Mathematics

Is the summation below true? [latex] \sum_{a}a * Pr[R=a] \leq \sum_{a\leq b}b * Pr[R=a]. [/latex] Where R is a random variable and Pr[R=a] means that the probability that the random variable is equal to some number 'a'. You can ignore that part and replace Pr[R=a] with x: [latex] \sum_{a}a * x \leq \sum_{a\leq b}b * x. [/latex] The first summation provides all 'a' values, so the summation is over larger amount of terms. The right hand side sums only those a<=b, so the right hand sums over less amount of terms. But at the same time the right hand is multiplied by b>=a. So it is not clear which one is bigger. I am not extremely familiar with Riemann sum, so …

Hello, This is a question for the professional mathematicians on this board. I want to become a mathematician. My background is in law. I would most likely be able to begin studies in the spring semester of next year. I am 25 years old. From your perspective, am I coming to mathematics too late in life? Do you have any advice to someone wanting to make the transition to math? A few other questions: In law, we approach problems using "legal reasoning". Legal reasoning is an approach to problem solving taught in legal schools, and learned with practice. Is there an analogous process of approaching mathematical problems along the lines of "mathematical reasoning"…

Hello again folks. Is the following of any interest if it can be proved? P: Relative to any finite set of primes there are infinitely many pairs of consecutive twin primes. Note 1. In case it's the wrong word - by 'relative' I mean that none of the primes in the set are factors of the pair of twin primes. Note 2. This is nothing like a proof of the TPC. Thanks for any replies.

While looking for a modular building block for a sieve of Eratosthenes, for example, an 8-bit block of zeros with composite multiples of 2 and 3 already marked as ones,I noticed something bazaar. If I grouped the digits from the sieve into groups of 8 and marked the composites, it takes the same number of groups of eight to form a repeatable block as the prime who's composites i was marking. For example, here are some primes and the groups of eight digits for the sieve. 2 == 10101010 3 == 10010010 01001001 00100100 5 == 10000100 00100001 00001000 01000010 00010000 7 == 10000001 00000010 00000100 00001000 00010000 00100000 01000000 11 == 10000000 00010000 00000010 00…

Of course it hasn't been solved yet, but it would be significant to consider other properties of Hailstone sequences after it has been solved(or the properties brought in this post will be solved with the solution to the problem). Before introducing these problems, here are things to be defined: A Collatz number is defined by a number in a Hailstone sequence that is represented by [math]c_{x}=6x-2[/math] where x is the index of the number. This is a result of [math]c_{x}=3(2x-1)+1[/math]. A Hailstone sequence is a sequence of numbers resulting from the Collatz conjecture rules. A Hailstone exception is a number that does not follow the pattern of a Collatz number …

So, something I've been doing lately is reviewing driver safety. I got my license in 2008, and I have reviewed driver safety the past few months. I think I'm a much better driver than in 2008, but I've been reviewing skills to prevent myself from ever getting into an accident. One of the mathematical models that I came across lately in driver safety is the Solomon curve. http://en.wikipedia.org/wiki/Solomon_curve It's a mathematical model describing the relationship between speed between drivers and the probability of getting into an accident. What I don't understand about the curve, and perhaps some mathematician here could do research and give me insight, becaus…

Hello everyone Here's a question from the acceptance exam for Med school: 6,000 people undergo an ABO-bloodtest. 1,846 are not positive for antigen A, nor B. 2,527 are positive for antigen A, while 2,234 are positive for antigen B. How many are positive for both antigens? First thing that came up in my head, was to substract First thing that came up was Boolean algebra, where: [math]6 000 = \neg(A\vee B) + A + B + (A\wedge B)[/math] (O, A, B and AB) [math]1 846 = \neg(A\vee B)[/math] (O) [math]2 527 = A\wedge (A\wedge B)[/math] (A and AB) [math]2 234 = B\wedge (A\wedge B)[/math] (B and AB) But there's a problem: [math]A\wedge (A\wedge B) = (A\wedge…

