Please  tell me questions in abstract&#92; linear  algebra   topology   real  analysis  for  interview?
539965
You need to do some serious studying, concentrate on concepts. They won't pose you with lengthy calculations hopefully.
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Try Google groups. Particularly sci.math. \n\nIf you can afford it you can try Kasamba.
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Analysis is the generic name given to any branch of mathematics that depends upon the concepts of limits and convergence. It studies closely related topics such as continuity, integration, differentiability and transcendental functions. These topics are often studied in the context of real numbers, complex numbers, and their functions. However, they can also be defined and studied in any space of mathematical objects that is equipped with a definition of "nearness" (a topological space) or "distance" (a metric space). Mathematical analysis has its beginnings in the rigorous formulation of calculus.\n\n\nMathematical analysis includes the following subfields:\n\nReal analysis, the formally rigorous study of derivatives and integrals of real-valued functions. This includes the study of sequences and its limits, series, and measures. \nFunctional analysis studies spaces of functions and introduces concepts such as Banach spaces and Hilbert spaces. \nHarmonic analysis deals with Fourier series and their abstractions. \nComplex analysis, the study of functions from the complex plane to the complex plane which are complex differentiable. \np-adic analysis, the study of analysis within the context of p-adic numbers, which differs in some interesting and surprising ways from its real and complex counterparts. \nNon-standard analysis, which investigates the hyperreal numbers and their functions and gives a rigorous treatment of infinitesimals and infinitely large numbers. It is normally classed as model theory.
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Anyone with matrix background
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this page has lots of links:\n\nhttp://www.mathtools.net/C_C__/Algorithms_and_Data_structures/index.html\n\nmy personal favourite (although very academic) book:\n\nhttp://www.brpreiss.com/books/opus4/
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go to www.google.com and type in \n\nriemann spaces  3 4 dimensions\n\nit will bring up alot of information for you to look at
624409
Clearly false. Let K={i}.\n\nDid you mean for K to be a subfield? In that case, K contains the rationals and so is dense in R.
910564
umm none that im aware of, what kind of mathamatics leval are you looking at?
574139
Do you want homeomorphism classes or actual different topologies?\nLet's count both with the set X={1,2,3}:\n1) The indiscrete topology: {{},X}\n2) The discrete topology: all subsets.\n3) one open set with one point: {{},{1},X}\n   There are three of these.\n4) One singleton open, the complement open also:\n   {{},{1},{2,3},X}\n   There are three of these.\n5) one singleton open, one pair with element open.\n   {{},{1},{1,2},X}\n   There are six of these.\n6) One singleton open, both pairs with that element open:\n   {{},{1},{1,2},{1,3},X}\n   There are three of these.\n7) Two different singletons open, one pair open:\n   {{},{1},{2},{1,2},X}\n   There are three of these.\n8) Two different singletons open, two pair open\n   {{},{1},{2},{1,2},{1,3},X}\n    There are three of these.\n9) One open set with two points: {{},{1,2},X}\n   Again, three of these.\n\nNow, if all three singletons are open, the topology is disrete. If all three pairs are open, all singletons are also, so the topology is discrete(2). If two pairs are open, their intersection singleton is open. In this case, one other singleton may be open(6,8). If only one pair is open, then one or both singletons in that pair may be open(5,7), or the complement can be open(4), or no singleton may be open(9). If no pairs are open, one singleton may be(3), or none may be (1).
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Evidently this is undecidable for regular spaces. It is equivalent to the question of whether herditarily separable implies hereditarily Lindelof. For hausdorff spaces, the answer is NO.\n\nThe link below is a discussion on a topology forum about this question. Very nice!
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click on the below link, and choose any one of the results. I would advise reading at least 3 of them to get a feel for theory before choosing one of the walkthroughs.\n\nBest of luck to you!
969006
I've done a good bit with linear transforms in general (LaPlace,Fourier, Z), so hopefully I can help you. The most important thing for your class is to know whether or not they will allow the use of tables or not. Even the simplest function will usually require integration by parts to compute a transform directly. Usually I use tables of transforms coupled with properties of transforms (like the differentiation property, which lets you use algebra instead of calculus to solve an ordinary linear DE). I really can't go into any depth without pencil and paper. Check out the link below (it contains an example of using LaPlace transforms to solve a linear ordinary DE).
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HI: I tried to answer your email but it said that your email address has not been confirmed and so the email didn't go through.\n\nalpha and beta are scalers for the vector space V.  This problem is actually so easy that people don't believe what they've done.  You really just need to show that Span S behaves like V.  \n\nSpan S must be a vector space itself.  Two elements from the span is \nu=a1*v1 + a2*v2...ak*vk\nand \nw=b1*v1 + b2*v2...bk*vk\n\nshow that alpha*u+beta*w is in Span S where alpha, beta are scalers for your vector space.\n\nalpha*u+beta*w = (alpha*a1+beta*b1)*v1 + ....\nis a linear combination of the vectors in Span S, thus it's in Span S.  \n\nSo, Span S is not empty and is closed, thus its a subspace.
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Yes, but you have to be more clear what you want in general.\n\nSuppose we are working in n-dimensional Euclidean space. Suppose also that you have a hyperplane going through the origin. If you take n-1 independent vectors in that hyperplane and do a determinant construction similar to that for the cross product, you will get a vector normal to your hyperplane. But you will need n-1 *independent* vectors and you will have to do a nxn determinant (with the top row consisting of the unit tangent vectors along the axes).\n\nIf you don't have a full hyperplane, you will be wanting a basis for the normal subspace. Other than the previously mentioned Graham-Schmidt process, I don't know a good way to do that. Hmmm.....
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You could be, but who knows? You might be brilliant! Doesn't one course build upon the other? (Except parts of Linear Algebra, which is somewhat different, however it does use integrals and infinite series and lots of stuff I seem to recall might require that you know differential equations and integration . ) It has been 17 years since I had this series of math in college, but that's what my vague remembrances tell me! I'm not sure how often basic math curricula change over time but probably not that much...
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Read the references at the end of the article or talk to an industrial engineer.\n\nhttp://en.wikipedia.org/wiki/Linear_programming
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http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/\n\nhttp://www.math.armstrong.edu/MathTutorial/