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  1. Karlx

    A book on Probability

    Hello MIB. I second the recommendation of PAllen. Feller's book is a very recommendable book. Volume I starts from a very intuitive conception of probability and then it goes on, from the very elementary concepts until more deep ones. And always with a lot of very interesting exercises...
  2. Karlx

    An introductory book on the Distribution of Prime Numbers and Riemann's Zeta Function

    Thanks a lot, Petek. At first glance, Jameson's book seems to me a good choice as an elementary first introduction to the matter. And Fine and Rosenberger's one seems interesting too. Apostol appears to me as the more technical of three. Thanks again.
  3. Karlx

    An introductory book on the Distribution of Prime Numbers and Riemann's Zeta Function

    Hi everybody. I would like to find a book about the Distribution of Prime Numbers and the Riemann's Zeta Function. I know about the "classical" books: 1) Titchmarsh's "The Theory of the Riemann Zeta-Function" 2) Ingham's "The Distribution of Prime Numbers" 3) Ivic's "The Riemann...
  4. Karlx

    A good book for an introduction to Algebraic Topology

    My course is a one-year elementary introductory course, first half on general topology and second half on algebraic topology. So, from your comments, I think the best choice for my elementary level in this matter, will be, perhaps, Kosniowski-Munkres for general topology and...
  5. Karlx

    A good book for an introduction to Algebraic Topology

    Thanks Vargo and mathwonk for your suggestions. I'll take a look on Kosniowski's, Massey's and Munkres's and I'll decide. Hatcher's is interesting, but a little away from the contents of my course.
  6. Karlx

    A good book for an introduction to Algebraic Topology

    Hi everybody. Next year I will start an undergraduate course on algebraic topology. Which book would you suggest as a good introduction to this matter ? My first options are the following: 1.- "A First Course in Algebraic Topology" by Czes Kosniowski 2.- "Algebraic Topology: An...
  7. Karlx

    Problem Intensive books on Probability

    Hi kamran60. These books have a good selection of (classical) problems: "An introduction to Probability Theory and Its Applications", Vol. I and Vol.II by William Feller.
  8. Karlx

    Statistics vs probability

    Just a recommendation for Intervenient. If you are in your first probability class, just take a look to the book "An introduction to Probability Theory and Its Applications Vol.I, 3rd.Ed.", by William Feller. This book is a high level one, but if you read only the Introduction and Chapters I...
  9. Karlx

    Transformation of two dimensional random var

    Hi dannee. The inequalities (0<y<1, 2y-x<2, 2y+x<2) define a region A in the (x,y)-plane. You can follow these steps, in order to graphically "visualize" the problem: 1) Draw the region A in the (x,y)-plane 2) Introduce the two dimensional transformation u=x , z=y-x 3) Obtain the...
  10. Karlx

    Proof of variance for functions of variable

    Hi Georg. I don't know which is definition 4.1, but it doesn't matter. If you take definition 4.3 and apply it to the random variable Y=g(X), you'll get it.
  11. Karlx

    Exactly 2 People have the same birthday

    Hi again ndrue. Your question is not a trivial one. So, let us proceed from the very beginning: Let r be the number of balls (people) to be distributed in n cells (n=365). First of all, let us focus ourselves in a prescribed cell, say cell i. If you call a success the event that cell i be...
  12. Karlx

    Exactly 2 People have the same birthday

    Hi ndrue. In order to calculate the probability that at least 2 people share a birthday it is easier to calculate the probability of the complementary event, that is, the probability that no birthday coincidences at all. That is the same as distributing m balls in N cells and ask for the...
  13. Karlx

    Proof of the formula for the probability in a region

    Hi Bijan. In your post #4, you got it yet !! The "divide and conquer approach" of your book is the fundamental theorem of calculus, a little hidden. It is useful to draw the rectangular area B, with its four corners (x_{1},y_{1}) , (x_{1},y_{2}) , (x_{2},y_{1}) and (x_{2},y_{2}), and try to...
  14. Karlx

    Mathematics, Creativity, and Anxiety

    Hi, Dschumanji. You have the passion for maths. You have also the love for them. Your professor is encouraging you to take a concurrent degree in maths. Don't let you disturb yourself about AMC competitions. Go on, take this degree. You will enjoy maths (you have the ability for that) and you...
  15. Karlx

