Mathematical Definition and 1000 Threads

Prove by mathematical induction: (2n)! < (2^(2n))*(n!)^2 , for all n=2,3,4... I know that to start you must prove that it is true for n=2, (2*2)! = 24 < 64 = (2^4)(2!)^2 Then you assume that n=k and show tha n=k implies that n=(k+1) (2k)! < (2^(2k))*(k!)^2 ... At this point I...

Hey guys, I have seen many posts on the same topic but I was unable to come to a coherent conclusion. I have seen people reffering to Arfken or Mary Boas. I have sufficient knowledge in linear algebra, statistics and calculus in many variables. I am presently taking a course in complex analysis...

Hi, I am a high school student and my fields of interest are physics and mathematics. I've been advised to apply for the mathematical physics undergraduate program but I don't want to rush so that I won't have to regret my decision afterwards. I have a few questions about the paths I can...

My 7th grader has enough mathematical background in algebra, geometry and trigonometry to start learning how to write out proofs. Are their good books that teach this step by step? I can certainly teach him myself with examples, but I figured there must be a systematic way to teach this...

With my term-end examinations fast-approaching, I sat down to revise my entire senior year physics syllabus. As I was reading through electromagnetic induction, I found myself in the same state of utter confusion that I found myself in when I first studied about Lenz's Law and Eddy Currents. But...

Dear all, I am new to this forum and this is my first post. I hope this is the right place to open this topic. I have a homework for my mathematical methods for physics course and i am kind of stuck into a question: v=ψ∇β show that ∇xv is perpendicular to v. Here v is a vector x is cross...

Hi, I hail from Chennai, India. 1. I would like to know if the B.Sc Physics(Hons.) course offered by the Chennai Mathematical Institute (CMI) is a reputed one. 2. What university is CMI affiliated to? 3. I read that the course span is 3 years. Can I pursue my Masters abroad after...

As opposed to guess and checking by inspection. Is there a method mathematically like with an algorithm or something to balance equations by hand (without the aid of any computer programs or anything like that except a simple calculator)?

Repeatedly in the past few months any attempt at learning more advanced physics has ended in hitting a brick wall: my maths knowledge is really not up to par. To put this into perspective, I am an A Level student but feel as though the current syllabus for the sciences is really not enough. I...

Hi all, I've been struggling with a large piece of coursework. been quite stressed latley and now I am struggling while aproaching my deadline. i need help answering this question. Use mathematical induction to show that S(n) = 3 × 2 n-1 -2 is the solution for the recurrence relation: T(n)...

I was wondering if anyone knows of a good book on the mathematical theory of continuum mechanics. I have looked online, and the only ones I can seem to find are like your average physics or applied mathematics book. I want something with rigorous theoretical formulation of the subject. It...

How do I prove a formula/rule or something by mathematical induction? Please give me a few examples or resources and explain it as best you can because I think I'm messing up some how.

Author: B.P. Demidovich Title: Problems in mathematical analysis Amazon link https://www.amazon.com/dp/B0007BNL1W/?tag=pfamazon01-20 Table of Contents: Preface Introduction to Analysis Functions Graphs of Elementary Functions Limits Infinitely Small and Large Quantities Continuity...

Is the magnetic field purely a mathematical abstraction or is there actually something there? In other words, if a proton floating in deep space, is there actually something that shoots out in all directions from the proton that will interact with another charge particle?

I am an high school student starting grade 11 this year . I have been interested in physics since class 6 and i have been studying advanced physics since then . IN grade 9 and 10 i have read and solved problems from Resnick ,Halliday and walker's book and completed it . I thought myself...

I was wondering what the typical approach is for creating a "mathematical object" such as the probability model kolmogorov made (I've also heard it called a probability space...not really sure what the difference is)... <\Omega,\mathcal{F},P> , where \Omega is the sample space...

Hello I'm taking a mathematical physics course which has heavy emphasis on algebraic structures. The course has no required textbook but I want one anyway for extra practice. All of the books I see at my library all have no solutions in them which makes it frustrating because then I don't know...

