Mathematical Definition and 1000 Threads

I've done some research, and I've looked at the derivation of the diffusion equation, but I don't want to reproduce even a more simple version of it. I'd like something that can I do almost exclusively myself. The point of this is not to plot some graphs, and extract some line of best fit or...

Hello, We had a short unit on mathematical induction, and I know my final exam will probably have one problem that says ''prove this relationship with mathematical induction''. I was wondering, is there some sort of step by step procedure to proving something using induction? Or is it...

Hello guys, I'm new in this forum, this is my first Thread. I've started reading Robert Geroch's Mathematical Physics recently and I've been having problems with some of the proofs that involve monomorphism. He defines monomorphism the following way (pg 4): let ψ be a morphism between A...

I have a math theory about finding the root of negetive one however now i have no clue how to get it out. How can i trademark it or patent it... I am a 10th grader in South Africa. I can't post it on some site as people may steal or something.

Hi there, Consider a related rates problem, Gas is being added into a balloon at a rate of dE/dt = x ft^3/sec Find the rate at which the radius is changing at time h. This is a completely false problem; I am just giving an example. My question is, How would you know if there is a...

$S_k>k^2$ $S_{k+1}:2^{k+1}>(k+1)^2$ $2*2^{k+1}>2(k+1)^2$ $2^{k+2}>2(k+1)^2$ Assume $x=k+1$ $\frac{2^{x+1}}{2}>x^2$ $2^{x+1}*2^{-1}>x^2$ $2^x>x^2$ right? $2^{k+1}>(k+1)^2$

In theoretical physics, why is the mathematical model favored over the mechanical model? Awhile back, I posted a thread asking about what each theory posits as real. For example, quantum field theory might limit the set of real things to fields, field quanta, the universe, and causality. It...

$S_k:5\cdot 6 +5\cdot 6^2+5\cdot 6^3+ ...+5\cdot 6^k=6(6^k-1)$$S_k:5\cdot 6 +5\cdot 6^2+5\cdot 6^3+ ...+5\cdot 6^k+ 5\cdot 6^{k+1}=6(6^k-1)+5\cdot 6^{k+1}$ what do i do now? to prove $S_{k+1}$

Definition/Summary Mathematical Induction is a method of proving a series of mathematical statement labelled by natural numbers. This method usually involves two steps. First one proves the base case, then one shows that if the statement holds for some natural number, it holds for the...

Did i do this right? $2^n>n^2$, $n \ge 5$ $S_{k+1}: 2^{k+1}>k^2+2k+1$ $2^k>k^2$ $2(2^k)>2k^2$ $2^{k+1}>k^2+k^2$ And $k^2+k^2>k^2+2k+1$ RHS: $k^2+2k+1$ So $2^{k+1}>(k+1)^2$

I don't know what forum to post this under. PLEASE HELP ME THOUGH! Principle of Mathematical induction: Let $S_n$ be a statement concerning the positive integer n. Suppose that, $S_n$ is true. For any positive integer k, k $\le$ n, if $S_k$ is true, then $S_{k+1}$ is also true. Then $S_n$ is...

Original Equation: 5+6+7+...+(n+4)=1/2n(n+9) Ok, I've tried everything to understand this. I'm just not getting it. I understand everything (n=1, k+1, etc) up until this point: "To continue with proof what must be done?". I know you must simplify the right side, but I don't understand how they...

To what extent, if any, is an understanding of mathematical proofs required for a scientist? I can empathize with a need for an understanding of the general machinery of the tools you are using (understanding, for example, how it is the chain rule came about, ie, how it was derived) but, using...

Homework Statement Homework Equations The Attempt at a Solution Hello, I am working on the problem in the attached image regarding induction based on the inequality 2^n \geq n + 1 I am confused how to do this by proving that if it is assumed to be true for ## n = k ##, then how it is true...

Hi guys, I was wondering whether atypical preparation is needed for admission to a mathematical physics program? i.e. Do you need to take Real Analysis, Topology, and other "rigorous" mathematics even if you are only a physics undergrad, or will such mathematics be taught from the ground up...

