Mathematical Definition and 1000 Threads

Hey everyone If you want the concise version, skip over the bit in italics. First I'll quickly introduce myself. I am an undergraduate student, studying physics. I have been reading these forums for some time now (mostly just re-reading the stickies to be honest). In Australia, the first...

Hey everyone, This is a really strange question and I wasn't sure where to post it, but I need those who are well versed in physics and math to help with this. I recently started a new band and we came up with the symbol "1_" as our logo. We had a name, One Unknown, but we found out that it...

Hi, all Going to take the Intro to mathematical proof class this coming quarter. It says the prerequisite is Cal III and linear algebra. I have taken those prereq years ago and forgot most of the materials. I don't know if the Intro to mathematical proof class has a lot of materials from...

Most if not all laws of physics are not mathematical, rather statements that define the way mathematical models must follow. They have been laid down by intuition and observation. So how can something like string theory based on maths be expected to achieve a GUT or TOE if it does not know...

I am having trouble proving these. I cannot figure out how to get to the conclusion. Here is my attempt. The stuff in red is just side work and is not part of the proof. I always get stuck on these types of problems, can someone offer some tips on how to approach these kind of problems in...

My school is offering a advanced mathematical methods classes next semester, taught by a supposedly world-renowned professor. Everyone to whom I've spoken, students and faculty alike, says he's an amazing teacher who gives you a unique education. However, here is the course description: My...

Hi, Some times the starting point in MA confuses me, for example (\sum_{i=1}^ni)^2=\sum_{i=1}^ni^3 have we start with 2 or it is enough to show it when n=1 Thanks in advance.

Homework Statement Let X1, X2, ..., X9 be a random sample from a normal distribution, Xi~N(6,25), and denote by Xbar and S^2 the sample mean and sample variance. Use the standard statistical table for normal distribution. Homework Equations E[S^2] = δ^2 = 25 S^2 = (ƩXi^2 -...

I believe that I have discovered a mathematical formula related to trigonometry. It is used for finding the ratio of areas of triangles (not just similar triangles, but all kinds). I asked my Mathematics professor if any such formula for finding ratios exist. He said no. I also counter-checked...

Homework Statement "The propositions of mathematics work like this: we believe them first, and only later do we try to prove them."Homework Equations N/A The Attempt at a Solution I read it in some philosophy book but I'm not sure if it's true because I thought the propositions were not...

Hello, I am new to the forum and I have made an account to ask this one simple question. Am I good at math or not? I have been deciphering whether I am or not for some time now. It's like a pendulum, I can pathetically fail a math test but answer immense logic problems easily. I taught myself...

Homework Statement I'm writing up a mathematics-based assignment and I want to type some formula into a MS Word document. I'd appreciate if anyone could let me know how to go about this. Thank you. Homework Equations The Attempt at a Solution

Please point me a way to a mathematical project! Hello everybody, As a part of my Maths program I need to write an essay of about 25-30 pages. Game theory is the main topics and I now need a direction to analyse in game theory using mathematical method such as linear algebra. As I don't have...

Hello, I have been reading quite a bit about Tegmark's mathematical universe hypothesis. I realize that it is overly speculative in nature, or at least perceived that way. I am unsure if my question is better suited for the philosophy forum as it seems to me inherently unfalsifiable. Despite...

I am trying to create a mathematical model from a table of possible permutations. The table essentially consists of a list of various combinations of variables (there are 7 of them) and then an education guesstimate of how long that combination would take. Each variable is restricted to a...

A question I'm working on and my math book doesn't clarify the answer well enough for me to follow. I'm having some issues at getting the math symbols to work correctly so bare with me!Prove by mathematical induction that if A1, A2, ..., An and B are any n + 1 sets, then: Base step = n = 1 so...

Hi, I'm wondering how far one can go in learning graduate level real analysis or functional analysis with only background in undergraduate analysis 1 and 2 and none in algebra or topology? That is, is there any requirement or benefit to taking courses in algebra and topology to understand...

class. I did a lecture last semester on financial mathematics and stochastic processes. Know of any cool topics that I could lecture on?