Author: Richard Courant, David Hilbert Title: Methods of Mathematical Physics Amazon Link: https://www.amazon.com/dp/0471504475/?tag=pfamazon01-20 https://www.amazon.com/dp/0471504394/?tag=pfamazon01-20 Table of Contents for Volume I: The Algebra of Linear Transformations and Quadratic...

Author: Seymour Lipschutz, Murray Spiegel, John Liu Title: Schaum's Outline of Mathematical Handbook of Formulas and Tables Amazon Link: https://www.amazon.com/dp/0071795375/?tag=pfamazon01-20 Prerequisities: None Table of Contents: Formulas Elementary Constants, Products, Formulas...

archeoastronomist are bufled at polinesian finding out longitude without a clock here the concept i just found out how to prove: you have a dial with two geared counterotating needles you move by hand every rotation of the sun around you you rotate a needle ten times with which the...

Author: George B. Arfken (Author), Hans J. Weber (Author), Frank E. Harris (Author) Title: Mathematical Methods for Physicists Amazon Link: https://www.amazon.com/dp/0123846544/?tag=pfamazon01-20 Prerequisities: Calculus 1,2,3 Table of Contents: Preface Vector Analysis Definitions...

Hi , I was thinking about this , as you know calculus was used many years before the explicit work of both Newton and Leibniz , it was used the hard way , unrecognized , scattered and buried among unrelated formulas and topics. The golden question is ; what if there is another revolutionary...

Prove that: 1 + 1/√2 +...+ 1/√n < 2√n Work: So I've done the base case of n = 1, and I've set up the Indutive hypothesis as assuming n=k as 1 + 1/√2 +...+ 1/√k < 2√k and for the inductive step: 1 + 1/√2 +...+ 1/√k + 1/√(k+1) < 2√k + 1/√(k+1) now I'm having trouble trying...

Author: V.I. Arnol'd (Author), K. Vogtmann (Translator), A. Weinstein (Translator) Title: Mathematical Methods of Classical Mechanics Amazon Link: https://www.amazon.com/dp/1441930876/?tag=pfamazon01-20 Prerequisities: Contents:

Author: Mary L. Boas Title: Mathematical Methods in the Physical Sciences Amazon Link: https://www.amazon.com/dp/0471198269/?tag=pfamazon01-20 Prerequisities: Calculus Table of Contents: Infinite Series, Power Series The Geometric Series Definitions and notation Applications of...

Author: Rudin Title: Principles of Mathematical Analysis Amazon Link: https://www.amazon.com/dp/007054235X/?tag=pfamazon01-20 Prerequisities: Rigorous calculus, including epsilon-delta proofs. Spivak's "Calculus" would be more than sufficient preparation. Table of Contents: Preface The Real...

Is there a mathematical proof that the positive feedback makes the op-amp saturated? http://i.imgur.com/71PNh.png

I am writing my first paper in applied mathematics.I would like to know how important is it to write a analytical proof for the numerical solutions arrived?I always thought these sort of things were left to the 'pure mathematicians' and one didn't need to bother.As a engineer,I was always used...

I'm having a lot of difficulty with proofs. I can understand them when I read them, but when asked to prove things myself, I usually fall flat on my face. How important are proofs for physics? Do I really need an intimate understand of the mathematics, or would that be irrelevant? I was...

Hello all, I am currently an undergraduate student (just finished my first semester) at Stony Brook University. Basically, I'm fairly certain that I want to go into pure math or theoretical physics, it's just that I feel like I may not be up to par with everyone else who will be competing...

HE'S A DEMON! Yep, a Demon, a Teufel if you like. Have you read this book there ↑ ? Plain statiscal question for statistical answers. Anything not covered in the poll shall be posted here. Go wild.

Is there a way to allot more resources for Mathematica to use? I have 16GB of RAM and the Intel i5 but Mathematica is still too slow at many things. Is there a way I can allot more of my computers resources to the program?

I have a question that is a little hard to explain, since i don't know the name of this method, but I'll try my best, if anyone knows the name please do tell me. So let's say we have three numbers, 1 2 3 (in this order) and we have a container for this numbers: C123 and we have some...

