Mathematics

Just discovered www.maa.org/devlin/lockhartslament.pdf and thought it worth sharing/possibly stickying.

Hey, so I think I know how to do disjunction elimiation... Where I am given A∨B I can assume A => C and B => C, so the result is C after disjunction elimination. Is this always the correct method? For example if I am given: A∨B --- ∨E A How can I prove that this is not sound? Simply by doing what I did above?

There's a tendency for the evolution of mathematics to branch. If we assume the basic line of mathematics to be basic arithmetic, then one of the earliest branchings would have to be algebra. More recent developments might include calculus, combinations and permutations, trigonometry, set theory, logic and computer science, and so on. One thing I'm curious about is whether there is a mathematics of patterns. You know, repetitions and regularities. Is there such a thing?

I am taught if it is over 30 observations it will be probably normally distributed. How the heck was 30 chosen as the magic number?

I'm working on a book on John von Neumann and need to gauge his importance in 21st century math. Any anecdotes or personal experience with his work and his legacy will be appreciated. Thanks.

Hi so i am preparing for my algorithms class exam and this question is the second last one in my text book with graphs, and i am not too sure how to obtain an algorithm that is just O(m+n). a) Prove that every connected graph G=(V,E) has a node v∈V such that removing v and all its adjacent edges will not disconnect G. (b) For a given connected graph G=(V,E), design an O(n+m)-time algorithm to find such a node. I have understood that i need to take a case such as say for nodes v,w there is a node in between the path from v to w such that if v - x - w is the path, and x is removed, the graph is still connected. Anyone have any ideas? TIA.

ok so i want to know if there is an easier way to figure out how many times you would have to double a number before getting to certain number. (other then going 2x2x2x2x2x2x2 question two lets say we take the number 1080 is there a way to figure out how many times it had been doubled assuming the start point is 1 what if the starting number was 4 any way to figure that out besides the long way and this is not homework, i was just folding a piece of metal on itself over and over (like Damascus steel but i used indium since its soft and doesn't require heat to get the layers to bond but it also doesnt add any strength i just wanted to see how many layers i cou…

Hi, I was wondering what applications exist for n-dimensional figures (eg tesseract, hypercube). Could we start with 4-space?

Three vectors: Vector A = (2,-5,-1) Vector B = (2,0,-1) Vector C = (-1,0,1) What does it mean to have an entire vector represented by cartesian coordinates? Do those points represent the head of the arrow? I know that squaring the components and rooting the entirety yields the magnitude of the vector, but can someone explain what these points represent? BTW Vector A can also be written as (a) with a right-facing arrow on top. In context, these three vectors are going to be used to define the volume of a parallelepiped.

Dear Sir , I am in IX std . I felt difficulty in solving these problems . So please help me to solve these . I will be very thankful to you . Q 1 . Factorise the following - x^2+x/4-1/8 Q.2 . (1+3x)^3 is an example of a) monomial b)binomial c) trinomial d) none of these Thankyou

Hi guys! So, yesterday was my first day as a grad student, and my first grad-level class. Yay. I'm also the only one in class that is not a computer-science major in undergrad, but rather a physics major. The teacher said that will help me in this class since it's more a 'math-oriented' course, but ... I'm... not so sure. I have a feeling that the approaches of how "proof" works or how to consider a proof varies drastically between what I am used to from Physics and what I'm supposed to follow here in compsci class. I might be wrong, though, but either I didn't manage to phrase my questions correctly in class or I completely misunderstood the process on the board.…

hi, what this distance metric is called that equal ∑ ABS(ai-bi) thanks

As many of you are aware, I post challenges in the Brain Teasers and Puzzles forum in order to help others expand upon their mathematical abilities. I actually have developed these challenges myself (except for the cow, a rope, and a round barn challenge) without looking them up in books or on the internet. I have been doing this since 1994 and have gotten pretty good at modeling - deriving mathematical equations that predict the behavior of a system. I have learned how to recognize patterns that allow me to reduce problems (series of numbers) into manageable equations that are put together much like pieces in a puzzle. Thus, mathematical modeling is the most extreme form…

a = 17 b = 83 p = 109 y = 161 f_gay = 0 f_guido = 3 s = 233 m = 2 trophies = 0 gamerpoints = 7985 games total = 113 Friendsy-1 = 55 Friendsy0 = 32 Can you guys get the final answer for me? I can't figure it out... It's not a pressing matter, I'm just really curious for the answer. P.S: Please explain how you answer this as well.

