Maths in Engineering  - Page 1
Forum section: electronics / beginners

author: Johnwicc
author_rank: Newbie
timestamp: December 28, 2019, 03:11:54 am
content: I have just graduated from my HSC (Higher School Certificate) from NSW (New South Wales) Australia. I have received on offer from Griffith University in Queensland (Nathan campus) for: Bachelor of Engineering Technology in Electronic and Computer Engineeringhttps://www.griffith.edu.au/study/degrees/bachelor-of-engineering-technology-in-electronic-and-computer-engineering-1586.I need to make a decision before 30 December 2019, to either accept/defer/decline the offer from the university. I'm not confident in my maths skills at all, I have revived a mid band 2 (57% overall mark) in General mathematics 2 for one of my HSC subjects. General mathematics 2 is the easiest maths course you can do in high school.But there is foundation mathematics class I can take at the university to learn higher level maths stuff.https://www.griffith.edu.au/study/courses/foundation-mathematics-1017SCG#trimester-1-gold-coast-campus.But I'm not sure if I would be able to cope with that class too, I have failed the easiest HSC maths in high school. So what should I do then, I don't have long to make a decision?

author: floobydust
author_rank: Super Contributor
timestamp: December 28, 2019, 04:16:23 am
content: I would say it is better to crash and burn trying to make it, instead of letting low confidence and official "rank" in mathematics scare you away. Not from Australia but I would both accept, and sign up for the extra foundation math course. I took one over the summer and it gave me a huge leg up on other students. If you get anxiety and worry, that alone can make a person do poorly in math, or a result from a crappy high school maths teacher.I had poor marks in Gr. 12 general, then took a 1st year Uni math course over summer session. I knew many students that were terrible at math and they made it through engineering. I'll never forget getting 28% on a vector calculus midterm and class average was 22% so I aced that sucker, lol. All the students used to getting 80%+ were in tears. The Bell-curve makes marks totally different than high school where it's arbitrary what the teacher sets is "50%".

author: anvoice
author_rank: Frequent Contributor
timestamp: December 28, 2019, 06:03:48 am
content: Do you enjoy engineering and technology? Or math for that matter? If so, no reason a little bit of effort can't make this work for you. Just don't expect to have the knowledge handed to you on a platter just because you accept.If you prefer something like what is called the fine arts here in the US, it may be more reasonable to apply for that...

author: Johnwicc
author_rank: Newbie
timestamp: December 28, 2019, 06:13:55 am
content: Quote from: anvoice on December 28, 2019, 06:03:48 amI love how technology works especially of how computer hardware works, but I find maths vary hard. I normally get around 20% to 40% on exam papers like this:https://educationstandards.nsw.edu.au/wps/wcm/connect/d6c0ee8f-7f12-4f19-a62c-716b74015186/2018-hsc-maths-general-2.pdf?MOD=AJPERES&CACHEID=ROOTWORKSPACE-d6c0ee8f-7f12-4f19-a62c-716b74015186-mVoxsTm

author: anvoice
author_rank: Frequent Contributor
timestamp: December 28, 2019, 06:38:36 am
content: Quote from: Johnwicc on December 28, 2019, 06:13:55 amThat's a pretty basic math test. In general electronics and engineering requires much more advanced stuff (like calculus, i.e. differentiation and integration). I do agree that if you do accept you should take some extra math fundamental courses in parallel with your main curriculum.There's something called abstraction in both computer programming and hardware, which basically means you treat some things as black boxes and build bigger systems out of them by just knowing their input/output behavior. In that sense, you can have a good level of success without knowing how all the internals work.Did you ever consider software development? Also has a lot to do with computers, and (depending on what you do) may not require as a rigorous a math experience.

author: IconicPCB
author_rank: Super Contributor
timestamp: December 28, 2019, 06:41:56 am
content: You have a lot of learning to do in order to take up engineering.Sisyphus comes to mind or in the vernacular deploying a pointed stick along a hillside might be deemed appropriate.Why did you apply for a STEM based course?

