• Free Textbooks in Mathematics

    Fri, 02/24/2017 - 08:00 — yonatan zilpa
    The 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.
    Tags: 
    math textbooks

  • Hahn Decomposition Theorem

    Thu, 11/24/2016 - 14:07 — yonatan zilpa
    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\}$
    1.   $\exists N\in \tilde{N}\Big(\exists P \in \tilde{P}\Big( N\cap P=\emptyset \; \mbox{ and }\; N\cup P = X\Big)\Big)$
    2.   $\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) $
    Tags: 
    theorems

  • Minimum way to move all circles

    Thu, 11/24/2016 - 13:04 — yonatan zilpa
    Moving circles
    Consider 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?
    Tags: 
    recreational mathematics

  • Emotions Relationship & Learning

    Wed, 12/07/2016 - 14:48 — yonatan zilpa
    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.
    Tags: 
    learning tips

  • Steinhaus theorem

    Thu, 11/24/2016 - 13:15 — yonatan zilpa
    Let $\lambda$ be Borel measure.
    1. 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 $0\in I$
    2. If $A, B$ are measurable sets and $\lambda(A), \lambda(B)>0$, then $A+B$ contains a segment I.
    Tags: 
    theorems

  • Four bottles - Equidistant mouth problems

    Sun, 04/17/2016 - 05:29 — yonatan zilpa
    How to place four identical bottles in the plane such that the distance between each pair of mouths will be the same?
    Tags: 
    math recriation

  • Google search tips

    Thu, 11/24/2016 - 14:40 — yonatan zilpa
    Tips and tricks on Google search techniques.
    Tags: 
    google

  • How many squares can be found here?

    Sun, 08/14/2016 - 13:40 — yonatan zilpa

    How many squares can be found here?
    Tags: 
    recreational mathematics

  • The circle of Apollonius

    Fri, 02/26/2016 - 17:05 — yonatan zilpa
    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.
    Tags: 
    geometry

  • Conceptual Language and Learning

    Mon, 12/26/2016 - 15:17 — yonatan zilpa
    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?

    concept map

    Tags: 
    learning tips

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