Mathematics

Ok, so I'm taking discrete mathematics this semester and I cannot....can not, for the life of me understand the basics of counting. I was in class an the professor was talking and everyone was agreeing and I was sitting there wondering about how many fries can go with a shake, because I saw my future and it involved flunking out of college *little bit of humor there* . Any help, any would be appreciated in understanding the concepts of counting. The first thing that I need help on is understanding the core principles behind the product rule and how it relates to set theory so that I can at least have some reference.

I am currently working on a GR related project, and I wonder if there is anyone here who has access to a MAPLE installation? I need help to save me lots of work with the following: suppose we have a GR spacetime endowed with the usual Levi-Civita connection and the metric \[ds^{2} =-\left( 1-\frac{2M( u)}{r}\right) du^{2} -2dudr+r^{2}\left( d\theta ^{2} +sin^{2} \theta d\phi ^{2}\right)\] wherein M(u) is an unspecified everywhere differentiable function. My task is now to find all non-vanishing Christoffel symbols (2nd kind) for this metric, in terms of the mass function M(u) and its derivatives. I could of course do this by hand with pen-and-paper, but th…

is there such a definition in the content of integral account/calculation courses or in the content of calculus? I remember something like this: [math] \int^{v(x)}_{y=u(x)} f(x,y)dy [/math] if in this integral [math]f(x,y)[/math] function ( [math] \alpha \leq x \leq \beta [/math] and [math] a \leq y \leq b [/math] ) is derivable in the D region that characterized with the given inequalites in the paranthesis,then this region would be called as "regular region" but I am not sure about the exact definition could someone provide some more context about regular region (if possible)? thanks

I was browsing the web and I came across something which claimed to be the principle of omniscience: for every function p: X → 2, ∃x ∈ X(p(x) = 0) ∨ ∀x ∈ X(p(x) = 1) I thought it looked interesting, but I can’t seem to make out just exactly how it works... is this something one can use in conjunction with absolute infinite? or is it spam... any input gladly taken. -Oliver

Dear maths lovers I need sources that classify functions/sequences or functional sequences (in broad view (wide count of examples)) ,such as; *** convergent functions / sequences *** divergent functions / sequences *** differentiable functions (>1 variables) *** differentiable functions (>2 variables) *** regular continous functions *** continuous functions *** integrable functions *** lipschitz criterion satisfied functions *** cantor theorem satisfied functions *** regular convergence (functional sequences) (note: thesis and/or books are preferred ,because the soruce(s) I look for should provide broad v…

Can someone explain to a layman what they do, Why are they important? https://en.m.wikipedia.org/wiki/Penrose_tiling

I am a layman trying to understand above theorems. This could be a stupid question. Does these theorems imply that we actually cannot prove that 2+2 = 4??? Is this one of the implications of these theorems???

Do most composite numbers have a large prime factor? First, I’ll define what I mean by a “large” prime factor. Let N be a number. If a prime factor of N is greater than the square root of N, then that factor is a large prime factor of N. As an example, 11 is a large prime factor of 22, because 11 is greater than the square root of 22, and so 22 has a large prime factor On the other hand, 3 is not a large prime factor of 12 because 3 is less than the square root of 12, and so 12 does not have a large prime factor. Below is a list of composite numbers with large prime factors: 6, 10, 14, 15, 20, 21, 22, 26, 28, 33, 34, 35, 38, 39, 42, 44, 4…

A person who can solve x2 − 92y2 = 1 in less than a year is a mathematician. Brahmagupta http://en.wikipedia.org/wiki/Brahmagupta's_formula This is mine whats yours? 1/1508996212705581.8 = 6.62692186753095e-16

Is it possible to determine a transformation matrix from just a x and y matrix and the resulted transformed matrix? Say for example you have a few points on an x and y graph. You transform these points into a matrix. Lets also say that you have another graph with x and y points and you change that into a matrix. Lets finally say that a transformation matrix exist between the first and second matrix, however you have no idea what it is. Is there a possible means of solving for that said transformation matrix. Also apologies for the slight vagueness, have some linear algebra knowledge however I need to study up on it some more in order to give more …

Hey guys, If anyone is struggling with algebra, 3Bue1Brown playlist on it is really helpful

In case of right angled triangles, C^2 = A^2 +B^2 - 2AB cos(Ψ) is shortened to C^2 = A^2 +B^2 because the cosine of the angle "Ψ" which is 90° is equal to 0. But how is its cosine equal to 0.

I remember hearing someone say "almost infinite" in this video. As someone who hasn't studied very much math, "almost infinite" sounds like nonsense. Either something ends or it doesn't, there really isn't a spectrum of unending-ness. In this video he says that ''almost infinite'' pieces of verticle lines are placed along X length. Why not infinit?

