Mathematics

Hello! Well my interest for math is growing alot and I want to know if there is some sort of math literature to sharpen my problem solving skills. So I just basically want to be good at solving math problems really. I know that you might think that solving math problems makes one become better at solving math problems and that is so true but I am looking for something beyond that. Perhaps a book with math problem solving techniques or just some hard as* questions with good explanations aswell. If something is still unclear or you just have a question mark in your head feel free to ask me. Regards!

Say there are two people with facebook accounts. Person A has 200 friends. Person B has 50 friends. It seems as though there is a higher probability that Person A has Person B as a friend than Person B has Person A as a friend. Of course, if person A is friends with person B then person B is friends with person A and vice versa. That would mean they would have the same probability of one having the other as a friend.

Along a road, there exists marks for every passed kilometer after every kilometer, at the start where the mark shows 0. A hiker who starts walking at the roads start devote himself to count the numbers on the marks. How many kilometers has the hiker walked/passed at the mark showing the number 2013? I have the solutions aswell but I don't understand the solution. You can see it below. If somebody could explain this I would be greatful. Regards!

So, after taking a lecture on the use of difference quotients for derivatives, I happened upon something interesting. The usual equation for the different quotient is the following(applied for derivative use): [math]\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}[/math] Now, I know that getting the derivative of the function 3x+1 and its inverse gets the following result from testing before: [math]f(x)=(3x+1)(\frac{x-1}{3})[/math] Of course, seeing this connection to a pattern I found in hailstone sequences I left it at that. However, I then began investigating the affects of the variable h on the result. Here is what I found. I thought this …

Convex pentagon MNPQR. $\angle{MNP}=\angle{MRQ}=90^o$ and $\angle{NMP}=\angle{RMQ}$. $NQ\cap PR={A}$. Prove that $MA\perp NR$.

Hey Everyone, What does it mean if the processing time of a certain job instance is generated according to an exponential distribution with a certain mean? I already know the mean so what does it add to know its distribution and how can I use it? Regards,

As it is known, with a constant such as phi, lim n->infty F_n/F_n-1 = phi, the function can approach but never reach the irrational constant. This can be observed with the following: Phi = lim n->infty F_n/F_n-1 = (1+sqrt(5))/2 Lim n->infty 2F_n = Lim n->infty F_n-1(1+sqrt(5)) Turn this into a function displaying the approach to the constant. A(n)=2F_n-F_n-1(1+sqrt(5)) Of course, the expected result is to see the function decrease towards 0, but the question I am asking is if this approach towards an irrational constant will always be exponential in nature? If so, is there a way to determine the equation of this decrease without the brute forc…

There's a free online course running ATM by Stanford University http://online.stanford.edu/course/how-to-learn-math-for-students-s14 It teaches how to learn maths, and it's brilliant, so anyone who's learning maths at ANY level, give this a whirl. It doesn't take long, you have until December 14th to complete it, and if you do complete it, you are sent a certificate of excellence from the uni, which looks good on a CV or applying to uni etc. There's no obligations to complete it, it's free, simple and extremely useful. I recommend it strongly to anyone studying maths.

Hey Everyone, I'm modeling a sensor node power consumed and lifetime using markov chain for two cases. Case 1: Assume that the node senses, processes and transmits the data. Energy and time spent in each state are considered random variables. I have no problems and I did my calculations for this case. It is similar to: http://thiagot.com/papers/jung_tosn09.pdf. Case 2: It is the simplest form and I need it for comparison reasons only. It assumes that only the sensor and the radio are awake and that the node sends whatever it senses. Does Markov Chain still hold to this case? Thanks a lot in advance,

Question: How could the ancient Egyptians have invented/mastered geometry, independently from a teacher source? I can see how mathematics can sprout out of necessity for mankind in general.

Hi everyone, First, let me say I can actually solve this problem without trouble using the prescribed method. I just don't like it, think it's kind of clunky and have been wondering about another way to go at it. Something more intuitive to me. As you can see from the pic, the problem to solve is pretty straightforward. What I was wondering is what would happen if the boat were to *not* compensate for the river current at all? Where would it end up? The triangle I drew up in the corner kind of illustrates what I think would happen. 15 represents the speed of the boat along the Y axis, and 4 is the perpindicular force acting upon it by the river current. Calculating the a…

Hey guys, so a few days ago I registered for the CLEP Exam to exempt myself from taking the course. If I pass, I can go straight to Calculus I my first semester in college as a freshman. Unfortunately I have not taken Precalc in high school, but I did take Trig for a full year and AP Physics for half a year (I honestly became bored with Physics due to my teacher so I had to switch out). I have one more week until the test (next Wednesday), and I have a general list of things I need to study. If anyone has taken the CLEP exam or has any tips/hints/insight/etc that they could offer me I would greatly appreciate it!

