Applied Mathematics

A Course on the Web Graph Anthony Bonato, Wilfrid Laurier University, Waterloo, ON, Canada Website: http://info.wlu.ca/~wwwmath/faculty/bonato/webgraph.html AMS Graduate Studies in Mathematics 2008; 184 pp; hardcover Volume: 89 ISBN-10: 0-8218-4467-9 ISBN-13: 978-0-8218-4467-0 List Price: US$45 AMS Member Price: US$36 Description: A Course on the Web Graph provides a comprehensive introduction to state-of-the-art research on the applications of graph theory to real-world networks such as the web graph. It is the first mathematically rigorous textbook discussing both models of the web graph and algorithms for searching the web. After intro…

does anyone know how to do this? my teacher said that she can prove it, she said that in ceartain instances, numbers may be forced to do things that they are not supposed to do.... alternatively, does anyone have any other simple problems like this that you could prove like 1+5=5 or something seriously, any ideas at all, no matter how absurd OR complex, would be appreciated

I used to want to study cybernetics, but it looks like the field of cybernetics is called "control theory" nowadays. I'm interested in Automation, so I start by looking at various journals listed by SCI as related to Automation: Automatica and System Control Letters, for example. These journals seem to have a lot of articles with advanced differential equations. Well, I guess that fits my intuition that dynamical systems are the basis of controlled systems; after all, one would expect to use differential equations to describe dynamical systems, right? But the first snag is that differential equations can describe almost anything, and the second snag is t…

Alright I was doing some statistics questions and I have a probelm. Here goes: The random variable Z is distributed such that Z find the probalility: P(lZl < 1.3) NB. < is actually less than equal to. My solution: P( -1.3< Z < 1.3) P(z<1.3) - [ 1- P( Z < 1.3)) After putting values from the table 0.9032 - (1-0.9032). 0.9032 -0.9068 = -0.0036 (probalility can't be negative so my answer is wrong, mark scheme is saying the answer is 0.8064) Thanks in advance.

Hello, Assuming I design an experiment containing N separate measurements to measure something (different samples, different factors etc). Each of these measurements has the same standard deviation of SD. How would I calculate the standard error of the final result after fitting the data to a model? I assume this will be better than the standard deviation SD. I know when repeating the exact same measurement N times, the standard error of the result is: SD /sqrt(N). But how is this for a DoE with N experiments? In particular I'm looking into a D-Optimal design, and the question is how many experiments do I have to do in order to achieve a certain acc…

Hi. I created this Java program where you click around anywhere as many times you want then click calculate. After its done thinking, it will find the pixel closest to all of the places you clicked. I can't really explain it well so please view my applet What do you think of it? I'm a new developer so please critique. I put a map of italy on the background and clicked every city except rome then clicked calculate. And then the closest pixel was very close to rome.

What does actually density and distribution function means?

Hi all, I put this in Applied Mathematics because I'm going to apply this in real life. I'll let you in on some background so you know why I'm asking. Me and my friend are building a hookah. Since were artistic maniacs who are creatively anti-talented, we want the water jar to be in a shape of an incomplete rhombicuboctahedron. The "incomplete" part is where this gets a little complicated. Since we can't levitate our hookah, and one of us holding it while the other one smokes is out of the question, we need it to be steady of course. So the actual shape of our hookah water jar will be as follows: Take a normal rhombicuboctahedron. It's basically made of an Oct…

If you have an ordered list of numbers and you randomly change them what is the chance that at least one number will stay on its previous position? Or more practically if you give everyone a number and you let them blindly pick a number. What is the chance that at least one persons picks his/her own number again.

I have two questions about loans. 1. How do I figure the value of each monthly payment for a loan I take out, knowing only the principal (including origination fee), interest rate, frequency of interest, and number of monthly payments? All the equations I've seen also require how much I'm going to end up paying in the end, and I don't know that for my situation. I know this can be done because there's financial calculators on banks' websites that do it. 2. Suppose I have multiple loans that all go into effect at the same time, but they all have different interest rates. Is there a shorter way of finding the sum of the monthly payments without finding each ind…

The standard formula for an interest-gaining investment (such as a certificate of deposit) is v=pit (end value equals pricipal times interest times time). However, that foruma only holds if the interest only piles once per year. If the interest piles multiple times per year, such as quarterly, then there's a complex formula where if the number if times the interest piles equals one, then it simplifies into v=pit, and if the interest piles continuously, then there's a REALLY weird formula that uses the constant e. What are these formulas? It's been several months since I've taken that class, so I've long forgotten.

