Mathematical Definition and 1000 Threads

A post doc in an area that differs from my PhD? I am currently doing a PhD in fluid mechanics but want to do mathematical physics tbh. In another thread I got an answer about a user who had done a PhD in accelerator physics and went to do a post-doc in condensed matter, vice versa even, but in...

What is a nice resource to learn about the mathematics of neuroscience? I read a little bit about the Hodgkin-Huxley model for propagation of action potentials and also stuff like synaptic junctions, but I like to learn some more about modelling networks of more than one neuron, stochastic...

Hi, you all, I am an undegrad Physics student and I'm choosing my optional courses for my third year. I'm looking for advice (or opinions, if you prefer) since I'm not sure what of the following mathematical, optional courses would be more "beneficial" (I know this term is abstract) to my...

is the concept of potential just a mathematical model

Lattices are studied in mathematics. What physicists call a "lattice theory" uses the mathematical object that is a lattice, but it involves other things, such as associating elements of a group with the links between nodes of a lattice. Is there a mathematical term for lattices with this...

I have gone through the principle of mathematical induction. I cannot understand why do we need to prove every statement for n=1. I mean why is it necessary? Why can't we start directly from n=k then n=k+1. For example see the below image. Thanks!

I am reading his excellent book "Mathematical Physics Part 1, Second Edition", which has benefited me a lot in many ways. However, I have a doubt about the correctness of the theorem 2.3.23, which states that for any subspace U of V, the map T ' : V/U -> T(V) defined by T ' ([a]) = T|a> is...

Need some sources on why PWM is widely used in inverters for DC - AC conversion applications, and their mathematical basis? Basically, I was wondering why inverters had to use PWM, instead of just getting a square wave of let's say a 50Hz frequency and just filtering out the odd order harmonics...

Maybe a bit of an odd question (not really sure where it would belong on this site to be honest), but I was wondering if anyone can explain, or at least knows of a source that explains in a quantitative way, the physics behind aurora? Now I've seen websites like this that discuss conceptually...

The Block Universe Theory, based on Einstein's Relativity, says that past, present and future exist at the same "time", the universe is static, eternal, and things doesn't change, movement is an ilusion because you have memories from the past. But if the universe don't evolve does this imply...

Hello. When does someone know a classification of some kind of mathematical objects has been completed? For example of differentiable manifolds, or abelian groups or ordered fields? Thank you.

Hi PF, What would you say is the level of importance of Geometry, as opposed to say, Algebra I or II, in a future Mathematician's mathematical foundation? Would not covering it thoroughly leave holes that would show up later in higher mathematics? Any thoughts?Thank you, Chandller

So which should be the best strategy to avoid this hurdle: maybe try and look for a different mathematical object as quantum fields? or rather try and avoid their multiplication in our ways to handle them to obtain predictions? any other ideas? perhaps leave it altogether as not very many...

##A ∖ B## can't include any elements that are not in ##A##, so it is the same as saying ##A∖(A∩B)##; it's exactly the elements of ##A## except those in ##A∩B##. ##A∖(A∖(A∩B))## is exactly the elements of ##A## except those in (exactly the elements of ##A## except those in ##A∩B##). This is the...

I learned that the Lorentz group is the set of rotations and boosts that satisfy the Lorentz condition ##\Lambda^T g \Lambda = g## I recently learned that a representation is the embedding of the group element(s) in operators (usually being matrices). Examples of Lorentz transformations are...

A book that has really caught my attention recently is Yuri Manin's A Course in Mathematical Logic for Mathematicians. I am very interested in the foundations of mathematics and mathematical logic, plus I noticed that it had some chapters on quantum logic, so I started skimming through it...

Is there a standard mathematical definition for "wave"? What is the definition? Assuming that there is a definition, what are the mathematical definitions of the properties of waves? For example, how is the "group" of a wave defined? ( as in the "group" that has a "group velocity"). I'm not...

Hey everyone, I am a new member. This post is about something that bothers me a lot and will affect my future. I am not sure whether I'm pursuing a carrer that is right for me. I graduated from the physics department of Middle East Technical University in Turkey with 3.45/4.00 CGPA this year...

I personally don't know of any physical process that can't be modeled without need for tetration or higher order hyperoperations. In my own experience, exponentiation suffices. Does anyone else know about a physical process that can't be well-modeled unless tetration is used in the math?

I am not clearly understand what the question requests for, is it okay to continue doing like this ? Kindly advise, thanks

Imagine that you are a librarian or a book-seller, and you come across a book which is a cross between mathematical fiction and mathematics popularization: that is, it is heavier on the mathematics explanations than a work of fiction has a right to be, yet it is heavier on plot, much of which...

I am a high school who will be graduating next year. I am almost done with Purcell and Morin which I worked through in my past holidays. However, I am still not proficient in various topics like Linear Algebra, Basic Analysis, and I quite often encounter various new things that I haven't even...

Not sure if this is the correct forum. But are there any video lectures that follow the book Pugh: Real Mathematical Analysis? Thanks.

