simply has to be proficient at it.
 

Offline nigelwright7557

  • Frequent Contributor
  • **
  • Posts: 706
  • Country: gb
    • Electronic controls
Re: Maths in Engineering
« Reply #29 on: December 30, 2019, 06:19:02 pm »
In 1980 I did 3 maths tests to get on a TOPS (training opportunities course) in industrial electronics.
The first two were just simple adding/subtracting/multiplying and division.
The third was probably up to about GCSE level general maths.
I failed the first time but not by much so I went away and studied what I couldn't do in the test.
I passed the next time and got on the course.
When I started the course on the first day we were given another maths test !
I failed it and along with a few others had to do extra maths lessons alongside the electronics theory.
I quickly caught up. We had to do weekly tests on what we had learned to make sure we were coping with the course.
To start with I wasnt doing very well.
Then things started to fall into place and I started getting regular 100%'s.

I guess what that taught me is if you cant do it to start with if you work hard and don't give up you can get up to speed.

Electronics is very maths heavy. If the basic maths skills aren't there you will struggle badly.

One of my part time jobs now is maths tutoring...….



 

Offline rstofer

  • Super Contributor
  • ***
  • Posts: 9964
  • Country: us
Re: Maths in Engineering
« Reply #30 on: December 30, 2019, 09:52:23 pm »
Do u think I would be able to handle the foundation maths class? https://www.griffith.edu.au/study/courses/foundation-mathematics-1017SCG#trimester-1-gold-coast-campus.

Is that a 3 semester course?  It sure will be a stiff climb if it is only 1 semester.  It goes up through differential and integral calculus but it start somewhere before pre-calc.  Around here that would be 2 semesters (1 year) for pre-calc, 1 semester for differential calculus and 1 semester for integral calculus.  Total:  2 years!  On a trimester system, including some extra emphasis, maybe a 1 year program but that means pre-calc is going to be just a single semester and there is a LOT of material.

But what do I know?  Maybe the goals of the course are different, maybe the level of mastery is reduced.  The thing is, the calculus courses are usually the first year (2 semesters) of a degree program and they are followed up by calc-3, differential equations and linear algebra.  Statistics is taught as a side  issue, I think..

I have no idea whether you can succeed.  It's up to you to put in the same level of effort all of the engineers around here put into their studies.  If you think working 40-60 hours a week and going to school 5 nights a week and finishing a 143 unit program in 4 years (trimester system) was easy, I would dissuade you of that opinion.  It only worked because I was young and driven.

I doubt that any of us would claim to be 'good at math'.  Most of us had to work very hard to get through the program, so will you.

And you absolutely need all 3 calculus courses and differential equations to make it through an engineering program.

Forget about sleep, buy caffeine in bulk and give up on a social life.  There's a reason that engineering students have a glazed look and no social skills.
« Last Edit: December 30, 2019, 09:54:45 pm by rstofer »
 

Offline rstofer

  • Super Contributor
  • ***
  • Posts: 9964
  • Country: us
Re: Maths in Engineering
« Reply #31 on: December 30, 2019, 09:57:53 pm »
I am with those who have been saying "go for it."  If the college already accepted you, it is the college telling you they think you can and they are giving you a go at it.
That's a very naive view. In much of the world colleges will accept practically anyone, and expect a huge drop out rate at the end of the first year.

And yet thousands of others make it through the program.  It is a matter of interest and drive.  All of the other students passed, there is no reason the OP can't pass also.  But it's going to take work.  All that math he didn't take in High School is going to jump up and bite him in the butt.  Just the way it goes...
 

Offline anvoice

  • Frequent Contributor
  • **
  • Posts: 258
  • Country: us
Re: Maths in Engineering
« Reply #32 on: December 30, 2019, 10:33:34 pm »
My economics teacher in college came from India. He told a story about how students back in his day in university would hand-copy textbooks because they couldn't afford them and go through their courses with those textbooks. Do you have that kind of drive? If so, you might be successful. If not, testing the waters using a gap year first to make sure you're ready for the math might be good.

