Mathematics Definition and 995 Threads

Is there any particular reason as to why certain texts use ##j## and others ##i## when looking at complex numbers? Maths is a relatively easy subject but at times made difficult with all this mix-up... i tend to use a lot of my time in trying to understand author's language and this is also...

My wife was in Las Vegas over the weekend to visit her sons and grandson, and saw this new structure there, the MSG sphere. In this image the sphere appears to be a very large basketball. Other images I've seen are of a huge eye, animated fireworks displays, an image of the earth, along with...

In mathematics, there is the Ramanujan summation: $$1+2+3+4+...=-\frac{1}{12}$$ https://en.wikipedia.org/wiki/1_+_2_+_3_+_4_+_⋯ This sum is used in physics for predicting the Casimir effect: https://en.wikipedia.org/wiki/Casimir_effect I have also heard that this sum was used in the string...

I'm trying to figure out how the mathematics of conservation of mass in compressible flow works for a simple setup. I posted this problem in hw physics section, and the conversation turned to the physics model and appears to have gone kaput. This was supposed to be a mathematics question (but...

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HI, I am an International Student studying in the US (at a "liberal arts" small college ranked in the Top 20 as per US News Rankings). I will graduate in 2024 and intend to apply for PhD programs in Mathematical Physics starting October 2023 for admission in 2024. GPA: I am a double major in...

I stumbled across this article from decades past written by the best EE instructor I ever had. I thought it might be of some passing interest to others in highlighting the difference between memorizing a mathematical result vs. truly understanding it. The essence of engineering, in effect. We...

Considering math as a collection of true/logically consistent statements, I see only two possibilities: either the statement is true and can be proven, which means it's a theorem. Or it's true but cannot be proven, which means it's an axiom. Is there a third possibility? Or maybe more? I feel...

I found one ages ago about the hyperbolic functions, but it hadn’t been translated to English from German yet. Anyone know of a good book on hyperbolic functions and other transcendental functions besides the circular functions (trigonometric)?

Hello I am from Egypt my interests fall into the sciences mainly mathematics and chemistry

TL;DR Summary: Suggestions for the publication of an article Hello everyone, I was reviewing and I can't find much content on truncated octahedron formulas, can it be useful to publish an article in a magazine on the subject?. Thank you.

##f(x) = \begin{cases} \frac {x^3-x^2}{x-1} & \text{if } x\neq1 \\ 1 & \text{if } x=1 \end{cases}## Find ##f'(1)##. Using derivative definition: ##f'(1)=\lim_{x \rightarrow 1} {\frac {\frac {x^3-x^2}{x-1}-f(1)} {x-1}}## ##f'(1)=\lim_{x \rightarrow 1} {\frac {\frac {x^3-x^2}{x-1}-1} {x-1}}##...

TL;DR Summary: Here I am asking for some opinions and recommendations for mathematically rigorous books that should be taken as an interested physics student. I know the question is quite subjective but any insightful answer is appreciated. I am willing to join undergraduate physics classes...

Hi, I need some textbooks about Mathematical models, thanks:cool:

Part (a) ##s=ab^t## ##\log s= \log a+ t\log b## Expression on the right hand side increases linearly with ##t##Part(b) ##s=120 ×1.15^t## ##\log s = \log 120+t\log 1.15## ##\log s =2.08+0.06t## From graph, y-intercept = ##2.08## ##m=\dfrac{2.45-2.08}{6-0}=0.06## Part (c)...

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A bit confusing here; what i did, Using gradient, we have, ##m=\dfrac{7-1}{0-3}=-2## ##y=-2x+7## Since there is a Vertex, we have the other ##m_2=2## thus, ##y=mx+c## ##1=2×3 +c## ##... y=2x-5## ##a=2, b=-5, c=12## or##a=-2, b=5, c=2##

I am studying Physics to get into a University to study masters in India. But, I do realize how vital a role mathematics plays and I am studying Mathematical Methods for Physical Sciences by Mary L Boas for that. I have some background in Physics, I did study Physics in high school and...

I have the solution: ## \dfrac{2x-3y}{3z+y} = \dfrac{z-y}{z-x} = \dfrac {x+3z}{2y-3x} ## (1) ## \dfrac{2x-3y}{3z+y} = \dfrac{3(z-y)}{3(z-x)} = \dfrac {x+3z}{2y-3x} ## (2) ##= \dfrac{(2x-3y)-3(z-y)+x+3z}{(3z+y)-3(z-x)+(2y-3x)} ## (3) ##=\dfrac{x}{y}## My question is how is it possible to go...

TL;DR Summary: I have heard detailed description of what to do when you study physics, but I don't know how to learn Physics in the first place, so this post tries to counter that. Here's How to Teach Yourself Physics and Math [Futurism] How To Self-Learn Physics: The Ultimate Guide How to...

I find it interesting that so many know how to use all kinds of apps on their cell phones, but so few are able to do simple algebra any more. If you ask around, engineers not included, I think you would find very few people e.g. to be able to find the axis of symmetry of the parabola ##...

I am an Indian and even though my English knowledge is somewhat better than that of an average Indian, there isn't a day I try to real highly technical books and fail to understand it at the first glance (or don't understand it at all). I understand why they use language which might seem...

In 12th and considering a career in research. Ik most of the collages ( IIT Kanpur, IISc Bangalore, IISERs etc ) but I am not sure of the research possibilities provided so if anyone can help out please do

Math qyuestion for AI (Skype) include an expression that x is resting on y (both straight line segments). AI insisted that x coincides with y, while my intent was only placing x on y. Does 'rest' have such a narrow definition?

