I'm interested in cutting edge string theory studied by research physicist. I'm wonder what  mathematics is needed and how far am I in terms of mathematics background needed and how much more mathematics do I need in order to study it properly and reach my goal. My mathematics level is at calculus/Linear algebra.
Can someone please give me the prerequisites and mathematics required for string theory? Are there some good references to study it, both online and in a book? Please consider I am a newbie in string theory, and only about up to the level explained in Hawking's Brief History of Time and Penrose's Road to Reality. I would prefer something which does not omit rigor, but builds it up.Also, are there good online lectures on this?  (I have covered most of GR, but I am not really comfortable with advanced Quantum mechanics. I have studied QM only from Griffith's book, and a few McGraw hill lecture notes.)
The terminal gave me these errors when updating the software with sudo apt update.    Hit:1 http://it.archive.ubuntu.com/ubuntu bionic InRelease Hit:2 http://it.archive.ubuntu.com/ubuntu bionic-updates InRelease                                                                                        Hit:3 http://it.archive.ubuntu.com/ubuntu bionic-backports InRelease                                                                                      Hit:4 http://security.ubuntu.com/ubuntu bionic-security InRelease                                      Hit:5 http://archive.canonical.com/ubuntu bionic InRelease                 Traceback (most recent call last):                       File "/usr/lib/cnf-update-db", line 8, in &lt;module&gt;     from CommandNotFound.db.creator import DbCreator ModuleNotFoundError: No module named 'CommandNotFound' Reading packages list... Done E: Problem executing scripts APT::Update::Post-Invoke-Success     'if /usr/bin/test -w /var/lib/command-not-found/ -a -e /usr/lib/cnf-update-db;       then /usr/lib/cnf-update-db &gt; /dev/null; fi'   E: Sub-process returned an error code     These are the results of sudo apt install --reinstall command-not-found  Reading package lists... Done  Building dependency tree         Reading state information... Done 0 upgraded, 0 newly installed, 1 reinstalled, 0 to remove and 0 not upgraded. Need to get 0 B/5.188 B of archives After this operation, 0 B of additional disk space will be used. (Reading the database ... 225797 files and directories currently installed.) Preparations for extracting ... / command-not-found_18.04.4_all.deb ... Extracting command-not-found (18.04.4) on (18.04.4) ... Configuring command-not-found (18.04.4) ... libdvd-pkg: Package libdvdcss2-1.4.2-1 was removed, stop processing...   When I tried the command sudo apt update again after reinstalling command-not-found, the results were the same as described in the first text block. Calculating CR of monsters that do not deal calculable damage The recent  about a new supermassive virus being discovered got me thinking about how we define viruses as non-living organisms whilst they are bigger than bacteria, and much more complex than we first gave them credit for.   What biological differences between viruses and cellular organisms have made viruses be deemed non-living? Let $b_n$ be a sequence which decreases monotonically to zero, prove $\sum b_nz^n$ converges for $|z|\leq 1$ and $z\neq 1$.  So I was able to prove it converges on the open unit disk in the complex plane, but except for a few special points on the boundary, such as $-1$ and $i$, where I was able to use the alternating series test, I can't seem to prove it converges in general on the boundary minus $z=1$.  I feel I have to somehow use the fact that all the numbers on the unit circle except $z=1$ rotate around and around as you raise them to higher and higher powers, thus you get the real and imaginary parts of your series to alternate between sets of positive and negative terms, but in a very irregular way for most initial angles.  I tried to simplify the problem by breaking the series into its real and imaginary parts, and then trying to prove they each converge separately, but I still can't prove either converges:  $$\sum_{n=0}^{\infty}b_ne^{n\theta i} = \sum_{n=0}^{\infty}b_n\cos(n\theta) +i\sum_{n=0}^{\infty}b_n\sin(n\theta).