If the college already accepted you, it is the college telling you they think you can and they are giving you a go at it.  If there is any chance at all that you can push yourself to the finish line.  Go for it.
I agree that is a bit off the mark. Colleges accepting people doesn't mean a thing if people aren't willing to put in the work to pass their courses. Especially if you have a huge handicap like the OP does, you better be prepared to put in five times the effort of everyone else to pass.

My concern here is why the OP has a problem with math. If he knew he was bad at it, but is extremely driven and wants to do hardware anyway, he might have found a way around this issue already, by working with a tutor, taking extra classes, or putting in extra work in general. If he isn't particularly driven in the first place, and bad at math, he won't fare well in university. Finally, if he is extremely driven but still unable to do math despite trying harder than anyone, it may again mean he'll face difficulty in class.
 

Online tszaboo

  • Super Contributor
  • ***
  • Posts: 8218
  • Country: nl
  • Current job: ATEX product design
Re: Maths in Engineering
« Reply #33 on: December 30, 2019, 11:29:30 pm »
University math is different than high school math. Profs have a lot of possibility to be crazy, both ways. I passed an exam, by saying "The solution is just the product of two matrices, and it is probably very boring to calculate it", because he released that I understand what the question is, and how to solve it, and thats enough.

Others will fail you on the same exam, if you write a + instead of a - somewhere. Talk to people who already finished the math course. Ask them.

I had a guy asking me, if you can become an EE if you are colorblind, because resistor codes. (in case you are wondering, yes, of course) If he never asked, he wouldn't be an EE.
 
The following users thanked this post: Nominal Animal

Offline m98

  • Frequent Contributor
  • **
  • Posts: 634
  • Country: de
Re: Maths in Engineering
« Reply #34 on: December 30, 2019, 11:56:45 pm »
Others will fail you on the same exam, if you write a + instead of a - somewhere. Talk to people who already finished the math course. Ask them.
Ouch, made that experience first-hand. Went from failing multiple exams to passing the same subjects with flying colors just by changing to another college.
If 90% of a course and its final exam consist of doing algebraic transformations on equations each spanning two whiteboards horizontally, something's off in my opinion…
 

Offline rstofer

  • Super Contributor
  • ***
  • Posts: 9964
  • Country: us
Re: Maths in Engineering
« Reply #35 on: December 31, 2019, 01:02:11 am »
Many universities have a web based rating system for professors and while the results tend to skew high, it is still worth investigating.  If there are multiple professors for a given course, it might be better to select the one with the higher rating.

Alas, some courses only have one professor.  The early courses (first 2 years) tend to have multiple professors simply because of the number of students.

Or, you can go to a university where the courses are televised and there will be hundreds taking the class from a single professor with a herd of teaching assistants.

Recon!  Know before you go!
 

Offline nigelwright7557

  • Frequent Contributor
  • **
  • Posts: 706
  • Country: gb
    • Electronic controls
Re: Maths in Engineering
« Reply #36 on: December 31, 2019, 02:07:47 am »
Learning can be hard work.
I recently converted a 500,000 line program from wpf .net to .net core 3.1.
Some of it was just straight copying of code but other parts were quite different and I had to rewrite chunks of code.
At one point I was doing 15 hours a day converting code.
I was going to bed afterwards and having long nightmares about my code not working !
But if you keep going you eventually get there.
 

Offline Rick Law

  • Super Contributor
  • ***
  • Posts: 3490
  • Country: us
Re: Maths in Engineering
« Reply #37 on: December 31, 2019, 09:13:38 pm »
...
...
If the college already accepted you, it is the college telling you they think you can and they are giving you a go at it.  If there is any chance at all that you can push yourself to the finish line.  Go for it.
I agree that is a bit off the mark. Colleges accepting people doesn't mean a thing if people aren't willing to put in the work to pass their courses. Especially if you have a huge handicap like the OP does, you better be prepared to put in five times the effort of everyone else to pass.