author: floobydust
author_rank: Super Contributor
timestamp: December 28, 2019, 06:43:42 am
content: Engineering is largely about problem solving and university uses maths to teach and characterize everything. The maths general exam you linked to has both in it.It would be good to know what aspect is difficult for you. Memorization, problem solving, equations etc.If you are more of a "hands on" person, then starting out as an electronics technician or similar would be better and not much math. I started off like that because in high school I had poor marks due to partying, university open house had old crappy equipment and buildings, and relying on equations to explain how something works seemed absurd to me. Everything was new at the tech college.Years later I went to engineering in university, I guess because I needed more challenges.

author: Johnwicc
author_rank: Newbie
timestamp: December 28, 2019, 06:49:46 am
content: Quote from: anvoice on December 28, 2019, 06:38:36 amYea, but I have more of an interest in the "hardware"side of things other then softwareQuote from: IconicPCB on December 28, 2019, 06:41:56 amI like how things work, but my maths skills a always poor

author: John B
author_rank: Frequent Contributor
timestamp: December 28, 2019, 06:55:50 am
content: Sounds like you should take a gap year to intensively address the math issue. While "giving it a go" is worth some praise, you need to balance that against the real life consequences of being saddled with potentially tens of thousands of dollars of extra debt because you failed the courses.Also if you are just grasping the fundamental prerequisites, that will detract from you absorbing the new engineering material that you are paying the big bucks to study. It doesn't seem like a good use of the amount of money it will cost. You can learn all the math for free in your own time.

author: anvoice
author_rank: Frequent Contributor
timestamp: December 28, 2019, 07:05:03 am
content: Quote from: John B on December 28, 2019, 06:55:50 amSounds like the best idea to me, assuming it's viable for you. If you truly like hardware and are willing to put in the effort to make this work, you'll probably get the math down with practice. I don't know how much education costs in Australia, but it could be expensive to try just to fail.

author: Johnwicc
author_rank: Newbie
timestamp: December 28, 2019, 07:07:42 am
content: Quote from: John B on December 28, 2019, 06:55:50 amI am thinking about a gap year. I need to make a decision before 30 December 2019, to either accept/defer/decline the offer from the university. I'm just frozen what to do atm. I'm really scared if I do accept the offer, I will fail all maths that is shown to me and I will become a dropout statistic.

author: anvoice
author_rank: Frequent Contributor
timestamp: December 28, 2019, 07:14:54 am
content: Quote from: Johnwicc on December 28, 2019, 07:07:42 amDoes deferring essentially give you another year to make up your mind? If so, that seems like your best choice. If you're really not confident, it means you personally don't know where you stand in terms of knowledge, and university is not that forgiving.

author: Johnwicc
author_rank: Newbie
timestamp: December 28, 2019, 07:19:31 am
content: Quote from: anvoice on December 28, 2019, 07:14:54 amYea, deferring is a gap year. That means I would still have my place in the coarse, but it would commence in feb 2021, other then feb 2020

author: Johnwicc
author_rank: Newbie
timestamp: December 28, 2019, 07:41:34 am
content: Quote from: floobydust on December 28, 2019, 06:43:42 amIn the General mathematics 2 course I found the hardest is: probably,simplifying algebraic expressions, financial maths,geometry and statisticsI found easy is: rearranging equationsSome of the question can be found herehttps://educationstandards.nsw.edu.au/wps/wcm/connect/d6c0ee8f-7f12-4f19-a62c-716b74015186/2018-hsc-maths-general-2.pdf?MOD=AJPERES&CACHEID=ROOTWORKSPACE-d6c0ee8f-7f12-4f19-a62c-716b74015186-mVoxsTm

author: IconicPCB
author_rank: Super Contributor
timestamp: December 28, 2019, 07:52:34 am
content: Think about an apprenticeship in high tech game.In fact try out for an apprenticeship with one of military services... Say navy.Air force may be too uptight. Foot soldiering may be too close to dirt.At the end of Your tour You end up with a qualification in technology and possibly man management. Sought after skills in civilian life.

