Different Ways to Conceptualize Math? 166
rook a asks: "I've always been an avid reader but my math skills were poor, and TV had taught me that math was difficult. I knew only the concepts of the basic operations. From seventh grade through high school, I did only what was needed to get by and so my math skills remained below par. Now, as a freshman pre-cal student, I am struggling. I believe that I have a flaw in the basic way I think about numbers. I can think logically, but it does not carry over to math. I read somewhere that Feynman gave a lecture on arithmetic but I could not find it. I believe that different people have different thought structures for the same ideas. Has there been any research or books on the difference between how a mathematician, or a Richard Feynman, thinks about math and the way that the average person thinks about math? Or, did any of you initially find math difficult in college but go on to higher maths? If so what changed for you?"
"I wanted to be an EE and want very much to be good at math but if my ability does not increase I will not be able to. I am willing to do anything to increase my skill. I hate rote and do not want to be merely 'good' at math, I want to speak it. If math is a mindset then it's one I want to be part of.
This is similar to another question, however I found several interesting books but no comments toward learning a more efficient way to think."
This is similar to another question, however I found several interesting books but no comments toward learning a more efficient way to think."
Re:Some answers that worked for me (Score:3, Informative)
Info on Richard Phillips Feynman (Score:2, Informative)
A summary of Richard Phillips Feynman [st-and.ac.uk]
Amazon search [amazon.com] for Richard Feynman
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Mod +1 informative -5 Karma Slut
Some thoughts (Score:5, Informative)
See if you can get your hands on a demo of Maple. There's a student version available, I don't know if it's crippled, but I know that it's a disgustingly great deal. It got me through EE school. Mathematica has better marketing, but I always found it to be a horrible program (at least, its syntax requires you not know anything about programming languages). Maple has some great somewhat-interactive graphing modes too. You can't / shouldn't use it for the math courses, but for EE courses, you'll need a really good math program to help you out.
Also see if you can get your hands on a HP48GX calculator. Real engineers use old-school HP calculators. Posers use TI. You'll thank me come EE exam time. I'm not convinced that the currently selling HP calculators fall in the "real calculator" camp, but they might be okay. You want RPN. Trust me, if you're an engineer, RPN is your friend. It also tends to keep people from swiping your precious calculator
See if any of the professors in the EE department teach math classes; usually there'll be a few people who have a foot in each department. Make friends and see if they'll help you out during their office hours. In general, I have found that math professors can't teach math worth anything. Or at least not to engineers. It's just a different mindset / world view. And the result is that they're teaching math the way they think of math, and you're just going W-T-F?! The EE professors can teach it with an engineering spin, and they have the very distinct advantage of being able to map math problems to the real world EE problems you need that math to solve. The worst math professor phrase is "suppose you want to..." - well, suppose that I don't, ya damn hippie! EE profs can put the horse back in front of the cart and tell you WHY you NEED to do this or that math, and that insight alone makes it much easier to learn.
In general, I must emphasize that EE is a math intensive major, and it gets very very much uglier than basic calculus. If you truly aren't good at math and you aren't willing to put yourself through dramatic pain and sufferring to learn it anyway, change majors now. Really, seriously. If you're going to hit your limit and change majors, you're better off doing it while you're not as far along and don't have as much work to throw away. If you decide to stick with it, good for you, just understand that it's going to get *a*lot*worse*.
If you want to improve... (Score:2, Informative)
http://www.learner.org/resources/series66.html [learner.org]
26 half-hour videos covering all topics of Intermediate and College Algebra. The webcast videos are free (registration required), just click on the VoD symbol to watch them. If you use SDP ( http://sdp.ppona.com/ [ppona.com] ) you can download the ASF steams for repeat viewing. BTW... I got an A+ in my College Algebra class... It's absolutely critical that you fully understand advanced topics of Algebra before starting a Calculus class.
Well, here's one hurdle you need to overcome (Score:4, Informative)
This insane allergy people have to simply memorizing some things gets in the way all the time. Just get over it. Despite what new-age bullshit you might be used to about how rote learning is 'just' memorizing lists of facts, it remains important to memorize those facts. Some things you just have to memorize, and math is full of them. What edges of the triangle a cosine relates to is an example. Once you start committing this stuff to memory things will start to fall into place. Worked for me. Got a degree in math and everything.
Miller's "Popular Mathematics" (Score:2, Informative)
See if you can find a copy of the 1942 book "Popular Mathematics" by Denning Miller. It goes from arithmetic to calculus, taking generally a more geometrical, physical, and historical approach than most math classes do these days.
I was pretty good in math, up until I hit differential equations; I bought this book just for curiosity, so I can't really say if it will help you. But it looks like copies can be found on eBay for just a few bucks [ebay.com], so I'd say it's worth the gamble.
Memory, time and visualization (Score:3, Informative)
For example, do you already have the habit of trying to find rational patterns, and enjoy visualizing them? If not, you could try that out and see if it fits with you. Visualization may be a two-edged weapon when it comes to math. Some people (including me) do it a lot and find it helpful. (But others handle math topics that may defy visualization, and claim that the visual-modeling habit ends up a hindrance.) Maybe you could find it stimulating to visualize. To find out, you could try reading about classical geometry and working through the essentially visual proofs there, and then go on with coordinate geometry. Visual modeling based on geometry helped me through calculus.
Then, do you have very good numerical memory? Would it stimulate you to try extending it anyway? Can you do simple mental arithmetic really easily, like adding up your purchases without needing the machine? You might try it regularly and enjoy making it come more easily.
But most of all you probably need to spend a lot of time with a chosen subject, and try to think about it and analogize it in lots of different ways and see which ways stimulate you and work for you.
Good luck.