Mathematical Definition and 1000 Threads

(Sorry if these are the wrong forums) All right, so, I know the difference between pure and applied mathematics as well as mathematical vs theoretical physics. But, I don't quite get the difference between mathematical physics and applied mathematics. Aren't they both working on mathematical...

1: If u: omega---> reals is a Von Neumann Morganstern Utiliy function and L is a lottery, prove that expectation E is "linear" ie: E(Au(L)+B)=AEu(L)+B2. Given none:The Attempt at a Solution : My attempt at a solution has gone nowhere. I found a stanford and princeton game theory notes that went...

Hi guys, I'm at the tail end of my BSc degree major in math, minor in physics and I am considering grad school in mathematical physics. I am looking for input on career prospects with a BSc in Math vs. MSc in Mathematical Physics. I am also wondering about entry level positions that one could...

Hi there, I am reading Chapter 9 of Jackson Classic Electrodynamics 3rd edition, and I don't see why this equality is true, it says "integrating by parts", but I still don't know... any help? http://imageshack.com/a/img673/9201/4WYcXs.png

Hi guys i need your help! How can i reduce this equation: (Nd-Na)*[B*sqrt((Nd-Na)^2) + n^2) - sqrt((Na-Nd)^2) + n^2)] into this: (B-1)*(Nd-Na) + (B+1)*sqrt(Nd-Na)^2) + n^2)? I'm totally depressed, I'm always stocked in sqrt part of the equation: if there's a techniques in dealing this kind...

Check out this collection of mathematics problems, published in 1991, by V.I. Arnol'd called "A Mathematical Trivium". Here's the link: http://www.math.upenn.edu/Arnold/Arnold-Trivium-1991.pdf Apparently, these problems are meant to be solvable by the end of your undergraduate (math) education...

Good Evening to everyone! I'm currently a student of theoretical physics. I have a Bachelor Degree in Physics and I'm from Italy. When you finish your B.D. you can choose to go on with your studies in order to get a Master Degree (other 2 years of study) and here you can choose your curricula...

This is occasioned by the thread https://www.physicsforums.com/threads/proof-multiplication-is-commutative.782057/ but being somewhat personal I thought the sometimes rather sobersided mods could find it out of place there. I was first interested by the proposition that (n + m) = (m + n) (1) -...

Is Our Mathematical Universe by Max Tegmark any good, as a work of popsci? Apparantly it's related to some TOE thing Tegmark's got, is that one actually something legitimate? (Edit: Sorry if this isn't appropriate for this forum!)

Author: Jonathan Lewin Title: An Interactive Introduction to Mathematical Analysis Amazon Link: https://www.amazon.com/dp/1107694043/?tag=pfamazon01-20

There is at least one story about mathematical discoveries caused my a misunderstood homework assignment, http://en.wikipedia.org/wiki/George_Dantzig . Are there any stories about mathematical discoveries caused by misprints?

There are different things in mathematics that are called space: Topological space, vector space, etc. Wikipedia defines space as below: And in the page related to the word "structure", algebraic structures are listed too. So why people never use the word "space" when talking about groups...

I have come about few mathematical problems related to Riemann Tensor analysis while learning General Relativity. Should I ask these questions in this section or in the homework section. They are pretty hard!

As some may know, I have been studying the Morris-Thorne wormhole metric for quite some time now. ds2= -c2dt2 + dl2 + (b2 + l2)(dθ2 + sin2(θ)d∅2) Now, from this space-time interval, it is easy to see how I would deduce the following metric tensor: g00= -1 g11 = 1 g22= (b2 + l2) g33= (b2 +...

Just a quick question. I've recently thought about the various equations I'm learning about calculating velocity or vertical motion and have wondered that sense these equations are using Gravity as a constant force (9.8m/s^2) Is it not true that Einsteins' theory would denounce this idea and...

