EEVblog Electronics Community Forum
General => General Technical Chat => Topic started by: fonograph on August 18, 2018, 11:28:31 pm
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I have to admit one embarrasing fact about myself,my math and particulary my equation skills are extremly bad.I didnt study after I got 15 years old,whats even worse,I failed to learn math past about second grade.I only got through elementary school by cheating and my teachers being too merciful.I only went to engineering unrelated middle school one year,dropped out and never did any official education after that.
I realized some time later in my life I have big passion for electronics and my goal is to become electronic engineer.For past two years I have been reading and watching videos about electronics alot but my math skill deficiency is becoming limiting factor.I went around my weakness by seeking material that is light on math and explains stuff with words but this cant go on forever.
In my antenna thread someone suggested learning Maxwell equations and I was sad becose I knew there is no way in hell with my current math skill to ever be able to understand them.I also bought metric funkton of EE books and while the noob oriented ones I can diggest,the advanced ones are like just pages and pages covered in equations.The authors of these books are skilled in math,explain everything with math,if you dont know math,its like you cant even read that book.
I realized I must get my shit together and learn math.So I ask you,people of eevblog forum,can you give me some guidence on how to learn equations? I know math is huge and I would rather only spend time learning whats important from EE perspective,but I dont know what is so thats why I am asking you for help.I prefer learning from internet, youtube,Khan academy etc
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I didnt study after I got 15 years old,whats even worse,I failed to learn math past about second grade.
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I realized I must get my shit together and learn math.So I ask you,people of eevblog forum,can you give me some guidence on how to learn equations? I know math is huge and I would rather only spend time learning whats important from EE perspective,but I dont know what is so thats why I am asking you for help.I prefer learning from internet, youtube,Khan academy etc
Hello.
Well I would have to say that if you are that far behind in math it would be best to either try free courses on the Internets (I haven't looked but I would bet there are quite a few). Either that or go take some basic algebra or perhaps even more basic than that, in your local community if you need the motivation of an instructor. If you really mean that you "failed to learn math past about second grade" you certainly have a lot of work to do. But I'm sure there are more suggestions coming.
Good Luck. :-+
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The beauty of the internet is not only its depth, but also its width. Traditional schools present material in one or a few ways and if that's not right for you, that's it. The internet allows you to look around and find someone who can explain things in a way that you understand. It really pays to look around, rather than looking at a source that's not right for you and getting discouraged.
When you've done that, it's a matter of doing it and doing it a lot. I always remind myself of Brian Cox, a reasonably famous physicist. He once said that he really was terrible at maths too and only got good by doing it a lot. Even the people we look up at have had to work to acquire the skills. The trick is to go at it and to keep going at it until you get better.
That being said, it seems you've already found Khan Academy. What's stopping you from progressing through the years there and learning ever more advanced maths?
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Become a software developer.
There innumeracy won't be noticed and might even be regarded as a badge of honour :(
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I realized I must get my shit together and learn math.So I ask you,people of eevblog forum,can you give me some guidence on how to learn equations? I know math is huge and I would rather only spend time learning whats important from EE perspective,but I dont know what is so thats why I am asking you for help.I prefer learning from internet, youtube,Khan academy etc
It's really difficult learn without starting from the foundations and building up. If you try to skip steps and jump straight to more advanced things you will have tremendous difficulty understanding them.
So I would say you really need to start with high school textbooks and work through the things you missed early on.
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I always remind myself of Brian Cox, a reasonably famous physicist. He once said that he really was terrible at maths too and only got good by doing it a lot.
When a physicist says they are "really terrible at maths" it may not mean what you think it means. It may mean they feel they are not quite up there with the super-geniuses of the world, but they may still be vastly better than you or I.
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Become a software developer.
There innumeracy won't be noticed and might even be regarded as a badge of honour :(
:phew:
;D
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The type of math that is about equations is called algebra?
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When a physicist says they are "really terrible at maths" it may not mean what you think it means. It may mean they feel they are not quite up there with the super-geniuses of the world, but they may still be vastly better than you or I.
This was before he was a physicist: "He said on The Jonathan Ross Show that he performed poorly on his maths A-level exam: "I got a D ... I was really not very good ... I found out you need to practise."
I think he elaborated more on another occasion, but the gist was that maths skills aren't given even to scientists. You need to put the work in to get better. It's easy to get discouraged when you see people who are seemingly naturals, but almost all have had to struggle through being bad before getting better.
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The type of math that is about equations is called algebra?
Yup - you study the symbols of basic math like + - / * = and also the substitution of unknowns with symbols like x such as x + 4 = 10. Then you learn basic rules for solving these equations. It's really kind of fun if you start out basic and work your way up. :)
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Thank you xrunner! I think my problem is not so much that I cant do the calculations,I think the actual calculating part is easy,the problem that kills me is knowing what do the symbols mean.I cant calculate something when I dont even know what the symbols mean.What stops me from being to able to solve them is that instead of numbers,these equations use letters and some weird hieroglyph looking things and it looks like wall of alien/chinese text.
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Thank you xrunner! I think my problem is not so much that I cant do the calculations,I think the actual calculating part is easy,the problem that kills me is knowing what do the symbols mean.I cant calculate something when I dont even know what the symbols mean.What stops me from being to able to solve them is that instead of numbers,these equations use letters and some weird hieroglyph looking things and it looks like wall of alien/chinese text.
That too sounds like a matter of familiarizing yourself with ever more complex maths. Sooner rather than later plugging numbers in stops working. You need to familiarize yourself with both what the symbols mean and how you solve the resulting equation. It doesn't help knowing a symbol means the integral of something if you don't know what to do with it. That's what exercises are for.
I see you've found Khan Academy. What's stopping you from progressing through the years and learning ever more complex maths?
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Thank you xrunner! I think my problem is not so much that I cant do the calculations,I think the actual calculating part is easy,the problem that kills me is knowing what do the symbols mean.I cant calculate something when I dont even know what the symbols mean.What stops me from being to able to solve them is that instead of numbers,these equations use letters and some weird hieroglyph looking things and it looks like wall of alien/chinese text.
Well I don't think we want to start a math class here but yea the symbols are just telling you to do an operation. Like () parenthesis means "do this shit in here and find the value then work on the stuff outside", ... just learn what the symbols tell you to do and it's not that bad.
