Mathematical Definition and 1000 Threads

Let's say that a treatment A has been proven to have an impact on the levels of B with a given confidence interval. Let's also say that we know that the treatment C causes the treatment A to be imposed on our sample. Before the testing on the effects of C has been done, which statistical models...

According to GR is space actually supposed to be bending around mass, or is the concept of "curvature" just abstract and purely mathematical idea?

[FONT=Helvetica]Suppose we want to prove that: 1/2 * 3/4 ... 2n-1/2n < 1/sqrt(3n) [FONT=Helvetica]for all positive integers. [FONT=Helvetica](a) Show that if we try to prove this inequality using mathematical induction, the basis step works, but [FONT=Helvetica]the inductive step...

I found myself having a hard time choosing what mathematical physics text should I stick with. I'd like to think of myself as mathematically inclined, and I would really prefer a mathematical physics book that emphasizes 'the maths' and the proofs and not just the methods while maintaining its...

Where does one attain the skill/ability (skill vs. ability is a good question in itself) to do proofs? By "do proofs" I mean prove existing theorems. For instance I am really no good with ε-δ proofs. The concept is so easy, but when I have to prove something using ε-δ I either have no idea what...

I am attempting to improve a spreadsheet I created back in uni some 5-6 years ago, which models all the velocities and accelerations of the pistons and rods, as well calculating pressure, temperature and resulting torque. It is only a simple model so far, originally it started simply by...

I wish to know why and how does hysteresis occur from a purely mathematical perspective, using analytical functions and multivariable calculus. Thank you!

Homework Statement Prove the following LEMMA: For every proposition A[P_{1}, \dots, P_{n}] and any two interpretations v and v', if v(P_{i})=v'(P_{i}) for all i=1, \dots,n, then v^{*}(A)=v'^{*}(A). Homework Equations The Attempt at a Solution Sure this is obviously an...

Hi, I have read on a website that the refractive index of glass is related to the number of electrons it has per unit volume. I don't recall which website it was, but is it true? & if so what is the quantitative description behind it? or is it a lot more complicated :) Many thanks for...

Homework Statement Prove that for all n>1, P(n) :1 + 1/2 + 1/3 +...+1/n = k/m where k is an odd number an m is an even number.Homework Equations The Attempt at a Solution 1)Base Case n =2 P(2) = k/m 3/2 = k/m which is true. 2) Inductive Step Assume P(n) is true for some arbitrary n. 3)...

Hi could you please help me out with a formula? So imagine this abstract cylinder and a piston moving in it , I have let's say an x amount of gas in it and all the other parameters like stroke diameter and so on , by what formula could I calculate the pressure that the gas will have when the...

What branches of mathematical logic are there? I've taken formal logic (that is, the logic where one has various operators, like conjunction, disjunction, etc). What other fields of logic should I take to become better at mathematical logic? Which fields of logic are the most useful and essential?

I graduated high school nine years ago. The highest math I took then was Algebra II, as I had little interest then. After a seven year career, I was able to go back to school and have made it to Calculus I this semester. I struggled some in college algebra, finding out that there were...

what is a mathematical methods in physics book that you all would recommend? I need One that shows enough steps, explains clearly, etc. At ASU, my mathematical methods in phyiscs book covers the following topics with excruciatingly little detail and cryptic wording/notation, skipping so many...

Homework Statement show n3 + n < 3n for all n >= 4 Homework Equations The Attempt at a Solution I.H : n3 + n < n for all n >= 4 3(n3 + n) < 3(3n) then (3n+1) = 3 x 3 n > 3((n3) + n ) by I.H...

I was wondering where the best place to study logic at postgraduate level in the UK. As far as I know it's Manchester but I could be wrong? Thanks for any help

Hi, I'm unsure if I'm posting this in the correct place, so apologies in advance if not. I looked at the study board, but the post template doesn't apply to my question. I'm a layperson who had previously only read popular science books on QM, but has recently been watching some more...