author: Johnwicc
author_rank: Newbie
timestamp: December 28, 2019, 12:51:44 pm
content: BUMP ^

author: coppice
author_rank: Super Contributor
timestamp: December 28, 2019, 04:02:04 pm
content: If things like basic calculus trouble you, you are likely to have a lot of problems in an engineering degree course. However, the options in most courses let you avoid the hardest maths in the later years of the course, so you can steer your degree to suit your interests and abilities to some extent. Much of the maths in an engineering course is less about preparing you for a lifetime of doing maths than about giving you the framework needed to understand what is going on in a wide range of physical processes. A life in engineering can be tough if you lack a feel for the maths, even if you aren't working through maths problems every day.

author: rstofer
author_rank: Super Contributor
timestamp: December 28, 2019, 04:28:37 pm
content: Being from the US, I have no idea how your system works or what the various levels mean. Nor do I understand what a BS in Technology means. Is it a full blown engineering degree (like our BSEE) or a technician certificate?In terms of engineering:You have identified a weakness and it needs to be fixed. Take the gap year and spend it doing math. Around here the course might be called "Pre-Calculus" and it would involve Algebra, Geometry, Trigonometry and definitely is focused on solving problems. It takes two semesters (a full year) and is considered a prerequisite for Calculus I which is a first semester class in an engineering curriculum. IF you don't have pre-calc skills, you just added a year to your graduation date.Around here we have Community Colleges that offer pre-calc and they are fairly inexpensive.You can get help at Khan Academy and, if you want to spend some money, at CalcWorkshop.com (highly recommended). There is a free course on "Limits" at CalcWorkshop to help you evaluate whether her style of teaching meets your needs.More advanced math is taught in parallel with engineering subjects but, first semester, you need to start with Calculus I. In turn, there will be classes for Calculus II, Calculus III, Differential Equation and Linear Algebra. That is 5 semesters of math or about 2-1/2 years of a 5 year program. Not to worry, there will be more math in the last 2-1/2 years. It just will have a different title, like "Field Theory" or "Signals" or "Control Systems" or "Circuits". There will be a math oriented class every single semester for 5 solid years!Get that pre-calc out of the way!

author: floobydust
author_rank: Super Contributor
timestamp: December 28, 2019, 07:59:29 pm
content: Taking a year gap is dangerous, many people get a job and relationship and get comfy. They never take any post-secondary and end up with a life of low wages and hard labour.What you do in that year is really important, it's easy to get lost in the freedom of not having to go to school.You say you want to climb a mountain but are not good at it. Where is the part of you that looks for help or wants to improve that, instead of worrying about falling off the mountain?To see if you have any chance at being a mountain climber, take a university entry math course like pre-calculus and see how you do.Many of my peers in engineering flunked courses, some flunked the same course twice. They stuck to it and graduated.

author: rstofer
author_rank: Super Contributor
timestamp: December 28, 2019, 09:15:37 pm
content: It's either use the gap year to get a foundation in math or plan on working twice as hard if you head off to the university now. Still, you can make it.I dropped out of college as a freshman the day Kennedy was assassinated. Not because of that but more because I was just tired of going to school. A couple of years in the Army, a few years of working and I started over (6 years late) but this time I had a family, a job and had to do classes at night. Not an easy way to get things done. I wouldn't recommend it.I would only recommend the gap year if you plan to spend every waking moment working on math. If not then you still have two choices: Start at the university or give up on the idea altogether. If you think pre-calc is tough or you think your first freshman semester is tough, just wait. It gets more intense as you go along. The good news is that you build the foundation to make it through as you go along. It's still going to be a lot of work but I always look at this kind of thing as: "Hundreds of thousands of people have done this, I can do it too!". My version of "The Law of Large Numbers". If enough people take the exam, I'll pass.It's easier if there are no side issues. Compliments of the US Navy Seals: "The only easy day was yesterday!"

author: coppice
author_rank: Super Contributor
timestamp: December 28, 2019, 09:24:20 pm
content: Quote from: floobydust on December 28, 2019, 07:59:29 pmMany others realise the path they were taking was just what was expected of them, and not what they wanted. In general, people who take a gap between school and university take university a lot more seriously, because they have a better understanding of why they are there. A lot of top universities make offers to be taken this year or next, so someone can choose to take a gap year with their course beyond that settled in advance. The universities prefer students who have experienced life a little more.