It's just a bunch of rules, which if followed lead to a correct answer. That why they say artificial intelligence can do math really well because it's just a bunch of rules. :-//
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Well I don't think we want to start a math class here but yea the symbols are just telling you to do an operation. Like () parenthesis means "do this shit in here and find the value then work on the stuff outside", ... just learn what the symbols tell you to do and it's not that bad.
It's just a bunch of rules, which if followed lead to a correct answer. That why they say artificial intelligence can do math really well because it just a bunch of rules. :-//
Wolfram Alpha is already pretty good at doing rather complicated things. If you get it to understand your question, it tends to have the right answer.
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Wolfram Alpha is already pretty good at doing rather complicated things. If you get it to understand your question, it tends to have the right answer.
Oh yea I haven't played with that in a while I'll have to check it out again.
Say I was just thinking, does somebody have an equation solver on the web that actually shows how the equation is solved for the student? Like if they type in any equation it shows them step-by-step how the equation is solved and not just the answer? Let's them enter any equation and it shows the steps done in order? I bet somebody has done that and it would be a good teaching tool for people like fonograph.
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Algebra does work a lot on equations but so does calculus, which is more the kind of tools you need for maxwell equations if that's why you asked.
Being said that, learning calculus without understanding algebra is tricky if not impossible, I had parallel courses of both but advanced(ish) algebra with basic calculus. You need some basic algebra tools to go for the rest of the cake.
Now, you need to build up in math, in my degree I was talking to a teacher after I gave my final test of the class, known as one of the harder of the career, signals and systems, and I said him I prepared for the test in 3 days, that the class didn't appear to be that hard to me or have that many new concepts, but my math formation was in a different university, which had much better math classes. He agreed with me that the math department of the university was kind of falling apart and he was paying for that, in a class that was supposed to use a lot of mathematical tools to learn applications instead of teaching mathematics to be able to do the applications.
What I mean with this, expend as much time in your math as you can, do simpler electronics in the mean while, or at least things where you don't need the math or was already done by somebody else, so you don't get bored of the journey. Once you get the math fluid all other stuff will come together pretty quickly.
The path is starting with all the high school math, then the university level my way was real function understanding, algebra, real calculus with single variable, then multiple variables, then complex variables and discrete math to finish, also some statistics.
After that as I said signals and systems, which takes tools from all the others and puts them together in useful ways. Control theory also uses a lot of math and is very useful for EE.
All that goes together with physics, and the electronics courses, I say this because if you get a good way to go meshing all together would be much more rewarding than waiting to have all the math tools available to start with the next step, which will be quite frustrating and you are likely to quit math again (let's hope you don't) before learning enough.
JS
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Oh yea I haven't played with that in a while I'll have to check it out again.
Say I was just thinking, does somebody have an equation solver on the web that actually shows how the equation is solved for the student? Like if they type in any equation it shows them step-by-step how the equation is solved and not just the answer? Let's them enter any equation and it shows the steps done in order? I bet somebody has done that and it would be a good teaching tool for people like fonograph.
I think the paid app for Wolfram Alpha does or did that. They change things occasionally and I haven't used it recently, so I'm not sure it still does that. It was popular amongst students for this reason.
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The basic math curriculum used in school is appropriate. Pick it up where you feel you dropped out. Start with arithmetic. The algebra. Somewhere in those two make sure you pick up number systems and logarithms. Traditionally geometry comes next, but you might be able to skip that. Next trigonometry and basic calculus. That takes you through what a good high school used to do. For engineering you will need additional calculus including vector calculus, differential equations and linear algebra at a minimum. The differential equations course will be the single most important key to understanding Maxwell's equations. More math beyond that is good to have but it branches many directions and you will be able to pick for yourself at that point. None of these is deadly difficult to understand, but as with anything else practice is required to make them into tools you can apply readily.
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Sign up on Khan Academy.
You can take aptitude tests to determine the level you are currently at. Then do the videos and lessons starting from that point. It is an amazing resource and can get you to some rather advanced topics. If you get stuck on a certain thing, just watch the videos once more, take the test again and/or look for alternate explanations on the web.
The key for me is practice and some repetition to the point where it 'clicks'. That is the point where I feel like I understand the concepts, not just memorized the steps. Mastery of the concepts is important because math is like a pyramid, it just keeps building on itself.
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It was Satan himself that added letters to mathematics!
Literally everybody has trouble with first semester Algebra. "Find X" "Well, it's right here on the diagram, how far can it go!"
Enough levity, this is a serious situation because engineering is ALL math. And I'll let you in on a secret: Many practicing EEs don't understand Maxwell's Equations either. Curl? Divergence? I struggled with that course!
Khan Academy is great! Literally, it starts at Pre-School and works up through Differential Equations, Laplace Transforms and Fourier Series. This is about the end of the line for EEs except those who take Field Theory (Maxwell's Equations).
CalcWorkshop.com is excellent. It starts with Algebra and works up through Differential Equations. It costs money but I gladly pay it to help my grandson through Calculus. He got an 'A' in Calc I last semester so the program is worth every dime it costs.
Here's the thing: You aren't going to learn math without thousands of hours of practice. Why should you get to the level required for engineering any faster than we did?
Now, for a hobbyist, elementary Algebra is about all it takes. Plus a little matrix math - just to the level of Gauss-Jordan Elimination. It is nice to understand the differential equations behind RC, RL and RLC circuits but it might not be necessary. That's why you take 4 semesters of Calculus and Linear Algebra before you get to Circuit Analysis. It just takes a ton of math.
So, get started! Pick a place to start in the Khan Academy series and go for it. Set aside an hour or so each night and work at it.
There's a problem with YouTube tutorials and that is that you have a tendency to just watch. That is not the same as 'learn'. You need to solve problems for yourself. Khan Academy has quizzes throughout the program. Be sure to work them all. Maybe even find text books at Alibris.com - something cheap. Almost every book will have problems and answers for some.
Desmos.com for plotting equations
Symbolab.com for solving more complex problems (like pre-calc and Calculus problems).
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Oh yea I haven't played with that in a while I'll have to check it out again.
