Abstract Definition and 506 Threads

I had some colleagues in College who took a degree in Math on their first two years. After finishing their second year, they shifted to a different course. They already finished from Algebra to Calculus and they were in an even higher math. They were asked to prove that 1 + 1 = 3 This is...

Is this a good idea (provided the university will allow it)? I'll be going into my sophomore year at my university. But I'm unfamiliar with exactly how much linear algebra an intro course in abstract algebra would require. In hindsight I probably should have taken linear last semester, but...

Hi folks! A QFT question: you start from the lagrangian, compute the hamiltonian via Legendre transform and promote the the fields to operators with canonical equal-time commutation relations. Now you can compute the relation [H,F(x)]=-\mathrm{i}\partial_0 F(x) \ , where H is the hamiltonian...

There is this congress for which I would like to submit an abstract. Authors of accepted abstracts will be invited to write a full paper which will be published in a preceeding series and will be indexed in isi. Now I was wondering what exactly is expected from such an abstract? Is it...

Homework Statement Prove that f(x)=x^3-7x+11 is irreducible over Q Homework Equations The Attempt at a Solution I've tried using the eisenstein criterion for the polynomial. It doesn't work as it is written so I created a new polynomial...

Hi, everyone: I was wondering if it makes sense to define a theory of integration in abstract spaces (i.e., spaces other than IR^n, or homeomorphs), and, if so, how to do it (and wether we can then define a theory of differentiation). If so, do we need to define a measure...

"Derivative" in an abstract polynomial ring Homework Statement Let R be any ring and define D:R[X]-->R[X] by setting D[\sum a_nX^n]=\sum na_nX^{n-1}. a) Check that, if f(X)=\sum a_nX^n and g(X)=\sum b_nX^n, then D[f+g]=D[f]+D[g] b) Check that...

Abstract Algebra Questions - Need help for exam! Homework Statement I am studying Abstract Algebra in college and my exams are approaching fast.I need somebody to help me out to do a few exam papers. I am going to post the questions below from the exam papers and if you can advise me how...

Hi, Next fall i will be taking Intro to Abstract Algebra so i was planning to give it a shot on my own during the summer break, but i don't know what would be a good book to buy online, that is not too expensive. I would like the book to be quite rigorous, like very proof based one, but that...

Homework Statement Show that G is isomorphic to the Galois group of an irreducible polynomial of degree d iff is has a subgroup H of index d such that \bigcap_{\sigma \in G} \sigma H \sigma^{-1} = {1} .Homework Equations The Attempt at a Solution I know that if G acts transitively as a...

I'm going insane. The question is: List all abelian groups (up to isomorphism) of order 144. There are 10 non-isomorphic groups of order 144 and I only have 9. Here they are: Z2 X Z2 X Z2 X Z2 X Z3 X Z3 Z2 X Z2 X Z2 X Z2 X Z9 Z4 X Z2 X Z2 X Z3 X Z3 Z4 X Z2 X Z2 X Z9 Z8 X Z2 X Z3 X Z3 Z8 X Z2...

I'm currently taking a course, "Abstract Algebra I & Number Theory" and I'm wondering: what is the difference between abstract algebra and number theory? the two topics seem meshed together. i tried googling both of them and it doesn't really help. it's hard to tell the differences between...

[SOLVED] Biology Lab Abstract: Photosynthesis Homework Statement I am having trouble understanding how increased transmission is an indication to photosynthesis occurring. My teacher gave us the prediction for this lab: if photosynthesis is happening then transmittance goes up. I know...

[b]1. On the set of real numbers, R the following operation is defined: *RxR implies (arrow) R, (x,y) implies (arrow) x*y=2(x+y)-xy-2 Find the neutral element of this operation. [b]3. since we know x*e=x, e*x=x, so i attempted: using e as y, because it would just mean y...

Hello folks! Do you have any suggestions for a book on abstract algebra? Someone gave me this suggestion Algebra - Michael Artin https://www.amazon.com/dp/0130047635/?tag=pfamazon01-20 however there are some bad (and convincing) reviews on amazon.com about this book (although the...

Anybody know the name of the MIT course number for Abstract Algebra . Is it even listed as a course on the MIT opencourseware website?

I just bought the book Art of Electronics that berkman recommended and I just started reading it. I already know what voltage is but if I didn't I would have made no sense of their explanation. They say "The voltage between two points is the cost in energy (work done) required to move a unit...