author: floobydust
author_rank: Super Contributor
timestamp: December 28, 2019, 10:57:35 pm
content: As long as the parents don't start playing the harp, "what are you going to do with your life?" during the gap year. It can be more pressure unless a good plan is there.A university classmate said to me "I don't think I like engineering" during 3rd year EEI asked why did he take it, "because my parents said I have to take either engineering or business". He side-transferred into the faculty of business and I was shocked because that was such a waste of much time and tuition fees and course material. Who knows if he even liked business, in the end. But his parents were paying for it all. I sure couldn't afford to do any of that it was my dime for all of it.OP is lucky to have some real interests in hardware, at least a direction to go after.My university only cares about your age past 25, as a "mature student".First year engineering I swear was a cash cow, they made tuition money from students dropping out yet keeping the enrollment numbers appearing high for government funding.From 1,000 down to less than 400 after first year, the attrition rate really was stunning.

author: IanB
author_rank: Super Contributor
timestamp: December 28, 2019, 11:33:09 pm
content: Quote from: Johnwicc on December 28, 2019, 06:13:55 amAlthough this is called a "maths" test, that is not really what it is. It is a test of logical and deductive reasoning with some testing of memory skills.This would be a problem for you, because engineering is very largely dependent on logical and deductive reasoning. If you struggle with a test like that you are really going to struggle with engineering, and not because of the mathematics.As others asked, you need to do a bit of introspection. What is it you find hard about such a test? Why do you only manage to get 20% to 40% marks? Do you not manage to remember the concepts the questions are asking about, or do you have trouble figuring what the questions are asking you to do? Is there some way you can practice, or take extra classes to improve on what you find hard?To be honest, I am not sure how you would pass an aptitude test for entry into an engineering program with such limited mathematics skills? Something doesn't quite add up here.

author: jmelson
author_rank: Super Contributor
timestamp: December 29, 2019, 05:45:44 pm
content: Quote from: Johnwicc on December 28, 2019, 07:07:42 amReal-world EE requires good algebra and a little specialized math (Laplace transforms and such) but all the heavy lifting can be done with computer assistance. You do need to learn the fancy maths for classes, but then hardly anyone ever uses it again, with tools like mathcad. But, it is real good to understand how the math works.It might be good to get in a couple advanced math courses during your gap year to get totally up to speed on trig, calculus, diff eq. and such things.Jon

author: james_s
author_rank: Super Contributor
timestamp: December 29, 2019, 06:19:03 pm
content: 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.

author: Johnwicc
author_rank: Newbie
timestamp: December 30, 2019, 05:47:49 am
content: Quote from: james_s on December 29, 2019, 06:19:03 pmYes 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 dateDo 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.

author: Rick Law
author_rank: Super Contributor
timestamp: December 30, 2019, 07:07:47 am
content: I am with those who have been saying "go for it." If the college already accepted you, it isthe college telling you they think you canandthey are giving you a go at it. If there isany 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-testsFrom 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.

author: coppice
author_rank: Super Contributor
timestamp: December 30, 2019, 10:48:56 am
content: Quote from: Rick Law on December 30, 2019, 07:07:47 amThat'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.

author: james_s
author_rank: Super Contributor
timestamp: December 30, 2019, 05:53:31 pm
content: 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.

author: nigelwright7557
author_rank: Frequent Contributor
timestamp: December 30, 2019, 06:19:02 pm
content: 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...….

author: rstofer
author_rank: Super Contributor
timestamp: December 30, 2019, 09:52:23 pm
content: Quote from: Johnwicc on December 30, 2019, 05:47:49 amIs 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.

author: rstofer
author_rank: Super Contributor
timestamp: December 30, 2019, 09:57:53 pm
content: Quote from: coppice on December 30, 2019, 10:48:56 amAnd 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...

author: anvoice
author_rank: Frequent Contributor
timestamp: December 30, 2019, 10:33:34 pm
content: My economics teacher in college came from India. He told a story about how students back in his day in university wouldhand-copytextbooks 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.Quote from: Rick Law on December 30, 2019, 07:07:47 amI 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 iswhythe 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.

author: tszaboo
author_rank: Super Contributor
timestamp: December 30, 2019, 11:29:30 pm
content: 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.