Say I was just thinking, does somebody have an equation solver on the web that actually shows how the equation is solved for the student? Like if they type in any equation it shows them step-by-step how the equation is solved and not just the answer? Let's them enter any equation and it shows the steps done in order? I bet somebody has done that and it would be a good teaching tool for people like fonograph.
I think the paid app for Wolfram Alpha does or did that. They change things occasionally and I haven't used it recently, so I'm not sure it still does that. It was popular amongst students for this reason.
Try symbolab.com If you subscribe you get a more detailed explanation but you get the big picture even with the cheap seats. I subscribe!
I think symbolab is focused on Calculus.
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You could look online and in 2nd hand bookstores for high school maths textbook sets. Maybe try abebooks.com
Pretty sure old HS math texts will be really cheap. Avoid anything from the modern 'common core' curriculum, it's brain-poison.
It's a lot more convenient reading physical paper books, than on screen. Also you can jot notes, work examples etc.
Another possibly good idea would be to ask around (local schools/Uni?) for someone willing to give you free or cheap math tutoring. Having someone who can evaluate your math state of knowledge and focus on advancing that, would help a lot. Since you 'don't know what you don't know' so to speak. Also they can make you do the necessary exercises. Sort of like a maths gym trainer.
This is actually what I need. If I had the motivation.
https://www.google.com/search?q=find+x+here+it+is+math+jokes (https://www.google.com/search?q=find+x+here+it+is+math+jokes)
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Thank you all for the avalanche of great tips! :)
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Try symbolab.com If you subscribe you get a more detailed explanation but you get the big picture even with the cheap seats. I subscribe!
I think symbolab is focused on Calculus.
Yea that's really nice for learners. We had nothing like that in 1985 at university we just got together in a study group. Like Bob Dylan says the times they are a changin'. :)
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It is a lot easier to learn maths as an adult, than as a child.
For a start, you are not as likely to be distracted by just about anything. :D
One thing that happens ( happened to me), is that if, when first being introduced to Algebra, you miss one
class due to illness, by the time the next one comes around, everybody has moved on, & you are still bobbing in their wake.
Teachers love to refer to "transferring" part of an equation from one side of the equation to the other, assuming the kids understand the basic rule of equations --"whatever you do to one side, you have to do to the other".
You can't do maths?
Well, just by functioning in society, you are using it all the time.
Here's one:-
How many cents in $10?
in. $100?
You will say - that's easy, just multiply the dollar amount by 100--------- (1)
OK, how many cents in $n?
Obviously the same rules apply, so Number of cents in $n = 100n----------(2)
We can now select any numerical value for n & always be able to determine this information for any value of n
But wait, isn't that what you already did in (1) above?
By the way, (2) is a bit long winded, so if we can represent "Number of cents in" as a letter, we can write it as , maybe "c" for cents, so we can say. c=100n ------(3)
(for the specific case of converting dollars into cents.)
But wait, there's more!
Maybe you have a lot of cents & want to convert them to dollars.
Can we use (3). In a different way?
As c=100n is an equation, we can do the same thing to each side.
If we divide both sides by 100, we get c/100= 100n/100 ----(4)
Obviously, 100 goes into 100n, "n" times so:- c/100 =n, which, as we want to
find out n, we would normally write it as---------------------------------n=c/100-----(5)
From the original discussion,we know that n represents the number of dollars, so for, say, 455cents you would end up with $4.55.
All stuff you do in your head whenever you sort out your change!
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Try symbolab.com If you subscribe you get a more detailed explanation but you get the big picture even with the cheap seats. I subscribe!
I think symbolab is focused on Calculus.
Yea that's really nice for learners. We had nothing like that in 1985 at university we just got together in a study group. Like Bob Dylan says the times they are a changin'. :)
I graduated in '73 - sliderule all the way!
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In my antenna thread someone suggested learning Maxwell equations and I was sad becose I knew there is no way in hell with my current math skill to ever be able to understand them.
Now I'm feeling guilty.
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I graduated in '73 - sliderule all the way!
Haha hardcore.
For me it was the HP 41C :clap:. Served me very well I loved it. :D
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I was also going to suggest Khan Academy, they have numerous topics but math seems to be their strong point. Start as far back as you need to go and keep going. I used them with success to re-learn some math I hadn't used in decades and had completely forgotten how to do.
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Here's the thing: You aren't going to learn math without thousands of hours of practice. Why should you get to the level required for engineering any faster than we did?
Precisely.
Wasn't it Arnold Palmer who said "The more I practice golf, the better I get".
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It is a lot easier to learn maths as an adult, than as a child.
For a start, you are not as likely to be distracted by just about anything. :D
I disagree. For a start there is this forum, then the rest of the web :(
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There are books that cover the foundations of mathematics in a way that is suited to adults and not to children (as a high-school textbook would be).
I'm thinking particularly of Courant & Robbins "What is Mathematics?". It's a nearly perfect book, there is nothing unnecessary in it at all.
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In my antenna thread someone suggested learning Maxwell equations and I was sad becose I knew there is no way in hell with my current math skill to ever be able to understand them.
Now I'm feeling guilty.
;D
No,I am thankful you did it.Small dose of saddness is good if it stimulates the action that removes the problem.I should have learned math long time ago.If I wasnt sad about not being able to learn Maxwell equations,I would be procrastinating god knows how long.
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I found until you run into something like a relevant differential equation IRL that its very difficult to learn. Once you observe a system and see how it behaves and ongulates and stuff you can start to appreciate the underlying mathematics as a decent approximation to begin to do some work on but always realize that when you get heavy into metrology the underlying equations will have a kind of fog of war or noise floor that seems to be related to things like materials properties and boundaries between different regimes of equations used in a piecewise manner which make exact mathematical solutions kind of irrelevant towards engineering design, these are always complicated and often not researched or explained well so your precise solution will still be covered in noise, so you wonder was the precise solution worth solving? Not to mention safety and reliable factors which often result in your precise solution being multiplied by six (or more if you have the budget).
I only began to have a understanding of PID theory when I began to work hands on with more complicated cooling systems, before that I watched a bunch of videos talking about cars approaching eachother and took some classes but it never really stuck.. I found myself bored usually, only when I had a problem that required that kind of understanding to figure out did the math look interesting enough to learn.
