### Self learning game theory and probability

I am teaching myself mathematics, my objective being a thorough understanding of game theory and probability. In particular, I want to be able to go through A Course in Game Theory by Osborne and Probability Theory by Jaynes.I understand I want to cover a lot of ground so I'm not expecting to learn it in less than a year or maybe even two. Still I'm fairly certain it's not impossible.However I would like to have a study plan more or less fleshed out just to know I'm on the right track. There were some other questions related to self learning ma...Read more

### reference request - Introductory Group Theory Book Recommendation

I am looking for an introductory book on group theory as I would like to know more about the subject. I am aware that this an extremely useful area of mathematics. What book would you suggest for a first course on group theory?...Read more

### graph theory - Fixed points of a group action on tree

Suppose a group $H$ acts on a tree $T$, and this action fixes a point. Let $T_1$ be an $H$ invariant subtree of $T$. How do I show that $H$ fixes a point in $T_1$?...Read more

### group theory - Automorphism of Tree

Let $\sigma$ and $\theta$ be two automorphisms of tree $X$. I want to show that min$_{v\in V(X)}d(v,\sigma(v))=$min$_{v\in V(X)}d(\theta^{-1}\sigma\theta(v),v)$.I know every automorphism of tree is either translation or inversion or rotation. So if $\sigma$ is rotation, then we done. But i do not have any idea for cases translation or inversion....Read more

### Virtually infinite cyclic groups act on a tree

A virtually infinite cyclic group $G$ is quasi-isometric to $\mathbb{Z}$ and thus has two ends; by Stallings theorem, $G$ acts (without inversion) on a tree with finite edge-stabilizers.But the construction of Stallings theorem works more generally for groups with more than one end; is it possible to find a simpler construction for virtually infinite cyclic groups?There is a purely algebraic classification of the virtually infinite cyclic groups which can be reformulated as simple HNN extensions and amalgations over finite groups, so (using Bas...Read more