author: m98
author_rank: Frequent Contributor
timestamp: December 30, 2019, 11:56:45 pm
content: Quote from: NANDBlog on December 30, 2019, 11:29:30 pmOuch, 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…

author: rstofer
author_rank: Super Contributor
timestamp: December 31, 2019, 01:02:11 am
content: 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!

author: nigelwright7557
author_rank: Frequent Contributor
timestamp: December 31, 2019, 02:07:47 am
content: 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.

author: Rick Law
author_rank: Super Contributor
timestamp: December 31, 2019, 09:13:38 pm
content: Quote from: anvoice on December 30, 2019, 10:33:34 pmThe "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.Quote from: rstofer on December 30, 2019, 09:57:53 pmCoppice: 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 withrstoferhere. 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.

author: Nominal Animal
author_rank: Super Contributor
timestamp: December 31, 2019, 11:10:28 pm
content: Quote from: NANDBlog on December 30, 2019, 11:29:30 pmVery 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 findananswer toaspecific 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 rememberMaxwell's equationsby heart. Idounderstand 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 insteadunderstandthem, and look the details up quickly and efficiently, at a young age. It takes more time and effort, but the results speak for themselves.)Quote from: NANDBlog on December 30, 2019, 11:29:30 pmAnd 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, isdimensional 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  = ) 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 remindyourselfthat 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.

author: WattsThat
author_rank: Frequent Contributor
timestamp: January 01, 2020, 01:39:16 am
content: 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 carB. Injury to the other driverC. Damage to the other driver’s carD. Cost of repairing a building damaged in the accident

author: coppice
author_rank: Super Contributor
timestamp: January 01, 2020, 01:50:28 am
content: Quote from: WattsThat on January 01, 2020, 01:39:16 amAre 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?

author: james_s
author_rank: Super Contributor
timestamp: January 01, 2020, 07:19:54 pm
content: 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.

author: coppice
author_rank: Super Contributor
timestamp: January 01, 2020, 08:43:35 pm
content: Quote from: james_s on January 01, 2020, 07:19:54 pmIn 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.

author: Rick Law
author_rank: Super Contributor
timestamp: January 01, 2020, 08:55:57 pm
content: Quote from: Nominal Animal on December 31, 2019, 11:10:28 pmThis 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 appliedto 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.

author: james_s
author_rank: Super Contributor
timestamp: January 01, 2020, 09:27:15 pm
content: Quote from: coppice on January 01, 2020, 08:43:35 pmHmm 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.

author: coppice
author_rank: Super Contributor
timestamp: January 01, 2020, 09:31:59 pm
content: Quote from: james_s on January 01, 2020, 09:27:15 pmDoes 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.

author: Nominal Animal
author_rank: Super Contributor
timestamp: January 01, 2020, 11:10:39 pm
content: Quote from: Rick Law on January 01, 2020, 08:55:57 pmWell, I'd say that math is the language in which we express science; science itself being the systematic application of thescientific methodto 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; andmathematical logicand 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 eitherFermat's principleorSnell's lawto 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 foryourneeds -- or you might have to do your own study notes from scratch, using several different sources, like I had to --, because us humans vary.

author: james_s
author_rank: Super Contributor
timestamp: January 02, 2020, 12:01:14 am
content: Quote from: coppice on January 01, 2020, 09:31:59 pmNo, 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.

author: Rick Law
author_rank: Super Contributor
timestamp: January 02, 2020, 05:25:42 am
content: Quote from: Nominal Animal on January 01, 2020, 11:10:39 pmWe 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.

author: Nominal Animal
author_rank: Super Contributor
timestamp: January 02, 2020, 10:48:00 pm
content: Quote from: Rick Law on January 02, 2020, 05:25:42 amThere 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.)Quote from: Rick Law on January 02, 2020, 05:25:42 amRight; to describe the interactions of the subatomic particles (electrons and photons in this case), we can use for exampleFeynman 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 analysisandequivalent impedance transformsare excellent examples of such.Quote from: Rick Law on January 02, 2020, 05:25:42 amOne of the reasons I lovecomputational materials physicsis 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 (thescientific method, obviously) to direct and guide a questioning mind to examine the phenomena. Models (usually in the form of atheoryorlaw, often called "somethinganalysis" 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 withab initiosimulations of electrons (usingdensity functionaltheory), 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: itworks 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 theBessel functionsyourself, to truly understand and correctly use them (in say solutions toLaplace's equationin 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 humanslikeit. It is important to get past that, and examineoneself, 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 usingEuler 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 togimbal lock. Very few are familiar withversorsorunit 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 usingHamilton 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.)