Hello, I am having some doubts/problems regarding my abilities in math. I am a math major, currently at a junior standing. I have taken calc I & II, linear algebra, probability, history of mathematics and an introduction to proofs class thus far, and I am taking calc III, Differential...

Does anyone have any suggestions for a good book or two on mathematical neurology? Thanks.

Homework Statement Find a distribution g_n which satisfies g'_n(x) = \delta(x - n) - \delta(x + n) and use it to prove \lim_{n \to \infty} \frac{\sin{nx}}{\pi x} = \delta(x) Homework Equations Nothing relevant comes up at the moment. The Attempt at a Solution Well the first...

I was making a PCB drilling machine at home with my brother, and came across this mathematical? problem. I needed to fix the drill machine. But I needed to determine where should it be fixed so that I could drill largest possible PCB boards. In other words, find the value of x so that you...

It is easily derived from trigonometric identities that cos(2*pi*f1*t)+cos(2*pi*f2*t)=2cos(2*pi*(f2+f1)*t)*cos(2*pi*(abs(f2-f1)*t)) which proves that superposition of two cosine wave will generate a beat frequency, but what about about a universal proof that applies to any kind of...

After 1-2 years of writing formal math proofs in undergraduate school, I now speak and write much more eloquently than I used to. Now, before uttering or writing a statement, I take a quick pause to ask myself whether it's logically valid; it's unambiguous; it's relevant and sequentially...

I'm working on the following two proofs: 1.) (x+y)2n+1 = x2n+1 + y2n+1 if and only if x=0, y=0 or y=-x and 2.) (x+y)2n = x2n + y2n if and only if x=0 or y=0 I've tried using induction and get stuck at a certain point. I've also tried playing around with...

I have an idea of what to do and I have reached the stage but when i am at final stage- I am struggling to simplify as i simply don't understand (1/2)+(2/2^2) +(3/2^3)+...+ (n/2^n) = 2 - (n+2/2^n) so I have done p(k) and p(k+1) this gives me p(k) (1/2)+(2/2^2) +(3/2^3)+...+ (k/2^k)...

I have a question about development of mathematical matury. First off, I'm a high school senior with almost all my college general education credits due to dual enrollment in Florida. I have been doing independed study since 10th grade and have self-taught everything (computation) from...

People have written about mathematical creativity and the joy and beauty of mathematics. What about the sleazy underside of mathematics? Has anyone written essays about Mathematical Confusion? As I recall my teenage studies of mathematics, the most common experience was "getting stuck". I...

Dear Forum: I am a senior chemistry major that has the typical science/engineering background in math - 2 quarters of single variable calculus, 2 quarters of multivariable calculus and vector analysis, 1 quarter of linear algebra and 1 quarter of differential equations. I am currently...

prove by induction that, 1) a^(m+n) = a^m + a^n 2) (a^m)^n=a^(mn) 2. Homework Equations -- mathematical induction 3. The Attempt at a Solution the equations hold for a = 1. let's say the equation hold for a = s; then s^(m+n) = s^m + s^n now for a = s+1; (s+1)^(m+n) = (binomial expansion of...

I searched for topics on relevant past questions but I didn't find any, so I hope you guys can help me. I'd like to get some suggestions of good graduate programs (master degree) in mathematical physics or theoretical physics (and here I'm pushing the envelope a bit) with a focus on research...

Can the ideal pendulum, i.e. massless string etc., be explained using torque?

I have taken courses in math up to calculus 2, after which my math ambitions came to a quick hault. I would like to pick it back up and attempt to casually learn some math on my free time. So I would like to know the sequence/order of math concepts that someone would normally take at a given...

Homework Statement Show that it is possible to arrange the numbers 1, 2, ... n in a row so that the average of any two of these numbers never appears between them. [Hint: Show that it suffices to prove this fact when n is a power of 2. Then use mathematical induction to prove the result when n...

