Mathematical Definition and 1000 Threads

Hello! First of all I have like 5 exercises I don't quite understand so will it be a problem if I create 5 new topics in the next 24h? Homework Statement Prove, by using mathematical induction that if x+1 \geq 0 then (1+x)^n \geq 1+nx. Homework Equations The Attempt at a Solution Basic step...

Is there any place on the Internet where I can pose questions on the text and get timely and reliable answers by those who are qualified enough? Besides the Harvey Mudd College, is there any other video lecture series on this text? Which is / are the most comprehensive and the most...

Hello, I am having trouble solving this problem. Maybe I'm just overreacting to it. In my two semesters in discrete math/combinatorics, I've never seen a problem like this (with two summations) and been asked to prove it. Can some one help? [SIZE="4"]\sum^{n}_{i=1} i^3 = \frac{n^2(n+1)^2}{4}...

I'm definitely messing up somewhere :P The Larmor Equation is \Delta H = \frac{2\mu}{\hbar Mc^2 e} \frac{\partial V(r_{ij})}{\partial r_{ij}} ( L \cdot S) I derived an equation stated as \nabla \times \vec{F}_{ij} \cdot \hat{n} = \nabla \times \frac{\partial V(r_{ij})}{\partial r_{ij}} How...

Im studying my bachelors degree in physics and math outside the UK, but inside the EU. I am just wondering how hard is it to get into this program? I probably could get funding from my home country so let's assume that money isn't a problem. If I get my bachelors with 1st class honors and...

Lack of Mathematical Ability I'm currently in Grade Nine (by the Canadian Education System) and enrolled in Tenth Grade mathematics, scoring top-marks. I've self-studied Algebra I-II, Trigonometry and Calculus I (not including integration). However, I've noticed when I participate in...

Hi, I was wondering if you can suggest good books on the techniques for mathematical proofs. I know this is quite a simple matter but I would be glad if you could suggest me with greats books for teaching proofs. More often than not I used the direct method and induction to prove problems in...

Homework Statement Hello! This is I want to prove using Mathematical Induction: 1+3+5+...+(2n-1)=n^2. The problem is: I don`t understand very much about Mathematical Induction :(Homework Equations The Attempt at a Solution Suppose n=1. Then 1=1. Now suppose 1+3+5+...+(2n)=(n+1)^2. Then...

In my chapter about electric fields in matter my book derives and expression for the potential due to the polarization of a dielectric material. For that you find that the polarization is equal to the potential of a collection of negative charges on the surface and positive charges inside the...

Hello. I would like to bring to discussion this paper called "Mathematical Foundations of the Relativistic Theory of Quantum Gravity", by Professor Fran de Aquino, from the Maranhao State University, in Brazil. The paper was published in the Pacific Journal of Science and Technology...

Hello Could anyone recommend a good introductory book for learning how to write mathematical proofs. Thank you.

Hi! I need some help here, please. In Principles of Mathematical Analysis, Rudin prove the uniqueness of the n-root on the real numbers. For doing so, he prove that both $y^n < 0$ and that $y^n > 0$ lead to a contradiction. In the first part of the proof, he chooses a value $h$ such...

Recently I went through a bunch of my old solution sets and realized that I've been quite sloppy with my use of punctuation; in particular, examining the quality of my writing in solution sets over a period time, it appears that the lack of proper punctuation is getting more and more pronounced...

Lately, I have been experiencing a sort of anxiety over not understanding some of these proofs in my calculus textbook. I just finished a calculus I course, and we did not spend any time learning them; so, I thought, since it is summer time now, I would go back over and try to learn those...

Homework Statement See attachment. f(t) is the input force and b1 and b2 are kinetic friction constants. There is no static friction. Homework Equations ƩF = m \ddot{x} F_s=kx F_f=b\dot{x} Ff is the force from friction and Fs is the force from spring. The Attempt at a Solution...

Homework Statement So I have to calculate the transmission of light, which goes through random black and "transparent" blocks (p=0.5), but the thickness (x) of each block is distributed exponentially dP/dx=1/t*exp(-x/t). When light goes through black block, it diminishes (I stands for...

