Search found 1798 matches

by btilly
Tue Nov 13, 2007 10:08 pm UTC
Forum: Serious Business
Topic: I'm 13 and wish to have a good education.
Replies: 95
Views: 10950

Re: I'm 13 and wish to have a good education.

I did mention that I am sixteen partially because I am quite aware that my opinion counts for little. However it is my opinion. I said what I said largely to stir people up, however I stick by it. The Times university list is one list. Universities are a very difficult thing to judge. And you may n...
by btilly
Tue Nov 13, 2007 7:53 pm UTC
Forum: Science
Topic: What has physics done for society lately?
Replies: 73
Views: 6759

Re: ammunition in the fight against those damn phil majors

miles01110 wrote:Tell those philosophy majors to shove it, by the way. A better question might be, "What hasn't physics done for society lately?"


Given the USA a better president? :wink:
by btilly
Tue Nov 13, 2007 7:32 pm UTC
Forum: Serious Business
Topic: I'm 13 and wish to have a good education.
Replies: 95
Views: 10950

Re: I'm 13 and wish to have a good education.

Perhaps a select few American 'colleges' or universities as the rest of us call them are indeed quite good (if you can pay your way in or get a scholarship), however the majority or mediocre and can not compare to Oxford, Cambridge or even a rather lower university such as Queen's of Belfast or New...
by btilly
Tue Nov 13, 2007 2:01 pm UTC
Forum: Serious Business
Topic: I'm 13 and wish to have a good education.
Replies: 95
Views: 10950

Re: I'm 13 and wish to have a good education.

This is extremely rare in society today methinks, what with all the anti-intellectualism and daily reminders that athleticism and social activities are more desirable than scholarly pursuits. I am known around the school for use of polysyllabic words. Supposedly, in a few years the US will no longe...
by btilly
Tue Nov 13, 2007 1:48 pm UTC
Forum: Science
Topic: What has physics done for society lately?
Replies: 73
Views: 6759

Re: ammunition in the fight against those damn phil majors

I'm a physics major, and when I get down to talking about scholastic matters with non-physics majors (especially those damn snooty philosophy majors) one of the questions that I tend to get asked a lot is "what has physics done for society lately?" I mean, everyone knows about the atomic ...
by btilly
Tue Nov 13, 2007 1:10 pm UTC
Forum: Books
Topic: Books you loved as a child, do they stand the test of time?
Replies: 82
Views: 8784

Re: Books you loved as a child, do they stand the test of time?

When I was in grade 5 I discovered the Norse mythology. It was a breath of fresh air compared with the Greek and Roman ones. I still like the Norse myths. I still don't like the Greek and Roman ones. :) As a kid I remember liking science books, fantasy and science fiction. (Confession, I learned mos...
by btilly
Mon Nov 12, 2007 5:56 pm UTC
Forum: Mathematics
Topic: Pythagorean Proofs
Replies: 24
Views: 3229

Re: Pythagorean Proofs

Torn Apart By Dingos wrote:It would be silly to define two proofs to be equal iff one of them has the same steps in the same order, but with added useless steps. No actual proofs have useless steps.


I take it from this comment that you've never had to grade math homework.
by btilly
Mon Nov 12, 2007 5:54 pm UTC
Forum: Computer Science
Topic: Calculating nCr algorithm
Replies: 28
Views: 9460

Re: Calculating nCr algorithm

blob wrote:Either Ruby's implementation of iteration is much slower, or
Spoiler:
If you have a running product x of 100 digits, and two more numbers y and z of 4 digits each, it's much faster to calculate x(yz) than (xy)z.


You get the brownie points. :D

Divide and conquer, it is your friend.
by btilly
Sun Nov 11, 2007 11:39 pm UTC
Forum: Mathematics
Topic: What is the smallest number with exactly X distict factors?
Replies: 32
Views: 9909

Re: What is the smallest number with exactly X distict factors?

