Mathematical Definition and 1000 Threads

john baez submitted a new PF Insights post Interview with a Mathematical Physicist: John Baez Part 2 Continue reading the Original PF Insights Post.

john baez submitted a new PF Insights post Interview with a Mathematical Physicist: John Baez Part 1 Continue reading the Original PF Insights Post.

Hello, I've read a few of the responses in the guidance section on this site and had some conversations with guidance personnel at my college, but I was hoping to get some other, potentially more objective insights from the group here. I will be 34 this year and am currently a sophomore at a...

I am not able to understand the mathematical expression of "change in Gibbs free energy", For a chemical reaction occurring at constant temperature and constant pressure, (ΔS)total = (ΔS)system + (ΔS)surrounding Considering that reaction is exothermic, ΔH be the heat supplied by system to...

In this puzzle, you use all integers from 0 to 9 to arrange a mathematical calculation whose result is the post number. There are only three rules: 1. No double posting 2. No approximation 3. No made-up variables Now since it is the first post here, let me do it first which results in 1...

Using these equations I am about to prove that photons have a rest mass of zero (mathematically) ________________________________________________________________________________________ E=hc/λ Photon Energy Equation E2=(pc+mc2)2 Mass-Energy Equivalence with Momentum Equation p=h/λ Momentum...

I am a CS student and have a very poor understanding of this field of mathematics. I don't properly know the difference in between symbolic logic, first order logic, propositional calculus, model theory and lambda calculus. But, I want to start studying logic formally from the very basic. I'd...

Homework Statement Restaurant Reservations for a given week were: Monday - 34 Tuesday - 27 (minimum value) Wednesday - 33 Thursday - 47 Friday - 58 Saturday - 61 (maximum value) Sunday - 42 Homework Equations I don't think you need these equations to help me solve what I'm stuck on Amplitude...

What are some of the top graduate programs in Europe (excluding the UK) on theoretical physics specializing in string theory, fields or mathematical physics?

Prof. S Lakshmi Bala from Department of Physics, Madras, India writes a blackboard of equations which show how beamsplitters used alone affect the wavefunctions of input photons. It seems that it depends on the number of photons you use and in which input port to get you a different entangled...

Hi all, just curious. I am just learning about user-defined functions in MSSQL2014. What kind of Math can we do with it? Didn't get much useful from my search.

Hello all, I have recently started a course at my University called Introduction to Mathematical Modeling. However, the course does not require/recommend a textbook, and I am someone who really depends on having a textbook in order to learn. I have asked the professor to recommend me some...

How does physicist translate their scientific concept into an image or illustration to make it comprehensible and visual. Does the physicist make use of computer-software to produce this illustrations? Who made the first very well-known illustration of gravity that causes space-time to curve...

Is this a valid statement? There are a hundred times as many donuts in box A as in box B. A B i.e. 0x100=0 I mean, I know it's a disingenuous statement, but is it valid?

Hello, i am currently enrolled in a Mathematics course which covers these subjects: -Calculus of Variations -Laplace Transform -Fourier Analysis -Special Functions -Integral Equations And as an introduction to the subject it has several things from calculus like maxima/minima of functions of...

Hello I VAGUELY recall reading somewhere (in the history of math), that there were intense and emotional (almost physical) arguments over who would use (claim?) what letter for what purpose in calculus: Δ δ d D ∂ Is this true? Can someone provide a reference? (I could be mistaken.) (My...

Let me introduce notation so my question makes sense. A set of orthogonal states can be distinguished by a Q-measurement, e.g. |0> and |1> (Q-computation notation) can be distinguished by measuring with the observable Z which has eigenvectors |0> and |1> with eigenvalues +1 and -1. But if those...

I have a small mathematical game. A random number with uniform distribution between 1 and 10 is drawn, the player must guess any number except the the one drawn.The method I have found is by selecting the same number for every draw, the player will win 9 times out of 10. My question is , is...

Mod note: Thread moved from HW section 1. Homework Statement My native language is not English,and I'm not good in reading hand writtings.I got a short passage on mathematics.Please tell me if you could help me with that.I've attached it as "Lif.pdf".Homework EquationsThe Attempt at a Solution

I have been learning topological insulators recently, and I become more and more curious about the link between topological insulators and mathematical theory these days. I know topological insulators have something to do with fiber bundles and K-theory. I have a relatively good background of...

Hello, I am a high school student who is supposed to start a project related to physics or mathematics - and I have to hand it in 3-4 months (but it is voluntary) . I am sorry that i haven't used the template, but i hope that someone will help me I haven't decided the topic yet. It doesn't...

What is the correct notation for Volumetric Heat Capacity? I see it written both ways (Wiki for example). I'm pretty sure one is more correct but which is it? (1) Btu/ft³·°F or (2) Btu/(ft³·°F)

Hello!can someone propose a good textbook for quantum mechanics and mathematical physics(including green function)?I would like to buy those books so i want something which is one of the best to have in your libraby!

What exactly is a mathematical operation? Wiki states that an operation in math is "a calculation from zero or more input values (called "operands") to an output value." That sounds oddly like a function, but I'm assuming that not all operations are functions? What is the relationship between...

Homework Statement Find t(τ), x(τ), y(τ), z(τ) for constant electric field E=E(sinθx+cosθz) and B=Bz, and constant magnetic field where E,B, and θ are all constants. I haven't seen this notation before, and I really just want to know what it means specifically. I know and up indice paired...