Hello there I am sorry if this sounds silly or out dated i want to ask anyone, how can i model the mathematical representation from music signal(time domain). lets say i recorded the signal from guitar through my music production software and print screen that signal as shown here...

I'm not quite sure if my question belongs to this section or not, so I hope I would be posting it in the right place. Anyway, I have troubles understanding Rudin's principals of mathematical analysis. To me, everything he says, is absurd. I can't understand what he says, neither do I want to...

In a mathematical model, a gas is under a pressure of the form P=e-v2 (v is volume). Find the work (in Joules) done on the gas as its volume decreases from infinity to zero.

I've been trying to decide on a mathematical logic textbook to teach myself a bit. I'm taking a course on it next semester, but I have never had a logic course before (I've had some CS courses though and proof-y math courses). I'm also taking a modal logic course the semester after math logic...

I have become so annoyed by the lack of mathematical detail in the physics textbooks. For example, to study Foundations of Quantum Mechanics, I had to spend hours and hours doing background reading from books, the net and Wikipedia until I got my way aroung vectors spaces and its nooks and...

I've been curious for some time about the concept of super position. my introduction to the idea was through the schrodingers cat paradox, which i assume most know, so i will stick with this example. is it not correct to assume super position is a concept to resolve the perceptual limitations of...

Homework Statement I am asked to prove: 2n < (n+1)! , where n≥2 The Attempt at a Solution Base step: set n=2, then test 22 < (2+1)! 22 = 4 (2+1)!= 3! = 3(2)(1) = 6 so 4 < 6 , which is true. Induction hypothesis is 2k < (k+1)! Using this, prove 2(k+1) < [(k+1)+1]! = (k+2)! Attempt to...

http://abcnews.go.com/blogs/health/2012/04/27/real-beautiful-mind-accidental-genius-draws-complex-math-formulas-photos/Don't know if he really is a genius at math now, but at least he can draw some cool pictures. So who wants to hit me on the head?

I am currently exploring if whether or not a fourth dimension exists or can be drawn. According to my professor, I have to use mathematical induction. I know that 2^n is the equation and "n" equals the dimension. Therefore 2^1 is 2. The first dimension is a line with 2 terminal points...

Here is the question: Transverse waves on a string have a wave speed of 8.00 m/s, amplitude of 0.0700m, and a wavelength of 0.320m. The waves travel in the -x direction, and at t=0, the end of the string (x=0) has its maximum upward displacement. a)What is the frequency, period, and wave...

Does anyone know where i can score a site with lots of problems pertaining to electronics equipment. Trying to understand the basics (resistors now) and when i google it i just get tons of crap but no problems to solve. anyone? Thx :)

Homework Statement (1/2!)+(2/3!)+(3/4!)+...+(n/(n+1)!) a) calculate for a few small values of n. b) Make a conjecture about a formula for this expression c)Prove your conjecture by mathematical induction. Homework Equations The Attempt at a Solution So for the first part I just used values...

Hey. So I have decided that I want to try to produce a math blog. The blog would essencially just consist of interesting problems and proofs, as well as expository notes on stuff that I'm reading (the symmetric group and it's reprepresentation theory). However, I have found no useful information...

This is neither homework nor independent study, it was a brain teaser( or so you could call it) I found. A new mathematical operation has been implemented , call it # It is used within our knowledge of numbers( it operates with all sets of numbers) and works together with our known operations (...

Dear fellows, my undergrad was not in maths, but I have quite a chance of getting into a master's program in pure maths, later this year. Long story, not particularly interesting. My question is due to the fact that I am quite prepared to the examination (basic real analysis and linear...

Hey guys I am in precalculus right now and we just started picking up mathematical induction. Our teacher assigned us a problem that I am stumped over and I tried looking all over for a clear explanation online but I can't find anything remotely helpful. The question is: Use mathematical...

Homework Statement show that the roots of a polynomial with real coefficients are real of form complex conjugate pairs .The inverse is not true ,in general. Homework Equations The Attempt at a Solution

I am curious as to where this book falls in the hierarchy of mathematical education. Could it be used effectively before a calculus course? Is calculus necessary before analysis?