I happened to find some random probability question im my book and im stuck on this one .... can anyone help me please, im really weak in probability so.... -There are two players A,B, player A gets to roll twice but player B only rolls once, whoever gets the higher number on the upper face wins ( A can choose the higher score of the two rolls), also note that if A and B draws, then B is automatically is the winner . What is the probability that player A will win? -For the same game, analyze the chance of any player winning 1) if both players can roll twice, 2) roll more than twice I will appreciate any help, thank you

I have 4 attributes A,B,C,D each of them takes value between [0,1] I want to make function F(A,B,C,D) such that: The more A and B, the more the function value is. The more C and D, the less the function value is. if C or D equals "one" the function value is zero. I want this function also to return value between [0,1] How can I do that ?

just saying...... racial bias

I am preparing to take a pre-algebra class in college. It's been 20 years since I've been in school, and in high school I failed algebra, because of this I have chosen careers that avoided math altogether. I never understood the need for combining letters with numbers. lol. As far as I was concerned, letters are for reading, writing, literature, etc. and numbers are for counting. The whole thing always looked like a jumbled mess and scared the crap out of me. I want to make sure that I have the right instrument for the job. The course simply calls for a Scientific Calculator. I have noticed on here that people have definite preferences about which calculators to use. Sinc…

Hi. So I understand the concept of degrees of freedom, as in we are not free to choose x many variables. Like if there are three numbers and the mean is 20, the degree of freedom is 2, because if we choose 2 numbers, the third one is defined. I don't get, however, why sample's of a population use n-1 in the denominator, when populations only use 1. Lets say this is a population: 1,3,5,2,7,8,6,9,2,7. The mean would be 50/10=5. The variance is 7.2. Let's take a sample of this population. 5+7+6+8+7. Let's take a sample of this population. 5+7+6+8+7. The mean would be 33/5=6.6. The variance, using N IN THE DENOMINATOR (which I know …

Ran across an interesting blog entry at Evolution Blog which reads, on part Of all the crazy things! What could possibly be wrong with set theory? I had not heard of this objection to mathematical principles, but I thought I would bring the discussion "home" as it were, as well as ask - has anyone here run into this denial of mathematics before? This is the first I am hearing about it.

hi, what are the numbers have to bee in similarity matrix? is it be the the large real vaule of comparison the element with itself? thanks

hi, If I have similarity matrix that I got it from sequence alignment, where each element of this matrix repersent the rate of similarity .i.e the max score represent mas similarity. say n*n symmetric that show the rate of similarity among n objects . ex. x=[10 3 2 3 6 4 2 4 5]; here obj. 1 is most similar to obj. 2 because the max score except diagonal(10) is 3 and so on. the diagonal here is represent the comparison the object with itsel so has the max value if I used distance metric such euclidean distance to cluster these objects, is it best to set the diagonal to zero, or leave it ? by the way , which the best…

Hi, I'm wondering if someone could give me a very good example of applying principal components analysis to a biology problem. thanks

Hello, Just had a question regarding statistical analysis. I'm trying to calculate the average of 4 numbers from a data set of 6 numbers in excel without manually choosing to average only the 4 numbers. e.g. 85 20 32 45 27 3 (total mean = 35.3 desired mean = 31) 100 30 27 40 21 1 (total mean = 21.5 desired mean = 29.5) ....etc The middle 4 numbers represent a more realistic result whilst the two end numbers are irrelevant. I've tried looking into weighted averages however I'm unsure how to apply this to an excel sheet. I'd prefer to find a formula which would discount numbers which vary wildly from the average amount and focus only on the …

1)in mathematics a0 =1 , when a not equal to zero. My question is how ' a multiplies 0 times is equal 1"?????? 2) vector a - vector a= null vector. What would be its direction?Is that a vector? 3) parameter of a circle is equals pi r 2 . why we use pi instead of a constant number 22/7?????