(Somewhat inspired by this website, particularly Section III. Also, I might be using a different definition of entropy than usual; what I am using is closest to the physics definition (the one I encountered first) of the amount of disorder in a system.) Consider the following two “random” 256-bit strings: 1110001011010010101000001111001100001100011111000111011011101000000000000001111110010110010100011101010010111110000010010101001001101100111110011000000110111111000111101111000011010100001001100010010010011000000011101110000000110001101100000110111001100011 …created via RNG, and: […]

Might come as a rather strange request but does anyone know a textbook on cryptography that is small and short, say around 300 pages max. I am tired of having a sore shoulder from carrying 5 heavy math textbooks. Want to carry around a cryptography textbook for anytime reading that is concise but I won’t […]

Let $f(x)\in \mathbb Q[x]$ be irreducible polynomial of prime degree , $L$ be its splitting field , then how to show that $f(x)$ is solvable by radicals over $\mathbb Q$ iff $L=\mathbb Q(a,b)$ for any two roots $a,b$ of $f(x)$ ? i.e. how to show that $Gal(L/\mathbb Q)$ is solvable iff $L=\mathbb Q(a,b)$ for any […]

I have a function with two variables say $$g(x,y)=f(x)−h(x,y)\ $$ where $$f(x)= ax-bx^2\ $$ and $$h(x,y)=(x+y)^2\ $$ and $$ y\ge0, x+y\ge0.$$ My purpose is to maximize $g(x,y)$ for $x$, simultaneously minimizing $h(x,y)$ for $y$. How I can do this? Is there any literature available related to this problem? Waiting your expert response.

I have an exam in combinatorics on Friday and the pigeonhole principle is a part of the material. Can someone give me a reference to a book with the hardest(!) questions on this material? Thank you very much, it can help me a lot!

The following system of ODEs – is it recognized as distinct system, with meaningful background and uses? $$\frac{dx}{dt} = – [x(t)]^2 – x(t)y(t)$$ $$\frac{dy}{dt} = – [y(t)]^2 – x(t)y(t)$$ This is probably not needed, but initial conditions: $x(t=0) = x_0, \space y(t=0) = y_0$

Is there any other text books on Group rings except The algebraic structures of Group Rings by D.Passman. This book is really good but it will help if I know about other books on the topic too. Thanks!

I have ran across the following theorem but the given proof does not convince me. Theorem Let $u, v \in H^s(\mathbb{T})$ with $s>1/2$. Then the pointwise product $uv$ is in $H^s(\mathbb{T})$ and $\lVert uv\rVert_s \le C\lVert u\rVert_s\lVert v \rVert_s$ for a constant $C$ not depending on $u$ and $v$. In functional terms, this theorem is […]

I’m a computer science student and is fairly familiar with basic probability (calculating the probability of a event occurring, pmfs and pdfs) but I find it very difficult to grasp the concepts of advanced probability like principles of data reduction (sufficiency, likelihood principle, etc), point and interval estimation, Hypothesis testing, etc. I think it is […]

I am looking for an online ODE course that would be matlab/project-oriented. A full online text/course in the spirit of this linear algebra text is preferred. I know about the following CODEE and its odetoolkit IDE the Interactive Differential Equations and its labs

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