How to go about it? I had abstract algebra in mind. Is the main thing to do as many solid examples as possible? So the only way to understand the abstract it is to think concrete then generalise?

Can some one help me, how to solve this problem?. Please explain me how is done, been having problem with the subject Let H be the subgroup of GL(2, R) under Matrix multiplication defined by H = {[ 1 n ]}| n E Z } 0 1 Let 0...

Homework Statement Let R be an Integral Domain. Prove that if a,b are elements of R and both a and b are units in R, then prove a*b is a unit of R. Homework Equations a is a unit in R if and only if there exists an element u in R such that au=1=ua where 1 is the identity element of R...

Homework Statement If G1, G2 are two groups and G = G1 times G2 = {(a,b) such that a is an element of G1, b is and element of G2}, where we define (a,b)(c,d) = (ac, bd), (a) Show that N = {(a, e2) such that a is an element of G1}, where e2 is the unit element of G2, is a normal subgroup...

Homework Statement If f is a homomorphism of G onto G' and N is a normal subgroup of G, show that f(N) is a normal subgroup of G'. Homework Equations The Attempt at a Solution Once again, I'm completely lost.

Homework Statement Let F be a field and f(x) in F[x]. If c in F and f(x+c) is irreducible, prove f(x) is irreducible in F[x]. (Hint: prove the contrapositive) Homework Equations So, I am going to prove if f(x) is reducible then f(x+c) is reducible. The Attempt at a Solution f(x)...

Abstract Algebra -- lifting up a factor group After spending an extended period with my Professor during office hours I must admit I am mystified. He kept on talking about "lifting up" factor groups. I think this has something to do with using a factor group, say G/N, to show that there...

Abstract Algebra -- no Sylow allowed Please note Sylow's theorem(s) may not be used. Using Theorem 1 as a tool, prove that if o(G)=p^{n}, p a prime number, then G has a subgroup of order p^m for all 0\leq m\leq n. Theorem 1: If o(G)=p^{n}, p a prime number, then Z(G)\neq (e). Theorem 1 uses...

Abstract Algebra -- group Show that in a group G of order p^2 any normal subgroup of order p must lie in the center of G. I am pretty sure here that p is supposed to be a prime number, as that is the stipulation in preceding and later problems. However, the problem statement does not...

I am studying the abstract theory of measure and I was wondering how the Lebesgue case for real functions of a real variable arises. But I did not find it. In the original theory of Lebesgue, a function f:E-->R was said to be measurable if for every real constant b, the preimage of ]-\infty, b]...

I have two problems I would like to discuss. 1.For any group G prove that the set of inner automorphisms J(G) is a normal subgroup of the set of automorphisms A(G). Let A be an automorphism of G. Let T_{g} be an inner automorphism, i.e. xT_{g}=g^{-1}xg The problem can be reduced to the...

1) find a group that contains elements a and b such that ︱a︱=︱b︱= 2 and a) ︱ab︱ = 3 b) ︱ab︱=4 c) ︱ab︱=5 2) suppose that H is a proper subgroup of Z under addition and H contains 18, 30 and 40. determine H? does anyone can help me out? and ...i am really in...

Abstract Algebra -- isomorphism question If N, M are normal subgroups of G, prove that NM/M is isomorphic to N/N intersect M. That's how the problem reads, although I am not sure how to make the proper upside-down cup intersection symbol appear on this forum. Or how to make the curly "="...

Homework Statement I am asked to show that if E is a semi-group and if (i) there is a left identity in E (ii) there is a left inverse to every element of E then, E is a group.The Attempt at a Solution Well I can't seem to find the solution, but it's very easy if one of the two "left" above is...

Homework Statement Prove that if (ab)^2=a^2*b^2, in a group G, then ab =baHomework Equations No equations necessary for this proofThe Attempt at a Solution Suppose (ab)^2=a^2*b^2. Then (ab)^2=(ab)(ab)=(abba)=(ab^2*a)=a^2 *b^2=> (ab)(ba)=(ba)(ab) = e By cancellation, (ab)=(ba) <=> (ba)=(ab)

Homework Statement Show that {1,2,3} under multiplication modulo 4 is not a group but that {1,2,3,4} under multiplication modulo 5 is a group Homework Equations a mod n=r ;a=qn + r The Attempt at a Solution I'm going to assume when the problem says modulo 4, the problem is read...