Granted it is useful to have the basic engineering mathematics courses with passing grades so you at least know what field of mathematics to look at when you are faced with a engineering problem, so things like gradients, multivariable equations, differential equations... even if you fail all the tests its good to sit through all the classes so you can kinda remember which text book you need to look in, when you are finally interested.
I always found pure mathematics related to topology and set theory MUCH more interesting from a 'dry' standpoint then any kind of engineering mathematics in terms of learning it in a classroom without any kind of force of will of your own to pursue a solution in. Engineering mathematics is horribly boring unless you are solving a problem.
For instance with hydraulics you can struggle to figure out exact pipe geometries for particular flows and stuff, but then realize later the thing you should really be thinking about is clogging and corrosion prevention. Nice math derived solutions often ignore real world problems that have a way larger threat, then when you tweak them to satisfy the other design criteron you start to kinda think, I could have used the first order approximation for this. Then when you compare your final design to your 'preicse' solution the error bars are humongous, then when manufacturability comes in it gets even more ridiculous.
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I am totally the same, worse is I have lot of interest in various fields of engineering, but the math is what will get me hung up. It's why I just do this stuff as a hobby and not professionally. I can try different parts, or use online calculators etc for stuff. In the pro world not so much.
If I'm building something, God help me if I need to calculate how much load it can handle, because I won't even know where to start, you can throw all the formulas you want at me but I won't know what to do with them or which one to use for what or what the variables are suppose to be etc. So instead I'll just over engineer the hell out of it and call it "good enough". >:D I guess that won't always work for every situation though, in things like radio you kinda have to be dead on. ex: antenna length, or spacing between elements on a yagi etc.
Suppose once I really do start to get into more serious projects I should take more time to try to learn math though. I made it through college, but I was always on the verge of failing. The general concepts would click, but as soon as it got more complicated I was lost.
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I am totally the same, worse is I have lot of interest in various fields of engineering, but the math is what will get me hung up. It's why I just do this stuff as a hobby and not professionally. I can try different parts, or use online calculators etc for stuff. In the pro world not so much.
If I'm building something, God help me if I need to calculate how much load it can handle, because I won't even know where to start, you can throw all the formulas you want at me but I won't know what to do with them or which one to use for what or what the variables are suppose to be etc. So instead I'll just over engineer the hell out of it and call it "good enough". >:D I guess that won't always work for every situation though, in things like radio you kinda have to be dead on. ex: antenna length, or spacing between elements on a yagi etc.
Suppose once I really do start to get into more serious projects I should take more time to try to learn math though. I made it through college, but I was always on the verge of failing. The general concepts would click, but as soon as it got more complicated I was lost.
I never saw the professionals get heavy on the math lol, the solution is usually cost related. You get ridiculous experiments done to see if money can be saved.
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I found until you run into something like a relevant differential equation IRL that its very difficult to learn. Once you observe a system and see how it behaves and ongulates and stuff you can start to appreciate the underlying mathematics as a decent approximation <snip>
For the last couple of years I have been playing with analog computers. What an amazing way to get a sense of differential equations! Problems that were a real drag to graph using nothing but a sliderule are readily displayed on an oscilloscope.
Engineering mathematics is horribly boring unless you are solving a problem.
Some universities have two math tracks: One for math majors which spends a lot of time on details and another for engineering students where they cut to the chase.
For EEs, math is for getting a handle on how things will work. There will be at least 2 semesters of Physics in the EE curriculum and this is a perfect place to use differential and integral calculus. In fact, those math classes may be pre-requisites to the Physics classes. How to explain the natural response of an RC circuit without calculus? It isn't super heavy duty calculus but it does involve both differential and integral forms. Lots of 1-e-t/T. EE is just full of exponential and logarithmic functions. And trig functions or, in the case of Eurler's Formula, both trig and exponentials at the same time.
In every case, solving word problems is the best way to get real experience with the tools. It just turns out that almost everybody hates word problems. It isn't solving the problem itself that causes pain, it's the inability to formulate the problem from the description.
Take the simple capacitor charging equation, solve it for parts you have on hand and then run it on a prototype board. It is awesome to see the trace look exactly like the equation predicted. That's when the math will make sense!
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In addition to the great resources identified above, check out Michel van Biezen's YouTube channel, and his website www.ilectureonline.com (http://www.ilectureonline.com)
On his channel and website, he specializes in showing how to solve, step by step, countless problems/questions by example. It is excellent supplementary material to a lecture or a book. Right now I am watching his (multiple) series on integration. He also has topics other than math, including electrical engineering and physics.
Best of luck, and don't quit. I ran away from math in my school days, and like many others, I regret it too. On a positive note, I can say that as an adult, I find myself genuinely attracted to the math as well as its application, and that the more I learn, the more interested I become. I would expect the same to happen for you. For the record, I started with algebra as an adult, having failed algebra twice in high school and developing a debilitating phobia of math that resulted in me running away from it entirely. Revisiting the topic in my late twenties and early thirties, I was able to tackle algebra and geometry/trigonometry, although that statement feels disingenuous because even these two fields are massive.
The point is, it can certainly be done, and you should definitely do it. I have found it rewarding thus far, and the experience is completely different than anything I had in school. I dare say it is mostly enjoyable and fascinating.
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Can you please help me lay out some roadmap how to progress with learning? My biggest obstacle is that there is so many things I dont even know where to start.I dont want to learn thing that I cant learn if I dont know some other thing.
I would like to have some rough step by step roadmap so I can tackle with one specific thing at a time.From the previous posts I so far come up with this plan :
Arithmetic > Algebra > Trigonometry > Calculus
Differential equations are another specific category or is it kind of a sub-category of the ones of the above?
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Earlier someone had suggested you sign up at Khan Academy and take the math placement test. I second this idea, and have done it, too. You should do this soon. It will help answer several of your questions and give you an idea of a logical progression.
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Earlier someone had suggested you sign up at Khan Academy and take the math placement test. I second this idea, and have done it, too. You should do this soon. It will help answer several of your questions and give you an idea of a logical progression.
Yes,that was great advice,I will take that test today but I still wanted some rough estimate of what areas of math will I need and what to learn first.Two users wrote algebra is must before calculus so thats already one guide rule I will obey.
