Mathematics

I have no clue how to do this one... let a= -1+i, b=-2-i, solve for z. b*=complex conjugate of b z-b*=Im(a^2/(2b+i))

Hello, I have a question about the change of radix, for example: Convert 1020304 base 10 into base 7: 1020304 / 7 = 145757 r 5 145757 / 7 = 20822 r 3 20822 / 7 = 2974 r 4 2974 / 7 = 424 r 6 424 / 7 = 60 r 4 60 / 7 = 8 r 4 8 / 7 = 1 r 1 1 / 7 = 0 r 1 => 11446435 There is a tip to divide a big number with a little number?, is posible with a simple calculator get the remainders from a divition like that?

Let's say we define a set [math]S[/math] in the following manner. [math] 0 < S_0 < 1 [/math] [math] S_n = (1-S_{n-1})^x[/math] If we take the example [math]S_0 = \frac{1}{2}[/math] and [math]x = 3[/math] then the set apears to not converge and to follow no set pateren, is this chaos?

I am interested in the ontological status of mathematical entities and statements, and the place for mathematics in a reductive, materialistic universe. The mathematician Kronecker is supposed to have said 'God gave us the integers, all else is the work of man.' Translated into a secular form, this statement is the claim that the integers are somehow part of the 'ultimate furniture' of the universe. However, when we see two chairs, we will find on closer inspection that they are in fact not the same. I think that however natural it may seem to do so, and however ubiquitously it is done amongst many animal species, grouping objects with 'family resemblances' into cate…

I have a funny problem here... Solve for X: (sinX)/X = 0.5

Anyone suggest a book that deals with (the sheaf of) distributions over a smooth manifold? I want to find out how this ties in with the n-point functions in QFT. Cheers in advance

I just glanced at the book Representation Theory: A First Course by William Fulton and in the book there is the symbol [math]\mathfrak{S}_{\lambda}[/math]. What does this symbol mean? [math]\mathfrak{S}_{d}[/math] means symmetric group but what does [math]\mathfrak{S}_{\lambda}[/math] mean?

Hi, does anybody know of an application of differential equations in any computer-related field? Note: Im not meaning to solve a diff. equation with a computer

I've just begun learning about category theory. I would love to share ideas with anyone else interested in the topic. Perhaps anyone can recommend some good learning material for it? I've started an introductory book on it, a rather small book of about 200-250 pages. I've finished the first section on general categories, subcategories, pre-categories, morphisms, and other things. I enjoy studying things at the most general level, like category theory, model theory, universal algebra, metamathematics; it intrigues me. I'm more of a generalist than a practitioner, and personally, being a man of pure ideas, I don't believe in anything merely because of its practical…

I'm currently reading this book called Set Theory and the Continuum Hypothesis, written by Paul Cohen, which is a model-theoretic investigation of the topics. I'm trying to rediscover the proof of Gödel's Completeness theorem for myself, but I'm kind of stuck on certain details of the proof provided in the book. In the preface, the author mentioned that he did not "polish up" the final draft of the book, so many important details are left out. Although it is written for people with little to no background in propositional logic, the book assumes that one has a background in abstract mathematics, namely in Model theory. I'm only an undergraduate student not yet knowled…

Let [math]X[/math] consist of four elements: [math]X= \{a, b, c, d\}[/math]. Which of the following collections of its subsets are topological structures in [math]X[/math]? [math]1. \emptyset , X, \{a\} , \{b\} , \{a, c\} , \{a, b, c\} , \{a, b\};[/math] [math]2. \emptyset , X, \{a\} , \{b\} , \{a, b\} , \{b, d\};[/math] [math]3. \emptyset , X, \{a, c, d\} , \{b, c, d\}?[/math] Are they all topological structures in X? If they are not, why are they not?

this forum is very good for mathematics.

If [math] f(x) = x^3 + x + 2[/math] and [math]f(a) = 9[/math] then: Calculate [math]f^{-1}(-5)[/math] at "a". This is the question that i'm thinking of it but i can't solve it at all! Does anyone know that how i can get to the answer?