Your conjecture is wrong. At least in its naive form. In the simple version of your conjecture, f(16) should be 210, and in fact it is 120. There is a brute force way to answer it, and your conjecture is on the right path to do that, but there is no easily stated universal answer that I see. Drat, ...
by btilly
Sun Nov 11, 2007 11:25 pm UTC
Forum: Computer Science
Topic: Calculating nCr algorithm
Replies: 28
Views: 9460

Re: Calculating nCr algorithm

And yes, there is a reason I used recursion in multiply_range. Brownie points to the first person who can explain why. :wink: The only reason I can think of is to make the algorithm work faster in a parallel-processing environment. Nope. It makes it faster in a single-threaded process. Such as the ...
by btilly
Sun Nov 11, 2007 3:03 am UTC
Forum: Mathematics
Topic: weird question
Replies: 25
Views: 3132

Re: weird questin

bob221 wrote:i was thinking if a car is going clockwise does the driver go farther than the passenger?


In the USA, yes. In England, no.
by btilly
Sat Nov 10, 2007 6:05 pm UTC
Forum: Mathematics
Topic: Show us your articles! Or what's your Erdos number?
Replies: 187
Views: 278872

Re: Show us your articles! Or what's your Erdos number?

If X doesn't have a topology on it, the basis is probably a Hamel basis, meaning you need to be able to form arbitrary elements of the vector space using only finite linear combinations of basis elements. So there's certainly a basis for the vector space containing each of those functions, but if X...
by btilly
Sat Nov 10, 2007 6:00 pm UTC
Forum: Coding
Topic: Teaching a beginner to program
Replies: 21
Views: 3708

Re: Teaching a beginner to program

Useful though higher level abstractions are, the fact is that someone just starting out will usually be overwhelmed by them. In fact, there's a lot of education you can do in the 20-30 line range. For the basic ideas you'll absolutely need, such as flow control, performing normal operations, and li...
by btilly
Sat Nov 10, 2007 3:57 am UTC
Forum: Computer Science
Topic: Calculating nCr algorithm
Replies: 28
Views: 9460

Re: Calculating nCr algorithm

For anyone who is interested, here is a fairly well optimized 10 line version of the choose function. It is somewhat slower than my last, but is much simpler. def nCr (n, r) return 0 if r > n r = n-r if r > n/2 p = 1 (1..r).each{|i| p *= n - r + i p /= i } return p end
by btilly
Sat Nov 10, 2007 3:14 am UTC
Forum: Computer Science
Topic: Calculating nCr algorithm
Replies: 28
Views: 9460

Re: Calculating nCr algorithm

I know it can be optimized w/ pascal and all that, but factorials using bignum classes works in a perfectly reasonable amount of time. These 7 lines of ruby return 300C25 instantly and 3000C25 in 1/2 second: def nCr(n,r) ncr=1 return 0 if r>n ((r+1)..n).each {|x| ncr*=x} (2..(n-r)).each {|x| ncr/=x...
by btilly
Fri Nov 09, 2007 10:04 pm UTC
Forum: Mathematics
Topic: Pythagorean Proofs
Replies: 24
Views: 3229

Re: Pythagorean Proofs

I definitely think there are different shortest proofs (if we use the string-of-symbols kind of pure logic proofs) for some theorems, but many "macroscopic" proofs that seem different on the surface will probably boil down to essentially the same thing. To compare proofs, they have to use...
by btilly
Fri Nov 09, 2007 9:59 pm UTC
Forum: Mathematics
Topic: What is the smallest number with exactly X distict factors?
Replies: 32
Views: 9909

Re: What is the smallest number with exactly X distict factors?

It is a nice combinatorics exercise, so I will leave it to the reader for now, but there is a reasonably nice formula for f(t). write t in its prime factorization and use that to generate f(t)... Your conjecture is wrong. At least in its naive form. In the simple version of your conjecture,...
by btilly
Thu Nov 08, 2007 8:25 pm UTC
Forum: Mathematics
Topic: On Linear Algebra
Replies: 35
Views: 4311

Re: On Linear Algebra

As for what it is, the basic idea of linear algebra is that in many cases you want to organize numbers into rectangular matrices and manipulate those in various ways. And by so organizing a bunch of numbers, you can model all sorts of interesting things. If this idea seems strange to you, consider ...
by btilly
Thu Nov 08, 2007 8:18 pm UTC
Forum: Computer Science
Topic: Mergesort and Quicksort work in O(n) time
Replies: 37
Views: 7243

Re: Mergesort and Quicksort work in O(n) time

You may have USED quicksort as part of your solution, but at that point it is not actually a quicksort. No, but you haven't really proved much to the students if they still see that using quicksort as part of the solution is faster than not using it. My point is that there are better examples of si...
by btilly
Thu Nov 08, 2007 4:38 pm UTC
Forum: Mathematics
Topic: Proof by contradiction is never needed!
Replies: 22
Views: 2873

Re: Proof by contradiction is never needed!

