Mathematical Definition and 1000 Threads

Homework Statement * note that I meant fields in the abstract mathematical sense, notphysical (i.e. electric) fields! * Finding the determinant of a matrix in GF(28) I want to know if it is using mod 256 or mod 255 in the field of GF(28) Homework Equations Just math The...

Hi I'm a high school student. I gave a proof for the following theorem, but I was told by some professors that this is trivial and using natural induction twice for the rationals will do the same thing. What do you think? Is it just redundant? Theorem: Let P(r) be a statement about r...

Hi, I am looking to get some good information sources on modelling nuclear power in power plants and related fields. Anyone got any good starting points ? P.S. I am a biomedical engineer looking into different fields.

Homework Statement Prove that H1 +H2 +...+Hn = (n +1)(Hn-n)? Homework Equations Hn denotes the nth harmonic number. The nth harmonic number is the sum of 1+1/2+...1/n, which is n / n +1. I'm not really sure if Hn = (1/ n) . Prove by Mathematical Induction Hn denotes the...

I'd like to get better at writing mathematical statements using logical symbols. Let's start out with something simple. "For every A with property x, there's a B with property y". How should I write that? I don't even know if there's a symbol for "with property". How about this? \forall...

Homework Statement Suppose r and s are two positive real numbers. Let Dr and Ds be defined as in part 3 of Example 4.3.1. What is D_r \circ D_s? Justify your answer with a proof. (Hint: In your proof, you may find it helpful to use the triangle inequality.) Homework Equations Example 4.3.1...

Homework Statement I originally made this thread for something else, but I have another problem that I need help with. Suppose a and b are nonzero real numbers. Prove that if a < 1/a < b < 1/b then a < -1. Homework Equations A hint was given for the problem: Assume a < 1/a < b <...

http://rjlipton.wordpress.com/2009/12/26/mathematical-embarrassments/: i didn't think the invariant subspace problem would be an embarrassment. i guess it's not all that hard for finite dimensions. only one person mentioned goldbach's conjecture, & nobody said anything about perfect numbers...

I don't know where to post this message, excuse me. I am taking the course "Matmematical Methods for Physicists." And my textbook is by Arfken. I wonder anyone here knows online sources that I might benefit for studying. I am in lack for good sources please help.

For another BRS thread, I looked up some information at http://www.genealogy.ams.org/ and was completely sidetracked by my attempt to look up the genealogies of my undergraduate mentors :smile: Seriously, physics needs a tool like this, because it really does give amazing insight into the...

I'm a sophomore in math.I intend to learn mathematical and physics something like differential geometry,topology and QFT in my next years and do some research in some relative topics.I know I need to learn many courses and I feel I don't have enough time.This semester we open a course called...

Hi, I need to translate some conditions/statements into mathematical notation but my mind is drawing blank right now. There are a set of processes p={1,2,...n} and a class of resources r={a,b,...x}. 1 set of resources must be assigned to each existing process (e.g. resource a is...

I am have trouble with a question, and how exactly each given part of this question relates to getting the answer. [b]1. The problemb] Assume that N,X1, X2...are independent. Let P(N = k) = qk-1p , k\geq1, p+q = 1 and let X1,X2,X3,...be iid with a common pdf f(x)...

Hello, In this problem I am trying to Determine the exact set of natural numbers n for which the inequality 2^n>=(n+1)^2 holds. (equation (1)) I have already dealt with the base case where n=6, (since the inequality does not hold for n<6), and so (1) holds for n=k, and I need to show that it...

Homework Statement \forall n \in Z^+, \sum_{i=1}^n \frac{\sqrt{i+1}}{2i} > \frac{\sqrt{n}}{2} Homework Equations I have to prove the above via mathematical induction. The Attempt at a Solution I did the base case, n = 1 and found it true for the base case. Then I assumed that...

I spent quite a lot of time trying to figure out this question that I read in a book. Through trial and error, I got a rough idea of what the solution should be like but can't figure out how I would derive it mathematically. Can anyone give me some directions? :) QUESTION: n people stand...

