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.
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.
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?
How 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.
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\}$
$\exists N\in \tilde{N}\Big(\exists P \in \tilde{P}\Big( N\cap P=\emptyset \; \mbox{ and }\;
N\cup P = X\Big)\Big)$
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?
