31–40 of 57 posts
http://www.artofproblemsolving.com/Books/AoPS_B_Texts_FAQ.ph...
Start with following two books
the Art of Problem Solving, Volume 1: the Basics
the Art of Problem Solving, Volume 2: and Beyond
These will give you a solid grounding in mathematical problem solving.
This would be absolutely awesome. I'm 14 and going into 9th grade. I'm taking algebra 2 / trig next year but I hate how they teach it so I use the internet to teach me. This would be a really cool idea, I'd definitely use it.
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Here is the thing I wish someone had told me my freshman year of high school. If you're interested in computer science, study topics in discrete mathematics, real algebra (the algebra where you compute with symbols instead of numbers, look into "rings", "groups", and "fields"), and some statistics. And if you have to scale back on something to make room, scale back on trigonometry. Discrete is a subset of math that w…
I disagree with you on trig. Trig is the study of straight lines and what you can do with them. The important part of calculus is the fact that you can approximate curves by straight lines [1]. A folk theorem in applied math is that 90% of the time, an approximation by straight lines is good enough (another 9% of the time, you'll need a parabola). You can drop some of the petty stuff (x,y,(180-x-y) triangles), but do…
When people argue about the math curriculum, they almost always argue the wrong question. The question is not, "Should we cover X?", because in isolation the answer is always yes! Should we cover trig? Yes! Should we cover set theory? Yes! Should we cover graph theory? Yes! etc. etc. The question is, "Given our limited time to allocate to math education, what are the best topics to focus on?", and once you consider the wealth of incredibly valuable topics neglected (elementary economics, elementary discrete math, actual algebra, game theory, computer programming, anything remotely resembling actual mathematical practices rather than memorized formulas stripped of all motivation and history), you'll find that spending umpteen weeks on trig is really shortchanging the students. The opportunity cost of trig is too high.
Statistics is in my to-do list too. Kind of unavoidable if you want to work on machine learning.
Will your project include samples and practice problems to make sure readers understand concepts?
I'd recommend using this book as a rough guide: http://tinyurl.com/nfe3gv Don't let the title fool you. It's really a guide to advanced applied mathematics. I'd also suggest the material be supplimented with a good bit of statistics. In my experience, statistical reasoning (particularly as it applies to noise, perturbation, and system reliability) tends to be weakness with hackers.
using tinyurl to hide your amazon referral url... nice
Earlier quoted context omitted.
I disagree with you on trig. Trig is the study of straight lines and what you can do with them. The important part of calculus is the fact that you can approximate curves by straight lines [1]. A folk theorem in applied math is that 90% of the time, an approximation by straight lines is good enough (another 9% of the time, you'll need a parabola). You can drop some of the petty stuff (x,y,(180-x-y) triangles), but do…
I think you may forget what is taught as "trig" in school. Yes, knowing what sin, cos, and tan are is important. No, wasting weeks on pointless identities and digging into the minutia of lines and triangles well beyond what you will ever need, even in the course of getting a degree in mathematics , is not a sensible use of time. The only reason it is done is "that is how things are done". When people argue about the…
Don't.
There is already Wikipedia and Wolfram Mathworld. I have no interest in another system where math geeks compete to put the biggest knowledge dumps and most obscure references into a great big technopeacock tail.
You know all that stuff about usability and simplification that Apple/Microsoft get and Linux/OSS don't? You want to help a lot of people? Be more like betterexplained.com and less like a math entry on wikipedia.
(You're pretty much helping people who know and like maths and can make sense of mathworld, or people who haven't done anything mathematical for years or decades).
(Also, including a mental pronunciation guide would be interesting. How do you pronounce equations in your head?)