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### Arda Ünlü

Research -√(x*y+((y-x)/2)^2)=(x+y)/2

Is this true?

Is this true?

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Deeparaj Bhat

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A more precise RHS would be |x+y|/2. Assuming the domain to be real numbers.

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### Krishna Viswanath

Research -I need to solve the following recursion relation:-

$A_{k+1} + A_kB_k + A{k-1}C_k + D_{k} = 0$, actually it trivially follows that this recurrence is directly related to the following one:-

$X_{k+1} + X_k + X{k-1}f(n) + g(n) = 0$......

Can you find the exact solution to the above recurrences.........or provide any valuable source........

Thanks in advance...... :)

$A_{k+1} + A_kB_k + A{k-1}C_k + D_{k} = 0$, actually it trivially follows that this recurrence is directly related to the following one:-

$X_{k+1} + X_k + X{k-1}f(n) + g(n) = 0$......

Can you find the exact solution to the above recurrences.........or provide any valuable source........

Thanks in advance...... :)

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### Paul Smith

Research -It is well known that contemporary mathematics includes many disci- plines. Among them the most important are: set theory, algebra, topology, geometry, functional analysis, probability theory, the theory of differential equations and some others. Furthermore, every mathematical discipline consists of several large sections in which specific problems are investigated and the corresponding technique is developed. For example, in general topology we have the following extensive chap- ters: the theory of compact extensions of topological spaces, the theory of continuous mappings, cardinal-valued characteristics of topological spaces, the theory of set-valued (multi-valued) mappings, etc. Modern algebra is featured by the following domains: linear algebra, group theory, the theory of rings, universal algebras, lattice theory, category theory, and so on. #mathematics

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i'm sorry for that, duplicate, I deleted one.

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### Josh Adams

Research -What Do Mathematics and Cooking Have In Common?

http://cosmoso.net/mathematics-spaghetti-alla-carbonara-and-you/

http://cosmoso.net/mathematics-spaghetti-alla-carbonara-and-you/

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(Euro-accent) um yes... nice and twisty. ;-)

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### Byron Fedele

Research -This may lead to a practical, feasible solution, to factor the product of two very large prime numbers (with thousands of digits), making many security systems vulnerable to new types of attacks: factoring encryption keys, en masse. Let's start with the pictures. The patterns (as well as how to leverage them) are explained below.

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Nothing in the article shows anything better than intelligent guessing.

Where"s the beef?

Where"s the beef?

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### Ian M

Research -Since there seems to be a Phi Ratio kick going on..here's how to derive it from the computer number systems.

Cheers

- Ian

Cheers

- Ian

3 photos

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### Efstratios Gavves

Research -http://www.uva.nl/over-de-uva/werken-bij-de-uva/vacatures/item/15-233.html?f=Qual

If you are looking for a PhD or postdoc on computer vision and machine learning, or you know somebody who is looking, there are 11 openings in total at the University of Amsterdam.

The lab and the projects offered are a joint endeavour between the University of Amsterdam and Qualcomm, the leading mobile chip manufacturer.

There are project descriptions in the link. The projects cover a broad span of interest, practically whatever is hot in computer vision and machine learning nowadays. Of course, there is a heavy interest in deep learning!

Please share!

If you are looking for a PhD or postdoc on computer vision and machine learning, or you know somebody who is looking, there are 11 openings in total at the University of Amsterdam.

The lab and the projects offered are a joint endeavour between the University of Amsterdam and Qualcomm, the leading mobile chip manufacturer.

There are project descriptions in the link. The projects cover a broad span of interest, practically whatever is hot in computer vision and machine learning nowadays. Of course, there is a heavy interest in deep learning!

Please share!

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### Math

Research -THE MATHS OF PASTA

George L. Legendre, the man with a mathematical knowledge and intimate understanding of pasta, did in his book Pasta by Design - the biggest visual and detailed collection of pasta shapes ever published, a triumph of design, mathematics and a project that's led to some interesting discoveries. Using the mathematical functions, George was able to write formulas that conveyed each pasta's shape. These formulas can then be fed into a computer which processes the data and presents perfect renderings of each pasta's individual shape.

George L. Legendre, the man with a mathematical knowledge and intimate understanding of pasta, did in his book Pasta by Design - the biggest visual and detailed collection of pasta shapes ever published, a triumph of design, mathematics and a project that's led to some interesting discoveries. Using the mathematical functions, George was able to write formulas that conveyed each pasta's shape. These formulas can then be fed into a computer which processes the data and presents perfect renderings of each pasta's individual shape.

spring-of-mathematics:
“ Mathematics and Traditional Cuisine
The mathematics of Pasta: A process analysis to find unity, formulas and ways to express structure mathematics of pasta shapes, by their...