Thanks to iNow, I was able to make this finding(unless this was already found before I found it). I was meaning to post this sometime or other, but now I have the time to do so. When I saw the equation for the prime test, I decided to mess with it. When I took it's derivative, I found that the equation, when solving for x when y = 0, would come up with complex numbers, where the real part is 1/2. I modified the equation(only the exponents) so it would fit the characteristics of the Riemann Zeta function(though an unorthodox method, I thought it would be important). [math]\zeta (x)=(x-1)^{s}-x^{s}[/math] Where s = p+1 and s must be an even number. Now, in t…

Hello everyone In class, we saw some stuff in probability and I wondered if they could also be written with these symbols: [math]P(A \; \text{and}\; B)=P(A\cap B)[/math] [math]P(A \; \text{or}\; B)=P(A\cup B)[/math] And so I also wondered if they could also be written with proposition logic symbols [math]P(A\wedge B)[/math] and [math]P(A\vee B)[/math] For the chance of 'not A', we saw this notation: [math]P(\bar{A})[/math], but I wonder if this: [math]P(\neg A)[/math] is also good, and which one is the 'best' (best known, most correct one). Thanks. F

Recently I'm learning about complex networks and I'm interested in similarity functions that give how similar two nodes are in a network/graph. I found couple similarity functions/indices that were described in the sense of undirected networks. However my concern is with directed networks. For example Preferential Attachment similarity between two nodes in an undirected graph is the degree of the first node multiplied by the degree of the second node. But what about directed graphs? Which degree should one use? In-degree or out-degree? Another index is Salton index which is defined as the number of common neighbors between two nodes divided by the square root of the m…

For the second derivative, why is (d/dx)(dy/dx)= [(d/dt)(dy/dx)]/(dx/dt)? I don't see the logic. Am I supposed to apply the quotient rule of differentiation on dy/dx? If I do that I get the second derivative is 0 because dy-dy=0. Am I allowed to use algebra on dy and dx?

So, I found something that was interesting that could related to the Collatz conjecture. Here is what I found. Take any regular function f(x) and multiply it by its inverse. take the derivative of that product. Repeat this step until you reach a pattern of 2x repeating. Here is an example: [math]f(x) = x+1[/math] [math]\frac{\mathrm{d} }{\mathrm{d} x}\left ( (x+1)(x-1) \right )= 2x[/math] [math]\frac{\mathrm{d} }{\mathrm{d} x}\left ( \left (2x \right ) \left ( \frac{x}{2} \right )\right )=2x[/math] (This is just a simple example) I have tested this with other functions and it seems to check out. I haven't seen this before, so if someone knows if …

I came across a formula derived by Ankur Tiwari, which he says enables division by zero. The website claims This formula enables us to divide in a unique way without using denominator. This formula is based on the principle that, If the value of X divided by Y (X/Y) is A than by using this formula we can find out A without dividing X by Y directly, that means without dividing X by Y we can find out its value. This is the reason why ‘Bhartiya New Rule for Fraction’ is capable of diving by Zero. The interesting points in regard of this formula are :- 1.‘Bhartiya New Rule for Fraction’ is based on present phenomenon and rules of mathematics. 2. It is ver…

I am trying to figure out how to make a function for this wave. I drew it terribly, but I think it works: So, how would I make that? I tried but I can't do it. This is not for home work, I'm just curious. If you can't understand that image, basically you have a sine wave on a sine wave. Sorry, I'm not good at explaining things.

Hello In July, I'm doing the approval exam for Medicine school. The exam is a multiple-choice-exam, which consists out of 2 parts: "knowledge and insight in sciences" and "gathering and processing information". The first part consists out of 40 questions (10 maths, 10 physics, 10 biology & 10 chemistry), with each 4 possible answers. A good answer (let's call the number of good answers [math]a[/math]) results in +1 point, a bad answer (let's call the number of bad answers [math]b[/math]) in -1/3 point (correction for guessing) and 0 points if you leave the question open (the number of questions to which no answer is given would then be [math]40-(a+b)[/math…

