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ASGARLI.WORDPRESS.COM

Cold and austere | a simple blog on math

a simple blog on math

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Cold and austere | a simple blog on math | asgarli.wordpress.com Reviews
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Cold and austere | a simple blog on math | asgarli.wordpress.com Reviews

https://asgarli.wordpress.com

a simple blog on math

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1

October | 2014 | Cold and austere

https://asgarli.wordpress.com/2014/10

A simple blog on math. Monthly Archives: October 2014. Solving the diophantine equation x 3=y 2 2. October 19, 2014. This will be a post illustrating how unique factorization in the ring helps us solve the diophantine equation . We first start by proving Lemma: The ring is a UFD. Proof. Define . The identity proves that So is a … Continue reading →. Solving the diophantine equation x 3=y 2 2. Compact space that is not sequentially compact. Every group of order 63 is not simple.

2

April | 2014 | Cold and austere

https://asgarli.wordpress.com/2014/04

A simple blog on math. Monthly Archives: April 2014. Goldbach’s Conjecture over Z/mZ. April 19, 2014. Goldbach’s Conjecture states that every even integer greater than can be written as sum of primes. This problem is notoriously difficult, and still open. However, one can prove the following version of Goldbach’s Conjecture for the ring : Proposition. Let … Continue reading →. Solving the diophantine equation x 3=y 2 2. Compact space that is not sequentially compact. Every group of order 63 is not simple.

3

Goldbach’s Conjecture over Z/mZ | Cold and austere

https://asgarli.wordpress.com/2014/04/19/goldbachs-conjecture-over-zmz

A simple blog on math. Cayley-Hamilton for commutative rings. Uncountability of real numbers — Topological proof →. Goldbach’s Conjecture over Z/mZ. April 19, 2014. Goldbach’s Conjecture states that every even integer greater than. Can be written as sum of. Primes. This problem is notoriously difficult, and still open. However, one can prove the following version of Goldbach’s Conjecture for the ring. Be a positive integer. Given any even integer. There exists an integer. Is trivial, so assume. You write...

4

June | 2014 | Cold and austere

https://asgarli.wordpress.com/2014/06

A simple blog on math. Monthly Archives: June 2014. Uncountability of real numbers — Topological proof. June 4, 2014. Perhaps the fastest proof of uncountability of is using the diagonalization trick. However, there’s another proof that I learnt from Topology by Munkres (Theorem 27.7 in page 176) which is nice in its own way. It is enough to show that … Continue reading →. Solving the diophantine equation x 3=y 2 2. Compact space that is not sequentially compact. Every group of order 63 is not simple.

5

Continuous bijection from (0, 1) to [0, 1] | Cold and austere

https://asgarli.wordpress.com/2013/10/26/continuous-bijection-from-0-1-to-0-1

A simple blog on math. Properties of Noetherian modules. Cayley-Hamilton for commutative rings →. Continuous bijection from (0, 1) to [0, 1]. October 26, 2013. I think the following is a good exercise for first course in real analysis. Does there exist continuous bijection from. Like the answer should be “no”. At least if the question was. Does there exist continuous bijection from. The answer would be a trivial “no”. Continuous image of compact set is compact; in particular,. Is compact, and. Continuous...

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theoremoftheday.org theoremoftheday.org

Theorem of the Day

http://www.theoremoftheday.org/Acknowledgements.htm

Theorem of the Day. M any organisations and people have contributed to this site. I have generally preferred to acknowledge this contribution here rather than clutter up individual theorems. Fatima Affif Chaouche, Reza Akhtar. George E. Andrews. David L. Applegate. Robert F. Bailey. Kathleeen Bednar, Lowell Beineke. Arthur T. Benjamin. Curtis D. Bennett. Valérie Berthé. Ethan D. Bolker. Petter Brändén. David M. Bressoud. Andreas Brusinsky, Edward B. Burger. Georgina Bygott, Peter Cameron. Allan Siu Lun Lo.

hippomath.blogspot.com hippomath.blogspot.com

Paul Liu: A curious identity

http://hippomath.blogspot.com/2011/08/curious-identity.html

Math Physics. And a touch of arrogant self-reflection. I was trying to do a question the other day when I found an interesting identity that is a corollary of the double angle formulae. I've searched online for its name, but it might be so trivial that it doesn't have one. Instead of revealing the identity, I'll let you figure it out for yourself:. Frac{1}{2 0} cos(x 1) = cos(x 1) ]. Frac{1}{2 1} left( cos(x 1 x 2) cos(x 1-x 2) right)= cos(x 1) cos(x 2) ]. Frac{1}{2 {2} left( begin{array}{c}. Subscribe t...

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Cold and austere | a simple blog on math

A simple blog on math. Solving the diophantine equation x 3=y 2 2. October 19, 2014. This will be a post illustrating how unique factorization in the ring. Helps us solve the diophantine equation. We first start by proving. Is a multiplicative function. We claim that. Is a Euclidean norm on. We need to show that there exist elements. So we can write. Be the closest integers to. Let’s turn our attention in solving the equation. Cannot be even because then. Which is impossible. So. We first show that.

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