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### Arindam Bose

Research -Did You Know : The History of Egyptian Mathematics – Part I

An Overview: The early Egyptians settled along the fertile Nile valley as early as about 6000 BC, and they began to record the patterns of lunar phases and the seasons, both for agricultural...

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Sphinx

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### Vineet George

Research -A method to generate Partition.

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Russell Edson

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That's a nice iterative way to do it. :)

There's also an elegant recursive way too. The set of all partitions for N is equal to the union of:

- the set of all partitions of N-1, where 1 is concatenated to (the front of) each partition,

- the set of all partitons of N-1, where for each partition we've collected the set of partitions that are created by incrementing each number in turn.

And then we simply take ((1)) as the base case.

eg.

N=1: ((1))

N=2: ((1 1)) U ((2)) = ((1 1) (2))

N=3: ((1 1 1) (1 2)) U ((2 1) (1 2) (3))

= ((1 1 1) (1 2) (2 1) (3))

etc.

And then the duplicates can be filtered out (eg. if (1 2) and (2 1) are to be considered the same partition.)

There's also an elegant recursive way too. The set of all partitions for N is equal to the union of:

- the set of all partitions of N-1, where 1 is concatenated to (the front of) each partition,

- the set of all partitons of N-1, where for each partition we've collected the set of partitions that are created by incrementing each number in turn.

And then we simply take ((1)) as the base case.

eg.

N=1: ((1))

N=2: ((1 1)) U ((2)) = ((1 1) (2))

N=3: ((1 1 1) (1 2)) U ((2 1) (1 2) (3))

= ((1 1 1) (1 2) (2 1) (3))

etc.

And then the duplicates can be filtered out (eg. if (1 2) and (2 1) are to be considered the same partition.)

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### David Radcliffe

Research -This is a simple JavaScript app for estimating the probability of winning a basketball game, based on the article "Safe Leads and Lead Changes in Competitive Team Sports" by A. Clauset, M. Kogan, and S. Redner.

Basketball win probability calculator. This calculator estimates the probability that an NBA basketball team will win, given the lead (point difference) and the number of seconds remaining in the game. The formula assumes that the two teams are evenly matched. This is based on the article Safe ...

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### Vincent Granville

Research -This may lead to a practical, feasible solution, to factor the product of two very large prime numbers (with thousands of digits), making many security systems vulnerable to new types of attacks: factoring encryption keys, en masse. Let's start with the pictures. The patterns (as well as how to leverage them) are explained below.

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It brought to mind these patterns

http://www.naturalnumbers.org/Qfactor2.html

http://www.naturalnumbers.org/Qfactor2.html

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### George Mpantes

Research -THE DEFEAT OF DEDEKIND'S LOGICISM ON THE INFINITE SET

https://www.academia.edu/8578042 · Logicism .

· The logicism of Dedekind

· The infinite set

· The logical contradiction

· The impredicative definition

· The axiom of reducibility

The inconsistency of the infinite set of Dedekind

https://www.academia.edu/8578042 · Logicism .

· The logicism of Dedekind

· The infinite set

· The logical contradiction

· The impredicative definition

· The axiom of reducibility

The inconsistency of the infinite set of Dedekind

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### Abhishek Singh Rawat

Research -Yet another great example of Women in STEM.

Via +David Roberts

A Great TED playlist on the Women in STEM : https://www.ted.com/playlists/253/11_ted_talks_by_brilliant_wome

Via +David Roberts

A Great TED playlist on the Women in STEM : https://www.ted.com/playlists/253/11_ted_talks_by_brilliant_wome

Neena Gupta

Last year, the Indian Statistical Institute’s Neena Gupta was awarded the Indian National Science Academy’s medal for young scientists for solving a mathematical problem that was open for almost seven decades known as the Zariski Cancellation Conjecture. The academy tipped its hat to Gupta’s work calling it "one of the best works in Algebraic Geometry in recent years done anywhere".

Last year, the Indian Statistical Institute’s Neena Gupta was awarded the Indian National Science Academy’s medal for young scientists for solving a mathematical problem that was open for almost seven decades known as the Zariski Cancellation Conjecture. The academy tipped its hat to Gupta’s work calling it "one of the best works in Algebraic Geometry in recent years done anywhere".

Despite inherent biases in the academic system, some Indian women are thriving at the cutting edge of science.

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+Neil Penning Environmental and social barriers — including stereotypes, gender bias and the climate of science and engineering departments in colleges and universities — continue to block women’s participation and progress in science, technology, engineering, and math (STEM).

So, there is a need for new ideas for what each of us can do to more fully open scientific and engineering fields to girls and women.

So, there is a need for new ideas for what each of us can do to more fully open scientific and engineering fields to girls and women.

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