Abstract Definition and 506 Threads

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Recently stumbled across [Unacceptable reference deleted by the Mentors] and the abstract says that an experiment that spanned 2000-2012 has proven that physics is superdeterministic. I have absolutely no background in quantum physics whatsoever which is why I can't verify or reject the claim...

Hi All, Glad to be on this forum, I'm an imaging software developer mainly turned physics researcher in photonics and it became apparent how closed off some science institutions can be contacting and getting any engagement with any science proffesional if your not affiliated to an institution...

I have my own thoughts and possible could provide sketch or instance use case, elaborate using evident setsettings. But I don't want to persuade, influence or lead other people who are actually educated and inadvertently guide and ultimately hinder the outcomes of their initial assessment. The...

Hello, I am looking for one or more books in combination for self-study of abstract algebra. Desirable would be a good structure of the book with good examples of sentences and definitions. Of course, exercise problems should not be missing. I am now almost tending to buy the Algebra 0 book by...

please offer me examples of: a) 3 vector spaces over the same field; and b) the same vector space over 3 fields.

Hello. So, we have curves and surfaces. We already know about generally manifolds and Riemannian manifolds but what i want to produce are ways to abstract curves or surfaces but i am not talking about manifolds. Do you have any ideas? Perhaps the feature of curvature would help? To make an...

Hello. Questions: how to give new definitions of things in abstract spaces?What are the criteria? Is it just acceptable to define things that do not contradict with other things on the abstract space?What are the motivations to give definitions of things?Also, what are the motivations for...

Hello. How to think in abstract spaces?Like manifolds? Or metric spaces? Or function or Banach spaces? Are they not just generalisations of the usual 2d or 3d Euclidean spaces we know? So they could be studied by generalising or extending things we know from 2d or 3d euclidean spaces and if they...

Dear Everyone, What are the strategies from proving a either-or statements? Is there a way for me to write an either-or statement into a standard if-then statements? For example, this exercise is from Dummit and Foote Abstract Algebra 2nd, "Let $x$ be a nilpotent element of the commutative...

My university offers two different two-semester sequences for learning abstract algebra, and I can't decide which one would be better for me, a physics major. Here are the two sequences and their course descriptions, copied and pasted from the university website: Algebra 1: Theory of groups...

Hello, In the sources I have looked into (textbooks and articles on differential geometry), I have not found any abstract definition of the electromagnetic fields. It seems that at most the electric field is defined as $$\bf{E}(t,\bf{x}) = \frac{1}{4\pi \epsilon_0} \int \rho(t,\bf{x}')...

When you're studying abstract mathematics what are some effective techniques to use? When studying something like abstract algebra do you think something like this sounds reasonable? First learn the relevant section until you reach the exercises. While learning that write down the main...

One of the last classes I'm taking before finishing my degrees as an undergraduate is abstract algebra. My professor uses the textbook 'Contemporary Abstract Algebra' by Joseph Gallian. The book isn't written terribly nor is the teacher a poor one, but I just find this subject so...

Homework Statement My specific question is: What is the value held in r7 (written in hexadecimal) after the following instructions execute? addi r5, r0, 0x30 ldw r7, 0(r5) Homework Equations N/A The Attempt at a Solution There's a few things I'm not understanding... Here are my...

I am reading The Basics of Abstract Algebra by Paul E. Bland ... I am focused on Section 3.2 Subrings, Ideals and Factor Rings ... ... I need help with another aspect of the proof of Theorem 3.2.19 ... ... Theorem 3.2.19 and its proof reads as follows...

Homework Statement In frame S particle 1 is at rest and particle 2 is moving to the right with velocity u. Now consider a frame S 0 which, relative to S, is moving to the right with velocity v. Determine the value of v such that the two particles appear in S' to be approaching each other with...

Hi. What do I call Instance Classes, Interface, Abstract Classes, Partial Classes, Static Class, Sealed Class collectively? Thanks.

