I am mathematically illiterate

[rstofer]

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!

[bsfeechannel]

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.

[xrunner]

I graduated in '73 - sliderule all the way!

Haha hardcore.

For me it was the HP 41C  . Served me very well I loved it. 

[james_s]

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.

[tggzzz]

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".

[tggzzz]

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.

I disagree. For a start there is this forum, then the rest of the web

[helius]

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.

[fonograph]

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.

 
 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.

[coppercone2]

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.

[Red Squirrel]

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".         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.

[coppercone2]

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".         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.

[rstofer]

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!

[Syntax_Error]

In addition to the great resources identified above, check out Michel van Biezen's YouTube channel, and his website 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.

[fonograph]

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?

[Syntax_Error]

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.

[fonograph]

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.

[Mr. Scram]

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.

[Mr. Scram]

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.

[fonograph]

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.

[Syntax_Error]

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.

[fonograph]

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.

[Syntax_Error]

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.

[IanB]

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.

[rstofer]

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.

[Mr. Scram]

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.