Before telling about my background, I'd like to say that I did look at several similar questions, but neither involved my case (at least, not as far as I could see).   Now the background: I majored in Computer Engineering. I have expected more of Computer Science, but it was mostly business-oriented coding education (maybe I am being a little too harsh on this). So in my second year, I applied for a double major in Physics, thinking it might be more satisfying. In fact, I did enjoy Physics more than CS (or, CE in my case), and found it much more challenging and meaningful.  However, I ended up finishing my main major (CE), before Physics, so I applied for MS in CE in the same university, feeling the workload might be too little otherwise. I got accepted, and am currently enrolled in this program while taking 2-3 courses left from undergraduate Physics program. (My subject in MS is Computer Vision.)  But one thing I noticed over these years is that, for Physics I do not feel like I have the right mindset (seems that I lack a practical approach to things), and CE feels a little meaningless. Considering that I focused on Mathematical Physics, and more of the mathematical stuff in CS, I thought maybe Mathematics is the right place for me. But I cannot yet tell if I genuinely want Maths, or just whining about what I have at my hands.   So I have two questions, actually:   What are my chances if I apply for PhD in Number Theory? Do you recommend changing the field? Can you share other people's experiences in similar cases?   For the application part, I must add that I do not have an outstanding transcript in neither of my majors (around 3.4 GPA in both fields -Physics might be around 3.5 too), although I did get a paper published which was about relativistic quantum mechanics.   Edit: This question is different from what is suggested as duplicate as this particularly involves the case of a double major background. Specifically, whether the case of double major suggests the admission committee a versatility in working different fields or not. So I do not think this should be regarded as a duplicate question.  Edit2: Experience in proofs I have taken Discrete Mathematics and Formal Languages and Abstract Machines, in which we mostly used induction to prove things. Apart from that, in the mathematical methods courses we have gone through the proofs of Stokes' theorem, divergence theorem, etc. Although I mostly can understand a proof reading through it, and working out some things that seem off, I would not say that I am good at mathematical proofs, nor that I am much experienced with them.
Can I be admitted to graduate school in a different field from my degree?  Specific cases include:   If I've taken plenty of advanced courses in field X in the process of completing a degree in another field, can I apply to graduate school in X? What if I haven't taken many courses in X, but I have acquired a good grasp of X through self-study or working in a related field? What if I've never studied X, but I have done very well in an unrelated field?  Could I be admitted to graduate school in X on the basis of general intellectual promise, and then make up the missing background after enrollment?   Note that this question is an attempt to provide a comprehensive answer, to avoid the need for a profusion of field-specific questions on this topic (see the associated ). Please feel free to edit the question or answer to improve them.
Why does my iPad keep asking for my iCloud password? I keep receiving an iCloud pop-up message to insert my iCloud password every time i switch on my iPad and I'm unable to do anything on it, inserting the password doesn't help. What should I do? On June 28, 2017, Apple  that     macOS High Sierra will be the last macOS release to support 32-bit apps without compromise.   How can I find out which apps on my Mac are 32-bit so that I can see if I need to upgrade them? How do I escape a backtick ` within in-line code in Markdown? How do I escape a backtick ` within a code block?  This is probably a duplicate, since I'm sure it's a common concern, but I can't find a question that addresses this specifically.  How do I write List'1 with the "1" character still in the code-text format? Find all integral solutions of $y^2=x^3+7$ Find all integral solutions of $y^2 = x^3+7$.  I tried to use many different moduli, but it never works. With modulo $9$, you can get $x$ is divisible by $3$. Is there a single word to describe a solution that hasn't been optimized? I am working with some code, and I would like to describe the difference in its performance when it is optimized versus when it is not optimized. Unfortunately, I can't find a word to describe the code before it is optimized; "sub-optimal" might work, but I want to emphasize that this is the first iteration of the code. If "unoptimized" were a word, I would use that, but I haven't found any references to it in any dictionary.  Perhaps "raw" or "original"? Add max value to a new column in R Ubuntu 18.04 opening system setting logs me out I've recently installed Ubuntu 18.04 in a dual-boot configuration with Windows 10. I noticed today that, when trying to open system settings, Ubuntu seems to log me out to the lock screen. When I log back in, all previously-running applications are now closed. Very unsure what to do from here, any help much appreciated. Family of irreducible polynomials Why do damaged hard drives freeze the entire system? I have heard that some issues in group theory prevent classifying all manifolds upto homotopy using the fundamental group invariant. Does anyone know what are those issues?  