However, there are genuine examples where this isn't easy, typically ones which use both the hypothesis and the negated conclusion in several different ways during the course of the proof. For those proofs by contradiction that don't submit easily to conversion, I leave them as is and figure that a...
by btilly
Thu Nov 08, 2007 4:35 pm UTC
Forum: Mathematics
Topic: On Linear Algebra
Replies: 35
Views: 4311

Re: On Linear Algebra

Correct me if I'm wrong, but isn't this just a system of equations in a matrix? Reduced Row Echelon Form, etc? What else do I get into? What purpose does Linear Algebra serve in the real world? I've never taken a pure linear algebra course, but I'm fairly sure there isn't a whole lot to linear alge...
by btilly
Thu Nov 08, 2007 4:24 pm UTC
Forum: Computer Science
Topic: Mergesort and Quicksort work in O(n) time
Replies: 37
Views: 7243

Re: Mergesort and Quicksort work in O(n) time

Just have them sort a dataset that is large enough that it has to live on disk. That will teach you that quicksort is not the best alternative! No? Well, how about taking RAM-sized (or even cache-sized) chunks of the dataset and quicksorting them, then merging the results? That's not really cheatin...
by btilly
Thu Nov 08, 2007 4:21 pm UTC
Forum: Mathematics
Topic: Proof by contradiction is never needed!
Replies: 22
Views: 2873

Re: Proof by contradiction is never needed!

I agree that sometimes proof by contradiction is unnescesary. For example, many times when you need to prove uniqueness of something (say a function), you would start with "let's say with have a function f and a function g which satisfy all the above conditions. Let's assume that f=/=g and we'...
by btilly
Thu Nov 08, 2007 4:17 pm UTC
Forum: Mathematics
Topic: Proof by contradiction is never needed!
Replies: 22
Views: 2873

Re: Proof by contradiction is never needed!

Take your favorite proof by contradiction and try to write it using the contrapositive instead. Not my favorite, just an example. Let's say you just genetically constructed Z (the ordered ring of integers) and you want to prove that Z has no lower (or upper) bound. Using a reductio ad absurdum argu...
by btilly
Thu Nov 08, 2007 9:44 am UTC
Forum: Mathematics
Topic: On Linear Algebra
Replies: 35
Views: 4311

Re: On Linear Algebra

If this idea seems strange to you, consider solving 3 equations in 3 variables. Or 4 equations in 4 variables. Or 5 equations in 5 variables. What purpose do the variable names have when you do that? None! You could state the same problem, and the same solutions, more compactly if you forgot your v...
by btilly
Thu Nov 08, 2007 7:43 am UTC
Forum: Mathematics
Topic: On Linear Algebra
Replies: 35
Views: 4311

Re: On Linear Algebra

To those who are/have taken Linear Algebra, how much background Calculus knowledge needs to be known, if any? I have talked to my math teacher right now (Currently in Calculus BC, not exactly sure how that translates to I, II, etc. (but if you have Calculus I-IV that's Calculus II & III, if tha...
by btilly
Thu Nov 08, 2007 6:53 am UTC
Forum: Computer Science
Topic: Mergesort and Quicksort work in O(n) time
Replies: 37
Views: 7243

Re: Mergesort and Quicksort work in O(n) time

Yeah, I know the quicksort can be fixed. My algorithms professor had a serious hatred of it, and I suspect a little of that rubbed off on me. I think he was just tired of silly students always saying "Quicksort!" when so often there are better or more appropriate answers. Though by the ti...
by btilly
Thu Nov 08, 2007 6:04 am UTC
Forum: Logic Puzzles
Topic: Calculator problem (this one is old)
Replies: 24
Views: 4984

Re: Calculator problem (this one is old)

EdgarJPublius wrote:
Spoiler:
.2-1+2=7
.2-1+22=9

That was the solution I was looking for. :-)

Well done.
by btilly
Thu Nov 08, 2007 3:27 am UTC
Forum: Logic Puzzles
Topic: Calculator problem (this one is old)
Replies: 24
Views: 4984

Re: Calculator problem (this one is old)

EdgarJPublius wrote:
Spoiler:
2/2=1
2=2
2+2/2=3
22=4
2/.2/2=5
22+2=6
???=7
22*2=8
???=9
2/.2=10
2.2/.2=11
2+2/.2=12