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I think I asked a few times earlier in this thread. You seem to have found Khan Academy already. What's keeping you from progressing through the lessons there? It's based upon the logical progression of the school system without keeping you bound to it. If you know something already you can skip it and if you have trouble with something you get to take it slow. Meanwhile, your progress is tracked for you perfectly.
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Yes,that was great advice,I will take that test today but I still wanted some rough estimate of what areas of math will I need and what to learn first.Two users wrote algebra is must before calculus so thats already one guide rule I will obey.
You'll find out that you don't know what you need to solve something soon enough, so I'm not sure roadmapping the thing in advance is entirely necessary or effective. You almost seem more worried about mapping everything out than just getting to it. Ultimately you won't know what you don't know, so it really boils down to getting your feet wet.
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I think I asked a few times earlier in this thread. You seem to have found Khan Academy already. What's keeping you from progressing through the lessons there? It's based upon the logical progression of the school system without keeping you bound to it. If you know something already you can skip it and if you have trouble with something you get to take it slow. Meanwhile, your progress is tracked for you perfectly.
Ofcourse,nothing is preventing me,infact,I just opened account there.My point of this thread was to get idea of what types of math should I learn and in what sequence.While I think Khan is great,I am not sure if it can tell me what math will I need as EE or in what order should I learn it.
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Earlier someone had suggested you sign up at Khan Academy and take the math placement test. I second this idea, and have done it, too. You should do this soon. It will help answer several of your questions and give you an idea of a logical progression.
Yes,that was great advice,I will take that test today but I still wanted some rough estimate of what areas of math will I need and what to learn first.Two users wrote algebra is must before calculus so thats already one guide rule I will obey.
Alright. Just realize this is one of those areas where there are multiple ways to go about it, not just one way.
A typical progression is similar to what you have specified: a sequence progressing from basic arithmetic to "pre-algebra" such as exponents, fractions/rational expressions and operations, radical notation and operations, basic probability, etc. Also in this phase basic geometry is taught, such as formulas for solving areas or various polygons and circles. Then algebra, more geometry, and more algebra. This is where you will learn all about functions and their properties, and also theorems such as Pythagoras' Theorem. Trigonometry follows, along with sequences and series, limits, and more probability.
At this point you are ready or close to ready for calculus. Remember I said this is only one way to go about it, and it is not how I went about learning it.
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Yes,that was great advice,I will take that test today but I still wanted some rough estimate of what areas of math will I need and what to learn first.Two users wrote algebra is must before calculus so thats already one guide rule I will obey.
You'll find out that you don't know what you need to solve something soon enough, so I'm not sure roadmapping the thing in advance is entirely necessary or effective. You almost seem more worried about mapping everything out than just getting to it. Ultimately you won't know what you don't know, so it really boils down to getting your feet wet.
You are mostly right but I think having sort of battle strategy is good.Correct me if I am wrong but you cant just jump into it,you cant learn some things until you learn some other things earlier.I would like to avoid these kinds of setbacks by having a roadmap.Even if its all bullschmitt,the entire math thing is from my perspective a massive intimidating mess,having a roadmap will bring much needed sense of order and I find relief in knowing what I need to learn.
Knowing how huge math is and not knowing how much of it will I need to learn is scary and overwhelming and in turn makes me say funk it and not even try.If I have set number of clear goals,I feel like I can do it,its psychological thing.
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I get where you are coming from, and I also think that once you get into it, and have some progress that allows you to "look back" just a little at how you have progressed, you will understand where the other posters' opinions are coming from, too.
Watch this video, and keep in mind the idea of a linear progression as taught in school, compared to the only semi-linear, more web-like connection of math topics. Also remember that in school, nobody knows how you will progress and specialize, so you are exposed to as much as possible at limited depth. As an adult, or those in college, you have the ability to pick and choose each topic and its depth as it suits you. Because of this, strict linear progression might be ok at the start, but it likely will become unsatisfying when it makes you stray from your true interest. When this happens, go back to your interests, every time. Usually, if you delve deep enough, your interests will force you to circle back to those uninteresting topics so you can solve a problem you have, and you will find that with your newfound motivation, the boring topic is now manageable where before it was not.
https://www.youtube.com/watch?v=OmJ-4B-mS-Y (https://www.youtube.com/watch?v=OmJ-4B-mS-Y)
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You are mostly right but I think having sort of battle strategy is good.Correct me if I am wrong but you cant just jump into it,you cant learn some things until you learn some other things earlier.I would like to avoid these kinds of setbacks by having a roadmap.Even if its all bullschmitt,the entire math thing is from my perspective a massive intimidating mess,having a roadmap will bring much needed sense of order and I find relief in knowing what I need to learn.
Knowing how huge math is and not knowing how much of it will I need to learn is scary and overwhelming and in turn makes me say funk it and not even try.If I have set number of clear goals,I feel like I can do it,its psychological thing.
From what others have said, it seems that Khan Academy will answer your questions. It isn't a question of how much math you need to learn for electronics. You need to learn all of math from the beginning, understanding each step as you go. Khan Academy will apparently do this for you.
There aren't any shortcuts here. You can't skip over things, or you will find the next things impossible to understand. Math is like a ladder. Every step builds on the previous step. You have to start at the bottom and work up one step at a time.
In high school, they take 10 years to bring students up the ladder. And after that students spend more years at college learning what is needed for engineering. It might not take you 10 years now, because maybe you will be a good student and progress faster, and maybe your concentration skills will be better as an adult than as a child. School teaching systems also waste a lot of time going slower than they need to. But you must still expect to spend a few years getting there. You can't do it in a few months.
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Can you please help me lay out some roadmap how to progress with learning? My biggest obstacle is that there is so many things I dont even know where to start.I dont want to learn thing that I cant learn if I dont know some other thing.
I would like to have some rough step by step roadmap so I can tackle with one specific thing at a time.From the previous posts I so far come up with this plan :
Arithmetic > Algebra > Trigonometry > Calculus
Differential equations are another specific category or is it kind of a sub-category of the ones of the above?
You omitted Geometry which usually comes before Trigonometry but otherwise, you have the general idea.
In algebra you deal with all kinds of equations involving one or more variables. There are usually two semesters of algebra called, oddly enough, Algebra I and Algebra II.