I'm thinking about taking the math GRE in December but I've never studied abstract algebra--all this about rings and groups just flies right over my head. Can anyone recommend a good introductory book? I'm thinking one of the Dover works might be good since they seem to emphasize problem...

I'm giving a talk entitiled "concrete analogies of abstract concepts", where I give examples of concepts in mathematics that might have arisen in things found in every day life. I already have "chess" for isomorphism and "acronyms" for homomorphisms, but I'm running a bit dry. Anyone got any ideas?

I am currently signed up for an intro abstract algebra course. I will be taking this course and calculus 3(stewart's book). I am pretty good at writing proofs. Do you have to know calculus 3 to do well in abstract algebra? Or can you take it concurrently? Is abstract algebra considered a...

This question links to a former discussion on the board. I'm confused regarding this thread: https://www.physicsforums.com/showthread.php?t=3622" Specifically, towards the end of the thread, the asker states (in regards to the union notation originally cited): "...if we say that x is an...

Another Abstract Algebra Question... Every symmetry of the cube induces a permutation of the four diagonals connecting the opposite vertices of the cube. This yields a group homomorphism φ from the group G of symmetries of the Cube to S4 (4 is a subscript). Does φ map G onto S4? Is φ 1-1? If...

Note: M22 is the set of all m x n matrices with real entries P3 is the set of all polynomials of degree at most n, together with the zero polynomial. 1) Find a basis of M22 consisting of matrices with the property that A^2 = A. I only found 2 of the vectors with a lot of hard work... [1...

Abstract Algebra Questions... Help Please! Any and all help on these problems would be greatly appreciated. Thank you in advance to any who offer help :smile:. 1. Let φ:G->H be a group homomorphism, where G has order p, a prime number. show that φ is either one-to-one or maps every element...

G is a finite group, |G| =p^n, p prime *:GxX -> X is group action. X is a finite set, I am required to prove the following |X|\equiv |X^G|modp Now we start by asserting that x_1, x_2, ...,x_m is the set of m orbit representatives. That orbit x <x_i> = {x_i} \\ iff x_i is a...

Homework Statement Aut(R) denotes the set of ring automorphisms of a ring R Show formally that Aut(R) is a group under composition. Homework Equations The Attempt at a Solution I Have a very similar question to which I have the solution viz Aut(G) denotes the set of group...

Homework Statement Prove that (a b c d) is a unit in the ring M(R) if and only if ad-bc !=0. In this case, verify that its inverse is (d/t -b/t -c/t a/t) where t= ad-bc. Homework Equations An element a in a ring R with identity is called...

Homework Statement From An Introduction to Abstract Algebra by T. Hungerford Section 3.2 #29 Let R be a ring with identity and no zero divisors. If ab is a unit in R prove that a and b are units. Homework Equations c is a unit in R if and only if there exists an...

Please I need your help for that qustion and how do slove that qustion's problem. can you help me for slove for that? Pleasee Let G be any group, and let a, b ∈ G. Show that there are c, d ∈ G such that ac = b and da = b. Hint: you have to give an explicit definition for c and d in terms of a...

ProbelmLet p and q be distinct primes. Suppose that H is a porper subset of the integers and H is a group under addition that contains exactly three elements of the set {p, p+q, pq, p^q, q^p}. Determine which of the following are the three elements in H. a.pq, p^q, q^p b. p+q, pq, p^q c. p...

I'm just wondering about the spectrum of abstract thinking among the math lovers here. How pure do you like math? Do you insist on visualizing your math problems to be more than a collection of sets and mappings? I couldn't phrase everything I wanted to say in my 5 choices (limited to only...

I'm having trouble understanding splitting fields. Some of the problems are find the degree of the splitting field of x^4 + 1 over the rational numbers and if p is a prime prove that the splitting field over the rationals of the polynomial x^p - 1 is of degree p-1. I'm really confused with these...

can anyone help me with my abstract algebra assignment? Let a be an fixed element of some multiplicative group G. Define the map β: Z > G from the additive inter group Z to G by β(n)=a^n. i. Prove that the map β is a homomorphism. ii. Prove/Disprove that the map β is an isomorphism. thanks!

In my uni I am forced to make a painful choice btw taking PDE or abstract algebra. I will take algebra, but I'd like to know what I will be missing? What is being taught in this class exactly? (BESIDES HOW TO SOLVE A PDE BY SEPARATION OF VARIABLES :rolleyes:)