I started with Mary Boas' book "Mathematical Methods in the Physical Sciences". Now it is stressed in the introduction to make homework and do the problems. However, I would very much like to know if I got the answers right, and I even prefer if the problems are worked-out. So I guess my...

I am reading the book Mathematical Logic by Ian Chiswell and Wilfred Hodges (C&H) ... and am currently focused on Chapter 2: Informal Natural Deduction ... I need help with what C&H call the 'dandah' or more specifically symbols with a dandah through them ... The relevant text in C&H...

I am reading the book Mathematical Logic by Ian Chiswell and Wilfred Hodges ... and am currently focused on Chapter 2: Informal Natural Deduction ... I need help with interpreting the notation of an aspect of Exercise 2.1.3 which reads as follows:In the above text after the text: "Possible...

Hi guys, iv been stuck on this problem for a while now and can't seem to make any headway construct a counterexample to the following statement: "for matrices A with real entries 'A^3=Identity impies A=Identity' im not restricted by size for the matrix. any hints would help because i just...

In, QFT, an elementary particles is an excitation of its quantum field. Quantum fields are just mathematical. For example an electron is excitation of the electron field. But is the excitation of the field physically real or just mathematical? What i mean is, is there something physically...

Homework Statement Okay so we're testing the effects different types and number of layers can have the heat released through conduction. in our results we found that the heat released was reduced by 50% for 2 layers compared to 1 layer and that the heat released was reduced to 34% for 3 layers...

Homework Statement Show that every 2-tree(Definition 3.2) with n internal nodes has n+1 external nodes Homework Equations A 2 tree is a tree which nodes have 2 children or no children. Internal nodes are nodes which have two children external nodes are leafs. The Attempt at a Solution Proof...

I'm studying the first year in physics university and I want to follow the career in QFT and this area requires a lot of math. In my university a lot of students who want to study theoretical physics are studying mathematics, and then to graduate school in physics. It will be a good choice...

Do we need a keyboard for that.There are apps. Or can we write some code or latex? Or does whatsapp or google having so many developers even accept mathematical symbols like the θ sign or ∫ sign?

I keep seeing that "An atomic orbital is a mathematical function that describes the wave-like behaviour of either one electron or a pair of electrons in an atom" or something similar. However I can't find what the mathematical function is. Can someone tell me or link me to it please?

Hello, i just discovered this site and i love the work you guys are doing, helping people like me with math and physics etc. I was wondering if anyone knows a website / list / etc with math-rules, like algebra, logarithms, power, rules for differentiation, elasticity, substitution, sequence...

Hello everyone I need a good book dealing with the mathematical foundations of GR. I am looking for a rigorous one but i don't need a book on Differential Geometry. Just the stuff i need for GR. Thanks for the replies!

I was just recently reading about Cauchy's proof of the AM-GM inequality by forward backward induction and was simply blown away by it's elegance. However, I have never seen forward backward induction in any of my discrete maths books (including the one devoted just to mathematical induction)...

Hey! :o A cycloid is a flat curve that is traced by point of the rim of a circle while the circle rolls without slippage on the line. Show that if the line is the axis $x$ and the circle has radius $a>0$, then the cycloid can be parametrized by $$\gamma (t)=a(t-\sin t, 1-\cos t)$$ Could you...

Hello, I'm looking for information regarding this equation: or specifically in my case, when a=1:. This equation supposedly describes a mathematical pendulum in a rotating plane, however, I'm unable to find information on this specific subject. I'd really appreciate it if someone could show me...

Mathematical Proof That a 45 Degree Angle Launch is Best for Displacement how do i solve this

I'm a highly determined (and slightly stubborn) high school freshman who wants to learn enough mathematics to conduct mathematics research with a mentor. Looking on the internet, I found a program called MIT Primes, where students can be matched with graduate students/professors at MIT to...

I am transfer student and this going to be my first year in university. My major is electrical engineering and one of my requirements is to take an upper level physics course. I chose mathematical methods however the title of the class is intro to mathematical physics and i am worried that...

Prove that n^5 - 5n^3 + 4n is divisible by 120. for every natural number n greater or equal to 3. First, i checked if it works for n=3 and it does, so i could assume it works for some k>=3 so i could write k^5 - 5k^3 + 4k as 120*a a is natural number so for k+1 i have: (k+1)^5 - 5(k+1)^3...

A rod is radially mounted on a motor shaft and provided with a flat end plate. By turning movement, the end plate will touch a pointed object, and the angle turned is measured.By the torque of the motor during acceleration and deceleration, a vibration and deflection happens on the rod. The...

Prove $\sqrt{2}+\sqrt{3}\gt \pi$.

Hi https://en.wikipedia.org/wiki/Mathematical_descriptions_of_opacity it is mentioned above that "in non attenuating media, the refractive index and angular wavenumber are related by: A complex refractive index can therefore be defined in terms of the complex angular wavenumber defined...

Hello, I want to start learning mathematical logic. I was wondering what would be a good "expansive" mathematical logic book that covers as much material as possible. My school has books by both Ebinghaus (et. al) and Monk. Are these good? I've heard good things about Schoenfield, but I was...

There is an article on Wikipedia gravity assist and in the explanation of the term, author gives an analogy: Isn't this violating the law of conservation of energy and momentum? Can someone make a mathematical proof of this? I tried, but the variables like the mass of the train and the tennis...

I have a set of class notes that I've been thinking about publishing as a book, and I wonder what y'all thought about it. The book is intended for people who have taken introductory physics, and it is organized by mathematical topic or technique, with a specific focus on calculus. There are...