Differential equations are different in that the variable and it's derivative (the rate at which the variable is changing, usually as a function of time) appear in the equation. This class is the culmination of a 4 semester program of Calc I, Calc II, Calc III (often called linear algebra) and Differential Equations.
Differential Calculus (Calc I) deals with Change and Motion
Integral Calculus (Calc II) deals with Area and Volume
Linear Algebra deals with matrices and vectors
Differential Equations deals with more complex equations and how the variables change (usually with time)
So when do you use a second order ordinary differential equation? Every time you drive your car! The classic Mass-Spring-Damper equation turns out to be the equation for the suspension system. The mass is the weight of the car on a specific wheel, the spring rate (inches of deflection per unit of weight) comes from the torsion bar or spring and the shock absorber is the damper. Every single day!
Oh, BTW, the exact same equation is used to describe the natural response of a parallel R-L-C circuit. It's amazing how certain equations keep cropping up with different constants but identical form.
There are math courses beyond Differential Equations in the EE curriculum. Remember, those 4 courses are taught in the first two years of a 4 or 5 year program, the lower division. You certainly don't expect to slide through the later years do you? No! They hide the math when the course is called Signal Processing and you spend full time deep in Fourier Analysis (100% math) or Control Systems where you get to play with Laplace Transforms or even electrodynamics where you can enjoy Maxwell's Equations to their fullest. Yes sir, those were the days!
You will also notice that the 4 courses fill up both semesters of both years of the lower division. Everybody assumes you have perfect command of pre-Calc before you get to college. And very few do! As I said earlier, pre-Calc at our community college is a two semester course and takes an entire year all by itself unless you beat yourself to death taking part of it over the short summer semester. And, as discussed above, Calculus is easy, it's the pre-Calc that will kill you. An absolute perfect command of pre-Calc is truly a pre-requisite.
Pre-Calc is algebra, geometry and trigonometry all rolled into a mashed together class covering everything. It is critical to later success.
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You are mostly right but I think having sort of battle strategy is good.Correct me if I am wrong but you cant just jump into it,you cant learn some things until you learn some other things earlier.I would like to avoid these kinds of setbacks by having a roadmap.Even if its all bullschmitt,the entire math thing is from my perspective a massive intimidating mess,having a roadmap will bring much needed sense of order and I find relief in knowing what I need to learn.
Knowing how huge math is and not knowing how much of it will I need to learn is scary and overwhelming and in turn makes me say funk it and not even try.If I have set number of clear goals,I feel like I can do it,its psychological thing.
I guess that's what I was getting at earlier. You let yourself be intimidated by maths to the point you are trying to gain control in ways that are possibly not entirely helpful and are avoiding the things that might be helpful. The best way to get to it and start chipping away. The veil will slowly be lifted and you'll get a grasp of where you are soon enough. You'll find out you don't know what you need to know soon enough if that's the case. Don't be so scared of not knowing something that you don't even want to look at subjects above your current pay grade. Compiling a roadmap seems to be a way of carefully avoiding subjects until you can bear them. Drowning yourself isn't productive but you'll know when that happens. Being overly conservative won't exactly excite and stimulate either. Scratch and sniff, see what's out there. Even if more than you can chew at the moment.
The first step of knowing something is knowing you don't know. As someone else has stated correctly, having something to actually apply the knowledge on is a wonderful motivator to get it down. You come across a bit as the child on the edge of the pool afraid to jump in and it's time to jump in and find out it's not that terrible at all. Don't worry, if you don't jump we'll push you. ;D
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Here is a resource for you. They are examples of elementary math exams typical of the British school system for students aged 15 or so. Try them out and see how many questions you can answer successfully. That will give you an idea of what you already might know and what you need to learn:
http://www.bbc.co.uk/schools/gcsebitesize/maths/mocks/ (http://www.bbc.co.uk/schools/gcsebitesize/maths/mocks/)
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Only you know where you really are with arithmetic. Khan Academy starts with pre-school and works up through the first couple of semesters of EE school. Everything is there!
Start where you think you need. If it suddenly becomes redundant, skip ahead.
Look at the list and pick a spot. Maybe pre-Algrebra is the place. It will assume certain arithmetic skills but they will be demonstrated in use. If you don't quite follow, back up and look at the video for that specific topic.
https://www.khanacademy.org/math (https://www.khanacademy.org/math)
I'm really old... As a result, teaching methods have changed vastly and the more modern explanations are often an eye opener. Every once in awhile I get one of the "Oh, that's where that comes from!" episodes while watching a modern presentation.
I also have troubles staying awake for YouTube lectures. What I should be doing is solving the problem on a scratch pad in front of me rather than just watching the lecturer. Hint! Have a scratchpad and pen/pencil immediately at hand! Even if I just duplicate what the presenter is doing, I will gain from the repetition.
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I have a separate concern: Studying math, by itself, is boring! Furthermore, you don't know where to focus because you don't have an application. When math is taught as part of a college curriculum there is a certain goal in mind. It might be Physics, it might be EE, it might even be business. But there is a goal and math is on the path. Math itself is seldom the goal unless the major is Math.
How to deal with that? I have no idea!
Community College seems like one approach but it really depends on where a person is starting from. There is usually a math placement test and how well that works out will depend on how far along a person gets with Khan Academy.
One of the reasons I like CalcWorkshop is that she presents every single step of every solution. She even emphasizes the basic arithmetic. No step is omitted. Unfortunately, she starts with Algebra and if that is a bridge too far, you have to start somewhere else.
You can see a demo of the Limits series without subscribing. Unfortunately, Limits comes at the beginning of Calc I and that is definitely a long way down the path. Nevertheless, you can see the style of instruction and this site might become a resource you use later.
https://calcworkshop.com/courses/
https://calcworkshop.com/limits/
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Everything in higher math is in the end just applying the algebra, the weird hieroglyphs are there just to hide this fact. :)
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Everything in higher math is in the end just applying the algebra, the weird hieroglyphs are there just to hide this fact. :)
That turns out to be true! Laplace Transforms exist to convert truly ugly differential equations that probably can't be solved into simple algebraic equations that can. When we struggled through Algebra I and II in high school, how little did we know how important they would be later on. We had no idea how important 's' would be.
