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If you've already taken a couple courses in Abstract Algebra, try reading dummit and foote and do the hard problems. As far as number theory books go, I'm not sure since I have not taken any Number Theory at my University. I used to look at the syllabi and homeworks for classes at top schools and also found them very difficult. Even at those schools, only ...
You will likely get as many different opinions on books and US programs as you get Comments and Answers. And you will likely have no way to assess the experience or qualifications of those who give their opinions. So I will give you some information that you can verify for yourself and discuss possible strategies. First, you need to consider your grades in ...
Take a look at my Teach Yourself Logic Study Guide, which gives a lot of detailed advice about logic books at different levels, suitable to different backgrounds. Check out the proposed syllabus of the course you are about to start to see what it covers and hence what's relevant in the Guide.
Haha, you're worried waaay too much! If you're studying out of those books and have a good solid foundation on what you've learned, then you should be fine. However, the probability of you being accepted, and as a consequence passing, any PhD program in Mathematics is up to you. Allow me to explain what I mean (though this was posted 3 years ago, it may be ...
If you tell readers what your current level of mathematical understanding is you'll get far more helpful answers to a soft question like this. I'll assume you're an advanced undergrad/beginning grad in math/stat/phys. Markov chains are simple stochastic processes and knowing about them can make studying diffusions and Levy processes much easier. I don't ...
Read from another source that's shorter in length and better formulated. Linear algebra is a hefty course, but the time used for examples could well be used for absorbing the theory better. And you can find that theory from numerous sources, e.g. in the internet. I've found that textbooks can also be too hefty, if one doesn't have the time for reading them ...
Trying to fill in gaps through reading the hefty text book takes hours, just reading one or two pages to get thorough understanding can take an hour or more. I'm a professional mathematician. Far from brilliant or earthshaking, but I think at least competent. When I'm reading about a topic I don't already know just reading one or two pages can take me ...
1) Is there a study hall where students can go to and ask for help ? 2) Team up with your fellow students who are arguably in the same boat as you are, fix timings when you get together to work on the exercises 3) How well is the textbook written? Does it have enough exercises to practice the concepts? If not, is there a library to consult other books? I ...
Rather than ploughing through just the text, do exercises. Lots of them. Doing them will familiarize you with the concepts that you already covered and you will then be quicker in learning new concepts.
There is an abundance of research at Aerospace firms, Trading Houses and Hedge Funds, Private Labs (such as Bell Labs), and lots of others that have R&D divisions that use mathematicians, physicists, and engineers, all of whom focus on applied mathematics research. Trading Houses and Hedge Funds absolutely do have research groups. Goldman Sachs ...
You're an undergraduate. You don't know that you like analysis or algebra yet. Give it time. Everything at higher levels blends together anyway. You like analysis? In functional analysis, you will deal with measure theory. Measure theory is probability.
I have waited to reply because my field is probability and statistics, so I was afraid you'd consider my views biased. Now I would like to agree with the Comments, but with a little more detail. For several reasons, based on my own experience and the paths of many students I have advised over the years, I believe it is too early for you to limit your ...
Do I really need to know number theory ? You don't “need” to know anything. Why the heck is number theory supposed to occupy a slave position with regard to the other branches of mathematics, and not the other way around ? On related news, almost all integers can be written as the sum of a prime and a perfect power.
There are two forms of fourier series namely trigonometrical and complex form As you are an EE undergrad you would be dealing mostly with complex form of fourier series which further leads to development of Fourier transform . the basic relation that is used is that of euler ie e^ix = cosx + isinx and no major part of complex theory is required
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