I'm currently taking an online course in mathematics. One of the subjects is about interesting properties that come out of certain number series (or number patterns). Right off the bat, I'll spell out the purpose of this thread so you know where the OP is leading: I'm wondering if we can say that there's something "special" about these number series just because they bear certain interesting properties, or should we say (or prove) that there's always going to be interesting properties of any arbitrary number series no matter what it is? As an example of a number series for which an interesting property emerges, take the following: 1 + 3 = 4 1 + 3 + 5 = 9 1 +…

Hello. I understand that [math]\frac{d|x|}{dx}=\theta(x)-\theta(-x)[/math] and then [math]\frac{d^2|x|}{dx^2}=2\delta(x)[/math]. But i DONT UNDERSTAND why when [math]\phi[/math] is a angular coordinate, then [math]\frac{d^2|\phi|}{d\phi^2}=2(\delta(\phi)-\delta(\pi-\phi))[/math]

In algebraic topology there is something called a chain complex. http://en.wikipedia.org/wiki/Chain_complex My question is: Why is the composition of any two consecutive maps [math]d_n \cdot d_{n+1}[/math] equal zero?

there is correct the expresion [math]\int^{-\pi+\epsilon}_{\pi-\epsilon} d\theta[/math]....where [math]\theta[/math] is a angular coordinate between [math](-\pi,\pi)[/math]....¿what means this?... i believe that this mean that the angular coordinate theta runs from [math]\pi-\epsilon[/math] to [math]-\pi+\epsilon[/math] in the sense anti clock (figure)

hi, I was wondering why, in simpsons rule - for calculating the area of irregular shapes, there is a 4 in the formula. like so- A = h/3 (df + 4 * dm + dl)

Hi, Wondering if anyone could tell me how the cosine rule can be the way it is - how it works the way/like it does... Or give me a link to a good explaination for the nature of the rule.. Cheers

I'm not very familiar with checkers, and even less so with chess. But after I heard of polar coordinates (has to have been more than half a year ago now) and its nature of being analogous to rectangular ones... I imagined, would you be able to play a game that uses a rectangular-coordinate grid... whether chess, or checkers, or something else... on a polar-coordinate grid?

While using several operators(e.g.grad,div,curl) we often separate them and treat them as vectors in their own right,performing most algebraic and vector operation on them.How is this possible? are not operators and their operands inexorably linked together.In order to separate them we would need to define a whole set of specialized rules just to use them. This is not an isolated example several times while solving differential equations we replace the differential operator with a variable ,say 's'(and hence this technique in some areas gets its name as the s-operator method) (ref:http://en.wikibooks.org/wiki/Circuit_Theory/Second-Order_Solution)and proceed to manipulat…

how can i calculate the surface aria of a parabolic mirror

A few years ago, I had a math class, which I needed a TI-83 calculator, for. I don't have the class, anymore, but I bought the calculator, myself, so I still have it. However, of all the nifty features that the TI-83 has over traditional "pocket" calculators, it seems to lack a memory function! Pocket calculators allowed you to save a number to memory. You could also add and subtract from that memory. If you wanted to multiply the memory by something, there was a way to do that. This allowed you to use a commonly-recurring, but large number, without having to tediously punch in that same number over and over again. How do I do that, on a TI-83?

I saw meteorite men and thought about where abouts meteorites fall. Then i decided to figure out how often they fall near me. I just want to know if the math is right? Please correct what is wrong. It is all based on 2 numbers, Earths total square miles and total meteorites per year which are both rounded, so it's not perfect. If you can help i'd appreciate it. P.S. .0005 came from 58,000,000 devided by 29,000. Thanks again The attachment has the chart. Also the 61 years thing i know is wrong, forgot to delete that. meteotie chart.pdf

Hello, I've been reading a bit about Gödel's Incompleteness Theorem. On this video ( ) of a talk at Google, the speaker mentions that there are true statements that cannot be proven. My question is: how can a statement be true and not be proven, in other words, how can we be absolutely certain that it is true if we cannot prove it? Hope this is clear. Thank you, David