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    Mathematica: How do I program this? Square free part of an integer

    I am attempting to program Mathematica to multiply the square free terms of an integer. Basically say we are looking at 252, its prime factors are 2^2*3^2*7. So what I want to do is have Mathematica return to me just 2*3*7 when I enter 252. So I have this S := FactorInteger[252]...
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    Good linear algebra book recommendation

    If you want a rigorous treatment of the subject, use this book:
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    Best Mathematics Books

    Hello. If you'd like to read ahead on Linear Algebra I would suggest this book, As for history and development of Mathematics as well as books on geometry I would suggest the books by John Stillwell. If you are interested in the...
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    Need help forgot my alarm code.

    There are a total of 120 combinations with those numbers for you can choose 5 of the entries for the first digit, then 4 for the next, 3 for the next and 2 for the last, thus 5*4*3*2=120.
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    Abstract Algebra: Finding Conjugates

    Yes. For take the identity element, I^-1*A*I=A So A is a conjugate of A, and likewise B is a conjugate of itself.
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    When I took it I used the Princeton Review's book to prepare from. Certainly do as many practice exams from here to the test date, and make sure you understand every problem you get wrong to the smallest detail. Good luck!
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    Orthogonal vectors

    Use the linearity of the dot product ( , ) so, (x,u)=(u,x)=0 and (x,v)=(v,x)=0, So consider, (u-v,x)=(u,x)-(v,x)=0 => (x,u-v)=0.
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    Schools Can I skip College Algebra?

    Yes. Speaking from experience, I taught myself calculus without really having a strong background in trig nor algebra beforehand. Naturally you won't be able to fly through the material as you'll have to reference some things, but after that it is smooth sailing. I personally feel in retrospect...
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    Looking for Complex Analysis Video Course

    Thanks for that link, had never seen that website before. I now have video lectures to go along with my self study in the summer =).
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    Programs Will my past keep me from getting into a top PhD program?

    If you apply to graduate school for Physics they will look at your coursework in Physics and your potential to do research in Physics. So PoliSci does not matter.
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    So many mathematics choices

    If you are planning on going to graduate school, then settle down for a postponement of Graph Theory until then. Or even better, check out two books on graph theory and teach yourself from them! But do not prolong on taking Real Analysis as that course is essential, and it is better you take it now.
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    Number of roots

    Fundamental Theorem of Algebra: Every polynomial of degree n (n=/=0) has exactly n roots counting multiplicity over the Complex numbers. In the case of the real numbers, it has d roots where d is less than or equal to n. For instance, the easiest example x^2+1=0 only has complex solutions...
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    Best Metal Bands ever

    Iron Maiden, 'nuff said =).
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    Onto vs into

    Same, all the books I have seen in Algebra use onto when the function is surjective, otherwise they say into.
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    Field of order p^2

    This is an application of the Frobenius endomorphism if I am not mistaken,
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    Abstract Algebra: Finding Conjugates

    For conjugates of A, G={I, A, B, C, D, K} I^-1*A*I=A B^-1*A*B=D*C=K C^-1*A*C=C*B=K D^-1*A*D=B*K=C K^-1*A*K=K*D=C So K and C are conjugates of A. Do same procedure to find conjugates of B.
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    How to study for finals

    I type up notes, a good way to refresh on material. But just make sure you are processing what you type, because if you are absent minded as you type them, then there is no purpose.
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    Comparing Infinities

    Well in terms of cardinals, the set of countable infinity has cardinality Aleph-0. The set of reals has cardinality Aleph-1, power set of the reals is Aleph-2 and so on. Aleph-n is what is called a cardinal number. You could also look into reading about the Generalized Continuum Hypothesis...
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    Comparing Infinities

    So you are asking in which ways you can compare infinities (so the countable infinity and the uncountable infinities). If this is so, then one way to describe the countable infinity is as the smallest infinity, which is the naturals. Any countable set can be put in a one to one correspondence...
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    Galois Extension of Q isomorphic to Z/3Z

    When I wrote the above I was thinking of x as a natural number or integer, in which case it should work as an example of a Galois group isomorphic to Z/3Z. But as for a complete generalization, I do not know of how to give it.
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    Advice on Books?

    So here is my suggestion, if you are planning to pursue Mathematics as your degree in college or beyond, challenge yourself now and struggle on the proof based books. It is better to get used to it now, for almost every book beyond LA does not have solutions at the book of the book nor a...
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    Galois Extension of Q isomorphic to Z/3Z

    Let d=cubic root of some number x s.t. d is not in Q. Then [Q(d):Q]=3 => o(Gal(Q(d)/Q))=3 and only group of order 3 is Z/3Z so you have your desired group.
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    Advice on Books?

    This is the book I used when I took Linear Algebra, "Linear Algebra Done Wrong" by Serge Treil. I personally feel it is a well written introductory level text on Linear Algebra. It is also less computational than similar books at an intro...