Needing inspiration for a functional equation

Hey guys! I am researching labeled trees for my diplom thesis right now, and i am a bit stuck with a functional equation i got. It’s like this: A(z) = z + z(A(z)²+A(z²))

So obviously this one is kinda difficult, i got it while trying to calculate generating functions for my problem. But even the simpler equation A(z) = z + zA(z²) is not solvable by Wolfram Mathematica, plus i cannot find any hints on how to tackle it. Could you give me some hints for where to look? Thanks a lot!

submitted by Nevin Manimala Nevin Manimala /u/Kylorin94
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Tips on presenting long proofs with slides

I have to present the core of my master’s thesis soon and I should explain the main ideas of the proofs. The proofs are generally not that long, about 3/4 of a page, so I think it’s easier just to show the full proof than to try to summarize it and miss important details.

I’m worried the slides will become too cluttered or hard to follow though. Are there some tips for how to prepare presentations of proofs?

What I have is essentially the proofs broken down into sections over four or five slides. My supervisors are extremely clever and I don’t think they’d have a problem following this, but it would be nice to have clean slides.

Thanks for the tips.

submitted by Nevin Manimala Nevin Manimala /u/steve233
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Is Monte Carlo estimate is same as Maximum Likelihood estimate?

Say I want to find out the probability of success p of an experiment. So I carry out the experiment n times and obtain k success. Then the simple Monte Carlo estimate gives p=k/n.

The other way ia using the likelihood function. Given the outcome, the probability of that outcome for p in [0,1] will be my likelihood function L(p). If I look at the value of p for which L(p) is maximum, it will be my maximum likelihood estimate of p.

My question is, are both of these estimates equal? And if so, is there a way of proving it?

The third way to estimate is by taking expected value of p assuming p is a random variable with PDF c*L(p) where c is some scaling constant. Is this estimate better than previous ones? Is there a way to prove this?

And a last question, how to obtain the confidence interval for the estimate obtained from likelihood function?

submitted by Nevin Manimala Nevin Manimala /u/TheFoolVoyager
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Lie group topology

So I’m taking a course on topology and we have to create a 10min talk on anything related to the field. I’ve decided to look at Lie groups.

I was hoping someone could tell me if my understanding of the topology is correct.

So a Lie group is a manifold and a group. And a manifold is a top space that is locally homeomorphic to Euclidean n-space. So the topology on a Lie group is the topology inherited from the manifold? I.e. it is the open sets created by the balls in Euclidean n-space.

There is obviously a lot of information on Lie groups around but most of them either assume you know the topology or just skip it to focus on the algebra.

Thanks everyone!

submitted by Nevin Manimala Nevin Manimala /u/seagull94
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How can I study maths in my free time?

Hey guys, I left school a few years ago and didnt really pay attention in maths, but I’m interested in going back and learning it again. Are there any bookswebsites with simple to complex math questions and good explanations on how to solve them? Basically just want to catch up on 12 years of maths that I screwed around in. Thanks

submitted by Nevin Manimala Nevin Manimala /u/javydog
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