User talk:Goodralph
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Math reply
Thank you for your explanation on Talk:Natural Number. I enjoyed your insight that the base case can start pretty much anywhere. One of those things that made me wish I had thought of it myself.
Personally, I don't normally think of 0 as a natural number, but I'm sure that's because my primary research interest is number theory. Only when I switch over to set theory, combinatorics, or something else do I mentally "switch over" in my mind.
In general, there are lots of definitions and notations in math that have no uniform standard. It's usually not considered a problem, because you just make sure to know the convention the author is following. Of course, this only goes so far -- calling ideals beanbags or compactness nastiness is ridiculous. But some people prefer analytic function rather than holomorphic function, although even here there's a slight distinction (they happen to be equivalent for complex functions). Sometimes fights break out, though, especially over notation, because notation can become very ingrained in one's mind.
As far as the comment on induction, this is part of a more general theory, and it makes more sense if you think in terms of this. I don't know how familiar you are with ordinal numbers or well-ordered sets. Basically, it turns out that the natural numbers aren't the only ordered sets you can do induction over; you can do induction over infinite sets -- the important thing is that they have an ordering on them, which is a well-order. But the elements themselves don't matter. This is why it doesn't matter where you start. Each of the sets {k, k + 1, k + 2,...} is identical in their ordering, if you just shift up or down the right amount (in fancy language, they're order-isomorphic).
You seem quite intelligent on topics math and non-math.
I hope my potential employers think so! Thanks for the comment, although I really don't think I'm terribly brilliant, (well, at least among math people [AT MATH...didn't mean to imply math people are more brilliant than everyone else]). As a number theorist, I have a working knowledge of many areas of math, but not a deep knowledge of anything in particular (except my own little problem). There are still a lot of things I want to learn about (the more math you learn, the more there is you don't know).
Now, User:Charles Matthews knows a lot more about math than me.
I noticed at the end of your user page, you mentioned a list of inspirational math books. What would you recommend to an undergrad who is not as mathematically mature as you?
It depends what your purpose is, what classes you've had, level of maturity. Higher Arithmetic is a good intro to number theory...starts kind of slow, but gets pretty sophisticated at the end. Math and the Unexpected doesn't have much math in it, but it's well-written and gives a flavor of topology. The World of Mathematics has tons of articles, but you have to get a used copy. Math Experience is a frighteningly accurate picture of the life of mathematicians. And just to gain more maturity, Intro to General Topology (Joshi) is great -- I read it in college and it prepared me as much as any class I took. But it's out of print, it took me several weeks to get a used copy.
What classes have you had? Any where you focused on reading and writing proofs?
Revolver 00:55, 3 Mar 2004 (UTC)
Memetic lexicon
from memetic lexicon, under memetic drift...
"The memes in this text probably mutated slightly when the original author, "Noone", compiled this article from copyrighted sources."
A joke? Goodralph 19:28, 26 Apr 2004 (UTC)
Partly :) But it is also true :P! Change it if you want to :) Noone 16:06, 27 Apr 2004 (UTC)
Real Estate
Do you have a real estate license? I plan to get a sales license this summer (sorta for the heck of it). --Jiang 08:34, 20 May 2004 (UTC)
- I don't personally have a sales license but I know a few folks in our Berkeley Undergraduate Real Estate Club have. If you want me to get you in touch with someone who has done it, just let me know.
- I'm not sure if it's the best use of time, though! I get the impression that being a residential agent is looked down upon by the MBA crowd. Then again, I know that there are folks who are doing very well in being residential brokers. If your interest is more academic (as it seems), why not kill the GRE or something over the summer? I get the impression it's pretty easy. Goodralph 13:18, 20 May 2004 (UTC)
Oh...forgot to check here...and I just discovered that you're "burma" on livejournal.
I have no plans to be a residential agent, even for buying/selling my own home. I don't think that stuff requires much college. It's just that whatever I do for a career, I'll end up doing something with real estate unless I choose to be a street bum. This information may become useful somewhere down the line, probably too soon for me to be looking into this stuff now...but it's summer so I thought why not. My dad was my age when he got his.
If my Chem 3A grade depresses me enough I'll start looking into alternatives, but for now, I have a MCAT book on my bookshelf. It's not going to be fun...
What's you're interest in real estate, being VP of the Real Estate club and all? --Jiang 05:24, 24 May 2004 (UTC)
Urban Sprawl
Hi Goodralph, I thought I might point out an error - On the Urban sprawl definition: http://en.wikipedia.org/wiki/Los_angelization ,the third paragraph states "The lowest density large urbanized area in the world is Atlanta, which covers 1,963 square miles, with a population of 3,500,000 for a density of 1.783 people per square mile." The math isn't right. At 1.783 people per square mile, Atlanta would consume 1,962,983 square miles. I guess you may have a rogue decimal point. Great article! Thanks for the read,
Jordan Edwards Kelowna, BC, Canada jordan_edwards@hotmail.com