Hi, so I have just a small question about cyclic groups. Say I am trying to show that a group is cyclic. If I find that there is more than one element in that group that generates the whole group, is that fine? Essentially what I am asking is that can a cyclic group have more than one generator...

So what is the purpose of an Abstract Class? Can I not get the same things by doing subclasses? For example. I can create a class called Vector_Space and then a subclass called Euclidean_Space We all know that Euclidean space is just a particular type of vector space. So I can just write the...

I know both are different courses, but what I mean is, will a proof based Linear Algebra course be similar to an Abstract Algebra course in terms of difficulty and proofs, or are the proofs similar? Someone told me that there isn't that much difference between the proofs in Linear or Abstract...

What does "linear" in linear algebra and "abstract" in abstract algebra stands for ? Since I am learning linear algebra, I can guess why linear algebra is called so. In linear algebra, the introductory stuff is all related to solving systems of linear equations of form ##A\bf{X} = \bf{Y}##...

Some posts in another thread lead me to a search which ended when I read the following "kets such as ##|\psi\rangle## are elements of abstract Hilbert Space". That lead me to this paper. http://www.phy.ohiou.edu/~elster/lectures/qm1_1p2.pdf "The abstract Hilbert space ##l^2## is given by a...

Homework Statement I can't understand how abstract aljebra helps in creating graphical patterns. I don't find eq related to Groups. Do we consider predefined structures [/B] Homework Equations No equation only patterns. one pattern is attached The Attempt at a Solution I don't know how it...

1. The problem statement, all variables and given/known If each element of a group, G, has order which is a power of p, then the order of G is also a prime power. Homework EquationsThe Attempt at a Solution I am not sure really where to get started. I know that the class equation will be used...

Homework Statement http://prntscr.com/ej0akz Homework EquationsThe Attempt at a Solution I know there are three problems in one here, but they are all of the same nature. I don't understand how this is enough information to find out if they are subspaces. It's all really abstract to me. I know...

Hello, well I am not sure how to search for this online, but I raise this question here: Suppose that I have several bins of let's say cuts, here I list 3 but the main idea is to make their numbers tunable by the user: cut1 = { "p10" : "p <= 10" , "11p20 " : "10<p && p<=20" ...

I am looking for an accessible textbook in group theory. The idea here is to use it to learn basic group theory in order to take up Galois Theory. My background includes Calculus I-IV, P/Differential Equations, Discrete Mathematics including some graph theory, Linear algebra, and am currently...

I have been reading some books (Allendoerfer, principles of math, Zakon, series of mathematical analysis, R. Courant, what is mathematics). I have learned that some of the basic fundamental, the msot bare bones of mathermatical concepts and definitions have to remain undefined. These are set...

I am taking a linear algebra course and an introductory physics course simultaneously, so I am curious about the connections between the two when it comes to vectors. In beginning linear algebra, you typically study vectors in ## \Re^{2}## and ## \Re^{3}##. Are these the same vector spaces used...

micromass submitted a new PF Insights post How to self-study algebra. Part II: Abstract Algebra https://www.physicsforums.com/insights/wp-content/uploads/2016/06/aastock6.png Continue reading the Original PF Insights Post.

Homework Statement Hello PF! Let E be a splitting field of a separable polynomial over F. Define the Norm N: E-->F by: N(a) = the product of all q(a) where q is an element of the group Aut(E). I must show that this is a well defined mapping. Homework EquationsThe Attempt at a Solution So I...

In Wald's "General Relativity", in his section on abstract tensor notation, he let's g_{ab} denote the metric tensor. When applied to a vector v^a, we get a dual vector, because g_{ab}(v^a, \cdot) is just a dual vector. Okay cool. But then he says that this dual vector is actually g_{ab}v^b...

Homework Statement Suppose X is a set with n elements. Prove that Bij(X) ≅ S_n. Homework Equations S_n = Symmetric set ≅ = isomorphism Definition: Let G and G2 be groups. G and G2 are called Isomorphic if there exists a bijection ϑ:G->G2 such that for all x,y∈G, ϑ(xy) = ϑ(x)ϑ(y) where the...