$$ How to flash a BIOS when only a Windows binary is provided? Split Java String by New Line I'm trying to split text in a JTextArea using a regex to split the String by \n However, this does not work and I also tried by \r\n|\r|n and many other combination of regexes. Code:  public void insertUpdate(DocumentEvent e) {     String split[], docStr = null;     Document textAreaDoc = (Document)e.getDocument();      try {         docStr = textAreaDoc.getText(textAreaDoc.getStartPosition().getOffset(), textAreaDoc.getEndPosition().getOffset());     } catch (BadLocationException e1) {         // TODO Auto-generated catch block         e1.printStackTrace();     }      split = docStr.split("\\n"); } Why is it dangerous to eat meat which has been left out and then cooked? ARMA lag selection for ARMA-GARCH models Response.Redirect to new window I want to do a Response.Redirect("MyPage.aspx") but have it open in a new browser window. I've done this before without using the JavaScript register script method. I just can't remember how? How to create a Geometric Polygonal Art portrait I've been interested in creating Geometric Polygonal art illustrations, i.e. making polygons and shapes with different color shading represent a face, or an object, see  set of .  How are they achieved? Is there some script for Illustrator which alters the image adding the shapes according to the colors or shades? How would I transform a normal image of Marilyn Monroe for example, to a polygonal illustration of her? Changing colors of lightning-button I need to find all group homomorphisms of $S_n\to\mathbb{C}^*$ (for $n\ge2$), and also all group homomorphisms of $A_n\to\mathbb{C}^*$ (for $n\ge2$).  Someone on this site, two years ago, seems to have already asked the same question (). I understand what the questioner says there, but I don't understand it when he says:     Therefore there is exactly one $g:\mathbb{Z}/2\mathbb{Z}\to\mathbb{C}^*$, so all elements of $a\in\mathbb{C}^*$ give us $\operatorname{ord}(a)\mid g[\mathbb{Z}/2\mathbb{Z}]$, so $a$ can only be $-1$ or $1$. Now we know that $f:S_n\to\{-1,1\}$ &hellip;   What is he saying there? And how to go on from there? (I do not understand the answer given either &hellip;)  I hope that someone here can help me further. (And if I'm not allowed to ask this question because is has already been asked two years ago, please tell me what to do instead).  Thank you in advance! Vector autoregression for mix of stationary and nonstationary variables I am currently investigating the impact of certain indicators such as GDP and inflation on the stock market. However some of my variables are non-stationary and some stationary in levels. All variables are stationary in first differences.  My question:   Since I have a mix of I(0) and I(1), I need to take the first difference of the I(1) variables and then use VAR. Say that I have a dependent variable $y$ which is I(0) and independent variables $x_1$ which is I(1) and $x_2$ which is I(0). Do I take the first differences of only $x_1$ and then apply the VAR model? Is that correct?  If I take the first differences, then might I lose the long-run relationship between the variables? Is ARDL the better method in this case?   If you have any references regarding the above I would be grateful. Let $f$ be an entire function and $L$ a line in $\mathbb{C}$ such that $f(\mathbb{C})\cap L=\emptyset$. Show that $f$ is constant function.  If $f$ is not constant  then $f(\mathbb{C})$ is dense set in $\mathbb{C}$, but how can I use that line does not intersect the image set? Splitting a large document into several files Here's an example question from the :     On the last day of a one-week sale, customers numbered 149 through 201 were waited on. How many customers were waited on that day?   Possible answers: 51, 52, 53, 152, 153.   The correct answer here is 53, which is the result of (201-149) + 1 = 53.  What's the reasoning in adding the +1? I forgot my iPhone 5 passcode when I was changing the code. A window appeared on the device screen saying that iPhone is disabled.  I have Apple ID and password for it. After signing in to iCloud I have erased the device in order to remove the passcode from my iPhone but it still says that device will be erased when device will connect to internet. What would i have to do? Understanding Group Permissions If random variables are drawn from an identical distribution, why doesn't this guarantee they are independent? Why is the derivative of a circle's area its perimeter (and similarly for spheres)?