If $G$ is a finite group of order $n$, prove that $G$ is isomorphic to a subgroup
of the alternating group $A_{n+2}$'
From 'Groups and Symmetry (Springer UTM) by M. A. Armstrong'Enjoy!
Open University pure maths study and research blog
If $G$ is a finite group of order $n$, prove that $G$ is isomorphic to a subgroup
of the alternating group $A_{n+2}$'
From 'Groups and Symmetry (Springer UTM) by M. A. Armstrong'Enjoy!
We solve DEs by guessing.I like to watch science documentaries, since I have seen all Horizon and other channel's docs on physics by now ( some of them even twice or more ), I watch introductory physics stuff instead. Prof. Shankar lectures in an entertaining fashion.
Augustin-Louis Cauchy (1789–1857) was a French mathematician who is generally regarded as being the founder of mathematical analysis, including the theory of complex functions. Cauchy emerged as one of the most prolific mathematicians of all time. He authored at least 789 mathematical papers, and his collected works fill 27 volumes, this is on a par with Cayley and second only to Euler. It is said that more theorems, concepts, and methods bear Cauchy’s name than any other mathematician.
From Matrix Analysis by C. Meyer
2.15. (Fibonacci computational system) Prove that each positive integer admits a unique representation in the form $a_1f_1 + a_2f_2 + \cdots$, where $f_n$ are the Fibonacci numbers, each of the numbers $a_i$ is either $0$ or $1$, the number of ones in the representation is finite, and no two subsequent elements of the sequence $a_i$ are equal to $1$ simultaneously. For example, the first few representations are $1 = f_1$, $2 = f_2$, $3 = f_3$, $4 = f_3 + f_1$, $5 = f_4$, $6 = f_4 + f_1$, $7 = f_4 + f_2$. (Pay attention to the fact that the number $f_0 = 1$ is not used in this computational system, so that the Fibonacci sequence starts with $1,2,3,5,8,\cdots$). Invent algorithms for converting numbers from the Fibonacci system to the decimal positional number system and back, and algorithms for adding and multiplying numbers written in the Fibonacci sequence.
( "Lectures on Generating Functions by S.K. Lando, AMS 2003" )
This lecture is about vectors and how to add, subtract, decompose and multiply vectors. Decomposing vectors in 2 (or 3) dimensions is a key concept that will be used throughout the course.
Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before
(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)