Thanks, K. Does the potential energy of a single object exist? I know that potential energy exists for a system of objects. But why? Is there no potential energy for a single object system? I assume that there is.  Consider the earth-object system. Suppose an external force lifts the object above the earth. Then the work done by it gets stored in the earth-object system as potential energy.Right?  Now, my question is that is the potential energy always zero for a single object system.   MY REASONING  If we consider the object only as the system and lift it above the Earth, we are doing positive work on it and filling it with energy and the gravitational field of the Earth is doing negative work on it and draining it of energy. Thus whenever the object is moving it has kinetic energy which is fine. But when it is not moving,i.e. when its weight is equal to the force applied by us, the net work done is zero and so the object should not have any kinetic energy. Does it have potential energy? Game Theory and Uniform Distribution question? In an Auction , two players are  bidding. Their bids will be a unknown fraction of their valuations. The valuations come from a uniform distribution $$[0,1] $$  If Player 2 bids $$ v/2 $$  and Player 1 bids $$b1&lt;1/2$$   What is the probability player 1 wins ? Clearly for player 1 to win,players 2 bid has to be less than player 1 bids. $$P(v/2 &lt; b1)$$  $$P(v &lt; 2b1)$$ I follow the question up to this stage. Now it says since its uniformly distributed the probability player 1 wins is $$2b1$$ Im confused how can you just get 2b1 from the inequality ?  Thanks in advance I am working to build a reinforcement agent with DQN. The agent would be able to place buy and sell orders for a day trading purpose. I am facing a little problem with that project. The question is "how to tell the agent to maximize the profit and avoid the transaction where the profit is less than 100$".  I want to maximize the profit inside a trading day and avoid to place the pair (limit buy order, limit sell order) if the profit on that transaction is less than 100$. The idea here is to avoid the little noisy movements. Instead, I prefer long beautiful profitable movements. Be aware that I thought using the "Profit &amp; Loss" as the reward.  "I want the minimal profit per transaction to be 100$" ==> It seems this is not something that is enforceable. I can train the agent to maximize profit per transaction, but how that profit is cannot be ensured.  At the beginning, I wanted to tell the agent, if the profit of a transaction is 50 dollars, I will remove 100 dollars, then It becomes a penalty of 50 dollars for the agent. I thought it was a great way to tell the agent to not place a limit buy order if you are not sure it will give us a minimal profit of 100$. It seems that all I would be doing there is simply shifting the value of the reward. The agent only cares about maximizing the sum of rewards and not taking care of individual transactions.   How to tell the agent to maximize the profit and avoid the transaction where the profit is less than 100$? With that strategy, what guarantee that the agent will never make a buy/sell decision that results in less than 100 dollars profit? Does the sum of reward - # transaction * 100 can be a solution? Can anyone make me understand in simple language why the second condition for being an Euclidean domain is superfluous ?  Why $v(a)  \leq v(ab)$ is not needed?  How we can deduce from the first one? I am downloading macOS Sierra from Mac App Store. But I have electricity problem here. Due to which my iMac will lose power after 2 hours. Now I want to pause the downloading so that I can resume the download later on. How can I do that?  Here is a screenshot. I'm trying to prove that for $p,q&gt;0$, we have $$\int_0^1t^{p-1}(1-t)^{q-1}\,dt=\frac{\Gamma(p)\Gamma(q)}{\Gamma(p+q)}.$$    The hint given suggests that we express $\Gamma(p)\Gamma(q)$ as a double integral, then do a change of variables, but I've been unable thus far to express it as a double integral.  Can anyone get me started or suggest an alternate approach?  Note: This wasn't actually given to me as the $\Gamma$ function, just as a function $f$ satisfying $$f(p)=\int_0^\infty e^{-t}t^{p-1}\,dt$$ for all $p&gt;0$, but I recognized that. This is in the context of an advanced calculus practice exam. "no such file or directory" message when deleting a file that exists on NTFS OS X El Capitan and older not available on App Store? So it turns out I can not install Sierra because I have a Mid2009 Macbook Pro. I wanted to update to El Capitan, but it turns out its no longer available on the app store?  Any ideas, how to get El Capitan? I have installed nodeJS on Ubuntu with following code   sudo apt-get install nodejs   Since I am a new user for ubuntu I also ran this code too  sudo apt-get install npm   Now when I type    nodejs --version   It shows   v0.6.19   I checked and saw latest nodeJS version is 0.10.26   How can I update my version of nodeJS to 0.10.26?  I tried with    sudo apt-get install &lt;packagename&gt;  sudo apt-get install --only-upgrade &lt;packagename&gt;   but no luck. Change default code page of Windows console to UTF-8 Currently I'm running Windows 7 x64 and usually I want all console tools to work with UTF-8 rather than with default code page 850.  Running chcp 65001 in the command prompt prior to use of any tools helps but is there any way to set is as default code page?  Update:  Changing HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Nls\CodePage\OEMCP value to 65001 appear to make the system unable to boot in my case.  Proposed change of HKEY_LOCAL_MACHINE\Software\Microsoft\Command Processor\Autorun to @chcp 65001&gt;nul served just well for my purpose. (thanks to )