I'm trying to understand common core, however it seems who ever is making up these equations is using arbitrary numbers to make their point. I could understand if the numbers were derived from the question, but that's not the case. Example: _______________________________________________________________ What does 26 + 17 =? 1.) First think: 4 + 13 = 17 ( why not use 16 + 1 or 12 + 5...why 14 + 3) 2.) Add 26 + 4 = 30 3.) Add 13 + 30 = 43 ________________________________________________________________ ~ee

Esteemed Mathematicians , I have tried to emulate a step further and put a model in place to find the mathematical model of Sudoku..this method simplifies all the techniques used in conventional solving method and break up the number into possible row, possible coloums and box numbers, http://www.scribd.com/doc/39235249/How-to-Solve-Sudoku-Mathematically details of the model can be found in above link, i am looking for expert views and further investigation by mighty minds... Some food for Mathematicians Soul....

Necromancy! I searched the forum for 'Möbius' and this thread was the only one returned. And wonder of wonders you have mentioned just the concept I had in mind, i.e. squashing. Before I launch into squashed space I would just point out that above you say 'at the ends' and a Möbius band has no ends. So a few years back I got to wondering if there was a limit of L to W beyond which I could not join W's to get a Möbius band. I made paper bands as well as sewed some of canvas. Anyway, yes Möbius bands beyond certain ratios must be squishified. At some ratios the band squishes into a hexagon. After seeing it [the hexagon] and having recently read about the mysterious hexa…

To calculate the day of the week for a given date, first of all we need to find out the number of odd days. Today I thought of sharing a beautiful problem I learned in my school, though it is easy, it is tricky too. Odd Days are number of days more than the complete number of weeks in given period. Leap Year is the year which is divisible by 4. A normal year has 365 days A leap year has 366 days One normal year = 365 days = 52weeks + 1day One normal year has one odd day One leap year = 366 days = 52weeks + 2days One leap year has two odd days 100 years = 76 ordinary years + 24 leap years = 5200 weeks + 124 days = 5217 weeks + 5 days 100 years have…

Hi everyone Let me get to the point: in my opinion, the equality between "chance" and "probability" isn't very well chosen... Let me illustrate this with an example: Imagine a sheet of paper, of whatever area. On this paper, a part is covered with honey or some other sort of sweet stuff. The chance that a wasp, or a bee, a fly, whatever, lands on a very specific point of the sheet of paper, not covered with honey, is almost 0 (1/infinity). This chance is equal to the chance it will land on a point covered with honey. In my opinion, though, the probability that it will land on a point covered with honey, is much larger than it will land on a point which is…

I realized sexual polyamory could result in lower STI frequency per partner per individual, but the decreases are only 0.0 to 0.1 even under extreme conditions and with everybody doing it. The idea is that exposing organism-A to organism-B also indirectly exposes A to all B's contacts, so it's safer for A to interact with the contacts of previous contacts, reducing the total number of contacts (direct or indirect). My equations can model other epidemiological scenarios, but I can't get a universal equation for situations involving indirect transmission within the interacting groups. yn = the probability of being healthy after the nth contact, hence... y0 = the probabil…

a ^ 2 = d ^ 2 / 2

I have been playing about with primes, But this is not a prime question, I was looking at the difference between each prime, Then the difference between that difference until I reached 1, To look for patterns. I was wondering what it is called when you take a certain amount of numbers has shown below and find the difference between the difference until you end with 1? (1 is the point of triangle). I have tried to look it up but end up with differences between everything but what I want to know, There is most probably a simple name but it escapes me at the moment. Each difference of the same number is the same colour,0 pink,1 purple, 2 blue, 4 yellow.

Hello I want to invent a mathematics theory I have been trying for several years But, I can get any result Can any one tell me about inventing theories? Are there any resources on the internet? Thank you very much

Hello everybody. This is my very first post and I warn you now it's going to be unusual. I have always been a very creative and imaginative person, I have ambitions of becoming an author someday maybe even producing my own animated TV shows. I have always regarded creativity as a realm of infinite possibilities, where anyone and everyone can bring something unique into this world. But lately I been feeling very depressed because of two scientific theories. The first one was introduced to me years ago by my father who has always been very interested in science. He told me that there is a finite limit on the number of books is possible to write. Not because hum…

diameter of sphere is 2 pi r, but from what point of view