author: rstofer
author_rank: Super Contributor
timestamp: January 03, 2020, 06:31:34 pm
content: The University of Florida has two separate math tracks: One for math majors and the other for engineers. As engineers, we really don't need the derivation, we don't need to see the inner beauty, we only need to be able to apply the results of the derivations. In fact, there is pretty much a slide away from even solving advanced equations by hand. At my grandson's university, MATLAB is used for everything. His Differential Equations course was more about problem solving with MATLAB than the underlying elegance of the derivations. Terrific! It's the application that's important!I don't personally care a whit about how the equations and derivations came to be, I just want to use the tool. I don't need the history of fire, I just asked for a match.Free hint to the up and coming student:MASTERpartial fraction expansion in Algebra or it will come back to haunt you for Inverse Laplace Transforms. This topic is usually skimmed over in Algebra because it has little application at that level. It is a make-or-break deal when you get to Laplace.https://lpsa.swarthmore.edu/LaplaceXform/InvLaplace/InvLaplaceXformPFE.htmlSo, pay attention!

author: coppice
author_rank: Super Contributor
timestamp: January 03, 2020, 08:43:06 pm
content: Quote from: rstofer on January 03, 2020, 06:31:34 pmThis is fine if you are content to spend your life retreading old ground, but its not a suitable grounding for doing novel things. Matlab is a blessing for the working engineer, but its a curse for students. I lets them avoid understanding anything they do, and they are increasingly encouraged to take this path. If they have any aspirations it will come back to bite them.

author: rstofer
author_rank: Super Contributor
timestamp: January 04, 2020, 01:23:39 am
content: In my view, the only reason for being on an engineering track is to get a job as an engineer. Scientists are in a different program.How much new grass is there going to be in Mechanical Engineering and what is the probability of grazing there? Most graduates are going to do grunt level engineering until they retire. Truth is, engineering is boring. I hired engineers, I didn’t actually do all that much. Tell them what you want, how much you want to spend and see what they come up with.I hired some great engineers. They made me look good.

author: Nominal Animal
author_rank: Super Contributor
timestamp: January 04, 2020, 01:37:50 am
content: Quote from: coppice on January 03, 2020, 08:43:06 pmFor years, I had the same position, coppice.Then, I realized that in math, unlike in most other fields, one does not need to "forget" things to learn a new approach, because the different approaches never contradict. In physics especially, we use approximations, and it is sometimes a hard knock to realize that stuff that you've been told is a hard law, is actually just a model that applies only in specific circumstances.So, the cost of that "bite" in math is just taking the additional courses: additional study time. Worst case, the quick Matlab/Octave path was just wasted time.

author: coppice
author_rank: Super Contributor
timestamp: January 04, 2020, 01:58:31 am
content: Quote from: Nominal Animal on January 04, 2020, 01:37:50 amA very common thing holding people back is when they don't know just how much they don't know. Its hard to fill in gaps when you don't even recognise their existence. That's why a solid grounding in your college years is such a boon throughout your life. The sad thing is this is being lost through universities migrating to trade schools. Students leave with a lot of tactical knowledge that will serve them for a few years, but far too little strategic knowledge that will serve them for life.

author: GerryR
author_rank: Frequent Contributor
timestamp: January 04, 2020, 12:57:50 pm
content: Quote from: coppice on January 03, 2020, 08:43:06 pmI agree here 100%. What I refer to is what I call "cookbook" engineering. You don't know why something works, you just look up a formula and move on. I believe we all do that to some degree, especially in areas that we are not accustomed to working in, but it shouldn't be that way in your professional area. If you learn the basic principles, you can derive what you need when you need it, and I believe it makes one more creative.