Search found 140 matches

Fri May 22, 2009 3:36 pm UTC
Forum: Mathematics
Topic: Why is calculus considered so complex?
Replies: 64
Views: 6753

Re: Why is calculus considered so complex?

The above presumes, however, that the material wealth and ability to technically innovate in a society are immaterial to the well being of a society. Calculus, as mentioned, produces exponential dividends. I don't think anyone would disagree with this, especially the engineers, scientists, and soci...
Fri May 22, 2009 1:57 pm UTC
Forum: Mathematics
Topic: Why is calculus considered so complex?
Replies: 64
Views: 6753

Re: Why is calculus considered so complex?

This conversation has sort of drifted from "why is calculus considered so complex" to "why are some people not so good at math". I'll run with that. On one hand, I agree with t0rajir0u that a student is generally only as good as their worst math teacher. I also think in the West ...
Sun May 17, 2009 4:16 am UTC
Forum: Computer Science
Topic: Recursion help
Replies: 5
Views: 1153

Re: Recursion help

My question is, is it possible to make a recursive function that would print the Fibonacci series in just one call, instead of having to call the function again for each new term, maybe using flags so the same number doesn't get printed more than once? As you have discovered, Recursion is horribly ...
Sat May 16, 2009 5:43 pm UTC
Forum: Mathematics
Topic: Simple Probability Problem
Replies: 4
Views: 508

Re: Simple Probability Problem

Try in this order:

ii) neither - P(A') * P(B')
iii) at most one -- (use answer from i)
iv) at least one -- (use answer from ii)
v) one and only one -- (use answer from iii or iv)

vi) Generalise to K events from there.
Fri May 15, 2009 10:57 pm UTC
Forum: Mathematics
Topic: Help! I'm trying to get a 14 year old interested in Maths.
Replies: 52
Views: 6877

Re: Help! I'm trying to get a 14 year old interested in Maths.

I like all of these ideas, thanks! (It turns out worse than I thought though, he refused to turn up to the last tutoring session. I guess it's hard to teach someone who doesn't want to be taught. I'm thinking bribes. ) I think if the student is being tutored because they don't like math and perform...
Fri May 15, 2009 9:47 pm UTC
Forum: Mathematics
Topic: Why is calculus considered so complex?
Replies: 64
Views: 6753

Re: Why is calculus considered so complex?

I think twenty-thirty years ago people probably spoke of "algebra" or "trigonometry" as the dreaded end-all be-all math course. I suspect calculus pedagogy has vastly improved over the last few decades and calculus is becoming more "mainstream" as time passes, and it wi...
Fri May 15, 2009 9:09 pm UTC
Forum: Mathematics
Topic: Maths summer school - any ideas?
Replies: 13
Views: 2086

Re: Maths summer school - any ideas?

Putting myself in your shoes, I would think about making a curriculum out of selections from Stephen Hawking's "God Invented the Integers", or something similar to that - a sort of "history of math" primer with a bit of rigour. Even if the students are already familiar with the &...
Mon May 11, 2009 9:31 am UTC
Forum: Computer Science
Topic: Math for a computer scientist
Replies: 23
Views: 2546

Re: Math for a computer scientist

In my program, we needed a minimum of five math courses: two terms of single-variable calculus, a term of linear algebra, a term of discrete structures, and a term of intro statistics. Of those five courses, by far the most important was discrete structures which is definitely useful for further com...
Thu May 07, 2009 3:27 pm UTC
Forum: Computer Science
Topic: Little-o versus Big-o
Replies: 18
Views: 5263

Re: Little-o versus Big-o

I will never use Θ(nlogn) for quick sort. Θ(nlogn) means that it is bounded above and below by nlogn, which quick sort is not. It is an abuse of notation at best, and completely wrong at worst. Of course, if you specify that it is on average before hand, then O(nlogn) and Θ(nlogn) is valid. Yeah, i...
Thu May 07, 2009 3:02 pm UTC
Forum: Computer Science
Topic: Little-o versus Big-o
Replies: 18
Views: 5263

Re: Little-o versus Big-o

i always think of big omega as meaning "as bad as in the worst case" Sure. it's use is slightly different for describing the complexity of functions and algorithms though, and i think that confuses some people. For example. if f(n) = nlogn, then f(n) is Ω (1). However I would not say quic...
Thu May 07, 2009 2:47 pm UTC
Forum: Computer Science
Topic: Little-o versus Big-o
Replies: 18
Views: 5263