Hi there! I would like to know, what kind of mathematical background is needed for cosmology? I'm about to reach 50% of undergraduate physics and I appreciate if you could point it out some interesting courses I can take to build a strong basis for a «future» cosmology masters or phd degree...

series expansion: ln(1+x)=1-x^2/2+x^3/3-x^4/4+x^5/5+......∞ ln(1+1)=1-1/2+1/3-1/4+1/5...∞ ln(2)=(1+1/3+1/5+1/7...)-(1/2+1/4+1/6+1/8...) ln(2)=(1+1/3+...)-2(1/2+1/4+1/6+1/8...)+(1/2+1/4+1/6+1/8...) ln(2)=(1+1/2+1/3+1/4+1/5+1/6...)-2(1/2+1/4+1/6...)...

Dear all, I am going to attend masters program in micro and nano technology. I would like to know what concepts of maths and physics I should be clear at and some good textbooks for the same. My study module includes nanoscience, nanomaterials and nano electronic design.

Homework Statement [/b] Develop a mathematical model that would lengthen the time until the shock stabilised by the given time. T= 2.51 show mathematical analysis of the situation d(t) = -5e^(-5t) cos (10t) is the original equation for a deflection of a rod in centimetres where t is time...

I'm currently a rising sophomore (undergrad), and I'm trying to fill in some gaps in my applied math background this summer. So far, I've taken linear algebra and multi/intro analysis, but they were both theory-only and had very few applications (ex: I finished LA without knowing the various...

What exactly is ∏? I've never quite understood why it is apparent in so many different equations and formulas. Why is it there? Why is it apparent in nature so much? And ∏ it's just a infinite set of numbers why is it any more relevant than any other set of infinite numbers. Why is 3.14... so...

Are these satisfactory answers? Question 1: http://i.imgur.com/EElOqwM.jpg Question 2: http://i.imgur.com/SlE2jza.jpg?1 Thank you :)

I'm looking to write a dissertation in the field of logic (for a philosophy degree). I'm deeply interested in logic, but whenever I consider the material beyond my courses it becomes pretty daunting. I'm reasonably familiar with: *First Order Logic *Set Theory and ZFC *Cantor's Diagonal...

Homework Statement Ideal rubber stirng with length L=1km.Ant is takng a walk on the string with speed v=1cm/s After every minute(Δt=60s) ,string is getting longer by ΔL=1km. 1)Will ant get to the end of string? 2)If yes,then how long it will take ? Homework Equations 1) So i used...

I was wondering if there is a mathematical difference between the RMS free path and the mean free path of molecules in an ideal gas. For example, When I calculate the mean free path, I use use the average velocity and the scattering rate which is a function of the average velocity. I then...

How good or bad are we at math? Mathematical ability obviously varies from one person to another. I propose a scale in which a zero is the inability to add 2 + 2, 5 is the ability to successfully complete college-level math courses, and a 10 describes the ability to come up with mathematical...

If you have a charged solid sphere with uniform volume charge density ρ, then the total charge on the sphere is Q = ρ*4/3*∏*R^3 , where R is the radius of the sphere. Now...

Hello, I've started a MS in mathematics at my university and I'm interested in mathematical physics or going to to physics for a PhD. The classes required for the MS are 2 semesters of real analysis, linear algebra, and one semester of algebra, everything else is up to the student to pick and...

See attachment, please. Six variables that can change individually and hence altering all connected. The goal is always to find the distance between A & C, "ACD" if you will. ACD = ... Given 6 flexible variables: (Abbreviated to perhaps make things easier: r, abd, wt, abl, pll, pld. Use or not...

I'm an udergrad, 2nd year physics. I recently got interested in solar physics - one reason being, that I was offered to cooperate on a project, where I'll be doing some sunspot simulations. I really like mathematics and I kinda like the mathematical modelling curriculum. However the...

Hello, all. My whole life, I've had a passion for physics and understanding the universe in general. For years since I was younger I've read layman's books on the subject, reading articles and journals, etc. I have deeply thought about physics (theoretical physics in particular) as being my...

When a mathematician says that mathematics is "beautiful", is it so in the same sense as e.g. art is beautiful? A recent research presents evidence that it is: http://journal.frontiersin.org/Journal/10.3389/fnhum.2014.00068/full

Consider the two species competition model given by da/dt = [[FONT=Calibri]λ1 a[FONT=Times New Roman] /(a+K1)] - r_(ab) ab - da, (1) db/dt = [[FONT=Calibri]λ2 b[FONT=Times New Roman] *(1-b/K2)] - r_(ba) ab , t>0...