My concern here is why the OP has a problem with math. If he knew he was bad at it, but is extremely driven and wants to do hardware anyway, he might have found a way around this issue already, by working with a tutor, taking extra classes, or putting in extra work in general. If he isn't particularly driven in the first place, and bad at math, he won't fare well in university. Finally, if he is extremely driven but still unable to do math despite trying harder than anyone, it may again mean he'll face difficulty in class.

The "why" is my concern too.  I am being repetitive here just in case the OP read this thread.  That "why" was the reason much of my original reply was to encourage an exploration and think about why the lack of confidence when it comes to math.  Most important perhaps is to take the practice SAT, feel the pressure and actually think about what how it felt.  That is a good way to see if it was pressure, foundational knowledge, or whatever may be driving that lack of confidence.  Can't solve a problem that is unknown so knowing it (defining it) is step 1.

Math is intimidating.  I hope that is the main hold back.  That can easily be fixed: courage and working harder.  Make yourself do it, and then you know you can.  Once you know you can, it is no longer intimidating any more.  You become the boss.  You control it then.

I am with those who have been saying "go for it."  If the college already accepted you, it is the college telling you they think you can and they are giving you a go at it.
That's a very naive view. In much of the world colleges will accept practically anyone, and expect a huge drop out rate at the end of the first year.

And yet thousands of others make it through the program.  It is a matter of interest and drive.  All of the other students passed, there is no reason the OP can't pass also.  But it's going to take work.  All that math he didn't take in High School is going to jump up and bite him in the butt.  Just the way it goes...

Coppice :  You do have a point there.  In my eagerness to encourage the OP not to ignore an opportunity, I overlooked how much downward spiral our colleges have suffered.  So, I assumed (and hope) OP did his home work and made sure that it was a reputable college.

I agree with rstofer here.  It is a matter of interest and drive.   "Gut check" time - how much of yourself are you willing to give to get this goal done.
 

Offline Nominal Animal

  • Super Contributor
  • ***
  • Posts: 7198
  • Country: fi
    • My home page and email address
Re: Maths in Engineering
« Reply #38 on: December 31, 2019, 11:10:28 pm »
University math is different than high school math. Profs have a lot of possibility to be crazy, both ways.
Very true.  There is also a huge difference in "math" math and "applied" math; i.e. between math as a research subject and math as a tool.  I'm horrible at the former (I fail at proofs, for example), but pretty good at the latter (using math to describe and solve problems), myself.

I was almost 30 when I realized I really like using math to find solutions for types of problems, rather than using math to find an answer to a specific problem.  (When I first told a friend I had realized I love this meta-problem-solving aspect of applied math, they called me a pretentious fool and laughed at me.  Fair enough, but my point was that although I am not that good at mathematics as a science, I really enjoy helping others find tools that allow them to solve and construct things neither of us could do alone.  Nothing pretentious in the idea, just poorly expressed.  I'm like a cook that has specialized in helping others learn how to create new recipes, instead of making new recipes, or just cooking the same dishes every night.)

As a personal example, I failed the first part of a split math course at university (applied math; about mathematical methods for physicists), but got a good grade (4 out of 5) for the latter part.  The difference was that I wrote my own "lecture notes" for the latter part.  (The structure of the course was more about math as a science, involving classes of special functions, with tools for solving different types of differential equations as side notes, scattered all over the math-as-a-science text.  My own notes skipped all the history, and instead concentrated on the solution methods, starting from how to determine which approach was likely to yield a solution, and so on.  Because that's what a physicist actually needs; math-as-a-science being useful and one possible approach to practical solutions, but non-critical.)

All the above is to illustrate to the OP, that their own work to find maths resources that helps them find the approach that works for them to learn the mathy tools they need, is absolutely crucial.  Nobody will "offer" it on a plate; it will be completely up to you yourself to find them.  It will take a lot of effort, but my own example is proof that it is not only possible, it can even become very easy.

As a corollary, I personally don't even remember Maxwell's equations by heart. I do understand their context and meaning, and given a problem, I can usually immediately see if (one or more of) the equations can be applied to solve the problem.  I just don't remember the details -- or I do not trust myself to remember the details correctly.  (I've always been poor at memorizing things like names and equations, but that hasn't been a hindrance: instead of memorizing things, I learned to instead understand them, and look the details up quickly and efficiently, at a young age.  It takes more time and effort, but the results speak for themselves.)