Re: Little-o versus Big-o

i always think of big omega as meaning "as bad as in the worst case" So do I, and probably most everyone else. Except for quicksort, which is O(n²) in the worst case, but is generally attributed a complexity of O(n log n), which is the average case. Quicksort is Ω (nlogn) (best case) , Θ(...
Wed May 06, 2009 11:47 pm UTC
Forum: Computer Science
Topic: Little-o versus Big-o
Replies: 18
Views: 5263

Re: Little-o versus Big-o

yeah i got it backwards. Turns out some multiple of the thing inside the O has to be greater than the thing on the outside. Is there notation for the opposite? Yep. f(x) is big-Oh g(x) implies g(x) is Omega f(x). f(x) = O(g(x)) ==> g(x) = Ω(f(x)) f(x) is little-oh g(x) implies g(x) is little-Omega ...
Wed May 06, 2009 10:34 pm UTC
Forum: Mathematics
Topic: convergence of a sequence.
Replies: 7
Views: 1042

Re: convergence of a sequence.

Ah, the part where I misread the OP's post and thought he was talking about series instead of sequences . Makes the desired answer somewhat different. Ohh I'm having a little bit of reading malfunctoion as well. I thought you were the OP when I responded. :) As an aside, the sequence vs series thin...
Wed May 06, 2009 9:56 pm UTC
Forum: Mathematics
Topic: convergence of a sequence.
Replies: 7
Views: 1042

Re: convergence of a sequence.

... -- it should be "the series 1/1^p + 1/2^p +...+ 1/n^p , which converges for p > 1 and diverges for p less than or equal to 1 . This is correct. You can prove it with the integral comparison test. It doesn't resolve the series vs. sequence problem, but at least it isn't quite as ridiculous....
Wed May 06, 2009 4:59 pm UTC
Forum: Mathematics
Topic: Conceptual math (just a random thought)--
Replies: 13
Views: 1874

Re: Conceptual math (just a random thought)--

...And to answer your question with Hilberts Hotel: Imagine a hotel with an infinite amount of hotel rooms that is fully booked. In room #1 we have guest 1, in room #2 we have guest 1/2, in room #3 with have gust 1/4, and so on...guest 1/2^n is in room #(n+1). In walks "2" looking for a ro...
Wed May 06, 2009 4:26 pm UTC
Forum: Mathematics
Topic: Conceptual math (just a random thought)--
Replies: 13
Views: 1874

Re: Conceptual math (just a random thought)--

You may want to google Hilbert's Hotel, which uses the analogy of a hotel with an infinite amount of rooms as an analogy to how "infinitely countable" sets differ from infinitely "non-countable" sets. If you want to really stew over it, here is something for you. The set of natur...
Wed May 06, 2009 4:34 am UTC
Forum: Mathematics
Topic: convergence of a sequence.
Replies: 7
Views: 1042

Re: convergence of a sequence.

Don't be confused between a series and a sequence : Example of a sequence with p=1: 1/1, 1/2, 1/3, 1/4, 1/5,...,1/n -- as n goes to infinity, the sequence converges at 0. Example of a series with p=1: 1/1+1/2+1/3+1/4+1/5+...+1/n -- as n goes to infinity, the series diverges For a sequence, if p > 0,...
Tue May 05, 2009 1:48 pm UTC
Forum: Mathematics
Topic: Quick Intergration Question
Replies: 8
Views: 1477

Re: Quick Intergration Question

To be pedantic, the answer to the question as quoted would be undefined. Funny, I thought the same thing. And keeping in line with being a pedant :D , wouldn't "from definition" mean you would need to show that the sums using left endpoints and the sums using right endpoints are equal? I'...
Mon Apr 27, 2009 3:20 am UTC
Forum: Mathematics
Topic: Good problem for a 10th grader?
Replies: 32
Views: 2977

Re: Good problem for a 10th grader?

I think you should choose problems within the scope of her curriculum and capabilities, wherever that is. For example, the suggestion you gave is fine if she would have covered a little bit of basic number theory, and in particular, if she is capable of reasoning from definition whether an integer i...
Sun Apr 26, 2009 11:32 pm UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 488577

Re: Favorite math jokes

Q: Why'd the chicken cross the Möbius Band?
A: To get to the other...umm...

(Props to Professor Ian Stewart)