The table below records the profits that are made when one unit of material is sold by factories A,B, C to dealers L,M,N, P. The output of each factory and demand from each dealer are given in brackets ( A,B,C ) -> L(30) M(30) N(30) P(45) A(100) -> 25 30 20 20 B(20) -> 30 25 15 10 C(15) -> 10 35...

One basic operator is addition. In order to add the any number x number of times, multiplication was invented. In order to multiply any number x number of times, exponentiation was invented. What if we want to raise a number to a power x number of times? How come we didn't invent that? Also...

If we were to consider a nucleon-nucleon interaction: We know that the incident wave (plane wave) is ψ= Ae^{ikz}, propagating in z direction But for some mathematical facilities, we tend to use spherical coordinates, the wave becomes = \frac{A}{2ik}[e^{ikr}/r - e^{-ikr}/r] How come...

Hi, I am wondering if there is a mathematical physics degree. I was thinking about doing consultant/contract work for applied or research physicists, insofar that I would be paid to help establish/confirm the mathematical foundations of their work or research. Thank-you.

I'm having difficulties trying to establish the best approach to create a mathematical model of a process that has a combined continuous and discrete (batch) element to it. I explain as follows: The system is a hopper (vessel), open to atmosphere, with dry granular material being fed in by...

Hello, I am really not very good with math... over the years, I totally lost it. But today, it caught up with me... LOL! I hope someone can help me. In my spare time I am fiddling around with proximity sensors. I have a proximity sensor that accepts 135 steps. Therefore, when I am at step 135...

Specifically I plan on specializing as a Mechatronics engineer. I recently bought the book "Mathematical Proofs: A Transition to Advanced Mathematics" and I plan to study it on my own due to curiosity and interest towards mathematics. I would like to listen on one's opinion on how useful it...

Hello folks, I have an induction problem that I have been working on, and I am at my wit's end. If anybody could provide me with a nudge in the correct direction, I would greatly appreciate it. I have attempted to factor out a number of terms to find something remotely intuitive here to present...

So I really want to get good at mathematical physics. Below is a list of books I could get from various libraries, but I don't know which one's I should start with and which to do next and so on. I currently understand intro CM, EM, and QM. My math skills are very basic (ODES as of now). I thank...

Homework Statement Here is this problem: I have the solution http://www.proofwiki.org/wiki/Leibniz%27s_Rule/One_Variable This is where I get stuck.. Where it says: 'For the first summation, we separate the case k=n and then shift the indices up by 1.' Why does this lead to the...

hi, Reading a book on thermodynamics and the guy often uses something like this : ∫1/T dQ = ΔS and then he says "this in differential form" : dQ/T = dS I kind of get the idea visually that one slice of "integral" will be dQ and you can think of it this way. But my question is how...

I am trying to solve a problem that includes a function of the light hitting a certain area. My question is, how would I change a function G(x) of photons hitting a certain area to include just photons of a certain wavelength, say red light. I feel like this could be accomplished using a Fourier...

im looking to become a theoretical physicist and i think i might want to do a program in mathematical physics for an undergrad. does anyone know which are best in Canada? i know the obvious ones, (i think) U of T, Waterloo, UBC, McGill, but can anyone be more specific please?

Hey guys, let's say I were to define a new mathematical object, a novel type of number for example, and I am trying to determine its various properties (arithmetic, exponential, logarithmic, etc). Now, let's say I am able to use these numbers to produce solutions that agree with expected...

One of the problems that I come across is my bad habit of glancing at the solutions. I usually look at them after I struggle on a problem for 20 minutes. Almost always its a proof problem like in linear algebra such as "Prove that there is one and only one way to write A as the sum of a...

Hi there, I am looking for books that treat signals and systems from a mathematical perspective. When I say "signals and systems", I am referring to the typical second/third year material taught in EE programs: system characteristics (causality, memory, stability), LTI systems, linearization...

Smoker Non-smoker Disease A B No disease C D Show the mathematical relationship between Relative Risk and Difference in Conditional Proportions. (Work the formulas algebraically so RR is on one side of the equation and the difference (plus some other...