## Search found 21 matches

Mon Jul 16, 2012 2:20 am UTC
Forum: Mathematics
Topic: How can I tell if Im good at "Real Math"? + Emphasis anxiety
Replies: 11
Views: 4840

### Re: How can I tell if Im good at "Real Math"? + Emphasis anx

As others in this thread have said the feeling of "faking it" is normal. You will likely have to memorize a formula here or there for a test before "really" understanding why it's true. Whenever I do this I feel like I'm faking it but that's ok, it's a temporary fix to buy myself...
Mon Mar 12, 2012 4:55 am UTC
Forum: Mathematics
Topic: Hw help: real analysis proof
Replies: 36
Views: 4733

### Re: Hw help: real analysis proof

For anyone interested, my professor gave us his proof. And he also commented that he was surprised that he saw so many "ingenious" things on this exercise because it was supposed to be one of the simpler ones. Anyways... Assume f is diff on R, f(0) >/= 1, and f'(x)>f(x) for all x in R. The...
Fri Feb 24, 2012 5:50 am UTC
Forum: Mathematics
Topic: Mathematical thinking
Replies: 6
Views: 2093

### Re: Mathematical thinking

Feeling mad with power is perfectly normal when studying math. Is that what you are describing?
Mon Feb 13, 2012 12:51 am UTC
Forum: Mathematics
Topic: Hw help: real analysis proof
Replies: 36
Views: 4733

### Re: Hw help: real analysis proof

Thanks everyone.
The MVT proof is pretty slick, I have to say. ln(f(x))/x>1 is pretty immediate.

I fully intend to bust out the Volterra function if any of my cohorts show up with integrals in their proofs tomorrow.
Sun Feb 12, 2012 10:01 pm UTC
Forum: Mathematics
Topic: Hw help: real analysis proof
Replies: 36
Views: 4733

### Re: Hw help: real analysis proof

jestingrabbit wrote:The Volterra function is also an antiderivative of its derivative, its just not unique. You need uniqueness, and you can't get that.

That makes sense, Thanks.
Sun Feb 12, 2012 9:45 pm UTC
Forum: Mathematics
Topic: Hw help: real analysis proof
Replies: 36
Views: 4733

### Re: Hw help: real analysis proof

Is there anything from stopping me from starting with define g(x)=f'(x)/f(x), Note G(x)=ln(f(x)) is an antiderivative for g(x)?*

Then I could avoid invoking whatever that evil Volterra function is.

*posted before thinking, edited a mistake.
Sun Feb 12, 2012 9:12 pm UTC
Forum: Mathematics
Topic: Hw help: real analysis proof
Replies: 36
Views: 4733

### Re: Hw help: real analysis proof

So it looks like I can't do something like this: Define g(x)=\ln{(f(x))}. It's derivative is this: g'(x)=\frac{f'(x)}{f(x)}>1. So this \int_0^x g'(t)\ dt>\int_0^x1\ dx = x. And \int_0^x g'(t)\ dt=g(x)-g(0)...
Sat Feb 11, 2012 6:52 pm UTC
Forum: Mathematics
Topic: Hw help: real analysis proof
Replies: 36
Views: 4733

### Re: Hw help: real analysis proof

It seemed natural to try this by contradiction. Assume there exists a>0 for which f'(a) is less than or equal to exp(a). Define g(x)=f(x)-exp(x). We have g(0) is greater than or equal to 0 and g(a) is less than or equal to 0. So on (0,a) g is decreasing. By MVT there must be some b in (0,a) where g...
Sat Feb 11, 2012 5:34 pm UTC
Forum: Mathematics
Topic: Hw help: real analysis proof
Replies: 36
Views: 4733

### Hw help: real analysis proof

Hello beautiful smartypantses, I'm having some trouble (running around in circles, pulling hair out) trying to figure out how to prove something on my current real analysis problem set. Assume f is continuous, differentiable on R. Given f(0) is greater or equal to 1 and f'(x)>f(x) for all x in R. Sh...
Wed Nov 09, 2011 7:37 am UTC
Forum: Mathematics
Topic: Writing Proofs - a plea for help
Replies: 2
Views: 862

### Re: Writing Proofs - a plea for help

There's plenty of information about the items on your list on wikipedia. You won't know what your confused about until you get with some other people and talk through these ideas, at least that's been my experience. If you have legitimate reasons you can't do this right now you might want to wait to...
Sun Oct 30, 2011 8:13 pm UTC
Forum: Mathematics
Replies: 5
Views: 3241

