Mathematical Definition and 1000 Threads

Hi, I seem to remember there is a book by Steven Weinberg that gives the mathematical basis for tensor calculus for relativity, but the name escapes me. Anyone know what I'm talking about?

I'll be in my 4th year of a Pure Math degree next year, and I'm think of what courses to fill up my timetable with. I'll be taking an overload, so I'll be taking 6.0 credits worth of courses (3.0 per semester). I'm only required to take 3.0 more courses in Pure Math to get my degree, so I have...

Homework Statement Prove by Mathematical Induction that the assertion, n ∑ r^2 = n/6 (n+1)(2n+1) r=1 holds for every natural number n. Homework Equations Ok, so basically, how do you solve this question? I have got to the Induction step but I'm not sure how to do it...

I'm looking for an English translation of Lagrange's treatise "Reflections on the algebric solutions of equations" (Reflexions sur la Resolution Algebrique des Equations). I've searched the internet for it but haven't found anything about it yet. Where can I find such truly classic treatises?

I have always loved math and have done independent theorem-proving and research. However, I have had absolutely no olympiad training but it seems that the math olympiad is quite important in applying to universities. I have started to do some of the questions myself and find that I progress...

Hey all! For awhile, I have been looking for a .pdf version of a math notation sheet, similar to these sites: http://www.rapidtables.com/math/symbols/Basic_Math_Symbols.htm http://en.wikipedia.org/wiki/List_of_mathematical_symbols I like the way they have the notation in LaTeX, have a meaning...

Just as a little background, by the time summer comes around, I will have taken mathematics classes up to basic differential equations, multivariable calculus, linear algebra, and some probability theory. In Physics, I will have taken up to classical mechanics and mathematical physics. I want to...

Hey guys! Which research departments are best? I was hoping to get the top 3-4 institutions names. Basically I am into mathematical string theory and geometry/topology-physics in general.

Are physics laws (even the laws) mathematical models of reality? Or they describe reality as it is? Are those laws just models, like for example a population's growth mathematical model (just an example that I remembered)? A maths teacher told me that in physics everything are...

What are they, how are they visualized? Is it like how basic equations when plotted form a shape (e.g. circle) but much more complex? When I think of the those words, I think of some sort of weird/cool looking shape.

I'm going through the book: Principles of Quantum Mechanics 2nd edition by R. Shankar 1. In the mathematical introduction to projection operators (page 22), it writes: "Consider the expansion of an arbitrary ket |V\rangle in a basis: |V\rangle=\sum_{i}^{} |i\rangle\langle i|V\rangle"...

Homework Statement Okay, so I'm going to be completely honest, I am really bad at math, and I have been struggling the past couple of weeks in my Quantitative Reasoning class. I am so lost. I don't know if it's my teacher's teaching method or what, but nothing is clicking for me at the moment...

I'm not sure myself.

Though this question is about medicine, the actual question has little to do with medicine and more to do with modelling .. Homework Statement A patient is put on an intravenous drip at time t=0, the drip supplies a drug into the patients bloodstream at a constant rate λ. At the same time...

Hi all, Can someone help me understand how mathematical discoveries are evaluated? If a new finding is made, how do you know if it's significant or not? What differentiates the content of the prestigious journals from others? I can understand that solving problems that have been unsolved...

Looking for an interesting Mathematical problem "family" And what do I mean by that. All right, I think this was the most fitting category, I hope I'm not too off-topic. So I want to write a puzzle game, but, as everyone who loses his time playing puzzle flash games (like me), knows that you...

I didn't know where to post this question, but the general math forum seemed like the best idea. Newton's Laws are invariant with respect to the Galilean transformations. Maxwell's equations are invariant with respect to the Lorentz transformations. My question is, is it necessary...

Homework Statement I need to prove that for any real number r, if 0 < r < 1, then for all positive integers n and m, if n < m, then r^n > r^m. Homework Equations No calculus techniques are permitted, only mathematical induction. The Attempt at a Solution I know that any...

Hello, I would like to know about a good introductory book on mathematical logic. It should start from set theory , include ZFC axioms and also touch on Godel's theorems.

Mathematical Methods in the Physical Sciences (3rd edition) by Mary .L. Boas, Does this book has separate solution manual?

I am hoping to do mathematical or theoretical physics after my undergraduate science degree. I have been advised to do more maths subjects than physics subjects in order to achieve this. I am double majoring in maths and physics and I am just wondering what area of maths I should be focusing on...

Hello, I have a question about inductive reasoning... Earlier this week my intro proofs class went over the logical structure of induction, and an example. The example was a proof of \Sigmai = n*(n + 1)/2 My main issue is the assumption that "p(k)" is true. What if it's not? I asked this in...

Wondering if this is mathematically feasible.

I am currently a double major in biology and math, interested in mathematical modeling of ecosystems and physiological systems. The math portion involves modeling and pure math, but there isn't a lot of concentration on knowing physical laws. I'm not sure if I would miss all the knowledge...

I am having difficulty with students understanding mathematical proofs. Even if they do understand them in the class they cannot reproduce them in the final examination. Majority of the students avoid doing the proof questions and concentrate on the numerical or technique application of...

Please I need Mathematical Model of Processor and Mathematical Model of Hard Disk because i want to study thermal behavior to discover strategy for cooling it

I'm looking for something like a books filled with theorems not typically covered in textbooks. For example Viete's formulas for roots and coefficients of polynomials, which, strangely enough, I find useful. They speed up my computational speed and give interesting relationships between objects...

I have been self studying this book by Mary L.Boas for a while which is a treat to study for its great depth. However, the problem of mine is though I have been able to solve most of the problems of this book, there are some really tough Questions in this book which are very hard to solve. So...

