## 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
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## 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?
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## Learning tips

Sun, 12/04/2016 - 14:54 — yonatan zilpaHow to make the most of your learning time? Efficient learning and good usage of time may be key ingredients. Each student may have his own unique style of learning, but there exist patterns and strategies that can help everyone. Here is a list of links to good webinars and lectures note that may help you chose your own style of learning.- Read more about Learning tips
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## 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
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## Minimum way to move all circles

Thu, 11/24/2016 - 13:04 — yonatan zilpaConsider a game with three vertical sticks and 5 circles, where each circle has a hole in the middle. The circles arranged in one stick as shown in the picture: The task is to move all the circles to a nearby stick, circles can be move from one stick to another, but a circle cannot be put over a smaller one. What are the minimum number of steps needed to complete this task?- Read more about Minimum way to move all circles
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How 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
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Let $f$ 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?

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
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Normally 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
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By 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.

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Let $\nu$ 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
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