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You should find a good book or a good teacher if you want to appreciate the beauty of mathematics. If you personally experienced finding a subject beautiful and interesting then there will be no problem learning it even if you are a beginner. Note that by the terms good book and good teacher that is in accordance to your taste and therefore subjective.


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Algebraic topology, by it's very nature,is not an easy subject because it's really an uneven mixture of algebra and topology unlike any other subject you've seen before.However,how difficult it can be to me depends on how you present algebraic topology and the chosen level of abstraction. If you want to use a high-tech and fully general approach, where ...


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The answers here are rather idealistic. They seem to be based more on trite cliches rather than concrete reasoning or evidence. The fact is, academia is competitive and jobs are scarce. Your grades matter. Your performance relative to your peers matters. Being passionate at math or being interested in the subject is a necessary but insufficient condition ...


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At some point, math has less to do with intelligence and more to do with patience and methodology in learning. If you really want to continue studying math, then why not "try" grad school. For me, grad school was less about getting a master's degree and more about learning more mathematics. Overall, grad school was one of the best experiences in my life ...


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Often what happens in mathematics, from my personal experience, is that the one with more exposure generally gets the upper hand. What you are talking about here is talent, which you feel you lack. Talent plays a role till a certain extent, but then I have seen talented people too struggling with high level mathematics (algebraic geometry, to be precise). ...


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Hopefully I can answer before the tide of "talk to someone who knows you personally" and "this question is off topic" rolls in and your question is inevitably closed. It is true that you should talk to someone who knows you better, but I can give you some general advice that is better than just "follow your heart." First, you should know that professors see ...


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I know I'm late to this party, and I more or less agree with what nomen said. However, it happens that this is related to pretty much the only advice I've ever found useful about studying math, so I thought I'd share. Ravi Vakil [who happens to be an algebraic geometer] has an advice page which answers your second question strongly in the negative. However,...


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The material in Chapter 1 of the book Primes of the Form $x^2+ny^2$ by David Cox would be a very nice topic for a project. The book is excellent but not for complete beginners. Chapter 1 is quite approachable. For a list of books, see Best book ever on Number Theory.


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Following dtldarek's answer above: Let the unit normal vector for the plane $P$ be $n=\dfrac{(p_0-p_1)}{\lVert p_0-p_1 \rVert}$. Then for any $x\in C_1$, $n^{\rm T}(x-p_0)<-\dfrac{d}{2}<0$ because $\frac{d}{2}$ is the distance between $C_1$ and the plane P. And for any $y \in C_2, n^{\rm T}(y-p_0)>\dfrac{d}{2}>0$. So $n^{\rm T}x-n^{\rm ...


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I have nothing but pleasant memories of my time with Spivak, and I am nostalgically delighted that he is still used. To some extent it depends on you and your personal taste and temperament. Some people want nothing but a box of tools to memorise, along with instructions for which to pick when. Others aren't satisfied unless they know how things work — ...


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I knew that this was actually what I wanted to do for the next few years or even the rest of my life. That's great! I feel like my skills don't develop fast enough, and therefore I don't know in which direction I'm heading right now. It's okay. Just enjoy the journey. I always think that there is something wrong with my way of approaching ...


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Your thoughts are certainly normal. In fact, one could generalise and say that no mathematician is ever a success in his own eyes. How can he be, given that so much of maths involves working for weeks on a problem which, once you have solved it, has a solution that can be understood in minutes? I strongly recommend that you read section VIII.6, "Advice to a ...


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When I started in college my calculus professor used Spivak's book as the textbook for the course, I remember that was really hard at the beggining and mostly of the problems I couldn't solve by myself, but at the end of the course I was solving the problems by myself, and I felt that I improved a lot just for trying hard with Spivak's book. So I think you ...


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I work in the Guidance, Navigation, and Control department for a big aerospace company and also did my undergrad in math/physics. Here's my advice: (1) Get a Master's in aero, since your math background alone has not taught you how to think like an engineer. A mistake most mathematicians/scientists who become engineers often make is assuming engineering is ...



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