Articles of reference request

Bifurcation Example Using Newton's Method

I am studying dynamical systems as part of a research project. I have been using Newton’s Method and studying the dynamic properties. Does anyone know where I could find a relatively simple example of bifurcation using Newton’s Method?

Connections of Geometric Group Theory with other areas of mathematics.

I’m a master’s student in the Turin University. At the end of my studies, I have to write a master thesis. My main interest is geometric group theory, but it is not a research area of the Turin’s mathematical department. My professors in algebra and geometry are principally interested in algebraic geometry, commutative algebra or […]

Proving Theorems

I’ve been struggling with the concept of proofs ever since I completed my introductory logic course “Axiomatic Systems”. In that course it seemed to be easy. We were pretty much just using various logical methods to prove the properties of real numbers. Now it doesn’t seem nearly as simple. I often find myself stumped when […]

Straightedge and compass theory in three dimensions

I’m looking for a reference on the theory of straightedge and compass constructions in three dimensions akin to Euclid’s Elements in two dimensions. More specifically, I mean a theory of geometric constructions where one is allowed lines between any two points, planes through any three non-colinear points, and spheres with a given center and radius. […]

To find all odd integers $n>1$ such that $2n \choose r$ , where $1 \le r \le n$ , is odd only for $r=2$

For which odd integers $n>1$ is it true that $2n \choose r$ where $1 \le r \le n$ is odd only for $r=2$ ? I know that $2n \choose 2$ is odd if $n$ is odd but I want to find those odd $n$ for which the only value of $r$ between $1$ and $n$ […]

Information on “stronger form” of Dirichlet's Theorem on Arithmetic Progressions

From Wikipedia: “Stronger forms of Dirichlet’s theorem state that, for any arithmetic progression, the sum of the reciprocals of the prime numbers in the progression diverges.” Can anyone direct me to a proof of this “stronger” fact, or a paper that discusses it? Thanks.

Are there (known) bounds to the following arithmetic / number-theoretic expression?

I apologize in advance if this is something that is already well-known in the literature, but I would like to ask nonetheless (for the benefit of those who likewise do not know): Are there (known) lower and upper bounds to the following arithmetic / number-theoretic expression: $$\frac{I(x^2)}{I(x)} = \frac{\frac{\sigma_1(x^2)}{x^2}}{\frac{\sigma_1(x)}{x}}$$ where $x \in \mathbb{N}$, $\sigma_1(x)$ is […]

Books with more problems on card/urn and ball problems

I am struggling with combinations and permutations. One particular concept that is bugging me is selecting outcomes. I posed a few questions in a forum. \What is the probability that you are dealt a “full house”? (Three cards of one rank and two cards of another rank.)\ I received following answer “”When counting the number […]

Topological Conditions Equivalent to “Very Disconnected”

Definition: Let $(X, \mathcal{T})$ be a topological space, where the set $X$ has more than one element. Suppose that for every pair of distinct elements $a, b \in X$, there exists a separation $(A,B)$ of $X$ such that $a \in A$ and $b \in B$. Then we say $(X, \mathcal{T})$ is very disconnected. Is this […]

Matrix Theory book Recommendations

I’m currently reading Sheldon Axler’s “Linear Algebra Done Right”. Can anyone recommend any good books on matrix theory at about the same level that might compliment it?