Hi, I don't want to list the exact problem I have to solve, as I would rather do it myself, all I would like is some guidance. The problem is a function like: Pk+1=a (Pk-1) with a few more constants and some brackets thrown about on the right hand side. I need to find all the equilibrium...

Hi my school has these two courses: Specific mathematical methods used in advanced courses in physics. 233. Differential equations, vector differential and integral calculus. 234. Laplace transforms, Fourier analysis, complex analysis. There is no indication that 233 is a prereq for...

When we refer to terms in an equation, what EXACTLY are we referring to? Suppose for example we have: ab + bc + cd = A Suppose somebody refers to term "ab". Are they referring to the syntactical NAME "ab", the IMAGE of ab (i.e., it's value), or the ARGUMENT (a,b) which belongs to some...

Hi All, Just wanted to know, what is a good way to learn mathematical modeling? I'm a social scientist working with simulation and data, and would like approach the issue more formally. Before trying modeling textbooks, what should I know beyond calculus? Any suggestions (books, tutorials...

Homework Statement 62. In physics, it is important to use mathematical approximations. (a) Demonstrate that for small angles (<20°) tan a ~ sin a ~ a = (Pia'/180 degrees) where a is in radians and a' is in degrees. (b) Use a calculator to find the largest angle for which tan a may...

For anyone who has taken mathematical probability, what prerequisite(s) did you have? At my school, Calc IV is the only prerequisite. I ask because we are notorious about not having prerequisites lined up properly so I don't want to waste my time with this class if I don't have the proper...

I am finished with the first bachelor year at Computer Science and the next courses are: Assembly, Linear Algebra, Statistics, Java. Many people from my class said that they will not take Statistics as it's not that helpful to them and I was thinking of how accurate that is. Is Statistics...

How can I find people who are interested in correspondence on mathematics and are also around my age on the net? By correspondence I mean emails. I can't see many people interested in mathematics on popular social networks, or if there are, it's not possible to find them through searching...

Hey as part of my Physics undergrad in second year I have to take a module in either Mathematical Modelling or Linear Algebra (both course descriptions below) In first year I preferred Linear Algebra ( a very basic intro course) but apparently in second year its just all proof and no...

3^3 = [3^3 - 3^2] +[3^2 - 3^1] + [3^1 - 3^0] + 3^0 Practical Demonstration: 27 = [27-9] + [9-3] + [3-1] + 1 27 = 18 +6+2+1 27 = 27 Is this property discussed in theory of games?

I'm having a bit of trouble understanding why the principle of induction is included as one of Peano's axioms. It seems like it should not be independent of the others. Obviously it can be stated as: If a predicate P is true only of natural numbers, P(0) is true, and also P(n)\rightarrow...

"Scientific Thinking Graphing" -Determining the Mathematical Expression Homework Statement Ok, so I recently got an assignment for "Scientific Thinking Graphing Practice". Basically, I need to take a data table that will produce a curve shaped graph and turn it into a straight lined graph...

Is there a name for this series: 1/2 + 2/3 + 3/4 + 4/5 + 5/6 + 6/7 + 7/8 + 8/9 +...+ n/(n+1) Thanks.

It's NOT a homework. I'm self-studying Rudin's Analysis and I came to this part that I can't follow the argument after a certain point: statement: if x,y \in R, and x<y, then there exists a p \in Q such that x<p<y. Proof: since x<y, we have y-x>0, and the Archemedean property furnishes a...

Hi. I am learning mathematical induction on my own and I came across this problem: Homework Statement Prove: 1*4 + 4*7 + 7*10 + ... + (3n - 2)(3n + 1) = n(n + 1)²2. The attempt at a solution Quick test for n=1: (3 -2)(3 + 1) = 1(1 + 1)² 4 = 4 Alright, so I rewrite this with, on the left...

I have found that for a number of students doing proofs is an unnecessary evil. For some of them it is like a painful visit to the local dentist. I thought I had explained the need for proves but it still puts a number of students off. What motivating reasons can I give students for them to at...

Homework Statement I'm having trouble understanding the relationship between pressure, speed, and displacement to answer the following question correctly: While you are stopped at an intersection turn lane, a large truck zooms by, just a few feet from your car. As the truck passes, your car...

I want to basically have a dedicated machine for running scientific computation programs and be able to access it remotely anywhere using a laptop/netbook. That means I don’t care much about GUIs. I’m used to using Unix and am perfectly fine with doing everything through a command window. At the...

Homework Statement Here's the problem. Verify the operator identity x - d/dx = -exp (-x^2 / 2) d /dx exp (-x^2 / 2) Can someone please help me? Thanks :) Homework Equations The Attempt at a Solution

Hi a want to code implicite scheme for PDEs u_t =a laplace u + L p_t p_t = laplace p + u pls help I made a classical FEM discretization, but i don't know how to programe it. (u(n+1)ij - un)/t = a ((u(n+1)(i-1j) -2 u(n+1)(ij) +u(n+1)(i+1 j)) /x2 + (u(n+1)(i j-1)-2u(n+1)(ij) +...

Ok so on the roulette table the odds against winning on red or black are 1.111 to 1. This is about a 47% chance to win. Payout is 1 to 1. Say minimum bet is 1$ and bets are allowed in multiples of 1$. up to some limit. Suppose I want to win 1$ for every spin I play. I bet 1$, and I...

Homework Statement Prove that \frac{d}{dz}z^n = nz^{n-1}\;\;\; \forall n\in\mathbb{N} using the Product Rule for differentiation and mathematical induction. Homework Equations \frac{d}{dz} f(z) = \lim_{\Delta z\to 0} \frac{f(z+\Delta z) - f(z)}{\Delta z} \frac{d}{dz}[f(z)g(z)] = f\,'(z)g(z) +...