Homework Statement Suppose a and b are real numbers with 0 < b < a. Show that, if n is a positive integer, then a^n - b^n \leq na^{n-1}(a-b) Homework Equations The Attempt at a Solution I'm trying to show this by induction. Let P(n) be the proposition that a^n - b^n \leq na^{n-1}(a-b)...

Oyez! I'm an amateur philosopher and I'd like to start up an interesting debate. The topic will be mathematics (and, in general, everything) and how it is not logically possible to prove such a system. This is my informal argument: 1. Humans live in a "reality" governed by laws, axioms...

I've been looking for curriculum (e.g. classes needed) for mathematical/theoretical neuroscience but with no success. Math, physics, and neuroscience are some of my prime interests, but I have no idea on how to go about thinking if I should pursue theoretical neuroscience instead of theoretical...

consider a U shaped wire piece. a movable wire is fixed on it and their is liquid bubble in between them. If we move wire through distance l what force we need to apply surface tension basic formula is F=Sl. so it should Sl but it is 2Sl i cn't understand can you please help.

What are the equations from which all of GR can be derived? Obviously one of the equations is Einstein's Field Equation: G^{\alpha\beta}=8\pi T^{\alpha\beta}. I would also guess that you would need the Euler-Lagrange Equations: -\frac{d}{d\sigma}(\frac{\partial L}{\partial...

1. I don't understand how to prove this. for all n≥1, 10n - 1 is divisible by 9. 3. I've done the basis step. Now I'm on the inductive step. I'm using (10k+1-1)/9=1. I don't know where to go from there. Using algebra just gets me down to 10k+1= 10. And I really don't think that's...

Homework Statement For what values of K does the DE xy''-2xy'+(K-3x)y=0 (1) has a bounded solution in (0, \infty)?Homework Equations Not so sure, Frobenius method maybe.The Attempt at a Solution First, I check what happens when x tends to infinity. I see that the DE behaves like \phi ''-2 \phi...

What fields / disciplines of that field does mathematical visualization fall under. I know numerical computational geometry is one , where you wright algorithms to develop programs to visualize mathematics.

Homework Statement I must find the constant K such that y''-\left ( \frac{1}{4}+\frac{K}{x} \right )y=0 for x>0 has a non trivial solution that is worth 0 when x tends to 0 and when x tends to infinity.Homework Equations Frobenius method.The Attempt at a Solution I proposed a solution of the...

I'm studying the MUSIC algorithm in order to implement it in some project of mine, but I have some difficulties understanding the mathematical derivations done in the original Schmidt paper. For those of you who have access to this paper, I'll appreciate your time and help. The author begins...

Hello there. Can you please explain the following: Let us suppose that δ is very much less than r, and expand |r+δ|^-1 in powers of δ/r. Keeping the lower order terms gives: |r+δ|^-1 ≈ 1/r.(1-r.δ/r^2) + 1/2r [3(δ.r/r)^2-(δ/r)^2] How did they reach here? is this kind of a mathematical...

How do they differ from theoretical physicists? I was looking into arXiv papers in the mathematical physics portion and saw things like the physics of hoolahoops..I hope no offense is taken but I thought that was bit funny haha. On a more serious note, how are theoretical and mathematical...

Mathematics is supposed to abstract the essential features of a situation. I have yet to see this done for the common task of answering a question about mathematics posted to the forum. For questions of the form: "How do I do ... X ...?", I offer the following general general patterns...

Hello everybody, I am doing my reading lately to prepare for some exams to join a mathematics department. And I would very much like, if anyone could help, the solution (or a hint) to the following induction proof. " Show that n^3 + (n+1)^3 + (n+2)^3 is a multiple of 9 " :smile: I...

Anyone have any candidates, and yes i know its a broad term.

Hi everyone, I have been trying to do this induction question... but can't seem to understand how to do it. Prove by induction that, for all integers n is greater than or equal to 1, (n+1)(n+2)...(2n-1)2n = 2^n[1x3x...x(2n-1)] This is what someone else has given as the answer: For n...