The way we proved generalized associativity in my real analysis 1 class was by induction on a few different cases. We first proved that "the insertion of any one pair of parenthesis does not change the value of an n-fold product." Our base case is for 3-fold products, which is given as an ...
Fri Oct 28, 2011 8:47 pm UTC
Forum: Mathematics
Topic: What is the name of this sequence: 0110100110010110…
Replies: 3
Views: 1885

### Re: What is the name of this sequence: 0110100110010110…

Wow, I would have never guessed someone else had this sequence playing in their head like this. I think this sequence first found me around the age of 11 or 12th, where it was "left, right, right, left, ..." And at the time I could tell it was some manifestation of my childhood OCD. I had ...
Wed Sep 07, 2011 3:35 am UTC
Forum: Mathematics
Topic: An interesting topic for a math talk
Replies: 8
Views: 2131

### Re: An interesting topic for a math talk

Who is your audience? What should we assume about their math background?
Thu Sep 01, 2011 10:02 pm UTC
Forum: Mathematics
Topic: Multiplication or the summation operator (sigma)
Replies: 28
Views: 4468

### Re: Multiplication or the summation operator (sigma)

gmalivuk wrote:What?

Pancakes v. waffles for people slightly more mathematically minded.

I think. I can't really tell, either.
Thu Aug 18, 2011 6:26 pm UTC
Forum: Mathematics
Topic: It's not a square root function, but... what is it?
Replies: 13
Views: 3975

### Re: It's not a square root function, but... what is it?

Since the distance is 2x + 1 between each perfect square and the next higher one (with x being the root of the square), you could form an approximation by doing (y-x) / (2x +1), where y is the square root you want the number for. Should "(y-x) / (2x +1)" be an equation you are solving? Ho...
Wed Aug 17, 2011 5:21 am UTC
Forum: Mathematics
Topic: How to start studying maths again?
Replies: 8
Views: 3064

### Re: How to start studying maths again?

I would suggest seeing what you can do on Khan Academy's knowledge map. You can also find lessons for any of the subjects on the map on his site. It's a good way to see what's coming around the corner, if you know what I mean.

Thu Jul 14, 2011 4:31 pm UTC
Forum: Mathematics
Topic: Why can't I do this? (Infinite sets and cardinality)
Replies: 14
Views: 4763

### Re: Why can't I do this? (Infinite sets and cardinality)

It's not nearly so obvious how to iterate real numbers to be guaranteed to eventually hit any particular one. My idea goes something like this. Consider the base 10 representation system, zero padded out to infinity in both directions. So 1 is going to be ....000001.000000.... and so on and so fort...
Thu Jun 30, 2011 5:22 pm UTC
Forum: Mathematics
Topic: Curvature of f(x) as x->infinity
Replies: 4
Views: 2553

### Curvature of f(x) as x->infinity

Greetings again forum community, For a function f(x), its curvature function K(x) = |f''(x)|/(1+f'(x)^2)^(3/2) I'm trying to find a proof of the fact that no function f(x) can have monotonically increasing curvature K(x). I would like to prove this for two cases, one where the curvature tends to inf...
Thu Jun 23, 2011 6:50 pm UTC
Forum: Mathematics
Topic: What's your approach to digesting proofs?
Replies: 7
Views: 1579

### Re: What's your approach to digesting proofs?

I have a friend that swears by latex. He studies by writing all his proofs in latex language. Something about that act helps solidify the concepts in his mind. I always "draw a picture" of the parts of the proof I don't understand. Meaning I look for a geometric interpretation, as was alre...
Tue Jun 14, 2011 4:16 pm UTC
Forum: Mathematics
Topic: unlimited abstraction implies {} but limited does not
Replies: 2
Views: 704

### Re: unlimited abstraction implies {} but limited does not

Thanks, and I think I see. Limited abstraction just tells you that if you were given a property and a set then there exists some set of elements with that property, but it doesn't actually give you any of these sets. You'd have to be given a set A as a separate axiom and some impossible property to ...
Tue Jun 14, 2011 12:59 am UTC
Forum: Mathematics
Topic: unlimited abstraction implies {} but limited does not
Replies: 2
Views: 704

### unlimited abstraction implies {} but limited does not

Hello forum community. I'm having some fun going through the axioms of ZF set theory. I'm confused as to why the unlimited abstraction principle implies the existence of the empty set but the limited abstraction principle does not. My information comes from a book called Set Theory and the Continuum...