## 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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## Google search tips

Thu, 11/24/2016 - 14:40 — yonatan zilpaTips and tricks on Google search techniques.- Read more about Google search tips
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## 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
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## 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
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## 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
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## 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
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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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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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Let $\lambda$ be Borel measure.

- If $A$ is mesuarable and $\lambda(A)>0$, then $A-A=\left\{ x-y\; :\; x,y\in A \right\}$ contains a segment $I$ such that $0\in I$
- If $A, B$ are measurable sets and $\lambda(A), \lambda(B)>0$, then $A+B$ contains a segment I.

- Read more about Steinhaus theorem
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It'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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