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The above scan from my physics text shows the type of force vector drawings that I can easily understand but somehow find impossible to draw on my own.
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The above Calculus examples are from the math review appendix of The Art of Electronics by Horowitz and Hill. You can do lots of of interesting projects knowing much less math than this, but you can do a lot more, with more confidence, if you know the math. .TD<C=top
I love math. Because of that I've taken about sixteen semesters of college math.
I love math. But I find it more than a little challenging.
I've taken first semester Calculus three times with generally improving grades and definitely improving understanding. Actually I've taken it about 3.2 times, but that drop was about life complications, not the math. Eventually I figured out that I was slow not because I wasn't understanding the concepts but because of my quirky memory. While everyone else was working on actual problems I was re-deriving basic formulas and transformations that wouldn't stick in my memory no matter how much I drilled.
Between iterations of first semester Calculus I took several semesters of Algebra. I'd always considered myself "a natural" at Algebra but I was hoping to discover some critical misunderstanding that would explain my struggles with Calculus. That seemed not to be the case. I was pretty good at Algebra. I enjoyed the classes even though they weren't challenging enough for my taste. But I like math so it was OK.
I started Calculus II several times and fell so far behind that I never finished. Take 0.5, 0.7 and a few others and that adds up to another couple of semesters of college math. Eventually I figured out that weakness in Trig was causing a lot of my problems. Intermixed with the Calculus II attempts were several repeats of Trig. I always finished and actually got fairly good grades. Trig just isn't that complicated. But I found it much harder than I thought it should be and unlike my experience with Algebra it didn't seem to get any easier when repeating. I found that a little disturbing, but I still enjoyed the classes overall. I like math so it was OK.
Eventually I got enough Calculus I and Trig bashed into my brain that I was able to get
through Calculus II with a reasonable grade.
I created a "cheat sheet" of formulas and re-read it compulsively.
With enough repetitions in the hall before class I could keep just enough of the formulas
in my memory to reduced my re-deriving work to a manageable level so
I could get through to the end of a test.
I was generally there to the bitter end with the other slow students but I was finishing most of the problems.
It was pretty frustrating. I really understood the concepts but it seemed that the part of my
memory that held previously derived formulas was broken.
Every step was a painfully slow process.
But I made it through.
And I like math so it was OK.
Physics is just a math class with more interesting problems. I love math word problems. Physics homework and tests are nearly all word problems. I thought Physics would be great fun. I read the problems. I worked to a solution. And I was wrong nearly every time. What? I'm used to getting stuck. I'm not used to being wrong without recognizing that I was stuck. It turns out that the hole I had in my memory for calculus truths was also the part of my brain needed to visualize force vectors. Whoops, that could be a problem. One afternoon I spent some time going over homework problems with my professor. I understood every step of the solutions. I walked out his office door, sat down on the floor and tried to re-do them on my own. Nada. I could not setup the problems properly on my own. Not even from memory. I could do the math working from my professor's drawing, but for the life of me I couldn't describe the angles on my own. Well, that certainly explained some of my Trig challenges. By the time I figured that out I was hopelessly behind and had to drop Physics I.
I'm not sure if that really adds up to sixteen semesters of college math, even with all the fractions. But is does add up to lots of time sitting in really uncomfortable classroom seats. And a lot of the time was pretty painful for reasons other than just the seats. But I learned a lot about math and about how my brain works. And I still love math so it was OK. I'm not done yet either. Near the top of my "bucket list" is making it through the Calculus and Physics sequences. Math is fun and important and I'm not a quitter.
I'm not an engineer either but I like doing engineering activities. The better I can do the math the better I can do the engineering. Every painful step I've taken to improve my math skills has also helped my engineering skills. It has definitely been worth the effort. I don't consider myself a math failure, I've just needed a very intense personal training program to achieve my current level of success. Just like a pro athlete.
When I belonged to a gym the trainer had me to do "reps" on the weight machine to build up my strength. I did that diligently. Just like I do my Calculus "reps." Maybe I'll be a pro some day. I started college hoping to get an engineering degree but eventually had to settle for a bachelors degree in Information Systems and an MBA. I haven't given up hope of getting that engineering degree some day.
An amazing amount of technology has moved from research centers to common use over the last few decades. Forty-some years ago I was one of the first high school students anywhere to have used a computer. Today its hard to find a high school student who doesn't carry around a vastly more powerful and connected computer in their backpack. Only today they call it a phone. We are now at the point where robotics technology is is starting to transition from research to daily use. Today you can buy a car that parks itself. It won't be too many years before your car drives itself down the freeway. Would that be a car or a robot zooming down the freeway? Lots of electronic and robotics parts are powerful and robust enough that you can by a pile of parts, plug them together and do interesting things without knowing much about them. Its surprisingly easy. It's very cool. But its not engineering. Engineers don't just know how to do things. They know how they work. They know how to make them better. They know how to do the math. That's what I want to do when I grow up.
I don't consider my obsession with math training any different than other people's obsessions with lowering their golf handicaps or improving their scoring averages. As a society we pay a lot of attention to sports. We idolize the winners and watch replays of thier every move. Even the loosers get a lot of attention and hearing them saying "we will be back and do better" is recognized as a sign of honor. For some reason we don't look at education the same way. Loosing at school is called failure. Liking to practice math identifies you as an oddball while practicing tossing balls through a hoop makes you a hero. There is something wrong with that. Its part of the reason why fewer and fewer kids are going into the science and engineering.
I have to listen to stories about sports all the time. There is nothing wrong with that, but I wish the nightly news had a regular segment on math, science and engineering challenges to balance the sports reports. For some reason I don't understand the sportscasters declare certain basketball shots as being made "with authority." MIT runs a Calculus Integration Bee. Why don't they show some of those problems being solved "with authority"? Is math too boring for TV? They find lots of time for golf ... enough said ...
If you've read this far you probably are working through your own math, science and engineering challenges. The nightly news might not want to hear your story, but I'd love to hear it. Send an email to .m2,al@biznode.com .. And if your challenge involves building something, please consider getting some of your parts from Hobby Engineering.
Thanks for reading. -- Al
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