    Proof of the formula for the probability in a region

    Hi Bijan. You may generalize expression (2) easily for the case of a random vector (X,Y). Just suppose B to be the rectangular region defined as B={(x,y):x_{1}<x\leqx_{2}, y_{1}<y\leqy_{2}}. From this how do you calculate P{(X,Y)\inB} ?
  16. Karlx

    Question on electromagnetism

    That's an interesting question. Which is the relative position of these two particles ? The geometry is an important point when thinking about electromagnetic fields. For instance, let us suppose the two particles are in fixed positions, separated by a distance a. Could you visualize the...
  17. Karlx

    Polar to cartesian coordinates for stream function

    x=x(r,\theta)=rcos\theta y=y(r,\theta=rsin\theta You are given V_{r}=\frac{dr}{dt}=0 V_{\theta}=\frac{d\theta}{dt}=cr How do you calculate V_{x}=\frac{dx}{dt} and V_{y}=\frac{dy}{dt} ?
  18. Karlx

    Exactly 2 People have the same birthday

    It may be useful if you think the problem with an image of distributing m balls in N cells. Your problem is equivalent to this one: You have N=365 cells, one for each day of the year, and you have to distribute m balls (people) into these cells. What you are asking for is the probability that...
  19. Karlx

    Future of number theory

    In science, when you get an answer, you get also several new questions. At the end of 19th century, physicists thought that Physics was nearly terminated. All the relevant questions had been yet studied and understood. It only left some "secondary" aspects that would be quickly dispatched...
  20. Karlx

    What are the applications of group theory?

    Yes, indeed. Group theory is extensively applied in Theoretical Physics: General and Spacial Relativity Elementary Particles Quantum Physics
  21. Karlx

    Can someone explain zeros and zeta function for Riemann Hypothesis? (Yr13)

    Hi 2710. A very good book you can read in order to understand what Riemann's Hypothesis is about is John Derbyshire's "Prime Obsession". It is a brilliant book, and I don't know any other book that can explain Riemann's Hypothesis in a more comprehensive way.
  22. Karlx

    Pancakes and Bayes' Rule

    Let's name the pancakes as B_{0}= Pancake with no burnt sides B_{1}= Pancake with one burnt side B_{2}= Pancake with two burnt sides The probability a priori, for a pancake of being at the top after stacking them is 1/3 for each one. I think there is no doubt about this. Now, let's take...
  23. Karlx

    Two point charges with electric potential energy?

    Hi netsurfer. Let q_{1} and q_{2} be the charges you are asked to find. How do these charges enter in your equation ?
  24. Karlx

    Finding the square with a fraction in the expression

    Hi Amaz1ng. You are asked to find if there is a value a so you can write x^{2}+x+1/4=(x+a)^{2}
  25. Karlx

    Combinations with limited repitition

    So, if I understand you, you have the number 362880 = 2^{7}\cdot3^{4}\cdot5\cdot7 and you want to calculate how may proper divisors does it have. If one of the factors has exponent n, then, counting also the zero exponent, this factor may arise in n+1 ways. So for the other factors. Thus the...
  26. Karlx

    Combinations with limited repitition

    Suppose you have the following list: {a,b,c}. In how many ways may you arrange these three members ?
  27. Karlx

    Combinations with limited repitition

    Hi Soandos. You have a list with 13 members, in groups of 7,4,1 and 1. Let us proceed step by step. 1) In how may ways may you combine 13 members ? 2) Among all these ways, how will you take into account the groups of equals members, of size 7,4,1 and 1?
  28. Karlx

    Probability Question

    A is the event that the first card is A. So pA=1/3. The same apply to B and C. Just calculate P(L).
  29. Karlx

    Probability Question

    Ok. According to your notation A is the event that the first (and rejected) card is the lowest one. So, if you reject A, the probability of accepting the lowest card is zero. So P(L|A) = 0. What about P(L|B) and P(L|C) ?
  30. Karlx

    Projectile motion problem

    What kind of motion do you think that has the ball on the y direction ?