Hello, I`m working on a mathematical model of a gas turbine and I need good compressor maps, especially function of efficiency vs. pressure ratio, inlet temperature, mass flow etc I`ve been looking for this for few days, but can`t find anything interesting. Do you know where I can...

Homework Statement Homework Equations The Attempt at a Solution Basically the first part of the question asks to prove the binomial theorem through induction which I've done. I'm basically lost as to how to even attempt these questions, I'm not asking for answers as I need to know this...

1. Define a sequence of numbers in the following way: a[k]=a[k-1]+a[k-2]+a[k-3] for k≥3, s.t. a[0]=1, a[1]=2, a[2]=3, a[3]=6... *The numbers in brackets will be subscripts for the whole problem Prove that a[n]≤2^n using complete mathematical induction. This is what I have so far. We'll use...

Homework Statement Hello, I now have a real practical mathematical problem to ask I have 14 files with different sizes to be burnt on DVD discs. Each DVD disc is 4.7GB. How to arrange the files so as to minimize the use of discs? The file sizes of the 14 files are 1) 2.25GB...

Okay so after tearing my face off trying to find a 2-cycle, I've managed to make significant process. I divided an enormous polynomial with another polynomial and got a god awful mess which incidentally was correct. Now I'm having trouble solving this equation with x in terms of c...

Advice on a good "Mathematical Methods for Physicists" Book? Hope this is the right area to be posting it in. I've checked out Tai Chow's book with the same title from my school library. There was a pretty brutal Amazon review on it, but overall I find it helpful. Does anyone have...

Homework Statement The problem is: Show that an \rightarrow \infty iff for all \Delta > 0, \existsN such that n \geq N \Rightarrow an \rightarrow \infty Homework Equations Not sure if there are any The Attempt at a Solution I can't really think of anything to do here because I have...

One would assume that: $$t \propto h^\alpha m^\beta g^\gamma$$ Where t = time taken for object to fall, h = height dropped from, m = mass, g = acceleration due to gravity. By doing some dimensional analysis one can find that: $$t \propto h^\frac{1}{2} g^\frac{-1}{2}$$ and that t is...

Greetings, I am an enthusiastic undergraduate university student in physics. In order to increase my mathematical knowledge and skills I would like to study a decent mathematical methods book. I came across two books whose names are: Mathematical Methods for Physics and Engineering by...

So I just got accepted into the University of Waterloo's mathematical physics program and I don't know anything about the program. What kind of career could I expect to get if I graduate from the program? If I take this program could I still get a major in accounting, actuary sciences, etc...

What is the general definition of energy? I already know that it means ability to perform work and that Work = ∫Force d(displacement) = Δ Kinetic Energy = -Δ Potential Energy ( in a conservative field "a closed path integral of the force = 0"), Σ Kinetic-Potential = constant, ∫Kinetic-Potential...

I intend to use the Gershgorin Circle Theorem for estimating the eigenvalues of a real symmetric (n x n) matrix. Unfortunately, I'm a bit confused with the examples one might find on the internet; What would be the mathematical formula for deriving estimates on eigenvalues? I understand that...

This question deals with a 1-parameter equation: fc(x)= (4/x)+(x/2)-c for 0≤c≤ 2.3 a.) Use algebra to find the positive fixed point p(c) of fc(x) (in terms of c) and identify its exact interval of existence a.) Ok so for the fixed point I got p(c)= -c+√(c2+8) I'm not sure if this is...

hi this question i just cannot do. i have no idea where to start: a student is trying to recall the formula for the sum of cubes of consecutive numbers. she thinks it may be (n^3(n+1)^3) /8 or (n^2(n+1)^2)/4 . show by counter example one is incorrect and the other is correct by induction...

Hello, this is my first post on this forum. I am a high school junior, and I am attempting to build onto my math foundation. Currently, I am finishing Algebra II. Next year, I will not be taking Trigonometry, as my teacher did not recommend me. We were supposed to have straight A's...

Which universities or instructors---anywhere in the world and particularly in the USA, Canada, UK, Australia, New Zealand, or India---use or have used Tom M. Apostol's landmark textbook on Mathematical Analysis? Are there any video lectures from a course based on the text available on the...