Good and thorough online and/or free Matroid Theory references? I'm studying a course on Matroid theory. Sadly, I can't really afford buying the textbook, so I only use the lecture notes, which aren't enough for me.   Are there any good and thorough online and or/free references on Matroid theory?   Thanks in advance for any assistance!
Books about matroids Could you recommend any approachable books/papers/texts about matroids (maybe a chapter from somewhere)? The ideal reference would contain multiple examples, present some intuitions and keep formalism to a necessary minimum.  I would appreciate any hints or appropriate sources.
A matrix inside a table Possible Duplicate:          I am trying to insert a matrix inside a table, and I am looking for a good way to do this. Usually when I write matrices in equations, I use array environment, so I naively defined an array inside tabular, and it sort of works. The only problem is that the matrix itself seems to take up a huge amount of space inside the cell. An example is   \begin{tabular}{|c|c|} \hline \textbf{EKF} &amp; \textbf{UKF}\\ \hline $Q = \left[ \begin{array}{cc} 0.1 &amp; 0 \\ 0 &amp; 0.1 \end{array}\right]$ &amp; $Q = left[ \begin{array}{cc} 0.01 &amp; 0 \\ 0 &amp; 0.01  \end{array}\right]$\\ \hline $R = 5 \times 10^{-3}$ &amp; $R = 5 \times 10^{-5}$ \\ \hline \end{tabular}   Is there any way to increase the spacing in the cell containing the matrix without that matrix taking up all the space? Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime. Determine the Galois group of $\mathbb{Q}(\sqrt{a+b\sqrt{d}})$ Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$ How do I backup my Ubuntu Phone? velocity of an object after leaving a ramp How to remove uninstalled snaps from cache? Review option on mobile phone not available? The other day I was looking at Stack Overflow on my Android phone. All is made very nice and all, but I could not find the Review button/link. Is it being implemented, did I miss it, or it is not available? Number of integer solutions of $x^2 + y^2 = k$ I'm looking for some help disproving an answer provided on a  I posted about computing the number of double square combinations for a given integer.    The original question is from the Facebook Hacker Cup       Source: Facebook Hacker Cup   Qualification Round 2011      A double-square number is an integer $X$   which can be expressed as the sum of   two perfect squares. For example, 10   is a double-square because $10 = 3^2 + 1^2$.   Given $X$, how can we determine the   number of ways in which it can be   written as the sum of two squares? For   example, $10$ can only be written as $3^2 + 1^2$   (we don't count $1^2 + 3^2$ as being different). On the other hand,   $25$ can be written as $5^2 + 0^2$ or as   $4^2 + 3^2$.      You need to solve this problem for $0 \leq X \leq 2,147,483,647$.      Examples:      $10 \Rightarrow 1$      $25 \Rightarrow 2$      $3 \Rightarrow 0$      $0 \Rightarrow 1$      $1 \Rightarrow 1$   In response to my original question about optimizing this for F#, I got the following response which I'm unable to confirm solves the given problem correctly.       Source:       Again, the number of integer solutions   of $x^2 + y^2 = k$ is four times the   number of prime divisors of $k$ which   are equal to $1 \bmod 4$.      Knowing this, writing a program which   gives the number of solutions is easy:   compute prime numbers up to $46341$ once   and for all.      Given $k$, compute the prime divisors of   $k$ by using the above list (test up to   $\sqrt{k}$). Count the ones which are   equal to $1 \bmod 4$, and sum. Multiply   answer by $4$.   When I go through this algorithm for $25$, I get $8$ which is not correct.          For each prime factor (pf) of $25$ ($5$, $5$ are prime factors of $25$)         if pf % $4$ = $1$ (true for both $5$'s), add $1$ to count      return $4$ * count (count would be $2$ here).          So for $25$, this would be $8$ How to disable all Vim-LaTeX mappings? I like some of the features provided by the Vim-LaTeX suite, but not all of them.  In particular, I dislike all of the mappings like [[ = \left[ \right] and the automatic placeholder stuff with &lt;++&gt;. I am a very fast typist but with that comes more typing mistakes, which I correct almost instantly by pressing backspace. Unfortunately, if something has automatically added a bunch of place-holders or expanded some expression, I then have to move around the document and remove more characters than necessary. For example, if I accidentally press [ twice, instead of only having to delete one character, I have to delete 10.  Having already looked through the documentation, and some of the source, I have managed to disable some of these "features", but not all of them:  In particular:  let g:Tex_SmartKeyBS = 0 let g:Tex_SmartKeyQuote = 0 let g:Tex_SmartKeyDot = 0   (Turn off maps for backspace, double quote and triple dot.)  let g:Imap_UsePlaceHolders = 0   (Turn off &lt;++&gt; placeholder insertion.)  But I can't seem to find a way of turning off the other stuff. Anyone have any suggestions?  