Mathematics

I was wondering what exactly 'standard form' is/means in the area of linear equations

I'm doing a presentation on statistics and statistical abuse and it got me interested in learning more about statistics, specifically in the context of data analysis and scientific experiments. Does anyone have a recommended textbook or resource for learning?

I have recently been studying algebra and came across this which didn't make sense - a(squared) + 1 / a + 1 and stated that it could not be simplified any further due to lack of common factors... however, can't the denominator 'a' be taken away from the numerator 'a(squared)', therefore just leaving 'a' with the two 1s being cancelled. Or is simplification (of algebraic expressions) different to solving them..

I know that the area of an ellipse is: Pi x Semimajor x Semiminor But after quite a long time of figuring, i thought, why can't we just treat the ellipse as a circle by hypothetically shortening the semimajor and lengthening the semiminor to the same length (averaging them) and then using Pi x Radius2 I know they give different answers, but i don't see why my way is wrong. I know that it is, but i would like someone to prove to me that it isn't, and prove to me that Pi x ab is thanks once again

Would someone be able to please explain to me what the following means - a^-1 = 1/a, a^-m = 1/a^m I've recently gone over the area of scientific notation and this part in particular didn't make sense. thanks.

The surface in above image is a portion of the graph of some mathematical equation. Let's do some brainstorming: Can you guess what's inside the surface? .

I was wondering does the rule - a plus and minus equals a minus - mean/hold the same for an expression such as -2 + 6 and 2 + (-6) and why is it so..

Hi all, I hope this is the right forum to post this question in, rather than one of the subforums, as it deals with notation, not actual mathematics. I've attached a pic of the problem I'm looking at: In Eq. (31), an implicit ODE is given; note how the last two derivatives are superscripted with a summation/capital sigma. What does this mean? I've Googled as best I can, but no luck. The only clue I have is that one of the terms superscripted with the sigma is a matrix of coefficients. There are more examples of this notation later on in the attachment. Any thoughts on this? Even a pointer in the right direction would be helpful. Thanks, TM

Say I have an ideal coin, and I keep throwing it until I get heads. What would be the average number of times I would have to throw the coin? I'd say the answer is one; I'm not familiar with the terminology so I'll have to use my own words, but since the chance of getting either heads or tails is 50%, the number of times I get heads should equal the number of times I get tails (after an unlimited number of throws), which means that I can think of the outcomes of the throws as alternating between heads and tails. Or so I think.

In the cutting Edge math theory thread, I provide a link to a very exciting DVD about Origami and its relation with math, science and art. The DVD is titled "Independent Lens: Between the Folds" and is great for getting high school students excited about math. Then this morning on the National Public Radio station, I heard about a book for children, done by a college professor. http://www.richardev...m/monsters.html Surely everyone has heard Pythagoras put down for treating numbers like beings with personalities, but that is exactly what the college professor has done. His number characters are monsters with individual personalities that children can ident…

note: this thread is based on my research .. in response to the tree request, ------------------------------------------------------------------------ Part I: Mind Encyclopaedia Fuzzy Neural Structures are a Logical Unit mapped to its corresponding object in reality, and unlike standard structures that need precise description, and appear to be unique, and seem clear ... Fuzzy Neural Structures have logical-identifiers, fuzzy-description, meta-data, history-bag (I will explain each later). The brain memory is a Fuzzy "Fuzzy Neural Structure" Encyclopaedia, this fuzzy encyclopaedia is a graph where every structure forms a tree, and all trees connects …

assume E is any even number, and O is any odd number E = O + 1 O = E + 1 E + E = E E + O = E + E + 1 = O O + O = ( O + E ) + 1 = O + 1 = E E * E = E E * O = E O * O = O note: if a given (O = O * O) then that O can only be factored by odd numbers. what do you think ..? I also think that, given that A & B & O are odd, and C & D & E are even ... C * D = E (A+1) * (B+1) = E AB + A + B + 1 = E odd*odd + odd + odd + 1 = odd+1 = even C * A = D, and C = B+1 (B+1) * A = D AB + A = D odd*odd + odd = odd+odd = even A * B = O (C+1) * (D+1) = O CD + C + D + 1 = O…

In math there is a lot of things that go in pairs, addition and subtraction, multiplication and division, real and imaginary, a function and its inverse, quite a few things that go in pairs. But I can't really think of any math structures that go in triplets. It should be possible since the idea of quark triplets should have a mathematical basis, but I can't think of any.

i'm sorry, i didn't know which specific subcatergory to put this in, there was no geometry section. According to mathematics you can draw a line. this is 1 dimensional. you can then draw another line at 90o to this; this occupies 2 dimensions: a square. you can then draw a third line which obviously cannot be at 90o to both of these, but represents it. this is 3 dimensional space: a cube. so far, this can all be realised in a physcial situation, as you can take for example 12 pieces of uncooked spaghetti and put them into a cube. all the intersections will be at 90o. now once again, according to modern mathematics, you can draw a fourth line, which connects 2 cubes, a…

For the following picture: The description for the picture said: source: Cycle Detection (2011). Wikipedia.org Shouldn't the table read more like "2,0,6,3,1" under f(x)?

Our cell use DNA as information storage medium. This is not 2 bit 0 1 , but 4 bit A T G C code. This is very developed method, which has been tested 4.5 billion years from the beginning of the earth. What is the benefit of this 4 bit storage method?

You have the following series Would anyone know what is causing the series to turn out like this? Like if the first couple of memebers in the number series can represented as the following: [math]{a}_{0} = 354[/math] [math]{a}_{1} = 180[/math] Is there some sort of recursive relationship that would allow one to find the value for [math]{a}_{i}[/math]?

Hi, simple question I have here. I was wondering how you would go from the following expression: to this one: ?

I need to do mathematics and computer science , where can i start in preparation for my course.

If you have Netflix check out the DVD "Independent Lens: Between the Lines. "Filmmaker Vanessa Gould takes you on a provocative odyssey into the mesmerizing world of modern origami, where artist and scientests use the ancient art form to craft works of delicate beauty and to model cutting edge mathematical theoriesl Pushing the envelope to include caricatured portraits and elaborate abstract designs, these experts examine how paper folding can reveal the profound connention between art, science and philosophy." This film is done by professors. Unfortunately, it goes over information too fast and does not give an in depth explanation of the math and physics,…

How would you represent Love mathematically ..?

Hello! Im new here so and in a hurry so I don't know if I'm posting at the right place but anyway here's my pickle! I'm trying to isolate y in this equation: (y^2) - 4y +10 = P anyone care to hint me ? I tried decomposition but it was in vain heheheeeeeeeee THanks!

I am average at simple Calculus, simple Probability & Statistics, simple Geometry & Linear Algebra ... and I'm very good at Mathematical Logic, Discrete Tomography & Graph Theory, Algorithm I have two questions --"i know they sound silly", Q1: Am I good enough to try solving one of the Seven Millennium Prize Problems ? Q2: If I propose a Paper using a simple proof using the simple principles in mathematics, do I have to know everything about the complex systems built over the simple principles of mathematics ?

Please, what is the function to create a rate depending upon a collection of other rates, some of which may be zero? Using a spreadsheet, functions harmonic mean can be applied to a range of rates (percentages), but this function fails when any rate is zero (which is required). Any advice of an alternative function to harmonic mean please?

The total land area of all continents is 148,647,000 square kilometres (57,393,000 sq mi) Approximatley, how much would it take for one average human feces spread out on the ground would it take to cover the entire land area of all continents?