Well done! Now what about those last 2?
by btilly
Thu Nov 08, 2007 3:26 am UTC
Forum: Logic Puzzles
Topic: Calculator problem (this one is old)
Replies: 24
Views: 4984

Re: Calculator problem (this one is old)

DrStalker wrote:I feel like I cheated.
Spoiler:
Even numbers: 2 [M+] [+] [MR] [+] [MR] ... as much as is needed.
Odd Numbers: As above, but append [+] [2] [/] [2]

I feel like you cheated as well. :-)

That isn't the answer I was looking for.
by btilly
Thu Nov 08, 2007 3:23 am UTC
Forum: Mathematics
Topic: Proof by contradiction is never needed!
Replies: 22
Views: 2873

Proof by contradiction is never needed!

Many years ago a mathematician told me that you never need to use proof by contradiction. In cases where people use it, you can prove the contrapositive instead and it will generally be clearer. (The contrapositive is the fact that A implies B iff not-B implies not-A.) The proofs that can't be rewri...
by btilly
Thu Nov 08, 2007 3:04 am UTC
Forum: Coding
Topic: Stand back! I'm new to regular expressions!
Replies: 33
Views: 3997

Re: Stand back! I'm new to regular expressions!

I'm trying to use regexp to figure out WHAT has been unwielded, and to automatically rewield the weapon/shield... Any ideas? There is a famous quote from Jamie Zawinski: Some people, when confronted with a problem, think “I know, I’ll use regular expressions.” Now they have two problems. This is a ...
by btilly
Thu Nov 08, 2007 2:18 am UTC
Forum: Logic Puzzles
Topic: Calculator problem (this one is old)
Replies: 24
Views: 4984

Calculator problem (this one is old)

Suppose that you have a standard scientific calculator. We can press any combination of keys, but the only digit that you're allowed to touch is 2, and you're only allowed to hit it 3 times. For instance we could press 2 - 2 / 2 = to get a 1. The puzzle, figure out how to produce every number from 1...
by btilly
Thu Nov 08, 2007 1:59 am UTC
Forum: Mathematics
Topic: Bad card shuffling and probability
Replies: 8
Views: 1757

Re: Bad card shuffling and probability

This reminds me of an article I saw in a Collectable Card Game magazine some time ago. For some reason, the author insisted that all players should riffle-shuffle their 60-card deck no less than 7 times before play, because it would (somehow) guarantee nearly-uniform randomness. The writer seemed t...
by btilly
Thu Nov 08, 2007 12:31 am UTC
Forum: Mathematics
Topic: Favourite Erroneous "Proofs"
Replies: 194
Views: 43822

Re: Favourite Erroneous "Proofs"

I've always liked the inflation theorem.

Code: Select all

1$ = 100 c
   = (10c)^2
   = (1/10$)^2
   = 1/100$
   = 1c
by btilly
Thu Nov 08, 2007 12:24 am UTC
Forum: Mathematics
Topic: when am I ever going to use this (help me choose a class)
Replies: 17
Views: 1902

Re: when am I ever going to use this (help me choose a class)

Given that list, I'm going to strongly recommend combinatorics. While it is true that, for instance, topology has lots of applications in certain areas of physics, if you go into them then you'll learn topology then. Similarly real analysis is critical if you plan to go on in math, but otherwise is ...
by btilly
Wed Nov 07, 2007 9:53 pm UTC
Forum: Mathematics
Topic: Show us your articles! Or what's your Erdos number?
Replies: 187
Views: 278872

Re: Show us your articles! Or what's your Erdos number?

I'm long out of mathematics. (Never quite finished my PhD.) But my official Erdos number is 3. My unofficial one is 2. The difference is because the official count does not include shared math monthly problems. I have 2 math papers and the aforementioned math monthly problem. http://links.jstor.org/...
by btilly
Tue Nov 06, 2007 7:29 pm UTC
Forum: Site/Forum issues
Topic: Is there any way to send comic suggestions?
Replies: 1
Views: 2020

Is there any way to send comic suggestions?

Several years ago the following puzzle appeared on a whiteboard at a Perl conference: "What does perl -penis have to do with pussy?" The connection is that perl -penis is an implementation of the Unix cat program. I'm curious what kind of comic this idea could turn into. Is there anywhere ...

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