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e(ho0n3

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Everything posted by e(ho0n3

  1. Basically you pick an element x from the list you want to sort, place all the elements greater than or equal to x on one side of the list, and the rest on the other. Then you recursively do the same procedure on both sides unitl the list is sorted. You can always google to find out more.
  2. In the worst-case, quicksort takes time O(nn) to sort a list of n items. Algorithms that use divide-and-conquer methods (like quicksort and mergesort) for sorting having average running times in the order of O(n log n) in general. I could do a proof for you if you desire.
  3. Good point. I had this professor for a couple of my CS courses who could not articulate herself properly in english when conducting a class (and she supposedly has 12 years of teaching expirience in the U.S.!). I guess nobody complains since everybody tends to pass her courses (e.g. I aced all of her courses without any trouble). At this stage, I don't really rely much on lectures anymore so all of the stuff I learn, I learn on my own. The professors, as I see it, are just there for support.
  4. I agree (and this has happened to me not only with maths. professors but with other professors as well). Problems arise however when they expect from you more than what you can provide.
  5. Seems this question isn't getting much attention. Perhaps it's too 'over-the-top'. Please forgive my shameless bumping.
  6. Ever heard of Lie groups and Lie algebras? I hear they are used extensively in quantum mechanics.
  7. I need some closure on this one: In how many ways can the vertices of an n-cube be labeled 0, … ,2ⁿ - 1 so that there is an edge between two vertices if and only if the binary representation of their labels differs in exactly one bit? Let G be an appropriately labeled n-cube. Pick an arbitrary vertex v in G. How many ways can one change labels of the vertices appart from v in G and still mantain the properties of the n-cube? Because of the nature of G, there are n incident edges on v with n adjacent vertices. The labels of these vertices differ from the label of v by one bit. If one swaps the labels of two of these vertices and makes the appropriate swaps elsewhere so as to maintain the n-cube (which can be done due to the symmetry of G), one obtains a new labeling. The number of combination of adjacent vertices that can be swapped is n(n - 1)/2, so the number of different labelings of the vertices in G without changing the label of v is n(n - 1)/2. The label of vertex v is arbitrary. Therefore, for every possible label of v there are n(n - 1)/2 labelings of the vertices in G. Because there are 2ⁿ - 1 possible labels for v, the number of possible labelings for the vertices in G is (2ⁿ - 1)(n - 1)n/2.
  8. Can you expound on this matter? Are you just developing your own little set theory or are you trying to do what Russell and Whitehead did with the Principia Matematica?
  9. Where does one learn about metric spaces? Do you learn this in a real analysis course or do you have to take a course on measure theory? I've never delved into this realm so I wouldn't know.
  10. You paper is too unorganized for me to follow (without getting a headache). What are you trying to accomplish with this set theory anyways?
  11. You can always find the degrees of an angle in a triangle with a protractor...OK, that was mean. What exactly is confusing you about the sine, cosine and tangent?
  12. The most advanced class I've taken is Calculus III (vector calc.). I'm studying alot of discrete math. at the moment. I've also done some abstract algebra (just groups and rings, never got into the fields chapters) and some tensor analysis. I took a course in applied statistics (but I found it too rudimentary). There is just so much math. that I still need to study, it's ridiculous. Linear algebra is probably the next thing I'll tackle.
  13. I feel very ashamed now. This problem was so easy. Maybe it's a sign that I'm getting dumber.
  14. I've used BIND before. It's very powerful and flexible. The downside to it is its complexity (took me like 3 hours of reading through the man. pages and tinkering to get it to do what I wanted).
  15. Depends on your definition of "good". Just google around until you find something.
  16. That cleared things up nicely. Thanks.
  17. Suppose a, b, and n are positive integers and a + b = n. For what values of a and b maximize ab? The only way I know of maximizing ab is by drawing a table of values and comparing numbers. It seems though that if n = 2k, then the maximum is obtained when a = b = k. If n = 2k + 1, the maximum is obtain when a = k and b = k + 1. Is there an intuitive way of showing/deriving this though. I can't seem to think of anything.
  18. I thought everyday was mating season for humans!?
  19. I have no idea how many transistors are used in an XOR gate. This sort of information is usually available in an IC's technical reference manual. Motorola makes XOR ICCs. I'm sure they have a PDF somewhere with the electrical diagram for it (so you can count the transistors yourself). P.S. I changed my avatar because the last one didn't look good. Why not HiMAT? It's a cool looking aircraft in my opinion.
  20. I'm not what you mean by "over and above 1 transistor". Transistors are one of the basic building blocks for building ICs, there is nothing "above" this as far as I know.
  21. The solutiion I gave you is explicit. What I would like to do is derive the solution.
  22. NAND and NOT gates are the simplest to make electrically (whether you are using TTL, CMOS, BiCMOS, GaAs, whatever). However, the amount of NAND gets used to make an XOR gate takes up too much space and therefore building a XOR gate from scratch (using CMOS or whatever) is sometimes preferred so not everything is made out of NAND and NOT logic. A microprocessor made entirely of pure NAND gates would require a larger surface area than one with mixed gate logic. The answer to your fourth question is no. Transistors alone can't do the job. You need other kinds of electrical circuits (resistors, capacitors, etc.).
  23. See here: http://mathworld.wolfram.com/CatalanNumber.html.
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