I vaguely (strong word there because I can no longer remember the source, but the idea sticks in my head for 30 years now) recall reading (somewhere long forgotten) that method of separation of variables is possible in only 11 coordinate systems. I list them below: 1.Cartesian coordinates...

Using integration by parts: $$I_n=\left. x(1+x^2)^{-n} \right|_0^1+\int_0^{1} 2nx^2(1+x^2)^{-(n+1)}dx$$ $$I_n=2^{-n} + 2n \int_0^{1} x^2(1+x^2)^{-(n+1)}dx$$ Then how to continue? Thanks

Good Morning (And apologies if this is not the right forum -- it is not a homework problem.) On the one hand, a vector is an arrow and a tail: it has magnitude and direction. It is used to describe direction, forces, acceleration, etc. However, there are more mathematical definitions: a...

Evaluate the integral $$\int_0^1 x\left\{\frac{1}{x}\right\}\, dx$$ where ##\{\frac{1}{x}\}## denotes the fractional part of ##1/x##.

Mathematics tends to be more progressive than any other field. But I've heard some people say that some math classes that they took were more difficult than the most advanced math classes that they took. For instance, I've heard people say that Calculus II is more difficult than Calculus III...

I was looking at this video, and have become quite interested:

Hi all! I've never been studied the identities and such of secant, cosecant and cotangent. Yet I think, it would be useful to have them in my toolbox. Thus I'm asking, if anyone would know a reasonable book or other kind of material (paper or pdf) about trigonometry that has brief theory...

Hi! I am 12, and will be a 13 in 9th grade ( I skipped 6th grade). I have a curiosity for mathematics and have started preparing to take the AMC 10 and 12 exams. I enjoy solving the ingeniously crafted problems, as I share the sentiment of many math competitors of not being challenged by the...

For this, Does someone please know why we are allowed to take limits of both side [boxed in orange]? Also for the thing boxed in pink, could we not divide by -h if ##h > 0##? Many thanks!

These are the two tables I developed trying to untangle how the Collatz Conjecture operates, and this certainly helps clear the water a bit

I noticed this https://www.physicsforums.com/forums/quantum-interpretations-and-foundations.292/ about Indeterminism in Physics and "Intuitionistic Mathematics" but it was already closed. I just wanted to add that, although the value of these ideas are aren't clear from abstract of quick...

Dear everyone, I'm an HDR student in Condensed Matter Physics. I want to enhance my math ability with the aim is learning physics. I found two books, they seem all fit my purpose. 1. Mathematical Physics 2nd by S.Hassani 2. Physical Mathematics 2nd by K.Cahill I want to choose one of them to...

TL;DR Summary: Imagine you have infinite funds and cooperation to build a very ideal curriculum and student organization, both dedicated to quantum information science, at a university. What does this look like pedagogically? How would this be structured? What resources do students need access...

Since this is a "general lounge" area, I will assume this rather personal story is not out of line. I am 64 years old (relevance of my age should become clear shortly) and graduated from an Ivy League University in 1980 with a degree in Electrical Engineering. I also scored over 700 on my math...

TL;DR Summary: education, history I need to devise a module for next academic year which is an introduction to pure mathematics. They need to use this module as a stepping stone module such as number theory, group theory, combinatorics, real analysis. What should I cover to make this an...

The physical world is highly parallel; many things are happening side by side simultaneously. This is true not only at the macroscopic scales that we can see but as far as we know down to the subatomic scales. This is referred to as the principle of locality [1], which states that an object is...

Get your friends and family to play this simple little game that illustrates a key aspect of stochastic mathematics in application to finance. Draw on a big sheet of paper a sequence of 30 squares and label them consecutively 0 (bankrupt), 1, 1, 2, 2, 3, 3, 4, . . . , 14, 14, 15...

I am not sure if this is the right place to post this, so if not sorry in advance. I am a second-year physics major, thinking of switching to mathematics. I have always been interested in both, but I could never be sure whether I could become a mathematician. Understanding physics was...

Electrons are shot thru two slits separated by a distance s at a screen a distance ##z_0## away. The wave function for the particles is proportional to ## e^{ik \sqrt{(x-s/2)^2+z_0^2}} +e^{ik \sqrt{(x+s/2)^2+z_0^2}}## Taking the first one, we can manipulate the square root algebraically...

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Can someone please tell me what math is this (see below pic)? For example: algebra, calculus, etc.

Hi, I mostly do Self study and I was wondering how to build up a course ie the.different levels from beginner to advanced in the fields of linear algebra, optimization (rbfs etc), statistics and probability? Suggestions of books with the various levels is welcome. Please help me out in this as...

Is there a math that describes these shapes at least one frequency?

Homework Statement:: Recommend PDF books Relevant Equations:: . Hi, I'm a second-year physics student and my uni doesn't have any study material in the syllabus. Only lectures. I want to learn more. Can you recommend to me a good mathematics pdf book that is about calculus? General topics...

Hi everyone! I am looking for advice on what courses I should take to better flush out my degree/be more versatile. Currently, I am going into my sophomore year in Applied Mathematics. I originally wanted to change into a Math/CS degree, but it was full, so I had to settle with taking the...

Some textbooks I found online ( open source ) College Trigonometry 3rd Corrected Edition - STITZ ZEAGER OPEN SOURCE MATHEMATICS Precalculus 3rd, Corrected Edition - Lakeland Community College, Lorain County Community College A First Course in Linear Algebra - Robert A. Beezer Cheers.