As a kid, I liked science and I liked to draw. In 7th grade I was in the smart kid math class. However, at some point early on in high school, I determined that I was going to be an 'artist'. By 11th grade I was in the slow kid math class. I did poorly, and in 12th grade I didn't take a math course at all. After graduating, I learned that my parents wouldn't pay for art school. So, I squeezed into Michigan State University, and thought I was going into zoology. The one math class I had, pre-calculus, I began to fail, and I dropped it. I left MSU after one semester of drinking and gambling. I then went to Oakland University (also in Michigan), and avoided math classes. I took general ed classes, lots of art classes, but left after 2 years and went to Boston. For 2 years I worked in a hardware store and had a lot of fun. Much of this fun wasn't conducive to learning. After that, I returned to Oakland University and decided that I would go into astronomy. There is no undergrad in astronomy, so I figured that physics would be the place to start. I started delivering pizzas for money. At this time, I could not remember an address more than 1 minute, if that. I had to constantly check and recheck them. I wanted to start taking physics classes right away. But, you needed to pass Calculus I before you could. Since it was the winter, my plan was: Take precalculus in the spring, Calc I at the community college in the summer, and begin physics classes (and Calc II) in the fall. I took precalculus that spring and got a 2.0. -I barely passed. So, I decided that I would take precalculus again in the summer, and take Calc I at the same time at the community college. That summer, I got a 2.7 in precalculus, and failed Calc I. I lied to my school and told them I passed Calc I. I signed up for some physics courses and Calc II. I listened to nothing but classical music at this time. I did not go out and have fun. The only reading I did was physics related. I got a 2.0 in Calc II. My physics courses were a mix but I passed them. That winter I got a 2.9 in Calc III. The next winter, I took 18 credits of physics: (Quantum Mechanics, Modern Physics, Vibrations and Waves, Thermodynamics, Modern Physics Lab, plus grading papers, plus undergrad reseach that got published (while learning to code in FORTRAN for that), plus I delivered pizzas. I got a 3.6 that semeseter. Eventually, I got my PhD in medical physics. My math skills have since atrophied, but at one point, there were few physics problems that I couldn't tackle given enough time. Math can be fucking hard, but it's beautiful stuff. When you really get into it, it's like poetry. The secrets to the universe are in it. More interestingly, it uses your brain in a way that nothing else does. You learn about yourself when you do crazy math. I do not have a natural talent at math. I didn't lay a solid foundation in math early on. But, through sheer force of will I gained compentency enough that I could find eigenvalues for a wave function like a pro. Like kleinbl00, I've always sucked hard at arithmetic. If you are not good at math, you aren't doing enough of it. the best way to learn math is to find the limit of your problem solving abilities, and solve lots of those problems, -like hundreds of them. When you are really confident with those, move to the next chapter. Solve crazy amounts of those problems, repeat. I used to get every book I could at the library that had the type of problems I needed to learn to solve. I just kept doing them. I think what many people misunderstand about math, is that it isn't something that you look at. or are told about, and 'get'. You only 'get' math by doing a lot of it. It takes exercise. No one can tell you how to pole vault, where you just 'get' it. Youve got to try and try and try...
I suck HARD at arithmetic. Like, massively hard. If I can do it in my head, I get it right. If it's one of those things where i have to show my work, I blow it. Yet I have an engineering degree with post-graduate work in acoustics and biomechanics. I did more calculus and differential equations as an acoustical consultant than any other graduate I knew. "math" is the stuff you can't do with a calculator. The shit you can do with a calculator? That's just number crunching. We invented abaci and trig tables and slide rules and calculators and computers and Siri to deal with that shit. All you need to know is if the answer looks right. The trick to learning "math" is to make it through to Calculus. Calculus is pretty much where the mathematicians say "okay, enough of these bullshit numbers. Let's dance." Calculus is where you start to learn exactly how the world works and everything opens up like The Matrix. If you keep going things get aggro. I once had a 2-hour final that started with "imagine a function", had 3 problems on it, and the only number on the page was "1" (the problems were lettered a, b and c). I suck at arithmetic. My wife rules at it. Incidentally, she graduated Magna Cum Laude with a bachelor's in Math. And we see the world in remarkably similar terms.
Its interesting to see some math papers written before high power computers were available readily. At the time, numerical solutions were all calculated by hand, so you'll see a hand drawn graph with just enough points filled in that the reader gets the picture. I think that's one of the ways computers have helped in teaching math; they've made it easy for students to visualize what a given function means. The down side, of course, being that they've become a huge crutch in place of real learning.
