# Recent content by Karlx

1. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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} ?