Others will fail you on the same exam, if you write a + instead of a - somewhere.
And that really annoys me, especially since there isn't usually enough time to double-check ones own work!

One extremely useful method, often ignored by engineers, is dimensional analysis; essentially, keeping the measurement units with the numerical values within equations.  This has been extremely useful for myself, and made math so much easier/understandable for me.

As an example, consider a problem where you are given a circuit of some sort, and you need to find the power consumed in one specific component of it. You solve the current passing over the component [in amperes, A] and the voltage drop over it [in volts, V].   Let's say the current is 0.300 A and the voltage drop is 4.9 V. If you were used to using only the numerical values, you might simply multiply 0.300×4.9=1.47, and give that as the answer.  But, because of dimensional analysis, when seeing 0.3A and 4.9V, you know that to obtain the power, you need to know if the voltage is relatively stable direct current (in which case [VA] = [W]) or not; if not, you need to additionally know the waveform and phase difference of the voltage and current, to find out the true power.  A short note in the solution, say "because power P = U I for constant direct current, power P = 0.3 A × 4.9 V = 1.47 VA = 1.47 W", will not only show that you understood the situation correctly, but also remind yourself that for alternating current, you'd need to either know more about the voltage and current, or make assumptions about them, to be able to give an answer.
 

Offline WattsThat

  • Frequent Contributor
  • **
  • Posts: 788
  • Country: us
Re: Maths in Engineering
« Reply #39 on: January 01, 2020, 01:39:16 am »
Interesting question on that test document. I’m wondering what it has to do with math, logic or anything other than holding a license to operate a motor vehicle in Australia:

15 Sam is the driver at fault in a car accident.
Which of the following is covered by Sam’s compulsory third-party (CTP) insurance?
A. Repairs to Sam’s car
B. Injury to the other driver
C. Damage to the other driver’s car
D. Cost of repairing a building damaged in the accident
 

Offline coppice

  • Super Contributor
  • ***
  • Posts: 10035
  • Country: gb
Re: Maths in Engineering
« Reply #40 on: January 01, 2020, 01:50:28 am »
Interesting question on that test document. I’m wondering what it has to do with math, logic or anything other than holding a license to operate a motor vehicle in Australia:

15 Sam is the driver at fault in a car accident.
Which of the following is covered by Sam’s compulsory third-party (CTP) insurance?
A. Repairs to Sam’s car
B. Injury to the other driver
C. Damage to the other driver’s car
D. Cost of repairing a building damaged in the accident
Are they trying to test if the candidate can logically identify what constitutes a third party? The odd thing to me is the answer appears to be B, C and D. Did they really mean what does it NOT cover?

 

Offline james_s

  • Super Contributor
  • ***
  • Posts: 21611
  • Country: us
Re: Maths in Engineering
« Reply #41 on: January 01, 2020, 07:19:54 pm »
I'm not familiar with the terms used in Australia but wouldn't it be D? "Third party" implies someone not involved in the accident who suffered a loss, which describes the owner of the building. They were not driving, they were not in a car accident, but their property was damaged as a result of the accident. That's how I would interpret it anyway.
 

Offline coppice

  • Super Contributor
  • ***
  • Posts: 10035
  • Country: gb
Re: Maths in Engineering
« Reply #42 on: January 01, 2020, 08:43:35 pm »
I'm not familiar with the terms used in Australia but wouldn't it be D? "Third party" implies someone not involved in the accident who suffered a loss, which describes the owner of the building. They were not driving, they were not in a car accident, but their property was damaged as a result of the accident. That's how I would interpret it anyway.
In most English speaking countries the first party is the driver, the second parties are the passengers accompanying the driver, and the third parties are anyone outside the car. That's why drivers are typically required to have third party insurance, to protect anyone not directly involved with the driver.
 