I am surrounded by Space and so I am curious to know what the name of this Space is. Is this Space given any name by a Mathematician? I suspect that this Space may be called Euclidean Space because Euclidean Space knows how to present point in three-dimensions. Euclidean Space talks about...

So, I'm a little confused and I thought I might get some help here. I have just started learning about manifolds and its super confusing because I've always worked with Euclidean spaces, too much that I didn't even realize it's euclidean and that it has different properties from others. So my...

Summary:: prove that (n 0) + (n 1) + (n 2) + ... + (n n) = 2^n is true using mathematical induction. note that (n n) is a falling factorial Hello! I have trouble dealing with this problem: Mod note: Thread moved from math technical section, so is missing the homework template. Prove that (n...

Real forces arise between pairs of interacting bodies. For any given system, classical physics tells you how to compute the forces (i.e. Coulomb/Newton inverse square laws etc.) acting one body due to another body, and then also tells you how different parts of the system move under the action...

I am really struggling with these problems and do not really know where to begin. In most cases I have just defined what the modelling means, e.g A rough surface is one upon which friction acts etc. I would really appreciate some help with suitably answering these questions comprehensively, and...

My attempt at solution is in the HW template, though this is not an HW question.

I am currently conducting a study that proposes a mathematical model. "mathematical model (n): a representation in mathematical terms of the behavior of real devices and objects."[1] The study composes of: AIM of the study: Create a mathematical model that represents a phenomena or happening...

Hello my dear physicists, I'm trying to model the varied generated (needed)Torque to rotate a washing machine Drum during a Washing Process so i assumed that the Model has as Input the target vilocity and as an Output the new needed torque to rotate the Drum(to be as a input for the motor...

I am trying to model an evaporator which evaporates water to steam in Matlab/simulink. Are there any governing equations i need to know and follow when modelling the evaporator mathematically? Please let me know.

I have been to other forum sites too where we need to encode a mathematical statement like this ... , some sites use $...$ before and after the mathematical things and some sites like this great forum use [itex]...[itex]. Why it this so? The latex software like Texstudio, Texmaker etc. uses $$...

I am trying to design a compressor in simulink. the mathematical equations has been modeled. but i just need, is there any relation to find the rate of change of volume with respect to time in compressor. Are there any equations or relations to find the rate of change in volume. As its a...

Prove by mathematical induction that $$7^n-2^n$$ is divisible by 5.What I've done so far:For n = 1 $$7^1-2^1=7-2=5$$ (true that it is divisible by 5) For n = k $$7^k-2^k=5a$$ (assumed to be true that it is divisible by 5) For n = k + 1...

My question is simple. Can one prove any theorem in mathematics by having only a pen and a paper, or a super-computer for that matter? Since math is essentially all about theorems, and we usually take them as true. I guess someone went in and proved them at some point in our history. But some...

A bit vague, I know, but I guess asking is worth a shot.

I know that sinhx = 1/2(e^x-e^-x) and that e^2x-1 = e^x(e^x-e^-x) and similar identities but don't know how to get any further. Any hints at where to go with this would be appreciated.

Summary: I'm planning making a guide of calculus so I am looking for a software that allows me to make illustrations like they show in the calculus books. do you know any? thanks in advance

I am reviewing and comparing a wide range of mathematical models that are being applied to a specific realm of wildlife biology. For the comparison of these models, and to weigh advantages/disadvantages of different aspects with regard to application, I need to characterize each model. As I do...

So I was trying to learn how to build a mathematical model of an oscillating system. The system and FBD is shown below. I just got confused why I got a different value of k from both x force and torsional equilibrium equation? Am I missing something?

Hi all, I am currently involved in a theoretical physics project and would like some advice. One of the main takeaways I hope to (well,) take away is the capacity to make simple physical/mathematical statements that are valid, which seems to be an important part of theoretical physics. How do...

Hi, I was told by someone to go for the above mentioned book (authored by Riley and a couple of other authors). I need a definitive tour de mathematica- something that I could use for the beginning of my Physics UG until the end of it (or even further if such a book exists!). Also, something...

https://www.upi.com/Science_News/2019/07/30/Mathematical-model-identifies-acoustic-signal-preceding-seismic-shake/4431564489814/

What are streams of mathematics that are generally not used by Physicists but you think can be used successfully provided they become more developed? I want to know about such things cause it is quite interesting. Also, can Projective Geo be used in physics?

Summary: Do physicists really need to master mathematical modeling? Do physicists really need to master mathematical modeling? As far as I know Mathematical modeling is a separate discipline form Physics?

Summary: damage on glasses plate by hitting ball If a ball hit a rectangular plate of glass and it cause a damage "but it didn't broken" how can i represent this damage using mathematics? I'll tell you my idea about it: let the ball move horizontally and hit the plate perpendicularly with...

I am in a process of making a mathematical model of an automobile driveline validation procedure called "Driveline impact". In this test, after the engine in cranked, first gear is selected. While clutch pedal is still pressed, engine rpm is raised unto its max. torque deliverable speed. In this...