Homework Statement For each ##n \in \mathbb{N}##, let ##A_{n}=\left\{n\right\}##. What are ##\bigcup_{n\in\mathbb{N}}A_{n}## and ##\bigcap_{n\in\mathbb{N}}A_{n}##. Homework Equations The Attempt at a Solution I know that this involves natural numbers some how, I am just confused on a...

Dear Physics Forum personnel, I recently got interested in the art of abstract proof, where the focus is writing the proof as general as possible rather than starting with a specific cases. Could anyone recommend an analysis book at the level of Rudin's PMA that treats the introductory...

Homework Statement Let g(x) ∈ ℤ[x] have degree at least 2, and let p be a prime number such that: (i) the leading coefficient of g(x) is not divisible by p. (ii) every other coefficient of g(x) is divisible by p. (iii) the constant term of g(x) is not divisible by p^2. a) Show that if a ∈ ℤ...

Homework Statement Let T:R-> S be a homomorphism of rings. Show that T(0_r) = 0_s. Homework EquationsThe Attempt at a Solution First off, the terminology used is kinda confusing. I take 0_r to be the zero in R. Is this correct? For some reason I recall my teacher quickly saying that it was...

I will be giving a speech for my class and my teacher wants an abstract. I will be talking for about 45 minutes and i want to explain time dilation, length contraction, Einstein postulates, twin paradox, and the Muon experiment. But I am not sure how to put it all into an abstract.

Homework Statement Let R be a ring and suppose r ∈R such that r^2 = 0. Show that (1+r) has a multiplicative inverse in R. Homework Equations A multiplicative inverse if (1+r)*x = 1 where x is some element in R. The Attempt at a Solution We know we have to use two facts. 1. Multiplicative...

Homework Statement Suppose R is a commutative ring with only a finite number of elements and no zero divisors. Show that R is a field. Homework Equations Unit is an element in R which has a multiplicative inverse. If s∈R with r*s = 1. A zero divisor is an element r∈R such that there exists...

Hi everyone, good day to you. A friend and I think that the process of writing a papers (especially in sciences and maths) are rather troublesome due to the following reason: 1. Long journal review process 2. Selection of papers to be published are not transparent, a few negative reviews can...

I'm taking an abstract algebra course that uses Hungerford's "An Introduction to Abstract Algebra" 3rd Ed. And while I feel like I'm following the material sufficiently and can do most of the proofs it's hard to learn and practice the material without a solutions guide. How am I supposed to know...

Inspired by stevendaryl's description of an EPR-like setting that doesn't refer to a particle concept, I want to discuss in this thread a generalized form of his setting that features a class of long-distance correlation experiments but abstracts from all distracting elements of reality and from...

Homework Statement Simplify the following statement as much as you can: (b). ##(3<4) \wedge (3<6)## Homework Equations ##\wedge= and## The Attempt at a Solution I figured that I could just write this as ##3<4<6##, but then I considered what if I didn't know that ##4<6## If it was just...

Hi As I am venturing in graduate level mathematics, I am having a recurring problem; I keep getting stuck in the abstraction of it. Usually it involved set theory; I never get "fluent" in it. However, the main problem is abstraction. For instance, this semester I had topology, and the...

Homework Statement Let (S,\cdot ) be an algebraic structure where the operation \cdot is associative and commutative and also the following axiom is satisfied: \forall x,y\in S,\exists z\in S: zx = y\ \ (1) Prove that if for every a,b,c\in S, ac = bc, then a=b. Homework EquationsThe Attempt...

I have a question about Automorphisms. Please check the following statement for validity... An automorphism of a group should map generators to generators. Suppose it didn't, well then the group structure wouldn't be preserved and since automorphisms are homomorphisms this would be a...

Good day, Did anyone here use Serge Lang's "Algebra" as an undergraduate text?

This isn't homework, I'm just trying to refresh my memory on cyclic groups. My question is, in this problem solution, how does ##{\sigma_i}^m=1## follow from ##\sigma_i## being disjoint?