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04:47 PM on 12/09/09 
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tonyC4L
tech-savvy at-risk youth
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Lake Forest, CA
Male - 25 Years Old
Just finished the last of my math finals today, so no questions from me for a few weeks. Unless someone wants to take a stab at this one from my complex analysis final:

Let f(z) be entire (i.e. analytic on all of C) and let |f(z)| > 1. Prove that f is constant.

My first thought was to use the the theorem that the only bounded entire functions are constant functions (and then be done), but f is not bounded so I didn't know what to do. If only the inequality were the other way...
12:54 AM on 12/18/09 
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tonyC4L
tech-savvy at-risk youth
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Lake Forest, CA
Male - 25 Years Old
Apparently nobody likes complex numbers... anyway I think I got an answer to that problem. If f(z) is entire, then so is 1/f(z), and |1/f(z)| < 1, so it is bounded and entire and thus constant. Clearly then f(z) is constant as well.
10:33 PM on 01/12/10 
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Spenny
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Vienna, Austria
Male - 22 Years Old
If anyone has an interesting math problem to talk about, or needs help with something they're working on, bring it in here!
If you're still interested, I have one.

Express the function in the form (f o g).

You're given g(x) = cuberoot(x/1+x)
02:21 PM on 01/13/10 
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John JD Dorian
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St Louis, MO
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If you're still interested, I have one.

Express the function in the form (f o g).

You're given g(x) = cuberoot(x/1+x)

i'm confused. express what function?
02:39 PM on 01/13/10 
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fishguts182
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New Mexico
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anyone here ever taken discrete math or linear algebra?
11:55 PM on 01/13/10 
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Spenny
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Vienna, Austria
Male - 22 Years Old
i'm confused. express what function?
My bad. It gives you G(x) = cuberoot(x/1+x) and tells you to express it in the form f of g, or f(g(x))

I discovered that all you have to do is give what f(x) and g(x) are, which are f(x) = cuberoot(x) and g(x) = x/1+x
06:16 AM on 01/14/10 
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John JD Dorian
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St Louis, MO
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anyone here ever taken discrete math or linear algebra?

yeah ask away.
08:16 AM on 01/14/10 
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fishguts182
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New Mexico
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im gonna be taking them this semester. How tough should these classes be?
11:15 AM on 01/14/10 
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John JD Dorian
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St Louis, MO
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im gonna be taking them this semester. How tough should these classes be?

what level?
11:15 AM on 01/14/10 
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fishguts182
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New Mexico
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both are 300 level class at my university.
07:53 AM on 01/15/10 
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John JD Dorian
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St Louis, MO
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both are 300 level class at my university.

same at mine.

is the text you're using for linear algebra david lay's 'linear algebra'?
and what text are you using (if any) for discrete math?

that class here is called 'foundations for higher mathematics' and isn't really purely discrete math but there's a lot of overlap. aside from the graph theory, i'll be able to help.
12:21 PM on 01/16/10 
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Spenny
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Vienna, Austria
Male - 22 Years Old
Okay, here's another question that I have absolutely no clue how to do. If anyone could help explain what to do, that would be much appreciated. :)


01:43 PM on 01/16/10 
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TotalCollapse
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Maryland
Female - 21 Years Old
Okay, here's another question that I have absolutely no clue how to do. If anyone could help explain what to do, that would be much appreciated. :)


I'm completely sure that my answer is correct. To find the volume of the pool, you can change the shape of the pool into a rectangular prism. Let's say that the water is 8 ft. in the deep end and 3 ft. in the shallow end. You want to find the average depth, which would be 5.5 ft. The volume would be 30*40*5.5 = 6600 cubic ft. 5.5 is 11/16 of 8; therefore, regardless of what the height of water in the deep end is, the average depth must be 11/16 * h. V(h) = 30 * 40 * 11/16 * h > V(h) = 825h. This function is only valid when h >= 0 and h <= 8 (domain). The range would be V(t) >= 0 and V(t) <= 6600. If h < 0 then V(t) = 0 (since the pool cannot have a negative volume). When h > 8, V(t) = 6600 (because the pool cannot hold more than 6600 cubic ft. of water without overflowing.
11:05 AM on 01/17/10 
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Spenny
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Vienna, Austria
Male - 22 Years Old
I'm completely sure that my answer is correct. To find the volume of the pool, you can change the shape of the pool into a rectangular prism. Let's say that the water is 8 ft. in the deep end and 3 ft. in the shallow end. You want to find the average depth, which would be 5.5 ft. The volume would be 30*40*5.5 = 6600 cubic ft. 5.5 is 11/16 of 8; therefore, regardless of what the height of water in the deep end is, the average depth must be 11/16 * h. V(h) = 30 * 40 * 11/16 * h > V(h) = 825h. This function is only valid when h >= 0 and h <= 8 (domain). The range would be V(t) >= 0 and V(t) <= 6600. If h < 0 then V(t) = 0 (since the pool cannot have a negative volume). When h > 8, V(t) = 6600 (because the pool cannot hold more than 6600 cubic ft. of water without overflowing.
Thank you so much! Very clear explanation. :)
02:07 PM on 01/17/10 
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TotalCollapse
You are my blanked out pages.
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Maryland
Female - 21 Years Old
Thank you so much! Very clear explanation. :)
Sure, no problem.



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