Hello! This is my second thread in here. I'm just finished my high school and waiting for the results to get admission in an undergrad physics program. I was confused about career guidance and academic guidance feel free to move my thread if I'm in the wrong place I was wondering about major...

does point really exist in reality or it is mere a mathematical concep

Homework Statement Show that PV = E Homework Equations E= \int^\infty_0 D(\epsilon)n_{FD}(\epsilon) \epsilon \cdot d\epsilon n_{FD}=\frac{1}{(1+ e^{-(\alpha +\beta \epsilon_k)})} \psi(\alpha ,\beta, V) =\beta PV =\sum_\vec{k} \ln{(1+e^{-(\alpha +\beta \epsilon_k)}) } and in an...

Hello everybody! First of all, I would like to say that this is my first post in this forum, even though I've occasionally read some posts before. I'm a ChemE major from Mexico! I am currently taking Thermodynamics I, and I have trouble figuring out the expression: W = \int_{V_1}^{V_2} PdV I...

Consider the single species population model defined by dR/dt = [gR/(R+R_m)] - dR, t>0, where g,R_m and d are all positive parameters and R(0) =R_0 (a) Describe the biological meaning of each term in the equation. (b) Determine the steady-states of the system and discuss any...

Hi. My purpose is to take a phd in physics, and after few years as researcher to become a Quant. What phd is better for this purpose: computational, theoretical or mathematical physics? http://en.wikipedia.org/wiki/Computational_physics

I've been thinking about some common properties of mathematical objects and I've been wondering if they are redundant. Like: Aren't all associative operations also closed under a set? Doesn't the existence of inverses imply the existence of an identity element? So that stating associativity...

I'm trying to get get a good base for learning further mathematics. Would an intro abstract algebra, analysis, and category theory text be good places to start? There are so many different places you could start and I'd like to first learn about those areas of math which help most when learning...

Mclaurin Series with Division by Zero? Boas: Mathematical Methods for Phys Sci Pr.1.13.25 Homework Statement Using the methods of this section: (a) Find the first few terms of the Maclaurin series for each of the following functions. (b) Find the general term and write the series in...

Homework Statement Using the methods of this section: (a) Find the first few terms of the Maclaurin series for each of the following functions. (b) Find the general term and write the series in summation form. (c) Check your results in (a) by computer. (d) Use a computer to plot the...

Homework Statement 4. Write the Maclaurin series for 1/√(1 + x) in ∑ form using the binomial coefficient notation. Then find a formula for the binomial coefficients in terms of n as we did in Example 2 above.Homework Equations { \left( 1+x \right) }^{ P }=\sum _{ n=0 }^{ \infty }{ \left(...

Hi Usually when learning math, understanding the theorems and ideas helps tremendously to remember math. I get that... I got through calculus, linear algebra and complex analysis easily. The problem for me started with three branches in mathematics: Real analysis, measure theory and abstract...

mathematical "connection" in the cartesian product What is the mathematical connection between elements of a cartesian product ##A\times{}B## and the elements of the sets ##A## and ##B##? In other words, what is the difference between the set ##A\times{}B## and just any set ##Z## with...

I want to study GR from a mathematical point of view but I know almost no physics. Is this possible? And what textbook would be more geared towards this? Also, what are the math prerequisites that I need? I have studied up to analysis on manifolds, some linear algebra and multi-linear...

Is this equation equal to: (e^(hf/kT)) - 1 or e^( (hf/kT) - 1 ) http://s29.postimg.org/le6iqy3rb/exp.png

I am no expert in formal logic, so please forgive me if this question sounds stupid. It's about a common pattern used in many mathematical proofs. For me it' "obvious" or "trivial" - but I can't prove it. For a friend of mine it's far from obvious or even wrong - but I don't get his point...

[FONT=Helvetica Neue]A ship has three cargo loads -forward, centre and after. The capacity limits are given: [FONT=Helvetica Neue]Commodity Weight (in tonne) Volume (in cu. feet) [FONT=Helvetica Neue]Forward 2000 100000 [FONT=Helvetica Neue]Centre 3000 135000 [FONT=Helvetica Neue]After...