Offline Rick Law

  • Super Contributor
  • ***
  • Posts: 3490
  • Country: us
Re: Maths in Engineering
« Reply #43 on: January 01, 2020, 08:55:57 pm »
University math is different than high school math. Profs have a lot of possibility to be crazy, both ways.
Very true.  There is also a huge difference in "math" math and "applied" math; i.e. between math as a research subject and math as a tool.
...
...

This is my opinion:

From my perspective as a Physics major, sometime between being a freshman and being in graduate school, I came to the conclusion that Math is science in it pure abstract form.  Physical science is when mathematics is applied to describe/explain the (kind of) physical. 

Remember, there is no spoon (just mathematics).

What we think of as physical is pure perception.  I am sitting on a chair right now, yet not a single part of my body really  "touch" the chair.  It is the electro-repulsive force between me and the chair that keeps me from "falling" to the ground.

When we have missing energy (in a consistent way), we think, okay, there is a particle that we haven't yet found that shoot off somewhere.  We hypothesis this particle, gave it the right mass, momentum, spin, color, whatever.   Geez, now we see that this particle "exist" in some other experiments as well since we found that missing mass, momentum, whatever.  Is it real?  Color in quantum properties of particles surely is not color as we see in rainbows.  But in quantum/particle physics, it is about as real as any other property such as electrical-charge.

We got this extra speed with the orbiting star - there must be some additional mass holding the star in orbit.  We'll call it dark matter.  We don't see it, it must be there or the star will not be able to be held in orbit at that speed...

So there was no spoon.  We found the mathematics to describe what we "saw" and... well... a spoon kind of fit the explanation well.

At some point, the level of abstraction becomes... well strange (it is and it is not not what "Strange" mean in particle physics).

Math is science in its pure abstracted form.  Nothing physical until your find some physical phenomenon that can be describe by a set or sets of mathematics.

There is/was a joke about Wolfgang Pauli (the joke is so because Wolfgang Pauli was the undisputed go-to guy with understanding the Fine Structure Constant and Quantum Mechanics):  When Pauli got to heaven, he asks God why the Fine Structure Constant is the value we know.  God told him why.  He then explain to God why that couldn't possibly be right.

If I should be able to ask God questions directly, I would have some math questions for him.  But I lack Pauli's expertise in the subject matter and I will have to take God's word for it.
« Last Edit: January 01, 2020, 09:14:32 pm by Rick Law »
 

Offline james_s

  • Super Contributor
  • ***
  • Posts: 21611
  • Country: us
Re: Maths in Engineering
« Reply #44 on: January 01, 2020, 09:27:15 pm »
In most English speaking countries the first party is the driver, the second parties are the passengers accompanying the driver, and the third parties are anyone outside the car. That's why drivers are typically required to have third party insurance, to protect anyone not directly involved with the driver.

Hmm here it's just called liability insurance, it covers damage and injury to others and their property but not the driver themselves, sounds like it's pretty much the same thing.
 

Offline coppice

  • Super Contributor
  • ***
  • Posts: 10035
  • Country: gb
Re: Maths in Engineering
« Reply #45 on: January 01, 2020, 09:31:59 pm »
In most English speaking countries the first party is the driver, the second parties are the passengers accompanying the driver, and the third parties are anyone outside the car. That's why drivers are typically required to have third party insurance, to protect anyone not directly involved with the driver.

Hmm here it's just called liability insurance, it covers damage and injury to others and their property but not the driver themselves, sounds like it's pretty much the same thing.
Does that mean your US liability insurance includes injuries to passengers in your car? That's more than just covering third parties, so its not directly equivalent.
 

Offline Nominal Animal

  • Super Contributor
  • ***
  • Posts: 7198
  • Country: fi
    • My home page and email address
Re: Maths in Engineering
« Reply #46 on: January 01, 2020, 11:10:39 pm »
University math is different than high school math. Profs have a lot of possibility to be crazy, both ways.
Very true.  There is also a huge difference in "math" math and "applied" math; i.e. between math as a research subject and math as a tool.
...
...
Math is science in its pure abstracted form.
Well, I'd say that math is the language in which we express science; science itself being the systematic application of the scientific method to find answers and solutions to all sorts of questions and problems.  (This is why I also prefer to call it a tool instead of a language.)