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It shouldn't be overlooked how important conceptual understanding is. To be successful it is not sufficient only to know how to mechanically manipulate symbols. There are underlying ideas that help everything to make sense. Much of the mathematical progression through high school is to build up the concepts.
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It shouldn't be overlooked how important conceptual understanding is. To be successful it is not sufficient only to know how to mechanically manipulate symbols. There are underlying ideas that help everything to make sense. Much of the mathematical progression through high school is to build up the concepts.
I actually feel the opposite. High school has taught me how to manipulate numbers, but when I revisit things now I learn a lot more about the why and how certain tricks and short-cuts actually work.
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Much of the mathematical progression through high school is to build up the concepts.
Which goes back to my point about application. Learning math for math's sake is a boring proposition. Taking Physics to emphasize the USE of mathematics is the real learning of math. At least to me...
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Everything in higher math is in the end just applying the algebra, the weird hieroglyphs are there just to hide this fact. :)
... Or to allow + - * and (if you are lucky) / operations to be used with the usual commutativity and associativity
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I am on Khan webpages and cant find that test that tells me what my skill level is.Can someone please link it there?
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I am on Khan webpages and cant find that test that tells me what my skill level is.Can someone please link it there?
There is no such test. You simply start at a level that seems reasonable and see how you do. If you fly through and pass easily - move up to the next level. Keep doing that until you get to where you are presented with the material you do not know.
You are responsible for deciding where to start.
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Resistors are used in almost all circuits, so resisters are all there is to complex circuits. NOT! Same thing is true about algebra. The tools of algebra are used in almost all mathematics, but there more to it than hiding behind complex symbols. This is not meant to discourage anyone, but to point out that there is more to learn at the higher level of math. Much has real, if occasional application to the real world. And much of it is fascinating in it's own right.
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I am on Khan webpages and cant find that test that tells me what my skill level is.Can someone please link it there?
Did you try the tests I linked above? Can you answer them, or or they difficult? You should print them out and actually try to do them. That will tell you a lot about where you need to start.
http://www.bbc.co.uk/schools/gcsebitesize/maths/mocks/ (http://www.bbc.co.uk/schools/gcsebitesize/maths/mocks/)
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There is no such test. You simply start at a level that seems reasonable and see how you do. If you fly through and pass easily - move up to the next level. Keep doing that until you get to where you are presented with the material you do not know.
You are responsible for deciding where to start.
There certainly used to be one, but they regularly fiddle with how things work.
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Yes, there definitely was one or more in the past. I remember taking it on a profile I had and I had my kids take it as well. It was an adaptive test where the difficulty of the questions increased or decreased based on your real-time successful/unsuccessful answering of questions.
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So I just created a new account, and literally the very first thing it presented me was a math quiz to judge where I am. It is called Mission Warm-up, and says "Complete your mission warm-up to unlock personalized practice skills!"
It is under dashboard: mastery challenge. Hopefully this helps you find it.
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So I just created a new account, and literally the very first thing it presented me was a math quiz to judge where I am. It is called Mission Warm-up, and says "Complete your mission warm-up to unlock personalized practice skills!"
It is under dashboard: mastery challenge. Hopefully this helps you find it.
Excellent - I never saw that before.
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Now I just need to figure out how to jump to a more appropriate level... It quite literally starts at "The Beginning" as in learning to count from 0 to 20. :)
EDIT: So after completing my sign-up by going to my email and clicking the link, I completed a profile and then noted two things:
1. On the progress tab, there is a dropdown to change the target material directly, but this is less useful than 2.
2. I clicked Home, and it asked me what grade I was in, and there was an Adult Learner option. Checking this then asked me what I wanted to learn. I checked five math options and two sciences (physics and electrical engineering) and two computer topics, and voila, I now have my curriculum.
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In my antenna thread someone suggested learning Maxwell equations and I was sad becose I knew there is no way in hell with my current math skill to ever be able to understand them.
Now I'm feeling guilty.
;D
No,I am thankful you did it.Small dose of saddness is good if it stimulates the action that removes the problem.I should have learned math long time ago.If I wasnt sad about not being able to learn Maxwell equations,I would be procrastinating god knows how long.
Well, I'm glad that my comment has not discouraged you. I was afraid of that.
Math, like a good oscilloscope or multimeter, is an invaluable tool in the hands of a competent engineer.
Go ahead and never give up. It's worth the investment.
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Also fonograph, remember that you are very fortunate to have nothing preventing you pursuing mathematics. In contrast I have some 'interesting life challenges' that absolutely must be solved first, before I have any hope of success with long term ambitions.
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Can someone please help me solve mathematical problem? If there is circle with 16 cm diameter on grid of 1cm squares and we count the total surface area of all the squares that the circle goes through or are within the circle,then what is the worst case difference between the area of the circle and area of all the squares intersected or laying within the circle...
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Can someone please help me solve mathematical problem? If there is circle with 16 cm diameter on grid of 1cm squares and we count the total surface area of all the squares that the circle goes through or are within the circle,then what is the worst case difference between the area of the circle and area of all the squares intersected or laying within the circle...
That's quite a difficult problem. Unless one of us knows the answer already, it would take quite some time thinking about it to come up with the solution. For example, I have no idea. I would have to spend ages thinking about it before being able to figure it out.
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The greatest difference (the worst case?) is the case with the maximum number of squares, so this is really a problem of how many squares you can fit under the circumference.
Each square is 1 cm2, so the answer is of the form \$ n - 64\pi \$ cm2
(since the area of a circle is \$ \pi r^2 \$ given r is the radius, and the diameter is twice the radius)
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Yes, it's clear the total number of squares enclosed or touched is an integer, but given that the circle could have any position on the grid, how would you figure out the position of the circle that touches the most number of squares, and what that number is?
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There are probably only two cases worth worrying about, the case where the circle is centered on a grid square, and the case where it's centered on a corner between 4 squares.
In the latter case, the whole circle is inscribed in a 16 x 16 square grid. In the former case, it's clear the grid needs to be 17 x 17.
How many squares does it touch? You could find out using a compass, or use algebraic geometry and the circle's defining equation, \$ x^2 + y^2 = r^2 \$ . There will be a limited number of integral solutions, which are the points where the circle traces a grid corner, and you can fill in between them to see how many squares it touches.