Hello, everyone. I understand the Standard Model and all of its quarks, leptons and bosons, but could someone show me the equation and simply explain it? I haven't been able to find it or an explanation of how it relates to the graphical representation of the Standard Model. Thanks in advance!

Homework Statement I am working on a mathematical induction problem, where I need to prove: (1 - (-7) ^ (k + 2)) / 4Homework Equations (1 - (-7) ^ (k + 1)) / 4 + 2(-7) ^ (k + 1) The Attempt at a Solution So I just need to add the two items in section two above. Now I know I need a common...

Hello I'm reading my old notes of QM, I found the definition of Pauli vector, as follow \vec{\sigma}=\sigma_1 e_x+\sigma_2e_y + \sigma_3 e_z Where e_x. e_y and e_z are unit vectors. So, here is my question. \sigma_i and e_i are elements of different nature. How can we define the product...

Homework Statement Use mathematical induction to prove the following statements are true for n≥1 a) 1^2+3^2+5^2+...+(2n-1)^2= [n(4n-1)]/3 Homework Equations The Attempt at a Solution Attempt at showing for n+1 is true: n[4(n+1-1)]/3+ 2[k+1-1)^2

hello! I think it would help a lot to visualize mathematical terms I would like to see the graphs of various f(x), then their f'(x), their f''(x), in order to understand what derivatives mean example: http://en.wikipedia.org/wiki/File:Graph_of_sliding_derivative_line.gif same with...

Homework Statement Let F: N->N be defined by f(1)=1 and f(2)=2 and f(n+2)=1/2(f(n+1)+f(n)) Use Theorem 1.3 to prove that 1<=f(n)<=2 for all n in N Homework Equations For each n in N let P(n) be a statement about the positive integer n. If a) P(1) is true, and b) for k>1, P(k) is...

Homework Statement See the attachment Once you read the question (attached) you'll notice that there are two different parts of the question, the first one asks to find the combined velocity of the system after collision while the 2nd one uses the result of the first part and states to find...

what is mathematical induction? explain with an example.

hello! is there a complete list of mathematical notations? thanks!

Can anybody provide some resources (books, websites etc. - preferably websites or course notes) for a (somewhat rigorous) introduction to Mathematical Finance? Basically, I want to have the background to understand stuff like this http://www3.stat.sinica.edu.tw/library/c_tec_rep/c-2002-10.pdf...

I am having a problem understanding the mathematical reasoning of finding the description of image in convex mirror... We know the relation, 1/v + 1/u =1/f is true for all mirrors... we can prove this for both concave and convex mirrors... In case of convex mirrors we use the conventional...

I'm a little confused about certain assumptions usually made in GR as to how rigorous they are mathematically speaking. For instance the assumption generally presented without proof that GR spacetime manifold is a Hausdorff space seems not to be warranted given the fact that pseudometric spaces...

Hi, as we know a density operator \rho is defined to be a non-negative definite operator of trace class (with trace 1). We also know that for a given observable A, which is a (possibly unbounded) self-adjoint operator, the expectation value can be calculated as \operatorname{tr}(A \cdot...

I've recently gotten into Mathematics more and more, and I wanted to do some mathematical modeling just to see where I stand on it and maybe try to get better at it. I've looked around as well as I could, and I didn't really find much, so I was wondering if anyone here knew of any good...

So I did QFT at university and didn't feel that I really understood what was being done. We just did some calculations, heuristic guesswork and dwelled on phenomenology. I want to do it the way I personally understand things best: by learning the mathematics in detail, almost at the level of a...

I am currently reading the book on quantum mechanics by N.Zettili. It's really a good book but has a lot of mathematical stuff which I am not able to absorb. There's a whole chapter on mathematical tools but it is difficult to.understand. Can anyone suggest me book or text on mathematics as...

Hey guys, I am trying to understand the concept of mathematical moments (as defined in this wikipedia page: http://en.wikipedia.org/wiki/Moment_%28mathematics%29), as some work I am doing relates to them. I am looking for more information to read up but when I search maths moments I get...