You see, math itself goes much, much deeper.  Most of what you described is still all "applied" math (i.e., using math to describe stuff) in my opinion, as there exists math about math, metamathematics; and mathematical logic and so on.

Even in physics, the exact same physical phenomena can be described using very different mathematical expressions.  My favourite example is optics: you can use either Fermat's principle or Snell's law to describe the path light rays take.  (It is not the best example, though, because a mathematician can derive the latter from the former by applying the wavelike properties of light.)

Circling back to the original topic, if we treat math as a tool or language to precisely describe physical phenomena, there are many different ways to learn that language, was my point.  Some believe in theoretical investigation, learning the syntax and grammar first, with the application left as an exercise.  Others believe in full immersion: dropping one in the deep end, and forcing them to learn to survive.  Yet others believe in memorizing most common phrases, minimizing the effort needed to work with a specific limited set of problems.  All work, none is obviously superior.  I have my own preferred methods I outlined already, but the optimum approach differs for each individual.  That is, although it is much more work initially, one should try to find out the study approach that works best for themselves; there is certainly enough material online and in books to suit just about anyone.  Even if a book or author is considered "the best" or "recommended", there may be other material better suited for your needs -- or you might have to do your own study notes from scratch, using several different sources, like I had to --, because us humans vary.
 

Offline james_s

  • Super Contributor
  • ***
  • Posts: 21611
  • Country: us
Re: Maths in Engineering
« Reply #47 on: January 02, 2020, 12:01:14 am »
Does that mean your US liability insurance includes injuries to passengers in your car? That's more than just covering third parties, so its not directly equivalent.

No, bodily injury is a separate thing and that's where it starts to get complicated and requirements vary from state to state. Thankfully I've never been in an accident where I was at fault so this is not something I've ever had to deal with.
 

Offline Rick Law

  • Super Contributor
  • ***
  • Posts: 3490
  • Country: us
Re: Maths in Engineering
« Reply #48 on: January 02, 2020, 05:25:42 am »
University math is different than high school math. Profs have a lot of possibility to be crazy, both ways.
Very true.  There is also a huge difference in "math" math and "applied" math; i.e. between math as a research subject and math as a tool.
...
...
Math is science in its pure abstracted form.
Well, I'd say that math is the language in which we express science; science itself being the systematic application of the scientific method to find answers and solutions to all sorts of questions and problems.  (This is why I also prefer to call it a tool instead of a language.)
...
...

We are in agreement.  I would "refine" it one step further (but by doing so, it also expose where I am fuzzy myself).  Math is a language for science when it comes to quantification.  Where quantification is not required, math does not seem necessary.

Electron flow in LED creates photon.  No one needs math to clarify that.  But one cannot describe the relationship between electron flow vs number of photons created without mathematics.

This is where I am fuzzy myself.  Say "dark matter", you do not need math to conceptually understand it exist.  Existence itself is a binary - a quantification between 0 and non-zero.  To prove that "there is something required to making the forces balance" requires math.  So if one can accept it exists without proof, one can forgo math.  But is that really "understand"?

We "accept" a lot of things.  V=IR is something we accept.  Most of us don't really dig deeper:  Why V=IR?  When will this relationship fail?  How will it fail?  And we all know it WILL fail!  When electron flow goes down to electrons you can count, V=IR doesn't apply anymore when you are talking a mere dozen electrons per minute.  Now you are talking statistics and probability.

May be that is why the Ph in the PhD stands for Philosophy...  Eventually, it all gets down to Philosophy.
 