Hello. I was wondering if anyone here could recommend a book on analog electronics that doesn't shy away from the math, but isn't too advanced for my level (electronics-wise, not math-wise). For reference, I've gone through Floyd's Electronics Fundamentals (although I don't necessarily...

-------------------------------------------------------------------------------- 1. Homework Statement Let H be a ten- element set of potive integers ranged from 1 to 99. Prove that H has two disjoint subsets A and B so that the sum of the elements of A is equal to the sum of the elements of B.

In Eq 11.72 in the QFT text by Peskin, the following equality is stated: i\int\frac{d^{d}k_{E}}{(2\pi)^{d}}\log(k_{E}^{2}+m^{2})=-i\frac{\partial}{\partial\alpha}\int\frac{d^{d}k_{E}}{(2\pi)^{d}}\frac{1}{(k_{E}^{2}+m^{2})^{\alpha}}|_{\alpha=0} This suggests that...

Homework Statement Let H be a ten- element set of potive integers ranged from 1 to 99. Prove that H has two disjoint subsets A and B so that the sum of the elements of A is equal to the sum of the elements of B.

Homework Statement I am writing a report for an Iodine clock lab, the questions I am having trouble with are: 1.What mathematical relationship exists between reaction rate and reaction time? 2.What mathematical relationship exists between concentration and reaction time? 3.What mathematical...

I'm a junior physics major at a school in the US and I've recently come to the conclusion that I think that I like math better than I like physics. I'm thinking I might like to do mathematical physics in grad school, but since I've spent the last 3 years thinking I'd go to grad school for...

Homework Statement There's a radioactive isotope placed inside an iron sphere (R=2cm), which acts as a source of constant heat (P=1W). The isotope is uniformly distributed over a very thin spherical layer (r=1cm). How much higher is temperature in the center of the sphere compared to...

Can someone please inform me what are the formal mathematical tools used in QFT? I plan to learn the maths beforehand or in parallel with QFT in the summer, and I don't like how physicists treat maths so that's it.

Is it possible to convert the statement 'Nothing matters' to a formula? Thanks in advance.

How to write "this per that" in mathematical terms? What is the mathematical equivalent of saying, for example, meters per second? If we want to say that something moves with the rate of 50 meters per 30 seconds--do we write this as a fraction or as an equation, or we can write as both? I...

Homework Statement The Fibonacci numbers are defined by f(1)=1, f(2)=1 and for n>2, by f(n) = f(n-2) + f(n-1). Prove by mathematical induction that f(3n) is even for all natural numbers n. Proof: Base case: (n=1) f(3) = f(2)+f(1) =1+1 =2 is even Induction hypothesis: (suppose the...

This is not homework, per se, but I have recently started reading Courant and Robbins' What is Mathematics? Homework Statement Prove by mathematical induction. (1+q)(1+q2)(1+q4) ... (1+q2n) = (1-q2n+1) / (1-q) Homework Equations Only the problem itself.The Attempt at a Solution Using the...

I want to write a program that can do algebraic transformations and mathematical deduction for me. It's not meant to do anything by itself, but rather check the transformations that I do myself for validity. The set of rule I will specify in advance. I want to capture all/most of the...

Hi, First of all, Happy new year to you all, I hope you enjoyed it as much as I did :), but its back to work for me now :(. I am an electronics Student and doing a project about control systems to control a vertical jet stream of air coming out of a pipe. My basic setup is a motor that...

Hey all, I will soon be graduating with a MSc in Transportation Engineering. I'm currently writing my thesis, and probably by May 2010 will be done. However, I am unsure I am willing to go for a PhD, at least not in this field. During my time in my Master, I found out I can only do...

Hi, I am just finished my Calc II class and a programming class and I am trying to write a computer graphics shader... My goal is to model this scenario: "Imagine a brick wall standing on a plane --- a shadow will be cast depending on the light source" ---my goal is to model the dispersion of...

Well, if we consider the universe as a closed, isolated system, then the law of conservation of momentum should kick in. P = MV We know that Hubble's law states that the velocity of bodies on an astronomical scale is increasing and P is a constant, so that means M must be decreasing...

