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  1. M

    Vector Quotient Spaces

    and the line comes from the vector definition of line.
  2. M

    Vector Quotient Spaces

    oh oh oh i see now. thanks
  3. M

    Vector Quotient Spaces

    Then i think my conception of adding vectors is incorrect. If i think of vectors as directed line segments, i cant think of a way to add vectors on the x-axis to other vectors to get something parallel.
  4. M

    Vector Quotient Spaces

    But if you add a vector to the x-axis, how can that be a line parallel to the x-axis. More importantly, what is an element of the x-axis? Is it just a point?
  5. M

    Vector Quotient Spaces

    I'm having a bit of trouble seeing Vector Quotient Spaces. Lets say I have a vector space $V$ and I want to quotient out by a linear subspace $N$. Then $V/N$ is the set of all equivalence classes $[N + v]$ where $v \in V$. For example, let me try to take $\mathbb{R}^{2} /$ x-axis. This...
  6. M

    Spivak calculus on manifolds solutions? (someone asked this b4 and got ignored)

    I've come to realize over time that it is better not to have a solutions manual.
  7. M

    Cal vs Chicago

    Hello, I am currently a high school student and I have been accepted into both UC Berkeley and the University of Chicago. I plan to major in math or physics, but I have no idea which college I want to go to. From what you know of their undergraduate mathematics or physics programs, which...
  8. M

    Really challenging IQ test

    IQ is the stupidest thing I have ever seen. What is it supposed to measure again?
  9. M

    Putnam Exam Prep Questions

    I use my extraordinary power of teleportation to get out.
  10. M

    Hey guys i need help in matrix

    I can help you. All you need is to move those things around and apply those theorems.
  11. M

    What the heck?

    Hm, I've already discovered mathematical and physical fallacies in his argument. Some people just can't do algebra i guess.
  12. M

    What the heck?

    This site was linked at the top of the physics forums website. www.relativitychallenge.com I guess everybody has freedom of speech. Do people just get a kick out of proving Einstein wrong?
  13. M

    Fields and new operations

    This problem comes from Halmos's Finite Dimensional Vector Spaces. Given that we can re-define addition or multiplication or both, is the set of all nonnegative integers a field? What about the integers? My thinking is that since the Rational numbers form a field, and they are countable, we...
  14. M

    Goursat and Analysis

    My library limit for Goursat's book(s) is dwindling down rapidly. Does anyone know where I can get a new copy? I hear dover had them before.
  15. M

    Goursat and Analysis

    Has anyone read Cours d'analyse mathématique (Course in Mathematical Analysis)? If you have, do you find some the the problems just a might challenging? I've found that this is pretty characteristic of books of that time period. Why have problems in textbooks today gotten so much easier?
  16. M

    Analysis or Abstract Algebra?

    you will eventually need both, so just flip a coin.
  17. M

    Medical Photographic Memory

    What is the Latest age at which one can acquire this ability? Are there people who can learn languages easily at older ages given that they had not been exposed at a younger age?
  18. M

    Probability and the Real Line

    Measure Theory. That sounds pretty cool.
  19. M

    Probability and the Real Line

    Wow, so many responses. I was just wondering and all. I have another question now. This is not homework, I was just thinking. Lets say we take a definite integral from 0 to 1 of an arbitrary real valued function, and answer is x. Clearly if we take away any random point from the interval 0...
  20. M

    Calculators Which Graphing Calculator to buy?

    HP 49 G+ man. I've had both, but i definetly prefer HP.
  21. M

    Excellent *teachyourself* Calculus books?

    A Course of Pure MAthematics by G. H. hardy
  22. M

    Probability and the Real Line

    Take the Interval [0,1] over the reals. Randomnly choosing a number, what is the probability that you will get an irrational number? A rational one?
  23. M

    Schools Possible to complete senior high school algebra&geometry course w/ 3 weeks cramming?

    Why do you need to graduate from high school? Is it because it is required to graduate from college? - Because it would be pretty cool to say, in the future when you become succesful, that you were a high school dropout.
  24. M

    Methods of Teaching Mathematics

    Where is mathematics learning going today? There are many books nowadays, that emphasis conciseness and rigour over all else. The Rudin "series" is a perfect example. There is hardly any motivation, and emphasis is put on rigour, rather than intuition. I am sure that this could be argued...
  25. M

    UC physics

    I think the school of engineering and the school of arts and sciences are two different schools. I think that if you want to major in physics you have to apply to the other college.
  26. M

    Hardest logic problem ever

    point to a road and ask if the other person would say if it was the road to gondor. This way if you are pointing to the correct road, and the person you are speaking to is the truth person, he would say no. Similiarily, if it was the lying person, then he would also say no. Thus you know to...
  27. M

    Hardest logic problem ever

    Ask the elf what the correct path is... Duh. I think it would be a lot more interesting if the orc and elf were indistinguishable.
  28. M

    Need to understand math better - advice?

    "I'm not looking to discover the Theory of Everything, but I'd like to be able to understand it when someone else finally does." Well if this is the case, then I am afraid most community college classes will not come close to the level of mathematics that is involved with the various theories...
  29. M

    Surgery Obstruction Groups

    First of all, it would be helpful to know what you have learned so far. There are quite a few prerequisites before surgery. You should have had a good graduate level classes in Algebra, Algebraic Topology, and some Differential Topology at very least. If you have enough Alg. Top. under your...
  30. M

    Surgery Obstruction Groups

    Surgery on Compact Manifolds: "Part 1 consists of the statement and proof onf our main result, namely that the possibility of successfully doing surgery depends on an obstruction in a certain abelian group, and that these 'surgery obstruction groups' depend only on the fundamental groups...
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