Homework Statement Prove that \frac{1}{n}\sum_{i=1}^n x_i\geq {(\prod_{i=1}^n x_i)}^{1/n} for positive integers n and positive real numbers x_i Homework Equations There is also a hint. It states that it does not seem to be possible to prove it directly so you should prove it for n=2^m...

Prove that f(n) = 4^n + 6n - 1 is divisible by 9 for all positive integers of n. I've proved this by considering that f(k) is divisible by 9, i.e f(k) = 4^k + 6k -1 = 9m where m is some integer. Rearranging to give 4^k = 9m - 4k + 1 and then considering f(k+1) = 4^(k+1) + 6(k+1) - 1 then...

Some time ago I had a thought regarding turning rules in the US, back when right turn on (a) red (light - unless otherwise marked) was becoming universal. If U-turn was legal on the cross street, then by smoothing out a sequence of legal maneuvers: - left turn on red should be legal (right...

Hello everyone, i am just wondering if a mathematical physics honours degree would benefit me more if i am wanting to get into theoretical astrophysics or theoretical high energy physics afterwards for my graduate studies? Or should i just stick with a physics honours degree? i'm...

Hi I have a question regarding notation. I have a function f(x, y), which I would like to integrate as \int_{x>0,y<x\frac{1}{\sqrt{\pi}}+1}{f(x, y) dxdy} My question is very simple, and probably very silly: What there a notation which enables me to write the condition for the integral (x>0, y...

Hello everyone, I needed to know more about measure theory so I'm reading in Rudin's Principle's of Mathematical Analysis, somewhere in the chapter, he says: We let E denote the family of all elementary subsets of $R^p$... E is a ring, but not a $\sigma$-ring. According to my understanding of...

What kind of mathematical "order" is this? Disclaimer: Sorry if this question is off-topic, I really don't yet know where it "belongs". I wrote a program that counts the number of "1" bits in a 16-bit value. My program is brute force right now (loop 0 to 65535, shift each number and count...

For those who aren't familiar with it, http://en.wikipedia.org/wiki/Pascal's_Wager"]Pascal's[/PLAIN] Wager, in it's bluntest manifestation, is the idea that being religious (Christian or Muslim) is worth any finite cost, because the possible consequence (eternal damnation) of not being...

I hope this is in the right section, otherwise please move it. This might be a long post and I hope someone will give it a shot. It is about books but not really a comparison between them. I will give some background first, so you might skip to the end (- Books * -) if you are only interested in...

Hi, I'm currently taking Discrete Mathematics and I'm working on a mathematical induction problem that's a little different than usual because it has a summation in it. What I basically want to know is did I do parts A and C correctly? Homework Statement Homework Equations The Attempt at a...

What is the mathematical equation or algorithm for alignment of four points in cartesian coordinates (X & Y). Say, we have 4 nominal points (Xn & Yn), and another 4 measured points (Xm & Ym)?. After alignment, what are the new locations of the measured points (Xmn & Ymn)?.

I've got the attached paper... It's interesting, because it deal with an old complex problem is a seemingly simple form, and just using high school algebra. Check it out! Here is the attackment:

I want to now the answer of this question and I think it relates to mathematical induction. The question is: -Suppose is a natural number. In how many ways can we place numbers around a circle such that each number is a divisor of the sum of it's two adjacent numbers? Who can answer this...

Please I need to combine these three equations to be one, though they have different domains, what can I do? RxLevel = -0.87RxQual - 72 RxLevel = -0.013Dis - 58 RxLevel - -0.2MOP - 81 Where RxQual, Dis and MOP are variables

"Mathematical Proof That The Media is Sexist and Bad at Math" Here's is a link to my favorite comedy website: Cracked.com (The website itself may be NSFW, but this particular article doesn't get vulgar). I thought that this was an interesting article that points out what is too obvious for the...

I need to design a voltage doubler that takes in 115V-50Hz a.c. and produces a doubled voltage output of 230V dc. I am using this circuit: I need help in the mathematics part: i) How do I find the optimum value of capacitance? (Using high capacitance values reduces ripples; but can...