Offline Nominal Animal

  • Super Contributor
  • ***
  • Posts: 7198
  • Country: fi
    • My home page and email address
Re: Maths in Engineering
« Reply #49 on: January 02, 2020, 10:48:00 pm »
University math is different than high school math. Profs have a lot of possibility to be crazy, both ways.
Very true.  There is also a huge difference in "math" math and "applied" math; i.e. between math as a research subject and math as a tool.
Math is science in its pure abstracted form.
Well, I'd say that math is the language in which we express science; science itself being the systematic application of the scientific method to find answers and solutions to all sorts of questions and problems.  (This is why I also prefer to call it a tool instead of a language.)
We are in agreement.  I would "refine" it one step further (but by doing so, it also expose where I am fuzzy myself).  Math is a language for science when it comes to quantification.  Where quantification is not required, math does not seem necessary.
There is math and logic for qualification as well; it's just in the abstract math-about-math domain.  Other tools, like dimensional analysis (which considers types or units instead of quantities), can be combined with math to handle non-quantification type problems.  (Thus, I do agree.)

Electron flow in LED creates photon.  No one needs math to clarify that.  But one cannot describe the relationship between electron flow vs number of photons created without mathematics.
Right; to describe the interactions of the subatomic particles (electrons and photons in this case), we can use for example Feynman diagrams.

I believe it is important to realize this in all subject matters where math is an important tool: it can be used in different ways (and one can approach it in so many different ways, it is important to find the way that works efficiently for oneself), but properly "applying" it with other, non-math methods, is crucial.

For electronics, network analysis and equivalent impedance transforms are excellent examples of such.

To prove that "there is something required to making the forces balance" requires math.  So if one can accept it exists without proof, one can forgo math.  But is that really "understand"?
One of the reasons I love computational materials physics is that every time you run a simulation, the first question both before and after, is always "Does this make any sense?"

Because math is only a tool, it cannot tell you how and when to apply it.  Science, on the other hand, gives us a method (the scientific method, obviously) to direct and guide a questioning mind to examine the phenomena.  Models (usually in the form of a theory or law, often called "something analysis" by mathematicians) bridge the two.

Newtonian physics is one such model.  We know the domain where it applies to an amazing accuracy, and where it fails.

We can even start with ab initio simulations of electrons (using density functional
theory
), and derive the electrical properties of semiconductor materials; in fact, this is what a lot of computational physicists do in practice.

Although this stack, science + methods + math, has completely arbitrary definitions (I'm sure many of those reading this post will disagree with my definitions), it is useful in the same way a well-organized workshop is: it works in practice, because it gives a logical place to store everything one uses.

And just like workshop tools, there are different approaches to math that one can choose.  Some woodworkers only use hand tools; this is roughly equivalent to those that say that you need to be able to derive the Bessel functions yourself, to truly understand and correctly use them (in say solutions to Laplace's equation in cylindrical coordinates).  Some only use a hammer, because all problems can be described as nails of various sorts, and so on.

Just because an approach is popular, does not mean it is optimal/best; just that a lot of humans like it.  It is important to get past that, and examine oneself, to find out which approaches work best for themselves.  This is particularly important in "higher learning", be that in an university, or in just-for-my-own-amusement type of thing.

A particularly good example of that, in my opinion, is in geometry or linear algebra: how to rotate 3D coordinates.  A lot of people learn how to do that by using Euler angles, but it is actually a horrible tool for that: it is vague (there being a couple of dozen different ways to define the angles, and practically nobody bothers to specify which one they mean!) and subject to gimbal lock.  Very few are familiar with versors or unit quaternions, which can describe any rotation; allows adding, subtracting, or interpolating between rotations; is numerically stable when "stacking" any number of rotations; has unambiguous forms for converting to and from rotation matrix form; and while the mathematical operations (like multiplying two versors is done using Hamilton product) look complicated, is in practice very easy and simple to use.
I would go as far as claim that anyone doing 3D computer graphics and using Euler angles, is a fool: doing a lot of hard work for unimpressive results, when a simple, efficient, and problem-free (no gimbal lock) solution exists.  (If someone is using Euler angles in a microcontroller dealing with 3D orientation or rotations, I'd say they are an idiot.  Harsh, but in my opinion, one must acknowledge crap is crap, even if a billion flies love it.)
 


Share me

Digg  Facebook  SlashDot  Delicious  Technorati  Twitter  Google  Yahoo
Smf