For example, Consider two shapes; a circle and rectangle. Both these shapes have same area but the perimeter of circle is less than that of rectangle. Why?

I am attempting to understanding implication in mathematical logic. I will start off by giving an example of its use and my interpretation of how to correctly under it. That way my process can be critiqued and corrected. Example if "f(a) =f(a')", then " a = a' " Interpretation the given logical statement above is like an "instruction manual" in which if I have f(some a) = f(some b) then it will always result in some a equaling some a'. And if I observe a counter example to this then that would mean that the overall example statement is wrong and therefore it is not defined as being that said thing, in this case being the definition of a …

Does anyone have any referencs to Oricycles ? I can't seem to find any. This is a (non Euclidian) geometrical question.

Hey whats up, question, Is there some underlying linear understanding for how one may go about understanding mathematical proofs? for example Definitions -> Postulates -> Theorems -> Proofs -> etc. Like is there a universal path of understanding for some logical statement? The reason I ask is because when reading a little of "Journey into Mathematics" and the Elements it would continuously go through this process like one thing is built on top of another. That is cool and all but is there like an existing quantifiable formula for this process? Thank you for your time

Hello everyone. 😃 In honor of Pi Day I'm going to be explaining the very beginning of set theory (which I consider the beginning of university math) live on Twitch in about two hours (1 PM GMT). For those who do not know Twitch, it's a completely free streaming platform - you can come in and watch without registering or anything. Starting university math can often be confusing so I'm hoping to be of some help to people with this. You can find the stream here: advertising link removed by moderator per rule 2.7 Anyone and everyone is welcome to join in. 😊 Hope to see you there, and good luck with your studies, Fluxistence.

If I understand the argument correctly, it's that if you compare a set of all whole numbers to a set of all whole + half numbers, when you look at each set up to number 2, set 1 would be 1 and 2 (and 0?) and set 2 would be 1/2, 1, 1 1/2 and 2 - so set 2 has more numbers, but that's only if you look up to 2. If you look at the whole sets the size of each is infinite, so neither is bigger than the other. What am I missing here?

Sir, I have recently published a paper that reveals THE EXTREMELY PRECISE Pi:Phi CORRELATION, which is firmly premised upon Classical geometric principles. Video Link: DELETED Paper Link: DELETED

Does anyone know of any research or math records on determining when a decimal number will terminate based on the inverse of its factors? Yes I know that I would be working with whole numbers not integers. But for integers what if you took the factors of a quotient, say circumference divided by diameter and factored the numerator and denominator. The equation would be = to itself, but if you multiplied the factors together you already know that those factors terminate at the product. Someone has probably done a similar technique. But factoring large numbers is recursive and then you add to the process recursion again to do the multiplicatio…

So I am taking my first proofs class this semester along with an application of it in mathematical statistics and I got to say. This is pretty awesome. Why have I never seen this stuff before in my lower level mathematics courses. Like it provides general reasoning and evidence for each mathematical equation. I am currently reading over "Journey into mathematics-an introduction to proofs" by Joseph J. Rotman and it answer ssooooo many questions. Like a proof for that cosine equation that was just given to me. I thought it involved like some super human levels of mathematics. It turns out it just uses the pythagean theorem and some geometry identification and relatio…

The reason you find or take a limit is when the values cannot give you an exact answer in an equation. Then the equation can be graphed, and the limit assumes the value that the function approaches on the graph. It is an extra step that can be taken to make a graphical analysis to find an approximate answer by looking at a graph. You can say that it is a certain value, even though the calculation of the variables in the equation cannot give you an answer. It is another way of trying to deal with infinity or infinitesimals in of itself. The main reason why this method isn't used in a lot of work is because it is not known if it has been proven to be reliable, bu…

Generally a tensor may be represented as a product of vectors. A “reducing tensor” may be represented as the average of vector triple products. A reducing tensor will also “reduce” to an average of scalar products. Acceleration may be represented as a vector. A field (gravitational, electric, or magnetic) may be represented using “reducing tensors” of acceleration. An “equivalent EFE” may be written as reducing tensors. The equivalent EFE will then reduce to scalar products of acceleration. Suitable definitions of acceleration will give the Schwarzschild metric. Christoffel symbols are not required. Is a “reducing tensor” mathematically valid? R…

Hi all, Forgive me if this post seems long, I tried to make it as short as possible by removing any unnecessary details, and leaving only the things needed. It would really mean so much to me if you would be able to read all of it to better understand my position, but if you're unable to read all of it, just jump to the Training Regime section. Ok, here's the thing. I'm preparing myself for the college entrance exam, and I hope that 6 months of intensive study regime will be enough time for me to pass it. I would like your opinion on it to see if there is anything I would need to change The entrance exam (July, 1st) is only 10 math-based que…