When studying the motion of particles in space, what are the mathematical considerations that have to made of spacetime? Could I say there exists a bijection between spacetime and ##\mathbb{R}^4##? Is the topology under consideration the usual product topology of ##\mathbb{R}^4##? Are there any...

Hello all, this is my first post here, so please excuse me if there are any mistakes or important information is left omitted. Now, my problem is quite intricate and specific so I will be thankful for any information I can get. Using Excel, I am looking to model the volume flow of air through...

Ok, so I don't doubt that this discussion has been had on these forums hundreds of times, but I want to take part in it rather than just read old threads, so here is the (admittedly trite) question: do you think that mathematical truths are discovered or are they merely invented?

One of the advantages of not all speaking the same language is that a great, dead but legendary mathematician might still author a book. It's only recently translated, apparently: https://www.amazon.com/dp/1470417014/?tag=pfamazon01-20

Hello, I was wondering what mathematical skills I would need to have in order to grasp classical mechanics as a whole; Newtonian, Lagrangian and Hamiltonian. I already have a small understanding of some classical concepts; such as motion in a two dimensional space (circular/arc motion...

Hello everyone! I am having difficulties interpreting mathematical phenomenons visually speaking. I am trying to create an image in my head to explain how the mathematics works, for example, I have tried explaining the term brightness with close results but still flaws. So how do you become...

Ok so i got step (a) and found that $\int_{0}^{\infty} \,d (x^0)*e^(-ax)dx=1/a$ But i do not get how i should go about starting the next steps using the info from the first step(have not done a similar problem before so i need to get a grasp on the method)

Homework Statement Draw out the game tree for tic-tac-toe Homework EquationsThe Attempt at a Solution I'm just thinking about it and I don't know how to start. To draw out the entire gametree, we'd have thousands and thousands of branches. So based on symmetry there is only 3 starting points...

Currently, I am a graduate student specializing in algebraic geometry. On the other hand, I have also become extremely interested in the mathematical physics. However, I am not sure what steps I should take to get to the modern frontiers of mathematical physics research. My mathematical...

I want to write to theory about math but I don't have enough information about writing process.What can I do to write correct theory or article. I use theory and article in same meanings. Example a physicist makes experiments to proof his theory.Whats a mathematician do to...

Which one of these statements is true? $$ \exists y >0 : \forall x > 0, y < x $$ or $$ \forall x > 0 \exists y > 0 : y < x $$I think the second statement is correct, since for all x greater than 0, there exists at least one value of y > 0 such that y <x. The first statement doesn't really...

It is seen that interlamellar spacing in pearlite becomes finer by increasing rate of cooling. theoretically this is because the rapid cooling rate produces more nucleation sites for lamella percipitation. so i tried to create a mathematical model using gibbs free energy change during...

Hello, I'm currently going through Agrawal's book 'Nonlinear Fiber Optics' and got stuck with some mathematical cosmetics (pp. 40). It is the substition of: \vec{P_L}(\vec{r},t) = \frac{1}{2} \hat{x} \left(P_L \exp{(-i \omega_0 t)} + c.c.\right) into \vec{P_L}(\vec{r},t) = \epsilon_0...

I am looking for the mathematical description of Hilbertspace. I am talking about a mathematical description not something like Hilbert space is a infinite or finite dimensional vector space commonly used in QM, it was named after David Hilbert a german mathematician...I know this is a very...

I was studying Dirac delta function, when I ran across this statement: The Dirac delta function is defined by: $$\delta(x) = lim _{K \to \infty } d_K(x), $$ where $$ d_K(x) = \int_{-K/2}^{K/2} \frac{dk}{2\pi} e^{ikx}$$ I was thinking that as $$K\to \infty$$ the integral won't be defined...

Does anybody know of a good Introduction to the mathematics of astronomy or astrophysics?

we all know that a tensor has a symmetric part and anti-symmetric part and the anti-symmetric product (of the anti-symmetric part) called [wedge product] in pic.(2). then what is the name of the product the represents the symmetric part of a tensor in pic.(1) ?