Central limit theorem is for the mean value of distribution. However not only the mean value but also the mode might follow similar limit theorem. I tried to prove it in the following site with experimental verification using Java applet; http://hecoaustralia.fortunecity.com/mode1/clt-mode.htm

Find asymptotic lines of the surface Z=X^2+Y^2 please give some definitions and suggestions.

I have been looking around the internet for something that could display what pi variations look like on a sphere. Most specifically 4pi & 4pi^2 and 8pi & 8pi^2 One source produced these such images. (quantum aether dynamics) 4[math]\pi ^2[/math] I do not fully understand if this would be accurate. Can anyone help me out. Are these shapes added correct? Must the curvature remained fixed?

Does anybody have any recommendations for books on game theory, (under-grad physics student) so from basics to intermediate...I can only find books aimed at post-grad Economics, Maths et.c which will be too technical for somebody at my level, maybe I havn't looked hard enough, not sure. I'm more interested in the purely mathematical side, rather than the complex computational use of game theory. I.E I'm not looking for a book filled with computational algorithms, instead starting with basic situations and use of matrices and onwards. How I missed this I have no idea...'An Introduction to Game Theory' by Martin Osbourne, but this seems to fit the bill. Has any…

The text book I borrowed from my school reads "you already know that the graph of y = ax^2 is a parabola whose vertex (0,0) lies on its axis of symmetry x=0." On the contrary, I know not of what it reads. I am unaware of what y symbolizes, as well as what a & x^2 symbolizes. The axis of symmetry as defined by the text book is "the line perpendicular to the parabola's directrix & passing through its focus. In particular, the axis of symmetry is the vertical line through the vertex of the graph of a quadratic function." So, from this, I've deduced that the axis of symmetry is the line perpendicular to a fixed line associated with the parabola, which passes through t…

How do calculators (and computers) add ,subtract etc.? I know it is done through code but how? I shall be grateful if someone helps me understand these very basic ideas.

[math]X =^{d} R(0,\theta)[/math] and we obtain five independent observations on X: 1.2, 3.7, 2.1, 5.9, and 4.0. The median [math]\hat{M}[/math] is 3.7 and I'm told that [math]var(\hat{M})=\frac{\theta^2}{28}[/math]. How is this obtained? Do I use the formula [math]var(\hat{M})=\frac{1}{4nf(m)^2}[/math]?

Does this symbol have anything to do with the tetrahedral constant? I would appreciate any opinions. http://thecompletefloweroflife.blogspot.com/

The angles in a tetrahedral molecular shape are 109.5 degrees according to my chemistry book. If I have only taken a geometry course is it possible for me to figure out why this is so? Could anyone give me a simplified explanation of how this is done? Thanks

Hi, My teacher and I were discussing my research project: A study of Potential Monogamy Behavior in the Family Dendrobatidae, and the conversation resulted in the my teacher telling me that I'd need to use some advanced statisticals formulas to determine what percentage of the females are required to repetitively choose the same male frog in order for it to be classified as "potential monogamous behavior". Any ideas? (there are 6 frogs. 2 females and 4 males, but everytime, only two males are introduced to a female at any given time.) Help is greatly appreciated! Thanks in advanced!

In linear regression: How can I demonstrate that expectation of hat-beta0 is beta0 ?? E(^Bo) = Bo I know that E(Yi) = Bo + B1·Xi ^Yi = ^Bo + ^B1·Xi ^B1 = SSxy / SSxx ^Bo = barY - ^B1· barX E(^B1) = B1 I would very grateful for your help.

How do calculators do this? From what I understand, a computer/calculator can only add or subtract, and nothing else. How exactly does it graph polynomials, calculate pi to hundreds of digits, etc. I know how it does some of the things: e.g. it sums a series when calculating the cos(1), but what does it do when its calculating anything complicated like logarithms?

what is the condition for a matrix to be linearly dependent or independent

for all you math and computor geniuses... this might be worded a bit weird(i'm not the greatest with words...) how do computors or programming languages come up with/define random sequences? example: if i tell a computer or write a program to pick a random positive integer between 1 and 100, what's going on behind the scenes? i hope my question makes sense. thanks to anyone with helpful replies... i've always been curious about this and until now have never really bothered to investigate(feel free to call me a lazy jackass...or whatever) -alex