Hah. I can beat the shit out of that. I learned to build cars long before learning engineering. By the time I took my courses on steel I'd been welding for about six years (and taught the welding section of my class - because apparently, it's gauche for engineering professors to know how to weld). And I was getting my ass kicked by Mohr's Circle and psychometric charts and all these rootin' tootin' high falootin' engineering calcs and then we got to 495, capstone engineering, and you learn that a) to do real engineering work, you take the answer that you think is correct and you stack six "bullshit factor" coefficients in front of it to get your real answer b) more likely than not you skip those "bullshit factor" coefficients and just go with 1.6 for military hardware, 2 for racing, and between 5 and 10 for consumer gear and even then, the most successful designs are those that "look strong enough." I've pulled engines with seat belts - they work really goddamn well. Meanwhile, we had an engineering homework question where we were supposed to use our "FS=2" bullshit factor, our "FS=1.6" bullshit factor and our "FS=5" bullshit factor to determine how thick the chain on a playground swingset needed to be to support a drunken, overweight frat rat of 250 lbs. You won't be surprised to find out that playground swingsets are actually sized such that they can support a drunken, overweight Buick LeSabre. I decided I hated engineering when my Finite Element Analysis instructor docked us points if our answers weren't "heavy" enough (these were printouts from a server-based FORTRAN program and if your report didn't tip the scales at half a pound of paper, you didn't do enough work - something that would have been nice to have known before I imported it all into excel and truncated the last half of all my data tables because you know what? I like trees). Then I decided I loved engineering when I learned what dimensional analysis was.
That said, safety factors can be important, mainly because material defects exist so often. Its easier to over-design by a factor of 2-10 than it is to perform quality inspections constantly (not to mention the whole lawsuit protection game).
The amazing thing to me wasn't that mine was far and away the cheapest approach, but that mine was the only successful approach. Here's all these 4th-year engineering students, and exactly two of them are capable of building a fucking hoist.
The thing is, I don't know if I'm good at "math" or not because I've never really tried my hand at it. I avoided math classes in college and only got as far as Algebra 2 in HS. I was afraid of it as a kid because I would easily fall behind in class and it's a lot easier to say, "I quit" than it is "hey, I need help" when you're 15. Along with learning to speak french and learning to read music, I suppose I should add ditch your fear of math and take an adult ed class to my list of things to get done. By the way, your wife sounds pretty damned fascinating.
As for Khan Academy, it's been a while since my last math exercise. I got as for as Multiplication 4, then stopped. I've always been "bad at math", but was also fascinated by it. I think Khan Academy is a good place to learn. Sal is a good teacher and I really felt like I was cleaning a dusty room in my brain. I quit trying to learn physics, math and chemistry in my final high school year, so I'm probably as "bad in math" as you can get.
Quite. http://www.reddit.com/r/scifi/comments/dzdd3/we_went_oldscho...
We took some publicity photos this morning (new lobby cards). I kinda played up the wrinkles and gray hair... most people can't believe she's over 30. She's probably the only naturopathic doctor in the United States that was management at a multinational insurance company for a decade.
Now here's a lady I'd pay good money to freeze a placenta: http://i.imgur.com/Io1u1.jpg
"The trick to learning "math" is to make it through to Calculus. Calculus is pretty much where the mathematicians say "okay, enough of these bullshit numbers. Let's dance." Calculus is where you start to learn exactly how the world works and everything opens up like The Matrix." This was the experience I had as well. It may sound cliche but a whole new world opened up before me. A new understanding.
Find a textbook or problem workbook and give yourself a regular assignment of 10 "easy problems" that just involve applying the formula, 5 medium-ish problems where the solution is not so straightforward, and 2 very hard problems that test your knowledge of each chapter, such as proofs. Vary the numbers as you see fit for sections as a whole, but try to keep a consistent challenge in your homework. Having a teacher can be helpful to explain some of the nuances of math, but isn't always necessary. I know plenty of students who skip out on class entirely and study directly out of a book. Just make sure you find decent textbooks for what you want to learn. (Unfortunately I have learned out of many terrible textbooks, which I cannot, in good conscience, recommend) If you finish those three subjects up (Students take more than a year sometimes, so don't rush yourself), then check out the undergraduate math curriculum available at a respectable university and grab a book or two on the subjects that look interesting. Knowing which fields of math that are relevant to your own work can also allow you to maintain your interest and have a practical application to the knowledge you've learned. Pretty much everyone can benefit from the ideas of linear algebra and differential equations, but multi-variable calculus tends to be geared more towards physicists, while discrete math shares more with the problems studied by computer scientists.
This is math: http://en.wikipedia.org/wiki/Eulers_identity
My only excuse.
What does bother me a bit is when people say "I can't do math." I am a shitty mathematician, pretty good at the overall concept, but it takes me forever to go through a long string of calculations. I'm positive that the two instructors in my life who really challenged and enlightened me in mathematics would both say that I was challenged, but hard working. Despite lack of innate ability I persevered and learned more math then the average bear. Almost everyone is able to learn college level algebra. Also. I know a few people who have/are pursuing graduate level degrees in mathematics. Most of them seem to ride a roller coaster of emotional well being that is a direct function of how well their understanding of the maths they are working on is progressing, I'd even say that they often feel like math sucks.
I got a "broken" VCR off of her for free because she couldn't wrap her head around "tracking."