I didn't know that students who think aloud while solving math problem solve faster and have more possibility of finding right solution. Can’t solve a mathematical problem? Just talk aloud and see your troubles disappear, suggests a new study Your thoughts, please.

Homework Statement Prove by matematical induction that (2^(n+1)+9(13^n)) divides by by 11 for all positive intergers Homework Equations The Attempt at a Solution I really have no idea where to start...

Hopefully you don't mind me saying this, I get the impression PhysicsForums is trying to tell me to turn my mind into a vegetable because all thoughts/feelings are automatically found in a book no matter what and so you have to purge all your feelings. I wonder if coming up with some...

I have a question for those who are cognisant with the study of economics. I've heard in economic classes they teach all sorts of mathematical models to describe/predict all the "laws" in the field, or at least approximations. I'm trying to hunt down the popular and useful economics...

I decided to take a math course based solely on proofs, no such courses are in my undergrad requirements and i thought it would be interesting experience. It seems like physicists have a working knowledge of mathematics rather than a really deep knowledge of it. I realized this after trying...

Homework Statement I derived this problem from back when I used to play Evony. I do not endorse this game whatsoever, and I think it has made enough of a mockery for itself with its plentiful supply of false and explicit advertisements such that I don't need to add to its shame. Anyway, my...

Homework Statement Is mathematical induction a deductive or inductive argument? Would appreciate the help. Thanks. Jeremy Homework Equations The Attempt at a Solution Its name suggests that the process is inductive, yet I know all of mathematics depends on deductive reasoning...

I'm looking for something like Arnold's "Mathematical Methods of Classical Mechanics" that applies to electrodynamics/SR/GR. I'd prefer it exterior calculus based. So far, I'm leaning towards Thirring: https://www.amazon.com/dp/0387406158/?tag=pfamazon01-20 Anyone know anything about...

i'm on first year of physics studies, but i got a little dilemma - do i want to be a mathematician, or phycist? I'm thinking about being theoretical physicist - but at the moment - math is much much more interesting to me than physics. I think that may change when i'll start to learn about...

Hi everyone. Little bit of my background: Im currently studying mathematics in the third year at university (or maybe you call it college in your country), and I have two more years left. I feel that I have affinity for physics and maths, and it is something I really want to master. My...

Although I haven't been too much into math in the past, with the exception of statistics being a college minor, all of a sudden I have an interest in coming up with mathematical equations to describe/predict how certain things work. I want to take data sets and come up with equations to...

Let's say all things are known in the Universe and magic doesn't exist, then: K is the set of all things known and Magic, M, doesn't exist. M \notin {K} Let {\neg K} be all things not known. {\neg K} \notin {K} Since Magic can not be defined by {K} Then M \in {\neg K} by...

Hi, I am wondering if anyone knows of a comprehensive book with tips/tricks/examples for manipulating various expressions. Things such as changing summation indices, \sum_{i,j,k=1}^{n}|a_{ik}b_{kj}|<=(\sum_{i,k=1}^{n}|a_{ik}|)^2(\sum_{j,m=1}^{n}|b_{mj}|)^2 or common(and not so common)...

Mathematical logic-- need some suggestion I'm planning to start self-study of mathematical logic and axiomatic set theory. In fact I have already started and but facing a lot of problems to grasp the conception and formalism used there. After studying Hilbert's program and Godel 's...

Do physicists know about mathematical undecidability? And do they believe it might play a part in Nature? Foundations of The Quantum Logic: http://steviefaulkner.wordpress.com/

Hi to all, Let A^{ik} be an antisymmetric tensor of rank 2; Why is A^{*ik}=1/2e ^{iklm}A_{lm} defined its dual? e^{iklm} is the completely antisymmetric unit tensor. Furthermore, e^{iklm} is a pseutotensor, what does it mean? Conversely, why the product e^{iklm} e_{prst} is a true tensor...

Greetings, I am a mathematics masters student applying for a PhD program in mathematics. I have a strong interest in mathematical physics. My credentials would not allow me to go to a top-rated math PhD program, so I'd have to settle for a second- or third-rate program. My question is...