## Free Textbooks in Mathematics

Fri, 02/24/2017 - 08:00 — yonatan zilpaThe following is a list of links to useful textbooks in mathematics, available for free on the Internet. All books are legally safe to download, The books are in printable format - Postscript (PS) or Portable Document Format (PDF). You are free to download, read and print them. This is a partial list of "free textbooks" in math, the list is to be updated regularly.- Read more about Free Textbooks in Mathematics
- Log in or register to post comments

## Hahn Decomposition Theorem

Thu, 11/24/2016 - 14:07 — yonatan zilpaLet $\nu$ be a signed measure over measurable space $(X,\mathcal{M})$. Denote $\tilde{N}=\left\{ u\in \mathcal{M} \; :\; \mbox{$u$ is $\nu$-negative} \right\}$ and $\tilde{P}=\left\{ u\in \mathcal{M} \; :\; \mbox{$u$ is $\nu$-positive} \right\}$- $\exists N\in \tilde{N}\Big(\exists P \in \tilde{P}\Big( N\cap P=\emptyset \; \mbox{ and }\; N\cup P = X\Big)\Big)$
- $\forall N,N^{'}\in \tilde{N}\Big(\forall P,P^{'}\in \tilde{P} \Big(N\sqcup P =N^{'}\sqcup P^{'}=X \; \Longrightarrow \nu( P\triangle \tilde{P})=\nu( N\triangle \tilde{N})=0\Big)\Big) $

- Read more about Hahn Decomposition Theorem
- Log in or register to post comments

## How many squares can be found here?

Sun, 08/14/2016 - 13:40 — yonatan zilpa- Read more about How many squares can be found here?
- Log in or register to post comments

## Four bottles - Equidistant mouth problems

Sun, 04/17/2016 - 05:29 — yonatan zilpaHow to place four identical bottles in the plane such that the distance between each pair of mouths will be the same?- Read more about Four bottles - Equidistant mouth problems
- Log in or register to post comments

## Conceptual Language and Learning

Mon, 12/26/2016 - 15:17 — yonatan zilpaNormally when we learn human spoken language we translate words to our own mother tongue language. But when we learn our mother tongue language we have no language to translate new words. How do we understand mother tongue without translating words? Is there some kind of conceptual language where we can translate mother tongue new words? And if so, can we use this conceptual language to become better learner?- Read more about Conceptual Language and Learning
- Log in or register to post comments

## Asymptotic Differentiable Function

Thu, 11/24/2016 - 14:45 — yonatan zilpaLet $f$ be any function asymptotic at zero. Prove/Disprove:

If $f$ is differentiable everywhere in its domain, then $\lim_{x\to \infty}f\;'(x)$ must be equal to zero?- Read more about Asymptotic Differentiable Function
- Log in or register to post comments

## Fibonacci Sequence, A Pattern of Natural Beauty

Fri, 02/26/2016 - 17:33 — yonatan zilpaThe sequence of Fibonacci can be found everywhere in nature. First mentioned by Leonardo Fibonacci who was a medieval mathematician that was trying to solve problem involving the growth of a population of rabbits. It became one of the most famous sequence in all of mathematics. Here is a mathematical description of some of its fundamental properties...- Read more about Fibonacci Sequence, A Pattern of Natural Beauty
- Log in or register to post comments

## Emotions Relationship & Learning

Wed, 12/07/2016 - 14:48 — yonatan zilpaIt's been said that "necessity is the mother of inventions", but necessity is the mother of learning as well. Learning is vital to survival it is a necessity, however necessity determines what we learn. This interaction between necessity and learning is part of "emotional relationship" between the learner his/her topic.- Read more about Emotions Relationship & Learning
- Log in or register to post comments

## The circle of Apollonius

Fri, 02/26/2016 - 17:05 — yonatan zilpaBy definition, a circle is the locus of all points equidistant from a fixed center. However, the circle of Apollonius is defined differently. In the following post I will define and construct an Apollonian circle.- Read more about The circle of Apollonius
- Log in or register to post comments

## Google search tips

Thu, 11/24/2016 - 14:40 — yonatan zilpaTips and tricks on Google search techniques.- Read more about Google search tips
- Log in or register to post comments