# All Questions

16 views

### conditional probability, logical product

I was working my way through Kruschke's textbook and got to Chapter 9 and the result on factoring out conditional probabilities for hierarchical models, seemed similar to something in Feller Vol1 ...
27 views

### Quick way to classify groups of small order

This is a past Qualifying exam on Algerbra : I'm curious if there is a quick way to solve Prob 1. To me, directly classifying groups takes too much time and I think I could not handle this in time ...
10 views

### Example of a non-regular curve which has the same geometric image as a regular curve parametrized by arclength

Give an explicit example of: $(a)$ a regular curve parametrized by arclength; $(b)$ a non-regular curve which has the same geometric image as the previous one. Could someone please help me with ...
30 views

17 views

### How to find isoclines of the following system?

If I had a system of equations such as: $$\dot{x}=(1+2x+y)x$$ $$\dot{y}=(4+6x+2y)y$$ How would I find the horizontal and vertical isoclines of such a system? I know ...
22 views

### Recursion in Integration by Parts

I'm trying to integrate by parts, but I keep getting recursive answers. $I=\int_0^\pi f(x)cos(x)dx$ where $f''(x)=3f(x)$, $f'(0)=-5$, and $f'(\pi)=4$ Thanks.
23 views

54 views

### Pythagorean triplets of the form $a^2+(a+1)^2=c^2$ and the space between them

I was searching for pythagorean triples where $b=a+1$, and I found using a python program I made the first 10 integer solutions: $0^2+1^2=1^2$ $3^2+4^2=5^2$ $20^2+21^2=29^2$ $119^2+120^2=169^2$ ...
25 views

### Representation of a group and its quotient

Let $G$ be a (finite) group and let $N$ be a normal subgroup of $G$. Suppose that we have a representation $(V,\rho)$ of $N$ and a representation of $(V, \tau)$ of the quotient group $G/N$. Here $V$ ...
### $\bf{x'}=Ax$ with eigenvalues of multiplicity greater than $1$
Given the system $\bf{x'}=Ax$, where $\bf{A}$$=\begin{bmatrix} -2 &0 &0 \\ 2& 1 & 0\\ 0 &0 &1 \end{bmatrix}$, if I solve it by first finding matrix $\bf{P}$ and then ...