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?

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 […]

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 […]

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. […]

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 $n$ […]

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.

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 […]

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 […]

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 […]

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?

Intereting Posts

Conditional probabilities from a joint density function
Positive integers $k = p_{1}^{r_{1}} \cdots p_{n}^{r_{n}} > 1$ satisfying $\sum_{i = 1}^{n} p_{i}^{-r_{i}} < 1$
Texts on Principal Bundles, Characteristic Classes, Intro to 4-manifolds / Gauge Theory
Prove the direct product of nonzero complex numbers under multiplication.
Evaluating $\sum\limits_{n=0}^{20} \frac{(-1)^{n}2^{n+1}}{3^{n}},$
Another method for limit of $/x$ as $x$ approaches zero
Homework: closed 1-forms on $S^2$ are exact.
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half sine and half cosine quaternions
Prove that $1+\frac{1}{3}+\frac{1\cdot 3}{3\cdot 6}+\frac{1\cdot 3\cdot 5}{3\cdot 6 \cdot 9}+…=\sqrt{3}$
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on the adjointness of the global section functor and the Spec functor
Tying some pieces regarding the Zeta Function and the Prime Number Theorem together
“Fat” Cantor Set
Probability question with interarrival times