Edit: I was able to "disable" some more things by setting:  let g:Tex_Leader = '`tex' let g:Tex_Leader2 = ',tex'   (Which stops some expansions but still not all. It's not really disabling it but just making it less likely that you're going to type in `texa as opposed to the potentially more common `a, for example.)  PS: Personally, I think it is very poor practice to make an optional package that, when installed, greatly changes the default handling of your system. I don't mind some intelligent source highlighting etc, or some new commands (that don't clobber any old ones), but it seems unhelpful to enable this drastic kind of key remapping by default. Is the collection of all functions between two sets a set? Possible Duplicates:             I heard a professor of mathematics explaining that the following conslusions are true.   $\textrm{False}\Rightarrow \textrm{True}$ $\textrm{False}\Rightarrow \textrm{False}$   Could someone please explain to me why both conclusions are true? I am especially interested in the first case. I'd like to hear two explanations if possible: One for mathematicians and one for non-mathematicians. :-) Let’s take an example of a movie site. So a well structured set of URLs for this site can be:     Movie page - example.com/movies/the-matrix Review for movie - example.com/movies/the-matrix/reviews Trailers for movie - example.com/movies/the-matrix/trailers Specific trailer for movie - example.com/movies/the-matrix/trailers/trailer1   where it’s possible to navigate the resource even by directly deleting/appending resource name seamlessly.  For SEO purpose I read somewhere that for two given pages, Google will prefer the page which have search query up in the URL hierarchy among other things. So for the given 2 URLs and the query "the matrix trailer"    example.com/movies/the-matrix/trailers example.org/trailers/the-matrix/    `     Google might prefer the second URL as it has the keyword "trailer" at first level comparing to first URL which has "trailer" at 3rd level (a resource deeper in URL hierarchy may be less important).    If it is correct, one may be tempted to create URL hierarchy somewhat like      Movie page - example.com/movies/the-matrix Review for movie - example.com/reviews/the-matrix/ Trailers for movie - example.com/trailers/the-matrix/ Specific trailer for movie - example.com/trailers/the-matrix/trailer1     which will break the seamless hierarchy.    My questions are:   Is it true that resource deeper in URL hierarchy is tend to be less important when comparing to URLs of other site?   Is sacrificing meaningful, seamless hierarchy worth for this SEO optimization? Events triggered by dynamically generated element are not captured by event handler when does a functor map products into products? How to add "Refresh" option to right click menu in Lubuntu? I have many users at the place I work, expressing the notion of switching to Ubuntu.  Most of them, for whatever weird reason wanting to know if its possible to have refresh added when you right click on the desktop.   Is that possible? SC2272-M4 Behaviour when using relay SRD-05VDC-SL-C 5V DC I'm currently encountering a problem when using a relay switch with a 5v receiver. When using the same receiver with a row of LEDS it works flawlessly. I've noticed that the relay keeps making the switching noise over and over like I'm pressing the transmitter really fast apart from the fact I'm not. Also, when the transmitter is moved closer to the receiver from 20" to around 1" the problem stops. Below is some circuits to help show you my setup.  Any help appreciated thanks.  Setup Specs   USB 5v DC (2AMPS) Receiver (XY-DJM-5V - SC2272-M4) Relay (SRD-05VDC-SL-C 5V DC) Transmitter (XY-04) Diode (1N4001) Transistor (2N2222A) Resistor (1.8K Ohms)          &ndash; Schematic created using   Antenna Signal Workaround or Booster  I believe this issue is related to wireless signal on D0. Basically above 20" inches the output to the relay drops from 5.05v to 0.5v and is obviously causing the problem. I think I need to boost the signal or replace the transistor with something that triggers at low and high current but have no clue. Any help appreciated, I'm new at this.  Board Setup How do I mount a qcow2 disk image? In the book Limit Theorems of Probability Theory by Valentin V. Petrov, I saw a distinction between the definitions of a distribution being &quot;continuous&quot; and &quot;absolutely continuous&quot;, which is stated as follows:  &quot;...The distribution of the random variable $X$ is said to be continuous if $P\left(X \in B\right)=0$ for any finite or countable set $B$ of points of the real line. It is said to be absolutely continuous if $P\left(X \in B\right)=0$ for all Borel sets $B$ of Lebesgue measure zero...&quot;  The concept I am familiar with is:  &quot;If a random variable has a continuous Cumulative Distribution Function, then it is absolutely continuous.&quot;  My questions are: are the two descriptions about &quot;absolute continuity&quot; in (1) and (2) talking about the same thing? If yes, how can I translate one explanation into the other one? Collinearity diagnostics problematic only when the interaction term is included