The above equation in integers is a diophantine equation, and its solutions are the pythagorean triples.
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I was imagining it in my head and I think the worst case error is somewhere around 16%.I imagined that the circle first starts in position where it touches least amount of squares,then I put it about half a square up so its 17 squares across in the up/down direction,that should give it maximum amount of squares.The square area will then be roughly 116% of the circle area.
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https://www.youtube.com/watch?v=rB83DpBJQsE (https://www.youtube.com/watch?v=rB83DpBJQsE)
Also 3blue1brown is amazing.
I feel like I should have watched some YT video and THEN studying on books that stuff.
But in 200X YT was not so popular.
BTW:
Thoroughly conscious ignorance is the prelude to every real advance in science.
― James Clerk Maxwell
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And in '73, we didn't even have HP calculators (the HP35 came out the year I graduated) or access to computers and simulation software.
I like the discussion of Predator-Prey (Lotka-Volterra) equations starting at 11:15. It is one of my favorite things to simulate on an analog computer or with Simulink/Matlab.
I truly hated the Field Theory course. We had virtually no way to visualize the fields and certainly no animations. For this reason alone, I stayed strictly in the digital side of electronics, a decision that remains 45 years later. Yes, Maxwell's equations still apply but at my frequencies of interest, they are a side issue.
I like the 3Blue1Brown videos and animations on a wide array of topics.
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And in '73, we didn't even have HP calculators (the HP35 came out the year I graduated) or access to computers and simulation software.
I like the discussion of Predator-Prey (Lotka-Volterra) equations starting at 11:15. It is one of my favorite things to simulate on an analog computer or with Simulink/Matlab.
I truly hated the Field Theory course. We had virtually no way to visualize the fields and certainly no animations. For this reason alone, I stayed strictly in the digital side of electronics, a decision that remains 45 years later. Yes, Maxwell's equations still apply but at my frequencies of interest, they are a side issue.
I like the 3Blue1Brown videos and animations on a wide array of topics.
May be a case of the wrong textbooks. We graduated virtually the same year, and the first few seconds of the video are color versions of illustrations from my books.
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And in '73, we didn't even have HP calculators (the HP35 came out the year I graduated) or access to computers and simulation software.
I like the discussion of Predator-Prey (Lotka-Volterra) equations starting at 11:15. It is one of my favorite things to simulate on an analog computer or with Simulink/Matlab.
I truly hated the Field Theory course. We had virtually no way to visualize the fields and certainly no animations. For this reason alone, I stayed strictly in the digital side of electronics, a decision that remains 45 years later. Yes, Maxwell's equations still apply but at my frequencies of interest, they are a side issue.
I like the 3Blue1Brown videos and animations on a wide array of topics.
May be a case of the wrong textbooks. We graduated virtually the same year, and the first few seconds of the video are color versions of illustrations from my books.
It was primarily an attitude problem...
I gave up on any part of electronics where Maxwell's Equations were directly involved. There's still a good bit of the sandbox to play in. I suppose "Who cares?" was part of the problem. I was tired, it had been a very long 4 years and I just wanted it over with. I was fried! Other than digital, I really didn't think much of my career choice.
I never did work in electronics. I worked in electrical design/construction but mostly in operations and project management. Electronics was always intended to be a hobby.
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Khan Academy is great! Literally, it starts at Pre-School and works up through Differential Equations, Laplace Transforms and Fourier Series. This is about the end of the line for EEs except those who take Field Theory (Maxwell's Equations).
What about frequency analysis? DSP? My Sig & Sys class we learned about Laplace, Fourier Series, and CTFT. This was all prep for our System & Controls course and DSP, the latter of which we had to do Discrete Time Fourier Transform, Discrete Fourier Transform, and Z transforms. This was with dealing with purely deterministic signals, without touching anything stochastic.
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Khan Academy is great! Literally, it starts at Pre-School and works up through Differential Equations, Laplace Transforms and Fourier Series. This is about the end of the line for EEs except those who take Field Theory (Maxwell's Equations).
What about frequency analysis? DSP? My Sig & Sys class we learned about Laplace, Fourier Series, and CTFT. This was all prep for our System & Controls course and DSP, the latter of which we had to do Discrete Time Fourier Transform, Discrete Fourier Transform, and Z transforms. This was with dealing with purely deterministic signals, without touching anything stochastic.
I'm a little hazy on the sequencing but I thought we had Control Systems and Signal Processing before Field Theory came along. Of course all those topics come up in the upper division classes but in terms of 'end of line', I thought it was Field Theory. There was no DSP in 1973.
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I had fields and waves class but pretty early on om the program, but needed only before some classes for comunications classes I never took, so I left it for the end. I did started earlier but classes were so boring and plain bad I never got around finishinh it till the last year I think. As I took all computers architecture classes and some control theory ones I never got around comunications so antenas will remain a mistery to me (not really, I gpt the basics but I don't get them as I do with other things of this vast field, more applicable to my line of work as are the other two)
JS
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Khan Academy is great! Literally, it starts at Pre-School and works up through Differential Equations, Laplace Transforms and Fourier Series. This is about the end of the line for EEs except those who take Field Theory (Maxwell's Equations).
What about frequency analysis? DSP? My Sig & Sys class we learned about Laplace, Fourier Series, and CTFT. This was all prep for our System & Controls course and DSP, the latter of which we had to do Discrete Time Fourier Transform, Discrete Fourier Transform, and Z transforms. This was with dealing with purely deterministic signals, without touching anything stochastic.
I'm a little hazy on the sequencing but I thought we had Control Systems and Signal Processing before Field Theory came along. Of course all those topics come up in the upper division classes but in terms of 'end of line', I thought it was Field Theory. There was no DSP in 1973.
Maybe its the curriculum I suppose. We had an Emags for Engineers were we learned Maxwell Equations (only lightly touching dipoles and E&M within matter) and then ended with transmission lines. This was spring fall of junior year though, taken along side the Sys & Sig classes I described above.
This fall im taking my last two courses outside of electives. Which is Electrical Communication Systems and VLSI
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Every branch of electronics can get into "fun" mathematics. Digital and communications get to do stochastic processes. Non-linear control people can get into calculus of perturbations and other fun topics. The solid state guys get all sorts of fun things.