In the previous version of PF, there was some sort of list from which one can select mathematical symbols (for the LaTex layman). However, I can't seem to find this option in PF 4.0. Can someone please tell me where it got moved to (if not deleted)? This feature was extremely helpful and...

i was just thinking over line that my teacher told - "Newton's second law is ultimate truth" i feel why one can say 'F=ma' is more prestigious th 'work energy method' Though i know they are one and same thing, i was planning to derive (using principle of reverse engineering) second law of...

Hi Guys, Can anyone provide links, books which explain the mathematical background of the field theory that explains the current accepted ^CDM model of the universe? Thanks Adarsh

If the bulk universe is infinite (IF it is), would mathematical physics have trouble describing it because infinity is not a number?

I've noticed that the vast majority of named or important mathematical constants, are what you might call small numbers. Their modulus lies very often in the range [0,5]. Here's two examples of tables: http://en.wikipedia.org/wiki/Mathematical_constant#Table_of_selected_mathematical_constants...

Hello, I need to prove the following: \sum_{i=0}^n\binom{n}{i} = 2^n by using something called mathematical induction. I understand, somewhat, what it is - we propose a statement and show that is true for n=1, then we assume that the statement is true for all n \in \mathbb{N}, which should also...

why the metric tensor is the dot product of two basis (co-variants or contra-variants) if it's a tensor then the metric tensor should be written as the tensor product of two basis (basis of a vector) >>> why ?!

Sometimes people ask a question and when I answer them in terms of equations, they say they want the physical reason, the real reason.. 1- Do you think there is a distinction between physical and mathematical reasons? 2- If your answer to the last question was yes, explain the distinction! if...

A theorem in mathematics can be beautiful in a lot of different ways. The result can be surprising or satisfying. Or perhaps the proof is very elegant and beautiful. Or maybe the theorem nice because it can be applied to other mathematics, or physics or engineering, or anything. So give here...

I'm not sure if I'm posting in the right subforum because there is one about proofs, but it requires the question not to be homework-like, but I also need an explanation... Homework Statement Prove by mathematical induction: Let m be the smallest element of A\subseteq\mathbb{N}. If A...

hello every body. may i know what is the difference between geometric product and tensor product ?

Can you help me with this exercise? 1^{1}+2^{2}+3^{3}+4^{4}+...+n^{n} = n^{n+1} Thanks! PD. I was trying to solve, and i have this: 1^{1}=1^{1+1} = 1 = 1 a) k^{k+1} b) k+1^{k+1} = k+1^{(k+1)+1} a in b) k^{k+1} + k+1^{k+1} = k+1^{(k+1)+1}...

I have gone through a mathematical modelling of a mass spring dashpot system in which if substitute differently we get different transfer functions. How does this really happen as we say Transfer function of a system is unique.

Hello, it is said that maths is the language of science, specifically physics. I am posting to ask which areas of mathematics are used in sections of physics. In a months time I will be studying: Solid state physics Thermal and statistical physics Maxwells equations, relativity and optics...

In mathematics, what is the name (type) for a curve given by velocity and time dilation? Specifically, I want to find a name for the curve y=1/(1-x^2)^{1/2} This curve is derived from the equation of a unit circle (x-a)^2+(y-b)^2=r^2 where y=(1-x^2)^{1/2}

Hello, I believe I presented myself before, but correct me if I'm wrong. I'm a math/physics major at a community college. I'm going to transfer to an university for spring. However, I don't know if I should major in astrophysics, Math, or Math/Astrophysics. I want to go to graduate school to...

Hello, How is it perceived the "Mathematical universe hypothesis" from Max Tegmark, in the scientific community ? Thank Patrick

Homework Statement Find the error in the following proof that \all horses are the same color" 4. Claim: In any set of h horses, all horses are the same color. Proof: By induction on ##h##: Base Case: For ##h = 1##. In any set containing just one horse, all horses are clearly the same color...