Hello everyone I played around with some binomials, variations etc. and I stumbled upon a problem. Let's first of all notice the following: [math]V^a_b=\frac{b!}{(b-a)!}=\binom{b}{a}\cdot a![/math] An equation which I have proven in "Variations formula", a topic of mine: [math]V^{n-m}_n\cdot(n+1)=V^{n-m+1}_{n+1}[/math] [math]\Leftrightarrow \binom{n}{n-m}(n-m)!(n+1)=\binom{n+1}{n-m+1}(n-m+1)![/math] [math]\Leftrightarrow \binom{n}{n-m}(n-m)!(n+1)=\binom{n+1}{n-m+1}(n-m+1)(n-m)![/math] [math]\Leftrightarrow \binom{n}{n-m}(n-m)!(n+1)=(n+1)\binom{n+1}{n-m+1}-m\binom{n+1}{n-m+1}[/math] [math]\Leftrightarrow \left(\binom{n}{n-m}-\binom{n+1}{n-m+1}…

Im doing distance between two points as its set out ---------------------------------- / 2 2 d = / (x2-x1) + (y2-y1) = and so i write the equation im doing out and follow the set rules to working it out.... x1,y1 x2,y2 ( 4 , 5 ) ( 1 , 1 ) --------------------------------------- / 2 2 d= / (1-4) + (1-5) = Now my text Book says the Answer is 5.. but i don't no how im getting 31.1.. im follow…

I have been trying to accelerate my math education, but I have found it difficult because most of the resources that I have been using haven't been to the point at all, or haven't been teaching just the concept. An example would be Khan Academy. I have been using them for a while but gave up because the videos are extremely slow for me. Are there any math books/resources out there that are to the point, maybe like a reference book, but not like a workbook? I also asked some of my teachers for some higher level books, but the same thing happened, they were slow, and had a lot of talking that was not related what so ever to the math.(I really couldn't care how high the …

Well, this is something that isn't really useful, but more fun. Well, here is the idea. The idea is there is a line of size x which then another line is placed at the other line's midpoint, or any given point for generalization, where one end of the new line is positioned at this particular coordinate. This is to repeat onto infinity. The idea is to find the distance between the end of the first line to the end of the last line that is placed in the particular fashion told about above. The distance of this is equal to the following function, given x as the length of the first line and F being the fraction at which to place the new line at on the original …

Im Using a Cas Calculator to work out the Following Equation x+11 2(x+14x) ------- = --------- 3 9 Now i no the Answer is -5 but when putting the following Equation in my Calculator i keep comimg up with 11 x= ---- 9 Just looking for a bit of Help if any one can help me at all.. thanks Matt

Sometime someone asked what zero divided by zero was. Someone answered if 0x=0, then 0/0=x. That's all fine in good, but isn't there a rule that anything divided by itself is one? So wouldn't you technically be turning nothing into one? How does that work? Can someone give a mathematical explanation on what is right? I don't get how 0/0=x, but how can that be true. Wouldn't 0/0=1, so x would equal one? But 0 does not equal one. Thanks for your thought and time.

m^2 = n^2 * 2 has no solution for integers m and n because root two is irrational. But m^2 = n^2 * 2 -1 does have solutions, the first of these being 7&5, 41&29, 239&169, 1393&985, 8119&5741. I believe that there are an infinite number of solutions, in other words for all N, there exists a solution with m and n both greater than N. Can anyone give me a proof ?

Does an algorithm exist that uses the most fundamental theorems of mathematics and creates even more theorems that build up mathematics? If not, I am thinking about pursuing a project as such. Though it might not be completely efficient to make one, I want to see if it is possible to produce one.

Hello For a research we have to do in class, I'd like to use mathematically correct notations. There is, however, one expression from which I don't know how it's written: a false equation. e.g. Fermat's big theorem: [math]\nexists (x,y,z,n) \in \mathbb{N}_0 : x^n+y^n=z^n[/math] [math]\forall(x,y,z,n)\in\mathbb{N}_0 : \left\{x^n+y^n=z^n\right\}=\emptyset[/math] [math]\forall(x,y,z,n)\in\mathbb{N}_0 : \left\{x^n+y^n=z^n\right\}=0[/math] Or just a very simple example: [math]\left\{1=0\right\}=0[/math] [math]\left\{1=0\right\}=\emptyset[/math] Is any of these notations correct? If not, which one could I use? Thanks. Function

Hello everyone For maths, we need to do a research of a mathematical subject. We chose the theorems of Fermat (both the big and small theorem). We are to make a question about this subject, a question worth investigating. (One big question and perhaps some smaller questions about that primary question) However, we can't seem to find one. Can someone help us? Thanks. Function